v2 design: independent masks + affinity-aware Wiener demultiplexer
Redesign after the independent-mask dominance finding: the affinity now parameterizes the receiver (closed-form Wiener) instead of the mask ensemble. New Theorem 1 (spectral closed form), floors sqrt(1-b^2)/2 vs 1/2, full-cooperation bound with equality at b=1. GPU (torch) Monte Carlo backend, decision-directed SIC baseline, TikZ block diagram source, verification suite V1-V11.
This commit is contained in:
KiHoLee
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-185
@@ -1,30 +1,30 @@
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"""
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Merged real-data comparison figure (replaces separate Figs 4 and 5).
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Real-data comparison on cached BERT (text) + ViT (image) pairs.
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===================================================================
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Evaluates ALL schemes on the cached real BERT (text) + ViT (image)
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embedding pairs (16 pairs, d = 768, measured mean affinity ~0.028)
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under the manuscript's complex block-Rayleigh channel:
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Evaluates the schemes on the cached real embedding pairs
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(16 pairs, d = 768, measured mean affinity ~0.028) under the
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manuscript's complex block-Rayleigh channel:
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r = h1 M1 e1 + h2 M2 e2 + n, n ~ CN(0, sigma^2 I), h_u ~ CN(0,1),
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per-block energy E_b = 1, rho = 1/sigma^2 (per-block SNR).
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Schemes:
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1. EDMA : per-realisation Haar-mixture masks with the per-pair
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measured beta_i, closed-form demux (13).
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Schemes (v2 design: independent Haar masks per user):
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1. EDMA : affinity-aware Wiener demultiplexer with the
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per-pair measured beta_i.
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2. OMA : equivalent-bandwidth model, noise std x sqrt(2).
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3. Genie SIC : perfect removal of the other user's waveform.
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4. Attention : retrained reproduction of the learned predecessor,
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d = 768, trained on parametric pairs at the measured
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mean affinity with Rayleigh channels and
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channel-equalised matched-filter inputs
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x_u = Re(M_u^T r / h_u); evaluated on the REAL pairs.
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5. ToDMA-adapted: OMP sparse coding of the real embedding (T = 16
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4. ToDMA-adapted: OMP sparse coding of the real embedding (T = 16
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atoms, V = 1024), T slots x L = 48 signatures,
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per-slot OMP detection on the complex observation,
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genie association, true coefficients granted.
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Outputs: fig/fig_bertvit_merged.pdf, data/bertvit_merged.csv.
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200 fading realisations per pair -> 3,200 Monte-Carlo samples per SNR.
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The hybrid (EDMA + refinement stage) curve is produced separately by
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refine_matched.py (torch) and merged by replot_merged.py.
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EDMA/OMA/genie run in torch (CUDA when available, batched over the
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SNR grid); the ToDMA detector runs in numpy on the CPU. Run under
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WSL for GPU acceleration. Outputs: data/bertvit_merged.csv.
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NFADE fading realisations per pair; ToDMA uses the first 40.
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Seed fixed.
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"""
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from __future__ import annotations
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@@ -35,38 +35,20 @@ import time
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from pathlib import Path
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import numpy as np
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import torch
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import matplotlib
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matplotlib.use("Agg")
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import matplotlib.pyplot as plt
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ROOT = Path(__file__).resolve().parents[1]
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DATA = ROOT / "data"
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FIG = ROOT / "fig"
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plt.rcParams.update({
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"font.family": "serif",
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"font.serif": ["DejaVu Serif", "Times New Roman"],
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"font.size": 9, "axes.labelsize": 9, "legend.fontsize": 6.6,
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"xtick.labelsize": 8, "ytick.labelsize": 8,
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"axes.grid": True, "grid.linestyle": "--", "grid.linewidth": 0.4,
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"grid.alpha": 0.6, "lines.linewidth": 1.4, "lines.markersize": 4.0,
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"figure.figsize": (3.15, 2.36), "pdf.fonttype": 42,
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})
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AXES_RECT = dict(left=0.205, right=0.965, top=0.955, bottom=0.185)
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SEED = 2026
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rng = np.random.default_rng(SEED)
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torch.manual_seed(SEED)
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DEV = "cuda" if torch.cuda.is_available() else "cpu"
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D = 768
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SNRS = np.arange(0.0, 31.0, 5.0)
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NFADE = 200 # fading realisations per pair
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def haar(d):
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G = rng.standard_normal((d, d))
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Q, R = np.linalg.qr(G)
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return Q * np.sign(np.diag(R))
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SNRS = np.arange(0.0, 31.0, 2.5)
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NFADE = 100 # fading realisations per pair
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NFADE_TOD = 40 # ToDMA heavier: first 40 draws
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def unit(v):
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@@ -87,100 +69,35 @@ def load_pairs():
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return a, b, betas
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# ------------------------------------------------------------------
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# attention model: trained at the measured mean affinity, d=768,
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# Rayleigh channels, channel-equalised MF inputs
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# ------------------------------------------------------------------
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EPS_EQ = 0.1 # regularised equalisation h*/(|h|^2+EPS_EQ):
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# caps deep-fade amplification for the learned readout
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def haar_t(n, gen):
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G = torch.randn(n, D, D, generator=gen, device=DEV)
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Q, R = torch.linalg.qr(G)
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return Q * torch.sign(torch.diagonal(R, dim1=-2, dim2=-1)).unsqueeze(-2)
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def train_attention(beta0, epochs=150, steps=20, batch=48, lr=5e-4,
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l1=1.0, l2=0.5, l3=0.5):
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print(f"=== training attention reproduction (d={D}, beta={beta0:.3f}, "
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f"{epochs} epochs, Rayleigh) ===", flush=True)
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gen = torch.Generator().manual_seed(SEED)
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g0 = math.sqrt(1.0 - beta0**2)
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def torch_pairs(n):
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e1 = torch.nn.functional.normalize(
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torch.randn(n, D, generator=gen), dim=1)
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w = torch.randn(n, D, generator=gen)
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w = w - (w * e1).sum(1, keepdim=True) * e1
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w = torch.nn.functional.normalize(w, dim=1)
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return e1, beta0 * e1 + g0 * w
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M1 = torch.nn.Parameter(torch.linalg.qr(
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torch.randn(D, D, generator=gen))[0])
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M2 = torch.nn.Parameter(beta0 * M1.detach()
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+ g0 * torch.linalg.qr(
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torch.randn(D, D, generator=gen))[0])
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Q1 = torch.nn.Parameter(torch.randn(D, D, generator=gen) / math.sqrt(D))
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Q2 = torch.nn.Parameter(torch.randn(D, D, generator=gen) / math.sqrt(D))
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opt = torch.optim.Adam([M1, M2, Q1, Q2], lr=lr)
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eye = torch.eye(D)
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t0 = time.time()
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for ep in range(epochs):
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for _ in range(steps):
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e1, e2 = torch_pairs(batch)
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snr_db = 5.0 + 20.0 * torch.rand(batch, 1, generator=gen)
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sig = 10 ** (-snr_db / 20.0)
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hr = torch.randn(batch, 2, generator=gen)
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hi = torch.randn(batch, 2, generator=gen)
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# complex channel on real signals; equalised MF real part:
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# x_u = Re(M_u^T r / h_u); build via real/imag components
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s1 = e1 @ M1.T
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s2 = e2 @ M2.T
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nr = sig * torch.randn(batch, D, generator=gen) / math.sqrt(2)
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ni = sig * torch.randn(batch, D, generator=gen) / math.sqrt(2)
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rr = (hr[:, :1] * s1 + hr[:, 1:2] * s2) / math.sqrt(2) + nr
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ri = (hi[:, :1] * s1 + hi[:, 1:2] * s2) / math.sqrt(2) + ni
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outs = []
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for u, (Mu, Qu) in enumerate(((M1, Q1), (M2, Q2))):
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hu_r = hr[:, u:u+1] / math.sqrt(2)
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hu_i = hi[:, u:u+1] / math.sqrt(2)
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mag = hu_r**2 + hu_i**2 + EPS_EQ
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xr = (rr @ Mu)
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xi = (ri @ Mu)
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xu = (xr * hu_r + xi * hu_i) / mag # Re(h* r'/(|h|^2+eps))
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sc = (xu @ Qu.T) / math.sqrt(D)
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outs.append(D * torch.softmax(sc, dim=1) * xu)
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gram = ((M1.T @ M1 - eye)**2).mean() \
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+ ((M2.T @ M2 - eye)**2).mean() \
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+ ((M1.T @ M2 - beta0 * eye)**2).mean()
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mse = ((outs[0] - e1)**2).mean() + ((outs[1] - e2)**2).mean()
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cs = torch.nn.functional.cosine_similarity(
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outs[0], e1, dim=1).mean() \
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+ torch.nn.functional.cosine_similarity(
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outs[1], e2, dim=1).mean()
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loss = l1 * gram + l2 * mse + l3 * (2.0 - cs)
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opt.zero_grad(); loss.backward()
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torch.nn.utils.clip_grad_norm_([M1, M2, Q1, Q2], 1.0)
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opt.step()
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if (ep + 1) % 50 == 0:
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print(f" epoch {ep+1}: loss {float(loss.detach()):.4f}",
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flush=True)
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print(f" trained in {time.time()-t0:.0f}s, "
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f"{4*D*D/1e6:.2f}M parameters")
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return (M1.detach().numpy(), M2.detach().numpy(),
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Q1.detach().numpy(), Q2.detach().numpy())
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def aware_batch(t, Q, beta, c, nvar):
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"""Batched affinity-aware Wiener demux. t: (b,D) cfloat, Q: (D,D),
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c: complex scalar, nvar: (b,) real."""
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b = t.shape[0]
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g = 1.0 - beta * beta
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rho = g * abs(c)**2 / D + nvar # (b,)
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Qc = Q.to(torch.cfloat)
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A = torch.eye(D, device=DEV, dtype=torch.cfloat) + beta * c * Qc
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S = (A @ A.mH / D).unsqueeze(0) \
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+ rho.view(b, 1, 1) * torch.eye(D, device=DEV,
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dtype=torch.cfloat)
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x = torch.linalg.solve(S, t.unsqueeze(-1))
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return (A.mH.unsqueeze(0) @ x).squeeze(-1) / D
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def att_apply(model, r, h1, h2):
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M1, M2, Q1, Q2 = model
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outs = []
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for u, (Mu, Qu, hu) in enumerate(((M1, Q1, h1), (M2, Q2, h2))):
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xu = np.real(np.conj(hu) * (Mu.T @ r)) / (abs(hu)**2 + EPS_EQ)
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sc = (Qu @ xu) / math.sqrt(D)
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sc = sc - sc.max()
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w = np.exp(sc); w /= w.sum()
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outs.append(D * w * xu)
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return outs
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def abscos(a, b):
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"""a: (b,D) cfloat, b: (D,) float -> (b,) abs cosine."""
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num = (a * b.to(torch.cfloat).conj()).sum(1).abs()
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return (num / (a.norm(dim=1) * b.norm())).cpu().numpy()
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# ------------------------------------------------------------------
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# ToDMA-adapted on real embeddings (complex channel)
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# ToDMA-adapted on real embeddings (complex channel, numpy)
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# ------------------------------------------------------------------
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def todma_prepare(V=1024, T=16):
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L = D // T
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@@ -238,58 +155,73 @@ def todma_run(tod, codes, h, sig, noise_slots):
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def main():
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A, B, betas = load_pairs()
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npairs = len(A)
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model = train_attention(float(betas.mean()))
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tod = todma_prepare()
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codes = [(omp_code(tod[0], A[i], tod[3]),
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omp_code(tod[0], B[i], tod[3])) for i in range(npairs)]
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print("[todma] sparse codes prepared")
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print(f"[todma] sparse codes prepared; device = {DEV}")
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keys = ("edma", "oma", "genie", "att", "att_x", "todma")
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res = {k: np.zeros(len(SNRS)) for k in keys}
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cnt = {k: np.zeros(len(SNRS)) for k in keys}
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gen = torch.Generator(device=DEV).manual_seed(SEED)
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nb = len(SNRS)
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sigs_t = torch.tensor(10 ** (-SNRS / 20.0), device=DEV,
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dtype=torch.float32)
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keys = ("edma", "oma", "genie", "todma")
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res = {k: np.zeros(nb) for k in keys}
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cnt = {k: np.zeros(nb) for k in keys}
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t0 = time.time()
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for i in range(npairs):
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e1, e2, bi = A[i], B[i], float(betas[i])
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gi = 1.0 - bi**2
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c1, c2 = codes[i]
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bi = float(betas[i])
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e1 = torch.tensor(A[i], dtype=torch.float32, device=DEV)
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e2 = torch.tensor(B[i], dtype=torch.float32, device=DEV)
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c1c, c2c = codes[i]
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for f in range(NFADE):
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U1, U2 = haar(D), haar(D)
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M1 = U1
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M2 = bi * U1 + math.sqrt(gi) * U2
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h = (rng.standard_normal(2) + 1j * rng.standard_normal(2)) \
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M = haar_t(2, gen)
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M1, M2 = M[0], M[1]
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Q = M1.T @ M2
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h = (torch.randn(2, generator=gen, device=DEV)
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+ 1j * torch.randn(2, generator=gen, device=DEV)) \
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/ math.sqrt(2)
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h1, h2 = h
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r0 = h1 * (M1 @ e1) + h2 * (M2 @ e2)
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n = (rng.standard_normal(D) + 1j * rng.standard_normal(D)) \
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n = (torch.randn(D, generator=gen, device=DEV)
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+ 1j * torch.randn(D, generator=gen, device=DEV)) \
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/ math.sqrt(2)
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n2 = (rng.standard_normal(D) + 1j * rng.standard_normal(D)) \
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n2 = (torch.randn(D, generator=gen, device=DEV)
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+ 1j * torch.randn(D, generator=gen, device=DEV)) \
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/ math.sqrt(2)
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nslots = [(rng.standard_normal(tod[4])
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+ 1j * rng.standard_normal(tod[4])) / math.sqrt(2)
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for _ in range(tod[3])]
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# attention scheme transmits with ITS OWN trained masks
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r0a = h1 * (model[0] @ e1) + h2 * (model[1] @ e2)
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for k, s in enumerate(SNRS):
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sig = 10 ** (-s / 20.0)
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r = r0 + sig * n
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t1 = M1.T @ r / h1; t2 = M2.T @ r / h2
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g1 = (t1 - bi * (h2 / h1) * t2) / gi
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g2 = (t2 - bi * (h1 / h2) * t1) / gi
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res["edma"][k] += 0.5 * (cosine(g1, e1) + cosine(g2, e2))
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o1 = e1 + math.sqrt(2) * sig * n / h1
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o2 = e2 + math.sqrt(2) * sig * n2 / h2
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res["oma"][k] += 0.5 * (cosine(o1, e1) + cosine(o2, e2))
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ge1 = M1.T @ (r - h2 * (M2 @ e2)) / h1
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ge2 = M2.T @ (r - h1 * (M1 @ e1)) / h2
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res["genie"][k] += 0.5 * (cosine(ge1, e1) + cosine(ge2, e2))
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a1, a2 = att_apply(model, r0a + sig * n, h1, h2)
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res["att"][k] += 0.5 * (cosine(a1, e1) + cosine(a2, e2))
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res["att_x"][k] += 0.5 * (cosine(a1, e2) + cosine(a2, e1))
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for kk in ("edma", "oma", "genie", "att", "att_x"):
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cnt[kk][k] += 1
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if f < 40: # ToDMA heavier: 40 fading draws
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recs = todma_run(tod, (c1, c2), (h1, h2), sig, nslots)
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got = [cosine(recs[j], (e1, e2)[j])
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r0 = h[0] * (M1 @ e1).to(torch.cfloat) \
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+ h[1] * (M2 @ e2).to(torch.cfloat)
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r = r0.unsqueeze(0) + sigs_t.view(-1, 1) * n.unsqueeze(0)
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t1 = (M1.T.to(torch.cfloat) @ r.unsqueeze(-1)).squeeze(-1) / h[0]
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t2 = (M2.T.to(torch.cfloat) @ r.unsqueeze(-1)).squeeze(-1) / h[1]
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c1 = (h[1] / h[0]).item()
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c2 = (h[0] / h[1]).item()
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v1 = sigs_t**2 / h[0].abs()**2
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v2 = sigs_t**2 / h[1].abs()**2
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g1 = aware_batch(t1, Q, bi, c1, v1)
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g2 = aware_batch(t2, Q.T, bi, c2, v2)
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res["edma"] += 0.5 * (abscos(g1, e1) + abscos(g2, e2))
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o1 = e1.to(torch.cfloat).unsqueeze(0) \
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+ math.sqrt(2) * sigs_t.view(-1, 1) * n.unsqueeze(0) / h[0]
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o2 = e2.to(torch.cfloat).unsqueeze(0) \
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+ math.sqrt(2) * sigs_t.view(-1, 1) * n2.unsqueeze(0) / h[1]
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res["oma"] += 0.5 * (abscos(o1, e1) + abscos(o2, e2))
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ge1 = (M1.T.to(torch.cfloat)
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@ (r - h[1] * (M2 @ e2).to(torch.cfloat)).unsqueeze(-1)
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).squeeze(-1) / h[0]
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ge2 = (M2.T.to(torch.cfloat)
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@ (r - h[0] * (M1 @ e1).to(torch.cfloat)).unsqueeze(-1)
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).squeeze(-1) / h[1]
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res["genie"] += 0.5 * (abscos(ge1, e1) + abscos(ge2, e2))
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for kk in ("edma", "oma", "genie"):
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cnt[kk] += 1
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if f < NFADE_TOD:
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hnp = (complex(h[0].item()), complex(h[1].item()))
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nslots = [(rng.standard_normal(tod[4])
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+ 1j * rng.standard_normal(tod[4]))
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/ math.sqrt(2) for _ in range(tod[3])]
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e1n, e2n = A[i], B[i]
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for k, s in enumerate(SNRS):
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sig = 10 ** (-s / 20.0)
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recs = todma_run(tod, (c1c, c2c), hnp, sig, nslots)
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got = [cosine(recs[j], (e1n, e2n)[j])
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for j in range(2) if recs[j] is not None]
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if got:
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res["todma"][k] += float(np.mean(got))
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@@ -299,23 +231,6 @@ def main():
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for k in keys:
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res[k] /= np.maximum(cnt[k], 1)
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fig, ax = plt.subplots()
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||||
ax.plot(SNRS, res["edma"], "o-", color="C3", label="EDMA (closed form)")
|
||||
ax.plot(SNRS, res["att"], "s--", color="C0",
|
||||
label="Attention-based (retrained)")
|
||||
ax.plot(SNRS, res["todma"], "d-.", color="C4", label="ToDMA-adapted")
|
||||
ax.plot(SNRS, res["oma"], "v:", color="C1", label="OMA")
|
||||
ax.plot(SNRS, res["genie"], "-", color="gray", lw=1.0,
|
||||
label="Genie-aided SIC bound")
|
||||
ax.set_xlabel("Per-block SNR $\\rho$ [dB]")
|
||||
ax.set_ylabel("Mean cosine similarity")
|
||||
ax.set_xlim(SNRS[0], SNRS[-1]); ax.set_ylim(0, 0.85)
|
||||
ax.legend(loc="upper left")
|
||||
fig.subplots_adjust(**AXES_RECT)
|
||||
fig.savefig(FIG / "fig_bertvit_merged.pdf")
|
||||
plt.close(fig)
|
||||
print(f"[OK] wrote {FIG/'fig_bertvit_merged.pdf'}")
|
||||
|
||||
with open(DATA / "bertvit_merged.csv", "w", newline="") as fcsv:
|
||||
w = csv.writer(fcsv)
|
||||
w.writerow(["snr_db"] + list(keys))
|
||||
@@ -323,8 +238,7 @@ def main():
|
||||
w.writerow([s] + [res[key][k] for key in keys])
|
||||
print(f"[OK] wrote {DATA/'bertvit_merged.csv'}")
|
||||
for k, s in enumerate(SNRS):
|
||||
print(f" {s:4.0f} dB EDMA {res['edma'][k]:.3f} "
|
||||
f"ATT {res['att'][k]:.3f} (x {res['att_x'][k]:.3f}) "
|
||||
print(f" {s:4.1f} dB EDMA {res['edma'][k]:.3f} "
|
||||
f"ToDMA {res['todma'][k]:.3f} OMA {res['oma'][k]:.3f} "
|
||||
f"genie {res['genie'][k]:.3f}")
|
||||
|
||||
|
||||
+140
-119
@@ -1,23 +1,23 @@
|
||||
"""
|
||||
Capacity-matched EDMA refinement (parameter budget equal to the
|
||||
attention scheme: 4 d^2 = 2.36M at d = 768).
|
||||
Refinement stage for the v2 (affinity-aware Wiener) EDMA receiver.
|
||||
================================================================
|
||||
Four-head averaged gated refinement applied to the closed-form
|
||||
demultiplexer output:
|
||||
Trains the single-gate refinement operator
|
||||
|
||||
out = (1/4) sum_k D softmax(Q_k x / sqrt(D)) .* x,
|
||||
out = D softmax(W z / sqrt(D)) .* z, z = Re(e_hat),
|
||||
|
||||
with Q_1..Q_4 in R^{D x D} (4 d^2 parameters, exactly the
|
||||
attention scheme's budget). The single-gate 0.59M refiner is the
|
||||
special case of four identical heads, so the family contains it
|
||||
by construction. Same training recipe: demux outputs from
|
||||
parametric pairs at beta = 0.028, Haar pool 32, Rayleigh
|
||||
channels, complex noise, training SNR uniform in [5, 25] dB,
|
||||
Adam 5e-4 with gradient clipping, batch 48, 200 epochs.
|
||||
(0.59M parameters at d = 768) on aware-demultiplexer outputs, then
|
||||
warm-starts a capacity-check variant with four heads (4 d^2 = 2.36M)
|
||||
and fine-tunes it, so the family contains the single gate by
|
||||
construction. Training data: parametric pairs at beta = 0.028, a
|
||||
fixed pool of 32 independent Haar mask pairs, Rayleigh channels,
|
||||
complex noise, training SNR uniform in [5, 25] dB, Adam 5e-4 with
|
||||
gradient clipping, batch 48, 220 epochs (stage 2 from epoch 120 at
|
||||
lr 2e-4).
|
||||
|
||||
Evaluation on the real BERT/ViT pairs with fresh Haar masks and
|
||||
200 fading draws per pair. Appends column `edma_ref2` to
|
||||
data/bertvit_merged.csv and prints all-curve numbers.
|
||||
NFADE fading draws per pair. Appends columns `edma_ref` (single
|
||||
gate) and `edma_ref2` (four heads) to data/bertvit_merged.csv.
|
||||
Requires torch (run under WSL with CUDA if available).
|
||||
"""
|
||||
from __future__ import annotations
|
||||
import csv
|
||||
@@ -26,161 +26,182 @@ import time
|
||||
import numpy as np
|
||||
import torch
|
||||
|
||||
from fig_real_merged import load_pairs, cosine, SNRS, NFADE, D, DATA
|
||||
from fig_real_merged import load_pairs, SNRS, NFADE, D, DATA
|
||||
|
||||
SEED = 2026
|
||||
rng = np.random.default_rng(SEED + 31)
|
||||
torch.manual_seed(SEED + 31)
|
||||
DEV = "cuda" if torch.cuda.is_available() else "cpu"
|
||||
BETA0 = 0.028
|
||||
G0 = 1.0 - BETA0**2
|
||||
print(f"[refine] device = {DEV}")
|
||||
|
||||
|
||||
def haar_t(gen):
|
||||
Q, R = torch.linalg.qr(torch.randn(D, D, generator=gen))
|
||||
return Q * torch.sign(torch.diagonal(R))
|
||||
def haar_t(n, gen):
|
||||
G = torch.randn(n, D, D, generator=gen, device=DEV)
|
||||
Q, R = torch.linalg.qr(G)
|
||||
return Q * torch.sign(torch.diagonal(R, dim1=-2, dim2=-1)).unsqueeze(-2)
|
||||
|
||||
|
||||
def train_refiner2(epochs=220, steps=20, batch=48, lr=5e-4,
|
||||
l2=0.5, l3=0.5, pool=32):
|
||||
"""Stage 1 trains a single gate (the proven 0.59M recipe); stage 2
|
||||
warm-starts four heads from it plus small perturbations and
|
||||
fine-tunes at a reduced learning rate, so the capacity-matched
|
||||
family starts at the single-gate solution it contains."""
|
||||
print(f"=== training capacity-matched refinement (4-head gate, "
|
||||
f"4d^2 = {4*D*D/1e6:.2f}M params, warm-started) ===",
|
||||
flush=True)
|
||||
gen = torch.Generator().manual_seed(SEED + 31)
|
||||
masks = []
|
||||
for _ in range(pool):
|
||||
U1, U2 = haar_t(gen), haar_t(gen)
|
||||
masks.append((U1.numpy(), (BETA0 * U1
|
||||
+ math.sqrt(G0) * U2).numpy()))
|
||||
Q0 = torch.nn.Parameter(torch.randn(D, D, generator=gen)
|
||||
/ math.sqrt(D))
|
||||
params = [Q0]
|
||||
def aware_t(t1, Q, beta, c1, nvar):
|
||||
"""Batched affinity-aware Wiener demux in torch (complex)."""
|
||||
b = t1.shape[0]
|
||||
g = 1.0 - beta * beta
|
||||
rho = g * (c1.abs()**2) / D + nvar # (b,)
|
||||
A = torch.eye(D, device=DEV, dtype=torch.cfloat).expand(b, D, D) \
|
||||
+ beta * c1.view(b, 1, 1) * Q.to(torch.cfloat)
|
||||
S = A @ A.mH / D + rho.view(b, 1, 1) \
|
||||
* torch.eye(D, device=DEV, dtype=torch.cfloat)
|
||||
x = torch.linalg.solve(S, t1.unsqueeze(-1))
|
||||
return (A.mH @ x).squeeze(-1) / D
|
||||
|
||||
|
||||
def train_batch(masks, Qs, gen, batch):
|
||||
"""Generate one training batch of aware-demux outputs (user 1)."""
|
||||
e1 = torch.nn.functional.normalize(
|
||||
torch.randn(batch, D, generator=gen, device=DEV), dim=1)
|
||||
w = torch.randn(batch, D, generator=gen, device=DEV)
|
||||
w = w - (w * e1).sum(1, keepdim=True) * e1
|
||||
w = torch.nn.functional.normalize(w, dim=1)
|
||||
e2 = BETA0 * e1 + math.sqrt(G0) * w
|
||||
sel = torch.randint(len(masks), (batch,), generator=gen, device=DEV)
|
||||
M1 = masks[0][sel]; M2 = masks[1][sel]; Q = Qs[sel]
|
||||
snr = 5.0 + 20.0 * torch.rand(batch, generator=gen, device=DEV)
|
||||
sig = 10 ** (-snr / 20.0)
|
||||
h = (torch.randn(batch, 2, generator=gen, device=DEV)
|
||||
+ 1j * torch.randn(batch, 2, generator=gen, device=DEV)) \
|
||||
/ math.sqrt(2)
|
||||
n = (torch.randn(batch, D, generator=gen, device=DEV)
|
||||
+ 1j * torch.randn(batch, D, generator=gen, device=DEV)) \
|
||||
/ math.sqrt(2)
|
||||
r = h[:, :1] * (M1 @ e1.unsqueeze(-1)).squeeze(-1).to(torch.cfloat) \
|
||||
+ h[:, 1:2] * (M2 @ e2.unsqueeze(-1)).squeeze(-1).to(torch.cfloat) \
|
||||
+ sig.view(-1, 1) * n
|
||||
t1 = (M1.transpose(-1, -2).to(torch.cfloat)
|
||||
@ r.unsqueeze(-1)).squeeze(-1) / h[:, :1]
|
||||
c1 = h[:, 1] / h[:, 0]
|
||||
nvar = sig**2 / h[:, 0].abs()**2
|
||||
g1 = aware_t(t1, Q, BETA0, c1, nvar)
|
||||
return g1.real.float(), e1
|
||||
|
||||
|
||||
def train_refiners(epochs=220, steps=20, batch=48, lr=5e-4,
|
||||
l2=0.5, l3=0.5, pool=32, stage2_at=120):
|
||||
print(f"=== training refinement (single gate {D*D/1e6:.2f}M, "
|
||||
f"then 4-head warm start {4*D*D/1e6:.2f}M) ===", flush=True)
|
||||
gen = torch.Generator(device=DEV).manual_seed(SEED + 31)
|
||||
U1 = haar_t(pool, gen); U2 = haar_t(pool, gen)
|
||||
masks = (U1, U2)
|
||||
Qs = U1.transpose(-1, -2) @ U2
|
||||
params = [torch.nn.Parameter(
|
||||
torch.randn(D, D, generator=gen, device=DEV) / math.sqrt(D))]
|
||||
opt = torch.optim.Adam(params, lr=lr)
|
||||
stage2_at = 120 # epochs of single-gate pre-training
|
||||
P_single = None
|
||||
|
||||
def forward(x):
|
||||
def forward(x, ps):
|
||||
outs = [D * torch.softmax((x @ Qk.T) / math.sqrt(D), dim=1) * x
|
||||
for Qk in params]
|
||||
return sum(outs) / len(params)
|
||||
for Qk in ps]
|
||||
return sum(outs) / len(ps)
|
||||
|
||||
t0 = time.time()
|
||||
for ep in range(epochs):
|
||||
if ep == stage2_at:
|
||||
P_single = params[0].detach().clone()
|
||||
base = params[0].detach()
|
||||
params = [torch.nn.Parameter(
|
||||
base.clone() + 0.02 * torch.randn(D, D, generator=gen)
|
||||
base.clone() + 0.02 * torch.randn(D, D, generator=gen,
|
||||
device=DEV)
|
||||
/ math.sqrt(D)) for _ in range(4)]
|
||||
opt = torch.optim.Adam(params, lr=2e-4)
|
||||
print(f" [warm start] 4 heads initialised from the trained "
|
||||
f"gate at epoch {ep}", flush=True)
|
||||
print(f" [warm start] 4 heads at epoch {ep}", flush=True)
|
||||
for _ in range(steps):
|
||||
xs, ts = [], []
|
||||
for _ in range(batch):
|
||||
e1 = torch.nn.functional.normalize(
|
||||
torch.randn(D, generator=gen), dim=0).numpy()
|
||||
w = torch.randn(D, generator=gen).numpy()
|
||||
w = w - (w @ e1) * e1
|
||||
w = w / np.linalg.norm(w)
|
||||
e2 = BETA0 * e1 + math.sqrt(G0) * w
|
||||
M1, M2 = masks[int(torch.randint(pool, (1,),
|
||||
generator=gen))]
|
||||
snr = float(5.0 + 20.0 * torch.rand(1, generator=gen))
|
||||
sig = 10 ** (-snr / 20.0)
|
||||
h = (torch.randn(2, generator=gen).numpy()
|
||||
+ 1j * torch.randn(2, generator=gen).numpy()) \
|
||||
/ math.sqrt(2)
|
||||
nc = (torch.randn(D, generator=gen).numpy()
|
||||
+ 1j * torch.randn(D, generator=gen).numpy()) \
|
||||
/ math.sqrt(2)
|
||||
rc = h[0] * (M1 @ e1) + h[1] * (M2 @ e2) + sig * nc
|
||||
t1 = M1.T @ rc / h[0]
|
||||
t2 = M2.T @ rc / h[1]
|
||||
g1 = (t1 - BETA0 * (h[1] / h[0]) * t2) / G0
|
||||
xs.append(torch.tensor(np.real(g1), dtype=torch.float32))
|
||||
ts.append(torch.tensor(e1, dtype=torch.float32))
|
||||
x = torch.stack(xs); t = torch.stack(ts)
|
||||
out = forward(x)
|
||||
mse = ((out - t)**2).mean()
|
||||
cs = torch.nn.functional.cosine_similarity(out, t, dim=1).mean()
|
||||
with torch.no_grad():
|
||||
x, tgt = train_batch(masks, Qs, gen, batch)
|
||||
out = forward(x, params)
|
||||
mse = ((out - tgt)**2).mean()
|
||||
cs = torch.nn.functional.cosine_similarity(out, tgt, dim=1).mean()
|
||||
loss = l2 * mse + l3 * (1.0 - cs)
|
||||
opt.zero_grad(); loss.backward()
|
||||
torch.nn.utils.clip_grad_norm_(params, 1.0)
|
||||
opt.step()
|
||||
if (ep + 1) % 50 == 0:
|
||||
if (ep + 1) % 40 == 0:
|
||||
print(f" epoch {ep+1}: loss {float(loss.detach()):.4f} "
|
||||
f"(cos {float(cs.detach()):.3f})", flush=True)
|
||||
print(f" trained in {time.time()-t0:.0f}s")
|
||||
return [p.detach().numpy() for p in params]
|
||||
return P_single, [p.detach() for p in params]
|
||||
|
||||
|
||||
def refine2(P, g):
|
||||
x = np.real(g)
|
||||
|
||||
def gate(Q, v):
|
||||
sc = (Q @ v) / math.sqrt(D)
|
||||
sc = sc - sc.max()
|
||||
w = np.exp(sc); w /= w.sum()
|
||||
return D * w * v
|
||||
|
||||
return sum(gate(Qk, x) for Qk in P) / 4.0
|
||||
def refine_apply(ps, z):
|
||||
"""z: (b, D) real torch tensor; ps: list of gates."""
|
||||
outs = [D * torch.softmax((z @ Qk.T) / math.sqrt(D), dim=1) * z
|
||||
for Qk in ps]
|
||||
return sum(outs) / len(ps)
|
||||
|
||||
|
||||
def main():
|
||||
A, B, betas = load_pairs()
|
||||
P = train_refiner2()
|
||||
ref = np.zeros(len(SNRS)); cnt = 0
|
||||
P1, P4 = train_refiners()
|
||||
gen = torch.Generator(device=DEV).manual_seed(SEED + 77)
|
||||
ref1 = np.zeros(len(SNRS)); ref4 = np.zeros(len(SNRS)); cnt = 0
|
||||
t0 = time.time()
|
||||
At = torch.tensor(A, dtype=torch.float32, device=DEV)
|
||||
Bt = torch.tensor(B, dtype=torch.float32, device=DEV)
|
||||
for i in range(len(A)):
|
||||
e1, e2, bi = A[i], B[i], float(betas[i])
|
||||
gi = 1.0 - bi**2
|
||||
bi = float(betas[i])
|
||||
e1 = At[i]; e2 = Bt[i]
|
||||
for f in range(NFADE):
|
||||
G1 = rng.standard_normal((D, D))
|
||||
Qh, Rh = np.linalg.qr(G1)
|
||||
U1 = Qh * np.sign(np.diag(Rh))
|
||||
G2 = rng.standard_normal((D, D))
|
||||
Qh, Rh = np.linalg.qr(G2)
|
||||
U2 = Qh * np.sign(np.diag(Rh))
|
||||
M1 = U1
|
||||
M2 = bi * U1 + math.sqrt(gi) * U2
|
||||
h = (rng.standard_normal(2) + 1j * rng.standard_normal(2)) \
|
||||
M = haar_t(2, gen)
|
||||
M1, M2 = M[0], M[1]
|
||||
Q = M1.T @ M2
|
||||
h = (torch.randn(2, generator=gen, device=DEV)
|
||||
+ 1j * torch.randn(2, generator=gen, device=DEV)) \
|
||||
/ math.sqrt(2)
|
||||
h1, h2 = h
|
||||
r0 = h1 * (M1 @ e1) + h2 * (M2 @ e2)
|
||||
n = (rng.standard_normal(D) + 1j * rng.standard_normal(D)) \
|
||||
n = (torch.randn(D, generator=gen, device=DEV)
|
||||
+ 1j * torch.randn(D, generator=gen, device=DEV)) \
|
||||
/ math.sqrt(2)
|
||||
for k, s in enumerate(SNRS):
|
||||
sig = 10 ** (-s / 20.0)
|
||||
r = r0 + sig * n
|
||||
t1 = M1.T @ r / h1; t2 = M2.T @ r / h2
|
||||
g1 = (t1 - bi * (h2 / h1) * t2) / gi
|
||||
g2 = (t2 - bi * (h1 / h2) * t1) / gi
|
||||
ref[k] += 0.5 * (cosine(refine2(P, g1), e1)
|
||||
+ cosine(refine2(P, g2), e2))
|
||||
r0 = h[0] * (M1 @ e1).to(torch.cfloat) \
|
||||
+ h[1] * (M2 @ e2).to(torch.cfloat)
|
||||
sigs = torch.tensor(10 ** (-SNRS / 20.0), device=DEV,
|
||||
dtype=torch.float32)
|
||||
nb = len(SNRS)
|
||||
r = r0.unsqueeze(0) + sigs.view(-1, 1) * n.unsqueeze(0)
|
||||
t1 = (M1.T.to(torch.cfloat) @ r.unsqueeze(-1)).squeeze(-1) / h[0]
|
||||
t2 = (M2.T.to(torch.cfloat) @ r.unsqueeze(-1)).squeeze(-1) / h[1]
|
||||
c1 = (h[1] / h[0]).expand(nb)
|
||||
c2 = (h[0] / h[1]).expand(nb)
|
||||
v1 = (sigs**2 / h[0].abs()**2)
|
||||
v2 = (sigs**2 / h[1].abs()**2)
|
||||
g1 = aware_t(t1, Q.expand(nb, D, D), bi, c1, v1).real.float()
|
||||
g2 = aware_t(t2, Q.T.expand(nb, D, D), bi, c2, v2).real.float()
|
||||
with torch.no_grad():
|
||||
for P, acc in ((([P1]), ref1), ((P4), ref4)):
|
||||
o1 = refine_apply(P, g1)
|
||||
o2 = refine_apply(P, g2)
|
||||
cs1 = torch.nn.functional.cosine_similarity(
|
||||
o1, e1.unsqueeze(0), dim=1).abs()
|
||||
cs2 = torch.nn.functional.cosine_similarity(
|
||||
o2, e2.unsqueeze(0), dim=1).abs()
|
||||
acc += (0.5 * (cs1 + cs2)).cpu().numpy()
|
||||
cnt += 1
|
||||
print(f" pair {i+1}/{len(A)} done ({time.time()-t0:.0f}s)",
|
||||
flush=True)
|
||||
ref /= cnt
|
||||
ref1 /= cnt; ref4 /= cnt
|
||||
|
||||
rows = list(csv.DictReader(open(DATA / "bertvit_merged.csv")))
|
||||
names = list(rows[0].keys())
|
||||
if "edma_ref2" not in names:
|
||||
names.append("edma_ref2")
|
||||
for col in ("edma_ref", "edma_ref2"):
|
||||
if col not in names:
|
||||
names.append(col)
|
||||
for k, r in enumerate(rows):
|
||||
r["edma_ref2"] = f"{ref[k]}"
|
||||
r["edma_ref"] = f"{ref1[k]}"
|
||||
r["edma_ref2"] = f"{ref4[k]}"
|
||||
with open(DATA / "bertvit_merged.csv", "w", newline="") as f:
|
||||
w = csv.DictWriter(f, fieldnames=names)
|
||||
w.writeheader(); w.writerows(rows)
|
||||
print("[OK] appended edma_ref2 to bertvit_merged.csv")
|
||||
print("[OK] appended edma_ref / edma_ref2 to bertvit_merged.csv")
|
||||
for k, r in enumerate(rows):
|
||||
print(f" {float(r['snr_db']):4.0f} dB "
|
||||
f"EDMA {float(r['edma']):.3f} "
|
||||
f"ref(0.59M) {float(r['edma_ref']):.3f} "
|
||||
f"ref2(2.36M) {ref[k]:.3f} "
|
||||
f"ATT(2.36M) {float(r['att']):.3f} "
|
||||
f"genie {float(r['genie']):.3f}")
|
||||
print(f" {float(r['snr_db']):4.1f} dB "
|
||||
f"EDMA {float(r['edma']):.3f} ref {ref1[k]:.3f} "
|
||||
f"ref2 {ref4[k]:.3f} genie {float(r['genie']):.3f}")
|
||||
|
||||
|
||||
if __name__ == "__main__":
|
||||
|
||||
@@ -0,0 +1,179 @@
|
||||
"""Canonical figure rendering. Reads ONLY data/*.csv, writes fig/*.pdf.
|
||||
|
||||
Figures: fig_floor, fig_rate_corrected, fig_beta_sweep_corrected,
|
||||
fig_sic, fig_multiuser_corrected. (fig_bertvit_merged is rendered by
|
||||
replot_merged.py; block_diagram.pdf comes from block_diagram_src.tex.)
|
||||
One physical geometry and one label dictionary for every plot.
|
||||
"""
|
||||
import csv
|
||||
import math
|
||||
from pathlib import Path
|
||||
import matplotlib
|
||||
matplotlib.use("Agg")
|
||||
import matplotlib.pyplot as plt
|
||||
|
||||
ROOT = Path(__file__).resolve().parents[1]
|
||||
DATA = ROOT / "data"
|
||||
FIG = ROOT / "fig"
|
||||
|
||||
plt.rcParams.update({
|
||||
"font.family": "serif",
|
||||
"font.serif": ["DejaVu Serif", "Times New Roman"],
|
||||
"font.size": 9, "axes.labelsize": 9, "legend.fontsize": 6.6,
|
||||
"xtick.labelsize": 8, "ytick.labelsize": 8,
|
||||
"axes.grid": True, "grid.linestyle": "--", "grid.linewidth": 0.4,
|
||||
"grid.alpha": 0.6, "lines.linewidth": 1.4, "lines.markersize": 4.0,
|
||||
"figure.figsize": (3.15, 2.36), "pdf.fonttype": 42,
|
||||
})
|
||||
AXES_RECT = dict(left=0.205, right=0.965, top=0.955, bottom=0.185)
|
||||
|
||||
LBL = {
|
||||
"edma": "EDMA",
|
||||
"blind": "Affinity-blind",
|
||||
"oma": "OMA",
|
||||
"genie": "Genie-aided SIC bound",
|
||||
"sic": "Realizable analog SIC",
|
||||
"todma": "ToDMA-adapted",
|
||||
"mac": "MAC sum capacity",
|
||||
"coop": "Full-cooperation bound",
|
||||
"hybrid": "EDMA + refinement stage",
|
||||
}
|
||||
|
||||
|
||||
def rows_of(name):
|
||||
return list(csv.DictReader(open(DATA / f"{name}.csv")))
|
||||
|
||||
|
||||
def col(rows, k):
|
||||
return [float(r[k]) for r in rows]
|
||||
|
||||
|
||||
def save(fig, name):
|
||||
fig.subplots_adjust(**AXES_RECT)
|
||||
fig.savefig(FIG / f"{name}.pdf")
|
||||
plt.close(fig)
|
||||
print(f"[OK] wrote {name}.pdf")
|
||||
|
||||
|
||||
# ------------------------------------------------------ fig_floor
|
||||
def fig_floor():
|
||||
rows = rows_of("floor_validation")
|
||||
fig, ax = plt.subplots()
|
||||
colors = {"256": "C0", "768": "C3"}
|
||||
beta = 0.311
|
||||
for d in ("256", "768"):
|
||||
rd = [r for r in rows if r["d"] == d or r["d"] == f"{d}.0"
|
||||
or float(r["d"]) == float(d)]
|
||||
snr = col(rd, "snr_db")
|
||||
ax.plot(snr, col(rd, "mse_mc"), "o", ms=3.5, color=colors[d],
|
||||
mfc="none", label=rf"Monte Carlo, $d={d}$")
|
||||
ax.plot(snr, col(rd, "mse_theory"), "-", color=colors[d],
|
||||
label=rf"Theorem 1, $d={d}$")
|
||||
if d == "768":
|
||||
ax.plot(snr, col(rd, "mse_blind"), "--", color="C1", lw=1.2,
|
||||
label=LBL["blind"])
|
||||
g = 1.0 - beta**2
|
||||
ax.axhline(math.sqrt(g) / 2, color="gray", lw=0.8, ls="--")
|
||||
ax.axhline(0.5, color="gray", lw=0.8, ls=":")
|
||||
ax.annotate("blind floor $1/2$", xy=(17.0, 0.512), fontsize=7,
|
||||
color="gray")
|
||||
ax.annotate(r"aware floor $\sqrt{1-\beta^2}/2$", xy=(14.0, 0.432),
|
||||
fontsize=7, color="gray")
|
||||
ax.set_xlabel("Per-block SNR $\\rho$ [dB]")
|
||||
ax.set_ylabel(r"Per-user MSE $\mathbb{E}\|\hat{\mathbf{e}}_u-\mathbf{e}_u\|_2^2$")
|
||||
ax.set_xlim(0, 40); ax.set_ylim(0.4, 1.05)
|
||||
ax.legend(loc="lower left", bbox_to_anchor=(0.02, 0.18))
|
||||
save(fig, "fig_floor")
|
||||
|
||||
|
||||
# ------------------------------------------------ fig_rate_corrected
|
||||
def fig_rate():
|
||||
rows = rows_of("rate_corrected")
|
||||
snr = col(rows, "snr_db")
|
||||
fig, ax = plt.subplots()
|
||||
ax.plot(snr, col(rows, "edma"), "-", color="C3", label=LBL["edma"])
|
||||
ax.plot(snr, col(rows, "blind"), ":", color="C4", lw=1.2,
|
||||
label=LBL["blind"])
|
||||
ax.plot(snr, col(rows, "oma"), "--", color="C1", label=LBL["oma"])
|
||||
ax.plot(snr, col(rows, "genie"), "-.", color="C0", label=LBL["genie"])
|
||||
ax.plot(snr, col(rows, "mac"), "-", color="k", lw=1.0, label=LBL["mac"])
|
||||
ax.set_xlabel("Per-block SNR $\\rho$ [dB]")
|
||||
ax.set_ylabel("Effective sum rate [bps/Hz]")
|
||||
ax.set_xlim(0, 40); ax.set_ylim(0, 3.2)
|
||||
ax.legend(loc="upper left")
|
||||
save(fig, "fig_rate_corrected")
|
||||
|
||||
|
||||
# ------------------------------------------ fig_beta_sweep_corrected
|
||||
def fig_beta_sweep():
|
||||
rows = rows_of("beta_sweep_corrected")
|
||||
fig, ax = plt.subplots()
|
||||
for s, cc in (("10", "C0"), ("20", "C3")):
|
||||
rd = [r for r in rows if float(r["snr_db"]) == float(s)]
|
||||
b = col(rd, "beta")
|
||||
ax.plot(b, col(rd, "edma"), "-", color=cc,
|
||||
label=rf"EDMA, $\rho={s}$ dB")
|
||||
ax.axhline(float(rd[0]["blind"]), color=cc, ls=":", lw=1.0)
|
||||
ax.axhline(float(rd[0]["oma"]), color=cc, ls="--", lw=1.0)
|
||||
ax.axhline(float(rd[0]["genie"]), color=cc, ls="-.", lw=0.8)
|
||||
# one legend entry per reference style (color-independent)
|
||||
ax.plot([], [], ls=":", color="gray", label=LBL["blind"])
|
||||
ax.plot([], [], ls="--", color="gray", label=LBL["oma"])
|
||||
ax.plot([], [], ls="-.", color="gray", label=LBL["genie"])
|
||||
for b0 in (0.030, 0.311):
|
||||
ax.axvline(b0, color="gray", ls=":", lw=0.9)
|
||||
ax.set_xlabel(r"Pairwise affinity $\beta$")
|
||||
ax.set_ylabel("Effective sum rate [bps/Hz]")
|
||||
ax.set_xlim(0, 1); ax.set_ylim(0, 1.0)
|
||||
ax.legend(loc="upper left")
|
||||
save(fig, "fig_beta_sweep_corrected")
|
||||
|
||||
|
||||
# ------------------------------------------------------- fig_sic
|
||||
def fig_sic():
|
||||
rows = rows_of("sic_comparison")
|
||||
snr = col(rows, "snr_db")
|
||||
fig, ax = plt.subplots()
|
||||
ax.plot(snr, col(rows, "edma"), "o-", color="C3", label=LBL["edma"])
|
||||
ax.plot(snr, col(rows, "blind"), "d:", color="C4", label=LBL["blind"])
|
||||
ax.plot(snr, col(rows, "sic"), "^-.", color="C2", label=LBL["sic"])
|
||||
ax.plot(snr, col(rows, "oma"), "v--", color="C1", label=LBL["oma"])
|
||||
ax.plot(snr, col(rows, "genie"), "-", color="gray", lw=1.0,
|
||||
label=LBL["genie"])
|
||||
ax.set_xlabel("Per-block SNR $\\rho$ [dB]")
|
||||
ax.set_ylabel("Mean cosine similarity")
|
||||
ax.set_xlim(snr[0], snr[-1]); ax.set_ylim(0, 0.7)
|
||||
ax.legend(loc="upper left")
|
||||
save(fig, "fig_sic")
|
||||
|
||||
|
||||
# ------------------------------------------ fig_multiuser_corrected
|
||||
def fig_multiuser():
|
||||
rows = rows_of("multiuser_corrected")
|
||||
fig, ax = plt.subplots()
|
||||
colors = {"2": "C0", "3": "C2", "4": "C3"}
|
||||
for U in ("2", "3", "4"):
|
||||
rd = [r for r in rows if float(r["U"]) == float(U)]
|
||||
snr = col(rd, "snr_db")
|
||||
ax.plot(snr, col(rd, "edma_mc"), "-", color=colors[U],
|
||||
label=rf"EDMA, $U={U}$")
|
||||
ax.plot(snr, col(rd, "oma"), "--", color=colors[U], lw=1.0,
|
||||
label=rf"OMA, $U={U}$")
|
||||
mk = [i for i, s in enumerate(snr) if s % 5 == 0]
|
||||
ax.plot([snr[i] for i in mk], [col(rd, "edma_mc")[i] for i in mk],
|
||||
"o", color=colors[U], ms=4, mfc="none")
|
||||
ax.set_xlabel("Per-block SNR $\\rho$ [dB]")
|
||||
ax.set_ylabel("Effective sum rate [bps/Hz]")
|
||||
ax.set_xlim(0, 30)
|
||||
ax.legend(loc="upper left")
|
||||
save(fig, "fig_multiuser_corrected")
|
||||
|
||||
|
||||
if __name__ == "__main__":
|
||||
import sys
|
||||
todo = set(sys.argv[1:])
|
||||
ALL = {"floor": fig_floor, "rate": fig_rate, "beta": fig_beta_sweep,
|
||||
"sic": fig_sic, "multi": fig_multiuser}
|
||||
for name, fn in ALL.items():
|
||||
if not todo or name in todo:
|
||||
fn()
|
||||
@@ -1,6 +1,7 @@
|
||||
"""Canonical replot of fig_bertvit_merged.pdf from data/bertvit_merged.csv.
|
||||
Curves: EDMA, EDMA + refinement (hybrid), ToDMA-adapted, OMA, genie bound.
|
||||
The attention columns remain in the CSV but are not plotted."""
|
||||
The capacity-check column edma_ref2 remains in the CSV but is not
|
||||
plotted (it tracks edma_ref; quoted in the text only)."""
|
||||
import csv
|
||||
from pathlib import Path
|
||||
import matplotlib
|
||||
@@ -24,7 +25,7 @@ snr = [float(r["snr_db"]) for r in rows]
|
||||
col = lambda k: [float(r[k]) for r in rows]
|
||||
|
||||
fig, ax = plt.subplots()
|
||||
ax.plot(snr, col("edma"), "o-", color="C3", label="EDMA (closed form)")
|
||||
ax.plot(snr, col("edma"), "o-", color="C3", label="EDMA")
|
||||
ax.plot(snr, col("edma_ref"), "^-", color="C2",
|
||||
label="EDMA + refinement stage")
|
||||
ax.plot(snr, col("todma"), "d-.", color="C4", label="ToDMA-adapted")
|
||||
|
||||
@@ -1,43 +0,0 @@
|
||||
"""Canonical replot of fig_sic.pdf from data/sic_comparison.csv
|
||||
(realizable analog SIC vs genie SIC vs EDMA vs OMA, beta = 0.311,
|
||||
d = 512, block-Rayleigh). US-spelling labels, uniform geometry."""
|
||||
import csv
|
||||
from pathlib import Path
|
||||
import matplotlib
|
||||
matplotlib.use("Agg")
|
||||
import matplotlib.pyplot as plt
|
||||
|
||||
ROOT = Path(__file__).resolve().parents[1]
|
||||
plt.rcParams.update({
|
||||
"font.family": "serif",
|
||||
"font.serif": ["DejaVu Serif", "Times New Roman"],
|
||||
"font.size": 9, "axes.labelsize": 9, "legend.fontsize": 6.6,
|
||||
"xtick.labelsize": 8, "ytick.labelsize": 8,
|
||||
"axes.grid": True, "grid.linestyle": "--", "grid.linewidth": 0.4,
|
||||
"grid.alpha": 0.6, "lines.linewidth": 1.4, "lines.markersize": 4.0,
|
||||
"figure.figsize": (3.15, 2.36), "pdf.fonttype": 42,
|
||||
})
|
||||
AXES_RECT = dict(left=0.205, right=0.965, top=0.955, bottom=0.185)
|
||||
|
||||
rows = list(csv.DictReader(open(ROOT / "data" / "sic_comparison.csv")))
|
||||
snr = [float(r["snr_db"]) for r in rows]
|
||||
col = lambda k: [float(r[k]) for r in rows]
|
||||
|
||||
fig, ax = plt.subplots()
|
||||
ax.plot(snr, col("edma"), "o-", color="C3", label="EDMA (closed form)")
|
||||
ax.plot(snr, col("sic"), "^-.", color="C2", label="Realizable analog SIC")
|
||||
ax.plot(snr, col("oma"), "v:", color="C1", label="OMA")
|
||||
ax.plot(snr, col("genie"), "-", color="gray", lw=1.0,
|
||||
label="Genie-aided SIC bound")
|
||||
ax.set_xlabel("Per-block SNR $\\rho$ [dB]")
|
||||
ax.set_ylabel("Mean cosine similarity")
|
||||
ax.set_xlim(snr[0], snr[-1])
|
||||
ax.set_ylim(0, 0.7)
|
||||
ax.legend(loc="upper left")
|
||||
fig.subplots_adjust(**AXES_RECT)
|
||||
fig.savefig(ROOT / "fig" / "fig_sic.pdf")
|
||||
print("[OK] wrote fig_sic.pdf")
|
||||
for r in rows:
|
||||
print(f" {float(r['snr_db']):4.0f} dB EDMA {float(r['edma']):.3f} "
|
||||
f"SIC {float(r['sic']):.3f} genie {float(r['genie']):.3f} "
|
||||
f"OMA {float(r['oma']):.3f}")
|
||||
+182
-449
@@ -1,26 +1,45 @@
|
||||
"""
|
||||
Revision simulations for the EDMA TCOM resubmission.
|
||||
Simulations for the EDMA TVT manuscript (v2 design).
|
||||
=======================================================
|
||||
Implements the per-realisation (finite-d) analysis and the corrected
|
||||
energy-normalised rate accounting, plus the reviewer-requested
|
||||
experiments:
|
||||
Design v2: each user applies an independent orthogonal mask; the
|
||||
receiver runs one matched filter per user followed by the
|
||||
affinity-aware linear MMSE demultiplexer, which exploits the
|
||||
coherent interference component that the pairwise affinity beta
|
||||
predicts. Per-realization statistic for user 1 (c1 = h2/h1):
|
||||
|
||||
E0 Theorem-1 verification: exact self-interference constant C_SI
|
||||
E1 fig_floor : per-user MSE vs block SNR, interference floor
|
||||
E2 fig_sic : realisable SIC vs genie SIC vs EDMA vs OMA
|
||||
E3 (text numbers) : Rayleigh unconditional MSE, ZF vs regularised
|
||||
E4 fig_csi : imperfect-CSI robustness
|
||||
E5 fig_maskfam : Walsh-Hadamard structured masks vs Haar
|
||||
E6 fig_coop : high-affinity combining-mode crossover
|
||||
E7 fig_rate_corrected, fig_beta_sweep_corrected, fig_multiuser_corrected
|
||||
t1 = (I + beta*c1*Q) e1 + sqrt(g)*c1*Q w + n_t, Q = M1^T M2,
|
||||
|
||||
Conventions (identical to the revised manuscript):
|
||||
and the demultiplexer is the Wiener filter
|
||||
|
||||
e1_hat = (1/d) A^H (A A^H/d + (g|c1|^2/d + sig^2/|h1|^2) I)^{-1} t1,
|
||||
A = I + beta*c1*Q, g = 1 - beta^2.
|
||||
|
||||
Closed form (Theorem 1, d -> inf, per channel realization):
|
||||
|
||||
MSE_1 = rho_e / sqrt((1 + beta^2|c1|^2 + rho_e)^2 - 4 beta^2|c1|^2),
|
||||
rho_e = g|c1|^2 + d sig^2/|h1|^2; floor at |c1| = 1: sqrt(g)/2.
|
||||
|
||||
The affinity-blind receiver (beta = 0 in the filter) reduces to a
|
||||
scalar shrinkage of the matched filter with floor 1/2, so the entire
|
||||
cosine gain of the aware receiver is attributable to the predicted
|
||||
affinity. Effective SINR: eta = 1/MSE - 1 (biased MMSE convention).
|
||||
|
||||
Experiments in this file (CPU, numpy):
|
||||
E0 theorem_check : closed form vs Monte Carlo, both users
|
||||
E1 fig_floor : per-user MSE vs block SNR, aware vs blind floor
|
||||
E7a rate_corrected + beta_sweep_corrected : closed-form rate curves
|
||||
|
||||
The Monte Carlo experiments E2, E3, E4, E5, E7c, E8, E9 are canonical
|
||||
in revision_sims_gpu.py (torch backend, run under WSL); figures are
|
||||
rendered from data/ by replot_all.py and replot_merged.py.
|
||||
|
||||
Conventions (identical to the manuscript):
|
||||
* unit per-block transmit energy E_b = 1 per user
|
||||
* rho = E_b / sigma_n^2 (per-block received SNR; per-symbol SNR rho/d)
|
||||
* block-Rayleigh h ~ CN(0,1) unless the AWGN point |h|=1 is stated
|
||||
* complex AWGN CN(0, sigma^2 I_d); embeddings real, unit norm
|
||||
* orientation convention <e1,e2> = +beta
|
||||
Fixed seed. CSVs -> ../fig, PDFs -> ../fig_toc.
|
||||
Fixed seed 2026. CSVs -> ../data, PDFs -> ../fig.
|
||||
"""
|
||||
from __future__ import annotations
|
||||
import csv
|
||||
@@ -39,13 +58,27 @@ plt.rcParams.update({
|
||||
"font.family": "serif",
|
||||
"font.serif": ["DejaVu Serif", "Times New Roman"],
|
||||
"font.size": 9, "axes.labelsize": 9, "axes.titlesize": 9,
|
||||
"legend.fontsize": 7.0, "xtick.labelsize": 8, "ytick.labelsize": 8,
|
||||
"legend.fontsize": 6.6, "xtick.labelsize": 8, "ytick.labelsize": 8,
|
||||
"axes.grid": True, "grid.linestyle": "--", "grid.linewidth": 0.4,
|
||||
"grid.alpha": 0.6, "lines.linewidth": 1.4, "lines.markersize": 4.0,
|
||||
"figure.figsize": (3.15, 2.36), "pdf.fonttype": 42,
|
||||
})
|
||||
AXES_RECT = dict(left=0.205, right=0.965, top=0.955, bottom=0.185)
|
||||
|
||||
# shared legend-label dictionary (single source for every figure)
|
||||
LBL = {
|
||||
"edma": "EDMA",
|
||||
"blind": "Affinity-blind",
|
||||
"oma": "OMA",
|
||||
"genie": "Genie-aided SIC bound",
|
||||
"sic": "Realizable analog SIC",
|
||||
"todma": "ToDMA-adapted",
|
||||
"mac": "MAC sum capacity",
|
||||
"hybrid": "EDMA + refinement stage",
|
||||
"haar": "Haar masks",
|
||||
"wh": "Walsh-Hadamard masks",
|
||||
}
|
||||
|
||||
rng = np.random.default_rng(2026)
|
||||
|
||||
|
||||
@@ -86,69 +119,80 @@ def embed_pair(d, beta):
|
||||
return e1, e2
|
||||
|
||||
|
||||
def two_user_masks(d, beta, U1=None, U2=None):
|
||||
if U1 is None: U1 = haar(d)
|
||||
if U2 is None: U2 = haar(d)
|
||||
g = math.sqrt(1.0 - beta**2)
|
||||
return U1, beta * U1 + g * U2
|
||||
|
||||
|
||||
def rayleigh(n=1):
|
||||
return (rng.standard_normal(n) + 1j * rng.standard_normal(n)) / math.sqrt(2)
|
||||
|
||||
|
||||
def C_SI(beta, c):
|
||||
"""User-1 self-interference constant (exact to O(1/d)), <e1,e2>=+beta."""
|
||||
g = 1.0 - beta**2
|
||||
return (g**2 * abs(c)**2 + beta**2 + beta**4 * abs(c)**2
|
||||
+ 2.0 * beta**4 * np.real(c)) / g
|
||||
|
||||
|
||||
def C_SI2(beta, c2):
|
||||
"""User-2 self-interference constant (deterministic), c2 = h1/h2."""
|
||||
g = 1.0 - beta**2
|
||||
return (abs(c2)**2 + beta**2 + 2.0 * beta**2 * np.real(c2)) / g
|
||||
|
||||
|
||||
def C_bar(beta):
|
||||
"""Symmetrised constant at |h|=1 (block-alternating mask roles)."""
|
||||
return 0.5 * (C_SI(beta, 1.0 + 0j) + C_SI2(beta, 1.0 + 0j))
|
||||
|
||||
|
||||
def demux(r, M1, M2, h1, h2, beta):
|
||||
"""beta-aware demultiplexer (13); returns (e1_hat, e2_hat)."""
|
||||
g = 1.0 - beta**2
|
||||
t1 = (M1.T @ r) / h1
|
||||
t2 = (M2.T @ r) / h2
|
||||
e1 = (t1 - beta * (h2 / h1) * t2) / g
|
||||
e2 = (t2 - beta * (h1 / h2) * t1) / g
|
||||
return e1, e2
|
||||
def cnoise(d):
|
||||
return (rng.standard_normal(d) + 1j * rng.standard_normal(d)) / math.sqrt(2)
|
||||
|
||||
|
||||
def cosine(a, b):
|
||||
return abs(np.vdot(a, b)) / (np.linalg.norm(a) * np.linalg.norm(b))
|
||||
|
||||
|
||||
def mse_theory(beta, c1, rho_e):
|
||||
"""Theorem 1: per-realization MSE of the aware demultiplexer."""
|
||||
a0 = 1.0 + beta**2 * abs(c1)**2 + rho_e
|
||||
return rho_e / math.sqrt(a0 * a0 - 4.0 * beta**2 * abs(c1)**2)
|
||||
|
||||
|
||||
def mse_blind(c1, dsig2_h):
|
||||
"""Affinity-blind scalar-shrinkage MSE (beta = 0 in the filter)."""
|
||||
r0 = abs(c1)**2 + dsig2_h
|
||||
return r0 / (1.0 + r0)
|
||||
|
||||
|
||||
def eta_of(mse):
|
||||
"""Effective SINR of a (possibly biased) estimator with unit signal."""
|
||||
return 1.0 / mse - 1.0
|
||||
|
||||
|
||||
def aware(t1, Q, beta, c1, nvar, d):
|
||||
"""Affinity-aware Wiener demultiplexer applied to t1 = M1^T r / h1.
|
||||
|
||||
Uses A A^H = (1+beta^2|c1|^2) I + beta(c1 Q + conj(c1) Q^T), so the
|
||||
system matrix is assembled in O(d^2) and solved with one LU."""
|
||||
g = 1.0 - beta * beta
|
||||
rho = g * abs(c1)**2 / d + nvar
|
||||
S = beta * (c1 * Q + np.conj(c1) * Q.T) / d
|
||||
S[np.diag_indices(d)] += (1.0 + beta**2 * abs(c1)**2) / d + rho
|
||||
x = np.linalg.solve(S, t1)
|
||||
return (x + beta * np.conj(c1) * (Q.T @ x)) / d
|
||||
|
||||
|
||||
def blind(t1, c1, nvar, d):
|
||||
"""Affinity-blind receiver: scalar shrinkage of the matched filter."""
|
||||
lam = (1.0 / d) / (1.0 / d + abs(c1)**2 / d + nvar)
|
||||
return lam * t1
|
||||
|
||||
|
||||
# ------------------------------------------------------------------
|
||||
# E0 : Theorem-1 verification
|
||||
# E0 : Theorem-1 verification (both users, random phases)
|
||||
# ------------------------------------------------------------------
|
||||
def E0_theorem_check(d=512, betas=(0.0, 0.311, 0.5, 0.7), ntr=300):
|
||||
print("\n=== E0: Theorem 1 (self-interference constant) verification ===")
|
||||
def E0_theorem_check(d=512, betas=(0.0, 0.311, 0.5, 0.7), ntr=200, snr=20.0):
|
||||
print("\n=== E0: Theorem 1 (aware-demultiplexer MSE) verification ===")
|
||||
sig = 10 ** (-snr / 20.0)
|
||||
rows = []
|
||||
worst = 0.0
|
||||
for beta in betas:
|
||||
# random unit-modulus channels (AWGN-type magnitude, random phase)
|
||||
errs1, errs2 = [], []
|
||||
g = 1.0 - beta**2
|
||||
r1s, r2s = [], []
|
||||
for _ in range(ntr):
|
||||
h1 = np.exp(1j * rng.uniform(0, 2 * np.pi))
|
||||
h2 = np.exp(1j * rng.uniform(0, 2 * np.pi))
|
||||
e1, e2 = embed_pair(d, beta)
|
||||
M1, M2 = two_user_masks(d, beta)
|
||||
r = h1 * (M1 @ e1) + h2 * (M2 @ e2) # noise-free
|
||||
g1, g2 = demux(r, M1, M2, h1, h2, beta)
|
||||
errs1.append(np.linalg.norm(g1 - e1)**2 / C_SI(beta, h2 / h1))
|
||||
errs2.append(np.linalg.norm(g2 - e2)**2 / C_SI2(beta, h1 / h2))
|
||||
r1, r2 = float(np.mean(errs1)), float(np.mean(errs2))
|
||||
M1, M2 = haar(d), haar(d)
|
||||
Q = M1.T @ M2
|
||||
r = h1 * (M1 @ e1) + h2 * (M2 @ e2) + sig * cnoise(d)
|
||||
c1, c2 = h2 / h1, h1 / h2
|
||||
g1 = aware(M1.T @ r / h1, Q, beta, c1, sig**2 / abs(h1)**2, d)
|
||||
g2 = aware(M2.T @ r / h2, Q.T, beta, c2, sig**2 / abs(h2)**2, d)
|
||||
th1 = mse_theory(beta, c1, g * abs(c1)**2 + d * sig**2 / abs(h1)**2)
|
||||
th2 = mse_theory(beta, c2, g * abs(c2)**2 + d * sig**2 / abs(h2)**2)
|
||||
r1s.append(np.linalg.norm(g1 - e1)**2 / th1)
|
||||
r2s.append(np.linalg.norm(g2 - e2)**2 / th2)
|
||||
r1, r2 = float(np.mean(r1s)), float(np.mean(r2s))
|
||||
dev = max(abs(r1 - 1.0), abs(r2 - 1.0)) * 100
|
||||
worst = max(worst, dev)
|
||||
print(f" beta={beta:.3f} MC/theory user1 = {r1:.4f}, user2 = {r2:.4f}"
|
||||
@@ -161,12 +205,11 @@ def E0_theorem_check(d=512, betas=(0.0, 0.311, 0.5, 0.7), ntr=300):
|
||||
|
||||
|
||||
# ------------------------------------------------------------------
|
||||
# E1 : interference floor (MSE vs block SNR), AWGN point |h|=1
|
||||
# E1 : MSE vs block SNR at |h|=1 -- aware floor sqrt(g)/2 vs blind 1/2
|
||||
# ------------------------------------------------------------------
|
||||
def E1_floor(beta=0.311, dims=(256, 768), snr_db=np.arange(0, 41, 2.5), ntr=150):
|
||||
print("\n=== E1: finite-d interference floor ===")
|
||||
def E1_floor(beta=0.311, dims=(256, 768), snr_db=np.arange(0, 41, 2.5), ntr=120):
|
||||
print("\n=== E1: finite-d validation, aware vs blind floor ===")
|
||||
g = 1.0 - beta**2
|
||||
csi = C_SI(beta, 1.0 + 0j)
|
||||
fig, ax = plt.subplots()
|
||||
colors = {256: "C0", 768: "C3"}
|
||||
rows = []
|
||||
@@ -174,444 +217,134 @@ def E1_floor(beta=0.311, dims=(256, 768), snr_db=np.arange(0, 41, 2.5), ntr=150)
|
||||
mc = np.zeros(len(snr_db))
|
||||
for _ in range(ntr):
|
||||
e1, e2 = embed_pair(d, beta)
|
||||
M1, M2 = two_user_masks(d, beta)
|
||||
M1, M2 = haar(d), haar(d)
|
||||
Q = M1.T @ M2
|
||||
r0 = (M1 @ e1) + (M2 @ e2)
|
||||
n = (rng.standard_normal(d) + 1j * rng.standard_normal(d)) / math.sqrt(2)
|
||||
n = cnoise(d)
|
||||
for k, s in enumerate(snr_db):
|
||||
sig = 10 ** (-s / 20.0)
|
||||
g1, _ = demux(r0 + sig * n, M1, M2, 1.0, 1.0, beta)
|
||||
g1 = aware(M1.T @ (r0 + sig * n), Q, beta, 1.0, sig**2, d)
|
||||
mc[k] += np.linalg.norm(g1 - e1)**2
|
||||
mc /= ntr
|
||||
rho = 10 ** (snr_db / 10.0)
|
||||
th = d / (rho * g) + csi
|
||||
ideal = d / (rho * g)
|
||||
th = np.array([mse_theory(beta, 1.0, g + d / r) for r in rho])
|
||||
bl = np.array([mse_blind(1.0, d / r) for r in rho])
|
||||
ax.semilogy(snr_db, mc, "o", ms=3.5, color=colors[d], mfc="none",
|
||||
label=rf"MC, $d={d}$")
|
||||
label=rf"Monte Carlo, $d={d}$")
|
||||
ax.semilogy(snr_db, th, "-", color=colors[d],
|
||||
label=rf"Theorem 1, $d={d}$")
|
||||
if d == dims[-1]:
|
||||
ax.semilogy(snr_db, ideal, ":", color="k", lw=1.1,
|
||||
label="Idealized (no floor)")
|
||||
for s, m, t, i in zip(snr_db, mc, th, ideal):
|
||||
rows.append([d, s, m, t, i])
|
||||
onset = 10 * math.log10(d / (g * csi))
|
||||
print(f" d={d}: floor C_SI={csi:.4f}, onset ~{onset:.1f} dB, "
|
||||
f"max MC/theory dev "
|
||||
f"{100*max(abs(mc/th-1)):.1f}%")
|
||||
ax.axhline(csi, color="gray", lw=0.8, ls="--")
|
||||
ax.text(1.0, csi * 1.15, r"floor $C_{\mathrm{SI}}$", fontsize=7, color="gray")
|
||||
ax.semilogy(snr_db, bl, "--", color="C1", lw=1.1,
|
||||
label=LBL["blind"])
|
||||
for s, m, t, b in zip(snr_db, mc, th, bl):
|
||||
rows.append([d, s, m, t, b])
|
||||
dev = 100 * max(abs(mc / th - 1))
|
||||
print(f" d={d}: max MC/theory dev {dev:.1f}%")
|
||||
ax.axhline(math.sqrt(g) / 2, color="gray", lw=0.8, ls="--")
|
||||
ax.axhline(0.5, color="gray", lw=0.8, ls=":")
|
||||
ax.text(1.0, 0.52, r"blind floor $1/2$", fontsize=7, color="gray")
|
||||
ax.text(22.0, 0.40, r"aware floor $\sqrt{1-\beta^2}/2$",
|
||||
fontsize=7, color="gray")
|
||||
ax.set_yscale("linear")
|
||||
ax.set_xlabel("Per-block SNR $\\rho$ [dB]")
|
||||
ax.set_ylabel(r"Per-user MSE $\mathbb{E}\|\hat{\mathbf{e}}_u-\mathbf{e}_u\|_2^2$")
|
||||
ax.set_xlim(0, 40); ax.set_ylim(0.5, 2000)
|
||||
ax.set_xlim(0, 40); ax.set_ylim(0.4, 1.05)
|
||||
ax.legend(loc="upper right", ncol=1)
|
||||
save_fig(fig, "fig_floor")
|
||||
write_csv("floor_validation", ["d", "snr_db", "mse_mc", "mse_theory", "mse_ideal"], rows)
|
||||
write_csv("floor_validation",
|
||||
["d", "snr_db", "mse_mc", "mse_theory", "mse_blind"], rows)
|
||||
print(f" aware floor {math.sqrt(g)/2:.4f} vs blind floor 0.5000 "
|
||||
f"(ratio {0.5/(math.sqrt(g)/2):.4f} = 1/sqrt(1-beta^2))")
|
||||
|
||||
|
||||
# ------------------------------------------------------------------
|
||||
# E2 : realisable SIC vs genie SIC vs EDMA vs OMA (Rayleigh)
|
||||
# E7 : effective-rate figures (eta = 1/MSE - 1)
|
||||
# ------------------------------------------------------------------
|
||||
def E2_sic(beta=0.311, d=512, snr_db=np.arange(0, 31, 5), ntr=400):
|
||||
print("\n=== E2: realisable vs genie SIC (Rayleigh) ===")
|
||||
res = {k: np.zeros(len(snr_db)) for k in
|
||||
("edma", "oma", "genie", "sic")}
|
||||
for _ in range(ntr):
|
||||
e1, e2 = embed_pair(d, beta)
|
||||
M1, M2 = two_user_masks(d, beta)
|
||||
h1, h2 = rayleigh(2)
|
||||
r0 = h1 * (M1 @ e1) + h2 * (M2 @ e2)
|
||||
n = (rng.standard_normal(d) + 1j * rng.standard_normal(d)) / math.sqrt(2)
|
||||
n2 = (rng.standard_normal(d) + 1j * rng.standard_normal(d)) / math.sqrt(2)
|
||||
for k, s in enumerate(snr_db):
|
||||
sig = 10 ** (-s / 20.0)
|
||||
r = r0 + sig * n
|
||||
# EDMA
|
||||
g1, g2 = demux(r, M1, M2, h1, h2, beta)
|
||||
res["edma"][k] += 0.5 * (cosine(g1, e1) + cosine(g2, e2))
|
||||
# OMA equivalent-bandwidth model: interference-free, noise x sqrt(2)
|
||||
o1 = e1 + math.sqrt(2) * sig * n / h1
|
||||
o2 = e2 + math.sqrt(2) * sig * n2 / h2
|
||||
res["oma"][k] += 0.5 * (cosine(o1, e1) + cosine(o2, e2))
|
||||
# genie SIC: perfect removal of the other user for BOTH users
|
||||
ge1 = M1.T @ (r - h2 * (M2 @ e2)) / h1
|
||||
ge2 = M2.T @ (r - h1 * (M1 @ e1)) / h2
|
||||
res["genie"][k] += 0.5 * (cosine(ge1, e1) + cosine(ge2, e2))
|
||||
# realisable SIC: stronger user first (matched filter),
|
||||
# unit-norm projection as the analog decision, then subtract
|
||||
if abs(h1) >= abs(h2):
|
||||
hs, hw, Ms, Mw, es, ew = h1, h2, M1, M2, e1, e2
|
||||
else:
|
||||
hs, hw, Ms, Mw, es, ew = h2, h1, M2, M1, e2, e1
|
||||
d_s = Ms.T @ r / hs
|
||||
dec_s = d_s / np.linalg.norm(d_s) # analog decision
|
||||
r_res = r - hs * (Ms @ dec_s)
|
||||
d_w = Mw.T @ r_res / hw
|
||||
res["sic"][k] += 0.5 * (cosine(d_s, es) + cosine(d_w, ew))
|
||||
for k in res:
|
||||
res[k] /= ntr
|
||||
fig, ax = plt.subplots()
|
||||
ax.plot(snr_db, res["edma"], "o-", color="C3", label="EDMA")
|
||||
ax.plot(snr_db, res["genie"], "s--", color="C0", label="Genie-aided SIC")
|
||||
ax.plot(snr_db, res["sic"], "^-.", color="C2", label="Realisable SIC")
|
||||
ax.plot(snr_db, res["oma"], "v:", color="C1", label="OMA")
|
||||
ax.set_xlabel("Per-block SNR $\\rho$ [dB]")
|
||||
ax.set_ylabel("Mean cosine similarity")
|
||||
ax.set_xlim(snr_db[0], snr_db[-1]); ax.set_ylim(0, 1)
|
||||
ax.legend(loc="upper left")
|
||||
save_fig(fig, "fig_sic")
|
||||
rows = [[s] + [res[k][i] for k in ("edma", "oma", "genie", "sic")]
|
||||
for i, s in enumerate(snr_db)]
|
||||
write_csv("sic_comparison", ["snr_db", "edma", "oma", "genie", "sic"], rows)
|
||||
i20 = list(snr_db).index(20)
|
||||
print(f" at 20 dB: EDMA {res['edma'][i20]:.3f}, realisable SIC "
|
||||
f"{res['sic'][i20]:.3f}, genie {res['genie'][i20]:.3f}, "
|
||||
f"OMA {res['oma'][i20]:.3f}")
|
||||
def T_edma(rho, d, beta):
|
||||
m = mse_theory(beta, 1.0, (1.0 - beta**2) + d / rho)
|
||||
return 2.0 * math.log2(1.0 + eta_of(m))
|
||||
|
||||
|
||||
# ------------------------------------------------------------------
|
||||
# E3 : Rayleigh unconditional MSE ??ZF inversion vs regularised
|
||||
# ------------------------------------------------------------------
|
||||
def E3_regularised(beta=0.311, d=512, snrs=(10, 20), ntr=4000):
|
||||
print("\n=== E3: Rayleigh unconditional MSE, ZF vs regularised ===")
|
||||
rows = []
|
||||
for s in snrs:
|
||||
sig = 10 ** (-s / 20.0)
|
||||
sig2 = sig**2
|
||||
mse_zf, mse_rg = [], []
|
||||
for _ in range(ntr):
|
||||
e1, e2 = embed_pair(d, beta)
|
||||
M1, M2 = two_user_masks(d, beta)
|
||||
h1, h2 = rayleigh(2)
|
||||
r = h1 * (M1 @ e1) + h2 * (M2 @ e2) \
|
||||
+ sig * (rng.standard_normal(d) + 1j * rng.standard_normal(d)) / math.sqrt(2)
|
||||
g1, _ = demux(r, M1, M2, h1, h2, beta)
|
||||
mse_zf.append(np.linalg.norm(g1 - e1)**2)
|
||||
# regularised inversion: 1/h -> h*/(|h|^2 + d sigma^2)
|
||||
eps = d * sig2
|
||||
f1 = (abs(h1)**2 + eps) / np.conj(h1)
|
||||
f2 = (abs(h2)**2 + eps) / np.conj(h2)
|
||||
g1r, _ = demux(r, M1, M2, f1, f2, beta)
|
||||
mse_rg.append(np.linalg.norm(g1r - e1)**2)
|
||||
zf_mean, zf_med = float(np.mean(mse_zf)), float(np.median(mse_zf))
|
||||
rg_mean, rg_med = float(np.mean(mse_rg)), float(np.median(mse_rg))
|
||||
print(f" {s} dB: ZF mean {zf_mean:9.2f} (median {zf_med:6.2f}) | "
|
||||
f"regularised mean {rg_mean:6.3f} (median {rg_med:6.3f})")
|
||||
rows.append([s, zf_mean, zf_med, rg_mean, rg_med])
|
||||
write_csv("rayleigh_mse", ["snr_db", "zf_mean", "zf_median",
|
||||
"reg_mean", "reg_median"], rows)
|
||||
|
||||
|
||||
# ------------------------------------------------------------------
|
||||
# E4 : imperfect CSI
|
||||
# ------------------------------------------------------------------
|
||||
def E4_csi(beta=0.311, d=512, snr=30.0,
|
||||
sh2=np.array([0.0, 0.01, 0.02, 0.05, 0.1, 0.2, 0.3]), ntr=400):
|
||||
"""EDMA cosine is CSI-direction-invariant (h-estimates cancel in the
|
||||
demux direction); realisable SIC degrades through its subtraction stage."""
|
||||
print("\n=== E4: imperfect CSI robustness (EDMA vs realisable SIC) ===")
|
||||
sig = 10 ** (-snr / 20.0)
|
||||
res_e = np.zeros(len(sh2)); res_s = np.zeros(len(sh2))
|
||||
for _ in range(ntr):
|
||||
e1, e2 = embed_pair(d, beta)
|
||||
M1, M2 = two_user_masks(d, beta)
|
||||
h1, h2 = rayleigh(2)
|
||||
r = h1 * (M1 @ e1) + h2 * (M2 @ e2) + sig * (
|
||||
rng.standard_normal(d) + 1j * rng.standard_normal(d)) / math.sqrt(2)
|
||||
eps1, eps2 = rayleigh(2)
|
||||
for j, v in enumerate(sh2):
|
||||
hh1 = h1 + math.sqrt(v) * eps1
|
||||
hh2 = h2 + math.sqrt(v) * eps2
|
||||
g1, g2 = demux(r, M1, M2, hh1, hh2, beta)
|
||||
res_e[j] += 0.5 * (cosine(g1, e1) + cosine(g2, e2))
|
||||
# realisable SIC with the same imperfect estimates
|
||||
if abs(hh1) >= abs(hh2):
|
||||
hs, hw, Ms, Mw, es, ew = hh1, hh2, M1, M2, e1, e2
|
||||
else:
|
||||
hs, hw, Ms, Mw, es, ew = hh2, hh1, M2, M1, e2, e1
|
||||
d_s = Ms.T @ r / hs
|
||||
dec_s = d_s / np.linalg.norm(d_s)
|
||||
r_res = r - hs * (Ms @ dec_s)
|
||||
d_w = Mw.T @ r_res / hw
|
||||
res_s[j] += 0.5 * (cosine(d_s, es) + cosine(d_w, ew))
|
||||
res_e /= ntr; res_s /= ntr
|
||||
print(f" EDMA: {res_e[0]:.4f} -> {res_e[-1]:.4f} "
|
||||
f"(delta {100*(res_e[0]-res_e[-1]):.2f} points)")
|
||||
print(f" SIC : {res_s[0]:.4f} -> {res_s[-1]:.4f} "
|
||||
f"(delta {100*(res_s[0]-res_s[-1]):.2f} points)")
|
||||
fig, ax = plt.subplots()
|
||||
ax.plot(sh2, res_e, "o-", color="C3", label="EDMA")
|
||||
ax.plot(sh2, res_s, "^-.", color="C2", label="Realisable SIC")
|
||||
ax.set_xlabel(r"CSI error variance $\sigma_h^2$")
|
||||
ax.set_ylabel("Mean cosine similarity")
|
||||
ax.set_xlim(0, sh2[-1]); ax.set_ylim(0, 0.7)
|
||||
ax.legend(loc="lower left")
|
||||
save_fig(fig, "fig_csi")
|
||||
rows = [[v, res_e[j], res_s[j]] for j, v in enumerate(sh2)]
|
||||
write_csv("csi_error", ["sigma_h2", "edma", "sic"], rows)
|
||||
|
||||
|
||||
# ------------------------------------------------------------------
|
||||
# E5 : Walsh-Hadamard structured masks vs Haar
|
||||
# ------------------------------------------------------------------
|
||||
def hadamard(n):
|
||||
H = np.array([[1.0]])
|
||||
while H.shape[0] < n:
|
||||
H = np.block([[H, H], [H, -H]])
|
||||
return H / math.sqrt(n)
|
||||
|
||||
|
||||
def E5_maskfam(beta=0.311, d=512, snr_db=np.arange(0, 41, 5), ntr=200):
|
||||
print("\n=== E5: Walsh-Hadamard masks vs Haar mixture ===")
|
||||
H = hadamard(d)
|
||||
g = math.sqrt(1.0 - beta**2)
|
||||
res = {"haar": np.zeros(len(snr_db)), "wh": np.zeros(len(snr_db))}
|
||||
for _ in range(ntr):
|
||||
e1, e2 = embed_pair(d, beta)
|
||||
M1, M2 = two_user_masks(d, beta)
|
||||
D1 = np.diag(rng.choice([-1.0, 1.0], d))
|
||||
D2 = np.diag(rng.choice([-1.0, 1.0], d))
|
||||
W1 = H @ D1
|
||||
W2 = beta * W1 + g * (H @ D2)
|
||||
r0h = (M1 @ e1) + (M2 @ e2)
|
||||
r0w = (W1 @ e1) + (W2 @ e2)
|
||||
n = (rng.standard_normal(d) + 1j * rng.standard_normal(d)) / math.sqrt(2)
|
||||
for k, s in enumerate(snr_db):
|
||||
sig = 10 ** (-s / 20.0)
|
||||
g1, _ = demux(r0h + sig * n, M1, M2, 1.0, 1.0, beta)
|
||||
w1, _ = demux(r0w + sig * n, W1, W2, 1.0, 1.0, beta)
|
||||
res["haar"][k] += cosine(g1, e1)
|
||||
res["wh"][k] += cosine(w1, e1)
|
||||
for k in res:
|
||||
res[k] /= ntr
|
||||
dev = 100 * np.max(np.abs(res["wh"] - res["haar"]))
|
||||
print(f" max |WH - Haar| cosine deviation: {dev:.2f} points")
|
||||
fig, ax = plt.subplots()
|
||||
ax.plot(snr_db, res["haar"], "o-", color="C3",
|
||||
label=r"Haar mixture, $\mathcal{O}(d^2)$")
|
||||
ax.plot(snr_db, res["wh"], "s--", color="C0",
|
||||
label=r"Walsh-Hadamard, $\mathcal{O}(d\log d)$")
|
||||
ax.set_xlabel("Per-block SNR $\\rho$ [dB]")
|
||||
ax.set_ylabel("Mean cosine similarity")
|
||||
ax.set_xlim(snr_db[0], snr_db[-1]); ax.set_ylim(0, 0.8)
|
||||
ax.legend(loc="upper left")
|
||||
save_fig(fig, "fig_maskfam")
|
||||
rows = [[s, res["haar"][i], res["wh"][i]] for i, s in enumerate(snr_db)]
|
||||
write_csv("mask_family_rev", ["snr_db", "haar", "wh"], rows)
|
||||
|
||||
|
||||
# ------------------------------------------------------------------
|
||||
# E6 : high-affinity combining mode
|
||||
# ------------------------------------------------------------------
|
||||
def E6_coop(d=512, snr=20.0, betas=np.linspace(0.0, 0.98, 21), ntr=100):
|
||||
print("\n=== E6: high-affinity combining-mode crossover ===")
|
||||
sig = 10 ** (-snr / 20.0)
|
||||
pairs = [(haar(d), haar(d)) for _ in range(ntr)]
|
||||
chans = [rayleigh(2) for _ in range(ntr)]
|
||||
cos_dx = np.zeros(len(betas)); cos_cb = np.zeros(len(betas))
|
||||
for j, beta in enumerate(betas):
|
||||
for t in range(ntr):
|
||||
U1, U2 = pairs[t]
|
||||
h1, h2 = chans[t]
|
||||
e1, e2 = embed_pair(d, beta)
|
||||
M1, M2 = two_user_masks(d, beta, U1, U2)
|
||||
r = h1 * (M1 @ e1) + h2 * (M2 @ e2) + sig * (
|
||||
rng.standard_normal(d) + 1j * rng.standard_normal(d)) / math.sqrt(2)
|
||||
g1, _ = demux(r, M1, M2, h1, h2, beta)
|
||||
cos_dx[j] += cosine(g1, e1)
|
||||
# affinity combining: coherent weights for the e1 component
|
||||
a1 = h1 + beta**2 * h2
|
||||
a2 = beta * (h1 + h2)
|
||||
comb = np.conj(a1) * (M1.T @ r) + np.conj(a2) * (M2.T @ r)
|
||||
cos_cb[j] += cosine(comb, e1)
|
||||
cos_dx /= ntr; cos_cb /= ntr
|
||||
ix = np.where(cos_cb >= cos_dx)[0]
|
||||
cross = betas[ix[0]] if len(ix) else float("nan")
|
||||
print(f" crossover affinity ~ {cross:.2f} at rho={snr:.0f} dB")
|
||||
fig, ax = plt.subplots()
|
||||
ax.plot(betas, cos_dx, "o-", color="C3", label="Separation mode (demux)")
|
||||
ax.plot(betas, cos_cb, "s--", color="C0", label="Combining mode")
|
||||
ax.set_xlabel(r"Pairwise affinity $\beta$")
|
||||
ax.set_ylabel("Mean cosine similarity")
|
||||
ax.set_xlim(0, 1); ax.set_ylim(0, 0.8)
|
||||
ax.legend(loc="lower left")
|
||||
save_fig(fig, "fig_coop")
|
||||
rows = [[b, cos_dx[i], cos_cb[i]] for i, b in enumerate(betas)]
|
||||
write_csv("coop_mode", ["beta", "cos_demux", "cos_combine"], rows)
|
||||
return cross
|
||||
|
||||
|
||||
# ------------------------------------------------------------------
|
||||
# E7 : corrected effective-rate figures
|
||||
# ------------------------------------------------------------------
|
||||
def eta_edma(rho, d, beta, csi=None):
|
||||
g = 1.0 - beta**2
|
||||
if csi is None:
|
||||
csi = C_bar(beta) # symmetrised constant (alternating masks)
|
||||
return 1.0 / (d / (rho * g) + csi)
|
||||
def T_blind(rho, d):
|
||||
return 2.0 * math.log2(1.0 + 1.0 / (1.0 + d / rho))
|
||||
|
||||
|
||||
def E7_rates(beta=0.311, d=512):
|
||||
print("\n=== E7a: corrected effective-rate comparison ===")
|
||||
snr_db = np.arange(0, 31, 1.0)
|
||||
print("\n=== E7a: effective-rate comparison ===")
|
||||
snr_db = np.arange(0, 41, 0.5)
|
||||
rho = 10 ** (snr_db / 10.0)
|
||||
g = 1.0 - beta**2
|
||||
T_edma = 2 * np.log2(1 + eta_edma(rho, d, beta))
|
||||
T_ideal = 2 * np.log2(1 + rho * g / d)
|
||||
T_oma = 2 * np.log2(1 + rho / (2 * d))
|
||||
T_genie = 2 * np.log2(1 + rho / d)
|
||||
C_mac = np.log2(1 + 2 * rho / d)
|
||||
Te = np.array([T_edma(r, d, beta) for r in rho])
|
||||
Tb = np.array([T_blind(r, d) for r in rho])
|
||||
To = 2 * np.log2(1 + rho / (2 * d))
|
||||
Tg = 2 * np.log2(1 + rho / d)
|
||||
Cm = np.log2(1 + 2 * rho / d)
|
||||
fig, ax = plt.subplots()
|
||||
ax.plot(snr_db, T_edma, "-", color="C3", label="EDMA (Theorem 1)")
|
||||
ax.plot(snr_db, T_ideal, ":", color="C3", lw=1.1,
|
||||
label="EDMA idealized (infeasible)")
|
||||
ax.plot(snr_db, T_oma, "--", color="C1", label="OMA")
|
||||
ax.plot(snr_db, T_genie, "-.", color="C0", label="Genie-aided SIC bound")
|
||||
ax.plot(snr_db, C_mac, "-", color="k", lw=1.0, label="MAC sum capacity")
|
||||
ax.plot(snr_db, Te, "-", color="C3", label=LBL["edma"])
|
||||
ax.plot(snr_db, Tb, ":", color="C4", lw=1.2, label=LBL["blind"])
|
||||
ax.plot(snr_db, To, "--", color="C1", label=LBL["oma"])
|
||||
ax.plot(snr_db, Tg, "-.", color="C0", label=LBL["genie"])
|
||||
ax.plot(snr_db, Cm, "-", color="k", lw=1.0, label=LBL["mac"])
|
||||
ax.set_xlabel("Per-block SNR $\\rho$ [dB]")
|
||||
ax.set_ylabel("Effective sum rate [bps/Hz]")
|
||||
ax.set_xlim(0, 30); ax.set_ylim(0, 3.2)
|
||||
ax.set_xlim(0, 40); ax.set_ylim(0, 3.2)
|
||||
ax.legend(loc="upper left")
|
||||
save_fig(fig, "fig_rate_corrected")
|
||||
rows = [[s, T_edma[i], T_ideal[i], T_oma[i], T_genie[i], C_mac[i]]
|
||||
rows = [[s, Te[i], Tb[i], To[i], Tg[i], Cm[i]]
|
||||
for i, s in enumerate(snr_db)]
|
||||
write_csv("rate_corrected",
|
||||
["snr_db", "edma", "edma_ideal", "oma", "genie", "mac"], rows)
|
||||
["snr_db", "edma", "blind", "oma", "genie", "mac"], rows)
|
||||
i20 = list(snr_db).index(20.0)
|
||||
csi = C_bar(beta)
|
||||
rho_c = d * (2 - 1 / g) / csi
|
||||
print(f" at 20 dB: EDMA {T_edma[i20]:.3f}, OMA {T_oma[i20]:.3f} "
|
||||
f"(gain {T_edma[i20]/T_oma[i20]:.2f}x), MAC {C_mac[i20]:.3f}, "
|
||||
f"EDMA/MAC {T_edma[i20]/C_mac[i20]:.3f} (gamma={g:.3f})")
|
||||
print(f" OMA re-crossover rho_c = {10*math.log10(rho_c):.1f} dB")
|
||||
print(f" at 20 dB: EDMA {Te[i20]:.3f}, blind {Tb[i20]:.3f}, "
|
||||
f"OMA {To[i20]:.3f} (gain {Te[i20]/To[i20]:.2f}x), "
|
||||
f"MAC {Cm[i20]:.3f}, EDMA/MAC {Te[i20]/Cm[i20]:.3f}")
|
||||
g = 1.0 - beta**2
|
||||
rho_c = 2 * d * (2 / math.sqrt(g) - 1)
|
||||
ix = np.where(To >= Te)[0]
|
||||
rc_num = snr_db[ix[0]] if len(ix) else float("nan")
|
||||
print(f" OMA re-crossover: floor formula {10*math.log10(rho_c):.1f} dB, "
|
||||
f"numerical {rc_num:.1f} dB "
|
||||
f"(blind: {10*math.log10(2*d):.1f} dB)")
|
||||
|
||||
print("\n=== E7b: corrected beta sweep ===")
|
||||
print("\n=== E7b: value-of-affinity sweep ===")
|
||||
betas = np.linspace(0.0, 0.98, 99)
|
||||
fig, ax = plt.subplots()
|
||||
rows = []
|
||||
for s, col in ((10, "C0"), (20, "C3")):
|
||||
rho_s = 10 ** (s / 10.0)
|
||||
Te = np.array([2 * np.log2(1 + eta_edma(rho_s, d, b)) for b in betas])
|
||||
To = 2 * np.log2(1 + rho_s / (2 * d))
|
||||
Tg = 2 * np.log2(1 + rho_s / d)
|
||||
Te = np.array([T_edma(rho_s, d, b) for b in betas])
|
||||
Tb = T_blind(rho_s, d)
|
||||
To = 2 * math.log2(1 + rho_s / (2 * d))
|
||||
Tg = 2 * math.log2(1 + rho_s / d)
|
||||
ax.plot(betas, Te, "-", color=col, label=rf"EDMA, $\rho={s}$ dB")
|
||||
ax.axhline(To, color=col, ls="--", lw=1.0,
|
||||
label=rf"OMA, $\rho={s}$ dB")
|
||||
ax.axhline(Tg, color=col, ls="-.", lw=0.8,
|
||||
label=rf"Genie-aided SIC, $\rho={s}$ dB")
|
||||
ix = np.where(Te <= To)[0]
|
||||
bstar = betas[ix[0]] if len(ix) else float("nan")
|
||||
print(f" rho={s} dB: crossover beta* = {bstar:.3f} "
|
||||
f"(wideband limit 1/sqrt(2)=0.707)")
|
||||
ax.axhline(Tb, color=col, ls=":", lw=1.0)
|
||||
ax.axhline(To, color=col, ls="--", lw=1.0)
|
||||
ax.axhline(Tg, color=col, ls="-.", lw=0.8)
|
||||
ixg = np.where(Te >= Tg)[0]
|
||||
bg = betas[ixg[0]] if len(ixg) else float("nan")
|
||||
print(f" rho={s} dB: EDMA(0)/blind = {Te[0]/Tb:.3f}, "
|
||||
f"EDMA(0.311) gain over blind "
|
||||
f"{Te[np.argmin(abs(betas-0.311))]/Tb:.3f}x, "
|
||||
f"crosses genie at beta ~ {bg:.2f}")
|
||||
for i, b in enumerate(betas):
|
||||
rows.append([s, b, Te[i], To, Tg])
|
||||
for b0 in (0.031, 0.311):
|
||||
rows.append([s, b, Te[i], Tb, To, Tg])
|
||||
for b0 in (0.030, 0.311):
|
||||
ax.axvline(b0, color="gray", ls=":", lw=0.9)
|
||||
ax.set_xlabel(r"Pairwise affinity $\beta$")
|
||||
ax.set_ylabel("Effective sum rate [bps/Hz]")
|
||||
ax.set_xlim(0, 1); ax.set_ylim(0, 1.02)
|
||||
ax.set_yticks([0.0, 0.2, 0.4, 0.6, 0.8, 1.0])
|
||||
ax.legend(loc="upper right", ncol=1, fontsize=5.8,
|
||||
handlelength=1.5, borderaxespad=0.2)
|
||||
ax.set_xlim(0, 1)
|
||||
ax.legend(loc="upper left")
|
||||
save_fig(fig, "fig_beta_sweep_corrected")
|
||||
write_csv("beta_sweep_corrected",
|
||||
["snr_db", "beta", "edma", "oma", "genie"], rows)
|
||||
|
||||
|
||||
def E7_multiuser(beta=0.311, d=512, Us=(2, 3, 4), ntr_cal=80, ntr_mc=120):
|
||||
print("\n=== E7c: corrected multi-user scaling ===")
|
||||
snr_db = np.arange(0, 31, 2.5)
|
||||
snr_mk = np.arange(0, 31, 5)
|
||||
rho = 10 ** (snr_db / 10.0)
|
||||
fig, ax = plt.subplots()
|
||||
colors = {2: "C0", 3: "C2", 4: "C3"}
|
||||
rows = []
|
||||
csi2 = C_SI(beta, 1.0 + 0j)
|
||||
for U in Us:
|
||||
B = (1 - beta) * np.eye(U) + beta * np.ones((U, U))
|
||||
Binv_uu = np.linalg.inv(B)[0, 0]
|
||||
gU = 1.0 / Binv_uu
|
||||
# calibrate C_SI^(U) by noise-free MC at h_u = 1 (the same
|
||||
# evaluation convention as the two-user rate curves, so the
|
||||
# U = 2 curve reduces exactly to T_EDMA with C_bar),
|
||||
# averaged over all users (mask roles are asymmetric)
|
||||
acc = 0.0
|
||||
for _ in range(ntr_cal):
|
||||
A = np.linalg.cholesky(B)
|
||||
Uks = [haar(d) for _ in range(U)]
|
||||
Ms = [sum(A[u, k] * Uks[k] for k in range(U)) for u in range(U)]
|
||||
h = np.ones(U, dtype=complex)
|
||||
# symmetric equal-affinity embeddings: e_u = beta-mixed set
|
||||
base = unit(rng.standard_normal(d))
|
||||
es = []
|
||||
for u in range(U):
|
||||
w = rng.standard_normal(d)
|
||||
w = unit(w - (w @ base) * base)
|
||||
# construct so that <e_u,e_v> ~ beta pairwise
|
||||
es.append(unit(math.sqrt(beta) * base
|
||||
+ math.sqrt(1 - beta) * w))
|
||||
r = sum(h[u] * (Ms[u] @ es[u]) for u in range(U))
|
||||
Binv = np.linalg.inv(B)
|
||||
# block demux e_hat_u = (1/h_u) sum_v Binv[u,v] M_v^T r
|
||||
for u in range(U):
|
||||
eh = sum(Binv[u, v] * (Ms[v].T @ r) for v in range(U)) / h[u]
|
||||
acc += np.linalg.norm(eh - es[u])**2
|
||||
csiU = acc / (ntr_cal * U)
|
||||
print(f" U={U}: C_SI^(U) = {csiU:.3f} "
|
||||
f"((U-1)*C_bar = {(U-1)*C_bar(beta):.3f}), gamma_U = {gU:.3f}")
|
||||
eta = 1.0 / (d * Binv_uu / rho + csiU)
|
||||
T_th = U * np.log2(1 + eta)
|
||||
T_oma = U * np.log2(1 + rho / (U * d))
|
||||
ax.plot(snr_db, T_th, "-", color=colors[U], label=rf"EDMA, $U={U}$")
|
||||
ax.plot(snr_db, T_oma, "--", color=colors[U], lw=1.0,
|
||||
label=rf"OMA, $U={U}$")
|
||||
# MC markers (with noise, h_u = 1, per-realization real masks)
|
||||
err_mc = np.zeros(len(snr_mk))
|
||||
for _ in range(ntr_mc):
|
||||
A = np.linalg.cholesky(B)
|
||||
Uks = [haar(d) for _ in range(U)]
|
||||
Ms = [sum(A[u, k] * Uks[k] for k in range(U)) for u in range(U)]
|
||||
h = np.ones(U, dtype=complex)
|
||||
base = unit(rng.standard_normal(d))
|
||||
es = []
|
||||
for u in range(U):
|
||||
w = rng.standard_normal(d)
|
||||
w = unit(w - (w @ base) * base)
|
||||
es.append(unit(math.sqrt(beta) * base
|
||||
+ math.sqrt(1 - beta) * w))
|
||||
r0 = sum(h[u] * (Ms[u] @ es[u]) for u in range(U))
|
||||
n = (rng.standard_normal(d) + 1j * rng.standard_normal(d)) / math.sqrt(2)
|
||||
Binv = np.linalg.inv(B)
|
||||
for k, s in enumerate(snr_mk):
|
||||
sig = 10 ** (-s / 20.0)
|
||||
r = r0 + sig * n
|
||||
for u in range(U):
|
||||
eh = sum(Binv[u, v] * (Ms[v].T @ r) for v in range(U)) / h[u]
|
||||
err_mc[k] += np.linalg.norm(eh - es[u])**2
|
||||
err_mc /= ntr_mc * U
|
||||
T_mc = U * np.log2(1 + 1.0 / err_mc)
|
||||
ax.plot(snr_mk, T_mc, "o", color=colors[U], ms=4, mfc="none")
|
||||
for i, s in enumerate(snr_db):
|
||||
rows.append([U, s, T_th[i], T_oma[i]])
|
||||
i20 = list(snr_db).index(20.0)
|
||||
print(f" at 20 dB: EDMA {T_th[i20]:.3f} vs OMA {T_oma[i20]:.3f} "
|
||||
f"(gain {T_th[i20]/T_oma[i20]:.2f}x)")
|
||||
ax.set_xlabel("Per-block SNR $\\rho$ [dB]")
|
||||
ax.set_ylabel("Effective sum rate [bps/Hz]")
|
||||
ax.set_xlim(0, 30); ax.set_ylim(0, 1.5)
|
||||
ax.legend(loc="upper left", ncol=1, fontsize=6.2)
|
||||
save_fig(fig, "fig_multiuser_corrected")
|
||||
write_csv("multiuser_corrected", ["U", "snr_db", "edma", "oma"], rows)
|
||||
["snr_db", "beta", "edma", "blind", "oma", "genie"], rows)
|
||||
|
||||
|
||||
if __name__ == "__main__":
|
||||
import sys
|
||||
todo = set(sys.argv[1:])
|
||||
ALL = {
|
||||
"E0": E0_theorem_check, "E1": E1_floor, "E2": E2_sic,
|
||||
"E3": E3_regularised, "E4": E4_csi, "E5": E5_maskfam,
|
||||
"E6": E6_coop, "E7a": E7_rates, "E7c": E7_multiuser,
|
||||
"E0": E0_theorem_check, "E1": E1_floor, "E7a": E7_rates,
|
||||
}
|
||||
for name, fn in ALL.items():
|
||||
if not todo or name in todo:
|
||||
fn()
|
||||
print("\nAll requested revision simulations complete.")
|
||||
print("\nAll requested simulations complete.")
|
||||
|
||||
@@ -0,0 +1,416 @@
|
||||
"""
|
||||
GPU-accelerated Monte Carlo experiments (torch backend).
|
||||
========================================================
|
||||
Computes the CSV artifacts of experiments E2, E3, E4, E5, E7c, E8
|
||||
of revision_sims.py with identical models and conventions, using
|
||||
torch (CUDA when available) for the dense linear algebra. All
|
||||
random draws come from the numpy generator with the documented seed
|
||||
2026, so the sample stream is platform-independent; torch only
|
||||
accelerates QR, matrix products, and linear solves in float32 /
|
||||
complex64 precision. Figures are rendered separately by
|
||||
replot_all.py, which reads only data/.
|
||||
|
||||
Run under WSL: python3 revision_sims_gpu.py E2 E3 E4 E5 E7c E8
|
||||
"""
|
||||
from __future__ import annotations
|
||||
import csv
|
||||
import math
|
||||
import sys
|
||||
import time
|
||||
from pathlib import Path
|
||||
import numpy as np
|
||||
import torch
|
||||
|
||||
ROOT = Path(__file__).resolve().parents[1]
|
||||
CSV_DIR = ROOT / "data"
|
||||
|
||||
SEED = 2026
|
||||
rng = np.random.default_rng(SEED)
|
||||
DEV = "cuda" if torch.cuda.is_available() else "cpu"
|
||||
print(f"[gpu] device = {DEV}")
|
||||
|
||||
|
||||
def write_csv(name, header, rows):
|
||||
p = CSV_DIR / f"{name}.csv"
|
||||
with open(p, "w", newline="") as f:
|
||||
w = csv.writer(f); w.writerow(header); w.writerows(rows)
|
||||
print(f"[OK] wrote {p}")
|
||||
|
||||
|
||||
def haar_g(d):
|
||||
"""Haar orthogonal on the GPU from a numpy Gaussian draw."""
|
||||
G = torch.tensor(rng.standard_normal((d, d)), dtype=torch.float32,
|
||||
device=DEV)
|
||||
Q, R = torch.linalg.qr(G)
|
||||
return Q * torch.sign(torch.diagonal(R)).unsqueeze(0)
|
||||
|
||||
|
||||
def embed_pair(d, beta):
|
||||
e1 = rng.standard_normal(d)
|
||||
e1 /= np.linalg.norm(e1)
|
||||
w = rng.standard_normal(d)
|
||||
w -= (w @ e1) * e1
|
||||
w /= np.linalg.norm(w)
|
||||
e2 = beta * e1 + math.sqrt(1.0 - beta**2) * w
|
||||
return (torch.tensor(e1, dtype=torch.float32, device=DEV),
|
||||
torch.tensor(e2, dtype=torch.float32, device=DEV))
|
||||
|
||||
|
||||
def rayleigh2():
|
||||
h = (rng.standard_normal(2) + 1j * rng.standard_normal(2)) / math.sqrt(2)
|
||||
return complex(h[0]), complex(h[1])
|
||||
|
||||
|
||||
def cnoise_g(d):
|
||||
n = (rng.standard_normal(d) + 1j * rng.standard_normal(d)) / math.sqrt(2)
|
||||
return torch.tensor(n, dtype=torch.complex64, device=DEV)
|
||||
|
||||
|
||||
def aware_g(t, Q, beta, c, nvar):
|
||||
"""Batched aware Wiener demux. t: (b,d) cfloat, Q: (d,d) float,
|
||||
c: python complex, nvar: (b,) tensor."""
|
||||
d = Q.shape[0]
|
||||
b = t.shape[0]
|
||||
g = 1.0 - beta * beta
|
||||
rho = g * abs(c)**2 / d + nvar
|
||||
A = torch.eye(d, device=DEV, dtype=torch.complex64) \
|
||||
+ beta * c * Q.to(torch.complex64)
|
||||
S = (A @ A.mH / d).unsqueeze(0) \
|
||||
+ rho.view(b, 1, 1) * torch.eye(d, device=DEV,
|
||||
dtype=torch.complex64)
|
||||
x = torch.linalg.solve(S, t.unsqueeze(-1))
|
||||
return (A.mH.unsqueeze(0) @ x).squeeze(-1) / d
|
||||
|
||||
|
||||
def abscos(a, e):
|
||||
num = (a * e.to(a.dtype).conj()).sum(-1).abs()
|
||||
return (num / (a.norm(dim=-1) * e.norm())).cpu().numpy()
|
||||
|
||||
|
||||
# ------------------------------------------------------------------
|
||||
def E2_sic(beta=0.311, d=512, ntr=400):
|
||||
print("\n=== E2: receiver comparison under block-Rayleigh fading ===")
|
||||
snr_db = np.arange(0, 31, 2.5)
|
||||
sigs = torch.tensor(10 ** (-snr_db / 20.0), dtype=torch.float32,
|
||||
device=DEV)
|
||||
nb = len(snr_db)
|
||||
res = {k: np.zeros(nb) for k in ("edma", "blind", "oma", "genie", "sic")}
|
||||
t0 = time.time()
|
||||
for tr in range(ntr):
|
||||
e1, e2 = embed_pair(d, beta)
|
||||
M1, M2 = haar_g(d), haar_g(d)
|
||||
Q = M1.T @ M2
|
||||
h1, h2 = rayleigh2()
|
||||
n = cnoise_g(d); n2 = cnoise_g(d)
|
||||
r0 = h1 * (M1 @ e1).to(torch.complex64) \
|
||||
+ h2 * (M2 @ e2).to(torch.complex64)
|
||||
r = r0.unsqueeze(0) + sigs.view(-1, 1) * n.unsqueeze(0)
|
||||
t1 = (M1.T.to(torch.complex64) @ r.unsqueeze(-1)).squeeze(-1) / h1
|
||||
t2 = (M2.T.to(torch.complex64) @ r.unsqueeze(-1)).squeeze(-1) / h2
|
||||
c1, c2 = h2 / h1, h1 / h2
|
||||
v1 = sigs**2 / abs(h1)**2
|
||||
v2 = sigs**2 / abs(h2)**2
|
||||
g1 = aware_g(t1, Q, beta, c1, v1)
|
||||
g2 = aware_g(t2, Q.T, beta, c2, v2)
|
||||
res["edma"] += 0.5 * (abscos(g1, e1) + abscos(g2, e2))
|
||||
res["blind"] += 0.5 * (abscos(t1, e1) + abscos(t2, e2))
|
||||
o1 = e1.to(torch.complex64).unsqueeze(0) \
|
||||
+ math.sqrt(2) * sigs.view(-1, 1) * n.unsqueeze(0) / h1
|
||||
o2 = e2.to(torch.complex64).unsqueeze(0) \
|
||||
+ math.sqrt(2) * sigs.view(-1, 1) * n2.unsqueeze(0) / h2
|
||||
res["oma"] += 0.5 * (abscos(o1, e1) + abscos(o2, e2))
|
||||
ge1 = (M1.T.to(torch.complex64)
|
||||
@ (r - h2 * (M2 @ e2).to(torch.complex64)).unsqueeze(-1)
|
||||
).squeeze(-1) / h1
|
||||
ge2 = (M2.T.to(torch.complex64)
|
||||
@ (r - h1 * (M1 @ e1).to(torch.complex64)).unsqueeze(-1)
|
||||
).squeeze(-1) / h2
|
||||
res["genie"] += 0.5 * (abscos(ge1, e1) + abscos(ge2, e2))
|
||||
# realizable decision-directed SIC: the stronger user is detected
|
||||
# with the same aware Wiener stage (a scalar-scaled matched-filter
|
||||
# decision would re-modulate to a multiple of r itself, because
|
||||
# M_s M_s^T = I, and cancel nothing), its re-modulated estimate is
|
||||
# subtracted, and the weaker user is read from the residual.
|
||||
if abs(h1) >= abs(h2):
|
||||
hs, hw, Ms, Mw, es, ew = h1, h2, M1, M2, e1, e2
|
||||
Qsw, csw, vsw = Q, c1, v1
|
||||
else:
|
||||
hs, hw, Ms, Mw, es, ew = h2, h1, M2, M1, e2, e1
|
||||
Qsw, csw, vsw = Q.T, c2, v2
|
||||
t_s = (Ms.T.to(torch.complex64) @ r.unsqueeze(-1)).squeeze(-1) / hs
|
||||
dec = aware_g(t_s, Qsw, beta, csw, vsw)
|
||||
r_res = r - hs * (Ms.to(torch.complex64)
|
||||
@ dec.unsqueeze(-1)).squeeze(-1)
|
||||
d_w = (Mw.T.to(torch.complex64) @ r_res.unsqueeze(-1)).squeeze(-1) / hw
|
||||
res["sic"] += 0.5 * (abscos(dec, es) + abscos(d_w, ew))
|
||||
if (tr + 1) % 100 == 0:
|
||||
print(f" {tr+1}/{ntr} ({time.time()-t0:.0f}s)", flush=True)
|
||||
for k in res:
|
||||
res[k] /= ntr
|
||||
rows = [[s] + [res[k][i] for k in ("edma", "blind", "oma", "genie", "sic")]
|
||||
for i, s in enumerate(snr_db)]
|
||||
write_csv("sic_comparison",
|
||||
["snr_db", "edma", "blind", "oma", "genie", "sic"], rows)
|
||||
i20 = list(snr_db).index(20)
|
||||
print(f" at 20 dB: EDMA {res['edma'][i20]:.3f}, blind "
|
||||
f"{res['blind'][i20]:.3f}, SIC {res['sic'][i20]:.3f}, "
|
||||
f"genie {res['genie'][i20]:.3f}, OMA {res['oma'][i20]:.3f}")
|
||||
|
||||
|
||||
# ------------------------------------------------------------------
|
||||
def E3_unconditional(beta=0.311, d=512, ntr=1500):
|
||||
print("\n=== E3: Rayleigh unconditional MSE of the aware receiver ===")
|
||||
rows = []
|
||||
for s in (10, 20):
|
||||
sig = 10 ** (-s / 20.0)
|
||||
mses, bl = [], []
|
||||
for _ in range(ntr):
|
||||
e1, e2 = embed_pair(d, beta)
|
||||
M1, M2 = haar_g(d), haar_g(d)
|
||||
Q = M1.T @ M2
|
||||
h1, h2 = rayleigh2()
|
||||
n = cnoise_g(d)
|
||||
r = h1 * (M1 @ e1).to(torch.complex64) \
|
||||
+ h2 * (M2 @ e2).to(torch.complex64) + sig * n
|
||||
t1 = (M1.T.to(torch.complex64) @ r) / h1
|
||||
c1 = h2 / h1
|
||||
nv = torch.tensor([sig**2 / abs(h1)**2], device=DEV)
|
||||
g1 = aware_g(t1.unsqueeze(0), Q, beta, c1, nv)[0]
|
||||
mses.append(float((g1 - e1.to(torch.complex64)).norm()**2))
|
||||
lam = (1.0 / d) / (1.0 / d + abs(c1)**2 / d + sig**2 / abs(h1)**2)
|
||||
b1 = lam * t1
|
||||
bl.append(float((b1 - e1.to(torch.complex64)).norm()**2))
|
||||
rows.append([s, float(np.mean(mses)), float(np.median(mses)),
|
||||
float(np.mean(bl)), float(np.median(bl))])
|
||||
print(f" {s} dB: aware mean {rows[-1][1]:.4f} "
|
||||
f"(median {rows[-1][2]:.4f}) | blind mean {rows[-1][3]:.4f} "
|
||||
f"(median {rows[-1][4]:.4f})")
|
||||
write_csv("rayleigh_mse", ["snr_db", "aware_mean", "aware_median",
|
||||
"blind_mean", "blind_median"], rows)
|
||||
|
||||
|
||||
# ------------------------------------------------------------------
|
||||
def E4_csi(beta=0.311, d=512, snr=30.0, ntr=400):
|
||||
print("\n=== E4: imperfect CSI robustness (EDMA vs realizable SIC) ===")
|
||||
sh2 = np.array([0.0, 0.01, 0.02, 0.05, 0.1, 0.2, 0.3])
|
||||
sig = 10 ** (-snr / 20.0)
|
||||
res_e = np.zeros(len(sh2)); res_s = np.zeros(len(sh2))
|
||||
for _ in range(ntr):
|
||||
e1, e2 = embed_pair(d, beta)
|
||||
M1, M2 = haar_g(d), haar_g(d)
|
||||
Q = M1.T @ M2
|
||||
h1, h2 = rayleigh2()
|
||||
n = cnoise_g(d)
|
||||
r = h1 * (M1 @ e1).to(torch.complex64) \
|
||||
+ h2 * (M2 @ e2).to(torch.complex64) + sig * n
|
||||
eps1, eps2 = rayleigh2()
|
||||
for j, v in enumerate(sh2):
|
||||
hh1 = h1 + math.sqrt(v) * eps1
|
||||
hh2 = h2 + math.sqrt(v) * eps2
|
||||
t1 = (M1.T.to(torch.complex64) @ r) / hh1
|
||||
t2 = (M2.T.to(torch.complex64) @ r) / hh2
|
||||
nv1 = torch.tensor([sig**2 / abs(hh1)**2], device=DEV)
|
||||
nv2 = torch.tensor([sig**2 / abs(hh2)**2], device=DEV)
|
||||
g1 = aware_g(t1.unsqueeze(0), Q, beta, hh2 / hh1, nv1)[0]
|
||||
g2 = aware_g(t2.unsqueeze(0), Q.T, beta, hh1 / hh2, nv2)[0]
|
||||
res_e[j] += 0.5 * (float(abscos(g1.unsqueeze(0), e1)[0])
|
||||
+ float(abscos(g2.unsqueeze(0), e2)[0]))
|
||||
if abs(hh1) >= abs(hh2):
|
||||
hs, hw, Ms, Mw, es, ew = hh1, hh2, M1, M2, e1, e2
|
||||
Qsw, csw = Q, hh2 / hh1
|
||||
else:
|
||||
hs, hw, Ms, Mw, es, ew = hh2, hh1, M2, M1, e2, e1
|
||||
Qsw, csw = Q.T, hh1 / hh2
|
||||
t_s = (Ms.T.to(torch.complex64) @ r) / hs
|
||||
nvs = torch.tensor([sig**2 / abs(hs)**2], device=DEV)
|
||||
dec = aware_g(t_s.unsqueeze(0), Qsw, beta, csw, nvs)[0]
|
||||
r_res = r - hs * (Ms.to(torch.complex64) @ dec)
|
||||
d_w = (Mw.T.to(torch.complex64) @ r_res) / hw
|
||||
res_s[j] += 0.5 * (float(abscos(dec.unsqueeze(0), es)[0])
|
||||
+ float(abscos(d_w.unsqueeze(0), ew)[0]))
|
||||
res_e /= ntr; res_s /= ntr
|
||||
print(f" EDMA: {res_e[0]:.4f} -> {res_e[-1]:.4f} "
|
||||
f"(delta {100*(res_e[0]-res_e[-1]):.2f} points)")
|
||||
print(f" SIC : {res_s[0]:.4f} -> {res_s[-1]:.4f} "
|
||||
f"(delta {100*(res_s[0]-res_s[-1]):.2f} points)")
|
||||
rows = [[v, res_e[j], res_s[j]] for j, v in enumerate(sh2)]
|
||||
write_csv("csi_error", ["sigma_h2", "edma", "sic"], rows)
|
||||
|
||||
|
||||
# ------------------------------------------------------------------
|
||||
def E5_maskfam(beta=0.311, d=512, ntr=200):
|
||||
print("\n=== E5: Walsh-Hadamard diagonal variant vs Haar ===")
|
||||
snr_db = np.arange(0, 41, 5)
|
||||
sigs = torch.tensor(10 ** (-snr_db / 20.0), dtype=torch.float32,
|
||||
device=DEV)
|
||||
nb = len(snr_db)
|
||||
H = np.array([[1.0]])
|
||||
while H.shape[0] < d:
|
||||
H = np.block([[H, H], [H, -H]])
|
||||
Ht = torch.tensor(H / math.sqrt(d), dtype=torch.float32, device=DEV)
|
||||
g = 1.0 - beta**2
|
||||
res = {"haar": np.zeros(nb), "wh": np.zeros(nb)}
|
||||
exact = np.zeros(nb)
|
||||
for _ in range(ntr):
|
||||
e1, e2 = embed_pair(d, beta)
|
||||
M1, M2 = haar_g(d), haar_g(d)
|
||||
Q = M1.T @ M2
|
||||
D1 = torch.tensor(np.sign(rng.standard_normal(d)),
|
||||
dtype=torch.float32, device=DEV)
|
||||
D2 = torch.tensor(np.sign(rng.standard_normal(d)),
|
||||
dtype=torch.float32, device=DEV)
|
||||
W1, W2 = Ht * D1.unsqueeze(0), Ht * D2.unsqueeze(0)
|
||||
q = D1 * D2
|
||||
n = cnoise_g(d)
|
||||
r0h = (M1 @ e1 + M2 @ e2).to(torch.complex64)
|
||||
r0w = (W1 @ e1 + W2 @ e2).to(torch.complex64)
|
||||
rh = r0h.unsqueeze(0) + sigs.view(-1, 1) * n.unsqueeze(0)
|
||||
rw = r0w.unsqueeze(0) + sigs.view(-1, 1) * n.unsqueeze(0)
|
||||
t1 = (M1.T.to(torch.complex64) @ rh.unsqueeze(-1)).squeeze(-1)
|
||||
g1 = aware_g(t1, Q, beta, 1.0, sigs**2)
|
||||
res["haar"] += abscos(g1, e1)
|
||||
tw = (W1.T.to(torch.complex64) @ rw.unsqueeze(-1)).squeeze(-1)
|
||||
a = 1.0 + beta * q # (d,)
|
||||
rho = g / d + sigs**2 # (nb,)
|
||||
wdiag = a.unsqueeze(0) / (a.unsqueeze(0)**2 / d
|
||||
+ rho.view(-1, 1)) # (nb,d)
|
||||
w1 = (wdiag.to(torch.complex64) / d) * tw
|
||||
res["wh"] += abscos(w1, e1)
|
||||
exact += ((g + d * sigs.view(-1, 1)**2)
|
||||
/ (a.unsqueeze(0)**2 + g + d * sigs.view(-1, 1)**2)
|
||||
).mean(1).cpu().numpy()
|
||||
for k in res:
|
||||
res[k] /= ntr
|
||||
exact /= ntr
|
||||
print(f" max |WH - Haar| cosine dev: "
|
||||
f"{100*np.max(np.abs(res['wh']-res['haar'])):.2f} points; "
|
||||
f"40 dB WH {res['wh'][-1]:.4f} vs Haar {res['haar'][-1]:.4f}")
|
||||
rows = [[s, res["haar"][i], res["wh"][i], exact[i]]
|
||||
for i, s in enumerate(snr_db)]
|
||||
write_csv("mask_family_rev", ["snr_db", "haar", "wh", "wh_exact_mse"],
|
||||
rows)
|
||||
|
||||
|
||||
# ------------------------------------------------------------------
|
||||
def E7_multiuser(beta=0.311, d=512, ntr=100):
|
||||
print("\n=== E7c: multi-user scaling (joint Wiener) ===")
|
||||
snr_db = np.arange(0, 31, 2.5)
|
||||
sigs = torch.tensor(10 ** (-snr_db / 20.0), dtype=torch.float32,
|
||||
device=DEV)
|
||||
nb = len(snr_db)
|
||||
rows = []
|
||||
for U in (2, 3, 4):
|
||||
B = (1 - beta) * np.eye(U) + beta * np.ones((U, U))
|
||||
A = np.linalg.cholesky(B)
|
||||
Bt = torch.tensor(B, dtype=torch.float32, device=DEV)
|
||||
err = np.zeros(nb)
|
||||
t0 = time.time()
|
||||
for _ in range(ntr):
|
||||
F = rng.standard_normal((d, U))
|
||||
Fq, _ = np.linalg.qr(F)
|
||||
E = (Fq @ A.T).T
|
||||
Et = torch.tensor(E, dtype=torch.float32, device=DEV)
|
||||
masks = [haar_g(d) for _ in range(U)]
|
||||
n = cnoise_g(d)
|
||||
r0 = sum(masks[u] @ Et[u] for u in range(U)).to(torch.complex64)
|
||||
Qs = [masks[0].T @ masks[v] for v in range(U)]
|
||||
Ret = sum(Bt[0, v] * Qs[v].T for v in range(U)) / d
|
||||
S0 = sum(Bt[v, w] * (Qs[v] @ Qs[w].T)
|
||||
for v in range(U) for w in range(U)) / d
|
||||
r = r0.unsqueeze(0) + sigs.view(-1, 1) * n.unsqueeze(0)
|
||||
t = (masks[0].T.to(torch.complex64)
|
||||
@ r.unsqueeze(-1)).squeeze(-1)
|
||||
S = S0.to(torch.complex64).unsqueeze(0) \
|
||||
+ (sigs**2).view(-1, 1, 1) \
|
||||
* torch.eye(d, device=DEV, dtype=torch.complex64)
|
||||
x = torch.linalg.solve(S, t.unsqueeze(-1))
|
||||
eh = (Ret.to(torch.complex64).unsqueeze(0) @ x).squeeze(-1)
|
||||
err += ((eh - Et[0].to(torch.complex64)).norm(dim=1)**2
|
||||
).cpu().numpy()
|
||||
err /= ntr
|
||||
T_mc = U * np.log2(1.0 / err)
|
||||
r0v = (U - 1) + d / 10 ** (snr_db / 10.0)
|
||||
T_bl = U * np.log2(1.0 + 1.0 / r0v)
|
||||
T_oma = U * np.log2(1 + 10 ** (snr_db / 10.0) / (U * d))
|
||||
for i, s in enumerate(snr_db):
|
||||
rows.append([U, s, T_mc[i], T_bl[i], T_oma[i], err[i]])
|
||||
i20 = list(snr_db).index(20.0)
|
||||
print(f" U={U}: at 20 dB EDMA {T_mc[i20]:.3f} vs blind "
|
||||
f"{T_bl[i20]:.3f} vs OMA {T_oma[i20]:.3f} "
|
||||
f"(gain {T_mc[i20]/T_oma[i20]:.2f}x), floor MSE {err[-1]:.4f}"
|
||||
f" [{time.time()-t0:.0f}s]")
|
||||
write_csv("multiuser_corrected",
|
||||
["U", "snr_db", "edma_mc", "blind", "oma", "mse_mc"], rows)
|
||||
|
||||
|
||||
# ------------------------------------------------------------------
|
||||
def E8_mismatch(beta=0.311, d=512, snr=20.0, ntr=200):
|
||||
print("\n=== E8: affinity mismatch of the aware receiver ===")
|
||||
sig = 10 ** (-snr / 20.0)
|
||||
bhs = [b for b in (beta - 0.1, beta - 0.06, beta, beta + 0.06,
|
||||
beta + 0.1, beta + 2 ** -8, 0.0) if b >= 0]
|
||||
accs = np.zeros(len(bhs)); msea = np.zeros(len(bhs))
|
||||
for _ in range(ntr):
|
||||
e1, e2 = embed_pair(d, beta)
|
||||
M1, M2 = haar_g(d), haar_g(d)
|
||||
Q = M1.T @ M2
|
||||
n = cnoise_g(d)
|
||||
r = (M1 @ e1 + M2 @ e2).to(torch.complex64) + sig * n
|
||||
t1 = (M1.T.to(torch.complex64) @ r)
|
||||
nv = torch.tensor([sig**2], device=DEV)
|
||||
for j, bh in enumerate(bhs):
|
||||
g1 = aware_g(t1.unsqueeze(0), Q, bh, 1.0, nv)[0]
|
||||
accs[j] += float(abscos(g1.unsqueeze(0), e1)[0])
|
||||
msea[j] += float((g1 - e1.to(torch.complex64)).norm()**2)
|
||||
accs /= ntr; msea /= ntr
|
||||
rows = []
|
||||
for j, bh in enumerate(bhs):
|
||||
tag = ("quant b=7" if abs(bh - beta - 2**-8) < 1e-12 else
|
||||
("blind" if bh == 0.0 else f"delta={bh-beta:+.2f}"))
|
||||
print(f" beta_hat={bh:.4f} ({tag}): cosine {accs[j]:.4f}, "
|
||||
f"MSE {msea[j]:.4f}")
|
||||
rows.append([bh, accs[j], msea[j]])
|
||||
write_csv("mismatch", ["beta_hat", "cosine", "mse"], rows)
|
||||
|
||||
|
||||
|
||||
|
||||
# ------------------------------------------------------------------
|
||||
def E9_ceiling(d=512, snr=60.0, ntr=200):
|
||||
print(chr(10) + '=== E9: cosine-ceiling verification (h=1) ===')
|
||||
sig = 10 ** (-snr / 20.0)
|
||||
rows = []
|
||||
for beta in (0.311, 0.8):
|
||||
g = 1.0 - beta**2
|
||||
acc_a = 0.0; acc_b = 0.0
|
||||
for _ in range(ntr):
|
||||
e1, e2 = embed_pair(d, beta)
|
||||
M1, M2 = haar_g(d), haar_g(d)
|
||||
Q = M1.T @ M2
|
||||
n = cnoise_g(d)
|
||||
r = (M1 @ e1 + M2 @ e2).to(torch.complex64) + sig * n
|
||||
t1 = (M1.T.to(torch.complex64) @ r)
|
||||
nv = torch.tensor([sig**2], device=DEV)
|
||||
g1 = aware_g(t1.unsqueeze(0), Q, beta, 1.0, nv)[0]
|
||||
acc_a += float(abscos(g1.unsqueeze(0), e1)[0])
|
||||
acc_b += float(abscos(t1.unsqueeze(0), e1)[0])
|
||||
acc_a /= ntr; acc_b /= ntr
|
||||
import math as _m
|
||||
pred_a = _m.sqrt(1.0 - _m.sqrt(g) / 2.0)
|
||||
pred_b = _m.sqrt(0.5)
|
||||
print(f' beta={beta}: aware MC {acc_a:.4f} pred {pred_a:.4f} | '
|
||||
f'blind MC {acc_b:.4f} pred {pred_b:.4f}')
|
||||
rows.append([beta, acc_a, pred_a, acc_b, pred_b])
|
||||
write_csv('cosine_ceiling', ['beta', 'aware_mc', 'aware_pred',
|
||||
'blind_mc', 'blind_pred'], rows)
|
||||
|
||||
|
||||
if __name__ == "__main__":
|
||||
todo = set(sys.argv[1:])
|
||||
ALL = {"E2": E2_sic, "E3": E3_unconditional, "E4": E4_csi,
|
||||
"E5": E5_maskfam, "E7c": E7_multiuser, "E8": E8_mismatch,
|
||||
"E9": E9_ceiling}
|
||||
for name, fn in ALL.items():
|
||||
if not todo or name in todo:
|
||||
fn()
|
||||
print("\nAll requested GPU simulations complete.")
|
||||
+225
-338
@@ -1,70 +1,35 @@
|
||||
"""
|
||||
Complete numerical verification of every closed form in the manuscript.
|
||||
=======================================================================
|
||||
Each check implements the formula EXACTLY as printed in main.tex and
|
||||
compares it against a direct Monte-Carlo or algebraic evaluation.
|
||||
Prints PASS/FAIL per item with the achieved deviation. Fixed seed.
|
||||
Monte Carlo verification of every closed-form claim (v2 design).
|
||||
================================================================
|
||||
Independent Haar masks + affinity-aware Wiener demultiplexer.
|
||||
Checks (d = 256 for speed; deviations shrink as O(1/d)):
|
||||
|
||||
V1 per-realization Gram identity M1^T M2 = beta I + sqrt(g) Q
|
||||
V2 Theorem 1 full MSE (noise + C_SI,u) vs MC, random complex h
|
||||
V3 noise-free calibration of C_SI,1 / C_SI,2 (several phases)
|
||||
V4 quoted constants: C_SI,1, C_SI,2, C-bar at (0.311, h=1);
|
||||
cosine ceiling 1/sqrt(1+C_SI,1) = 0.70; rho_f = 28 dB at d=768
|
||||
V5 SINR corollary eta_u = 1/MSE (per-coordinate accounting)
|
||||
V6 C_SI,u >= 1 for all beta (proof identities gamma*C_SI,1 =
|
||||
gamma + 4 beta^4, gamma*C_SI,2 = 1 + 3 beta^2 at h=1)
|
||||
V7 Proposition (MAC consistency) on a (beta, rho) grid
|
||||
V8 wideband limit T/C_MAC -> gamma
|
||||
V9 beta* crossover roots at 10/20 dB (0.700 / 0.590, d=512)
|
||||
V10 rho_c = d(2-1/gamma)/C-bar exact iff-condition + 25.7 dB value
|
||||
V11 idealized no-floor variant crosses C_MAC at 2 beta^2 d/gamma^2
|
||||
(~21 dB at d=512, beta=0.311)
|
||||
V12 mismatch identity (eq:mismatch) + bound value 8.8e-3
|
||||
V13 CSI-direction invariance: |cos| unchanged under wrong h-hat;
|
||||
eq:csi-free equals eq:correct
|
||||
V14 cross-moment lemma E[n^H M_u M_v^T n] = sigma^2 beta d
|
||||
V15 multi-user [B^-1]_uu Sherman-Morrison formula, U = 2..6
|
||||
V16 multi-user noise-free C_SI^(U) ~ (U-1) C-bar (within 10 %)
|
||||
V17 Walsh-Hadamard masks: exact orthogonality + expected cross-Gram
|
||||
V1 Theorem 1 MSE formula vs MC at several (beta, SNR), h = 1
|
||||
V2 Theorem 1 under random channel phases, both users
|
||||
V3 floors: aware sqrt(g)/2 vs blind 1/2, and the value ratio
|
||||
V4 cosine ceiling sqrt(1 - MSE) (Corollary: cosine)
|
||||
V5 blind receiver == matched filter in cosine (scalar shrinkage)
|
||||
V6 monotonicity of the MSE in beta (Proposition)
|
||||
V7 full-cooperation bound T <= log2(1+4 rho/d), equality at beta=1
|
||||
V8 MAC condition gamma^2 (2+k) >= 2 beta^2 k^2 boundary
|
||||
V9 Walsh-Hadamard diagonal variant: exact finite-d closed form
|
||||
V10 mismatch stationarity: MSE(beta_hat) - MSE(beta) = O(delta^2)
|
||||
V11 correlated-mask alternative floor 1 + 4 beta^4 / gamma
|
||||
(Remark and Appendix), dominated by the aware receiver
|
||||
|
||||
Pure numpy, fixed seed, ~2 minutes on a laptop.
|
||||
"""
|
||||
from __future__ import annotations
|
||||
import math
|
||||
import numpy as np
|
||||
|
||||
def hadamard(n):
|
||||
H = np.array([[1.0]])
|
||||
while H.shape[0] < n:
|
||||
H = np.block([[H, H], [H, -H]])
|
||||
return H
|
||||
|
||||
|
||||
def brentq(f, a, b, tol=1e-12):
|
||||
fa, fb = f(a), f(b)
|
||||
assert fa * fb < 0, "no sign change"
|
||||
for _ in range(200):
|
||||
m = 0.5 * (a + b)
|
||||
fm = f(m)
|
||||
if abs(fm) < tol or (b - a) < tol:
|
||||
return m
|
||||
if fa * fm < 0:
|
||||
b, fb = m, fm
|
||||
else:
|
||||
a, fa = m, fm
|
||||
return 0.5 * (a + b)
|
||||
|
||||
rng = np.random.default_rng(2026)
|
||||
FAIL = []
|
||||
|
||||
|
||||
def report(name, ok, detail):
|
||||
tag = "PASS" if ok else "FAIL"
|
||||
if not ok:
|
||||
FAIL.append(name)
|
||||
print(f"[{tag}] {name}: {detail}")
|
||||
D = 256
|
||||
|
||||
|
||||
def haar(d):
|
||||
Q, R = np.linalg.qr(rng.standard_normal((d, d)))
|
||||
G = rng.standard_normal((d, d))
|
||||
Q, R = np.linalg.qr(G)
|
||||
return Q * np.sign(np.diag(R))
|
||||
|
||||
|
||||
@@ -72,303 +37,225 @@ def unit(v):
|
||||
return v / np.linalg.norm(v)
|
||||
|
||||
|
||||
def pair(d, beta):
|
||||
def cosim(a, b):
|
||||
return float(abs(np.vdot(a, b)) / (np.linalg.norm(a) * np.linalg.norm(b)))
|
||||
|
||||
|
||||
def embed_pair(d, beta):
|
||||
e1 = unit(rng.standard_normal(d))
|
||||
w = rng.standard_normal(d)
|
||||
w = unit(w - (w @ e1) * e1)
|
||||
return e1, beta * e1 + math.sqrt(1 - beta**2) * w
|
||||
return e1, beta * e1 + math.sqrt(1 - beta * beta) * w
|
||||
|
||||
|
||||
def csi1(beta, c):
|
||||
g = 1 - beta**2
|
||||
n2 = 1 + beta**2 * abs(c)**2 + 2 * beta**2 * np.real(c)
|
||||
return (g**2 * abs(c)**2 + beta**2 * n2) / g
|
||||
def cnoise(d):
|
||||
return (rng.standard_normal(d) + 1j * rng.standard_normal(d)) / math.sqrt(2)
|
||||
|
||||
|
||||
def csi2(beta, c):
|
||||
g = 1 - beta**2
|
||||
return (abs(c)**2 + beta**2 + 2 * beta**2 * np.real(c)) / g
|
||||
def mse_theory(beta, c1, rho_e):
|
||||
a0 = 1.0 + beta**2 * abs(c1)**2 + rho_e
|
||||
return rho_e / math.sqrt(a0 * a0 - 4.0 * beta**2 * abs(c1)**2)
|
||||
|
||||
|
||||
# ---------------- V1: per-realization Gram identity ----------------
|
||||
d, beta = 256, 0.311
|
||||
g = 1 - beta**2
|
||||
U1, U2 = haar(d), haar(d)
|
||||
M1, M2 = U1, beta * U1 + math.sqrt(g) * U2
|
||||
dev = np.abs(M1.T @ M2 - (beta * np.eye(d)
|
||||
+ math.sqrt(g) * U1.T @ U2)).max()
|
||||
report("V1 Gram identity", dev < 1e-12, f"max dev {dev:.2e}")
|
||||
def aware(t1, Q, beta, c1, nvar, d):
|
||||
g = 1.0 - beta * beta
|
||||
rho = g * abs(c1)**2 / d + nvar
|
||||
S = beta * (c1 * Q + np.conj(c1) * Q.T) / d
|
||||
S[np.diag_indices(d)] += (1.0 + beta**2 * abs(c1)**2) / d + rho
|
||||
x = np.linalg.solve(S, t1)
|
||||
return (x + beta * np.conj(c1) * (Q.T @ x)) / d
|
||||
|
||||
# ---------------- V2: Theorem 1 full MSE, random complex h ---------
|
||||
d = 512
|
||||
for beta in (0.1, 0.311, 0.5):
|
||||
g = 1 - beta**2
|
||||
h = (rng.standard_normal(2) + 1j * rng.standard_normal(2)) / math.sqrt(2)
|
||||
h1, h2 = h
|
||||
rho_db = 15.0
|
||||
sig = 10 ** (-rho_db / 20.0)
|
||||
e1, e2 = pair(d, beta)
|
||||
mc = np.zeros(2)
|
||||
NT = 300
|
||||
for _ in range(NT):
|
||||
U1, U2 = haar(d), haar(d)
|
||||
M1, M2 = U1, beta * U1 + math.sqrt(g) * U2
|
||||
n = (rng.standard_normal(d) + 1j * rng.standard_normal(d)) \
|
||||
/ math.sqrt(2)
|
||||
r = h1 * (M1 @ e1) + h2 * (M2 @ e2) + sig * n
|
||||
t1 = M1.T @ r / h1
|
||||
t2 = M2.T @ r / h2
|
||||
g1 = (t1 - beta * (h2 / h1) * t2) / g
|
||||
g2 = (t2 - beta * (h1 / h2) * t1) / g
|
||||
mc[0] += np.linalg.norm(g1 - e1)**2
|
||||
mc[1] += np.linalg.norm(g2 - e2)**2
|
||||
mc /= NT
|
||||
th1 = d * sig**2 / (abs(h1)**2 * g) + csi1(beta, h2 / h1)
|
||||
th2 = d * sig**2 / (abs(h2)**2 * g) + csi2(beta, h1 / h2)
|
||||
dev = max(abs(mc[0] / th1 - 1), abs(mc[1] / th2 - 1))
|
||||
report(f"V2 Theorem 1 MSE (beta={beta})", dev < 0.02,
|
||||
f"MC/theory dev {100*dev:.2f}% (O(1/d) at d={d})")
|
||||
|
||||
# ---------------- V3: noise-free C_SI calibration ------------------
|
||||
d = 512
|
||||
for phase in (0.0, math.pi / 3, math.pi):
|
||||
beta = 0.311
|
||||
g = 1 - beta**2
|
||||
h1 = 1.0 + 0j
|
||||
h2 = np.exp(1j * phase)
|
||||
e1, e2 = pair(d, beta)
|
||||
mc = np.zeros(2)
|
||||
NT = 200
|
||||
for _ in range(NT):
|
||||
U1, U2 = haar(d), haar(d)
|
||||
M1, M2 = U1, beta * U1 + math.sqrt(g) * U2
|
||||
r = h1 * (M1 @ e1) + h2 * (M2 @ e2)
|
||||
t1 = M1.T @ r / h1
|
||||
t2 = M2.T @ r / h2
|
||||
g1 = (t1 - beta * (h2 / h1) * t2) / g
|
||||
g2 = (t2 - beta * (h1 / h2) * t1) / g
|
||||
mc[0] += np.linalg.norm(g1 - e1)**2
|
||||
mc[1] += np.linalg.norm(g2 - e2)**2
|
||||
mc /= NT
|
||||
t1v, t2v = csi1(beta, h2 / h1), csi2(beta, h1 / h2)
|
||||
dev = max(abs(mc[0] / t1v - 1), abs(mc[1] / t2v - 1))
|
||||
report(f"V3 noise-free C_SI (phase={phase:.2f})", dev < 0.02,
|
||||
f"dev {100*dev:.2f}%")
|
||||
def run_pair(beta, sig, h1=1.0 + 0j, h2=1.0 + 0j, d=D):
|
||||
e1, e2 = embed_pair(d, beta)
|
||||
M1, M2 = haar(d), haar(d)
|
||||
Q = M1.T @ M2
|
||||
r = h1 * (M1 @ e1) + h2 * (M2 @ e2) + sig * cnoise(d)
|
||||
t1 = M1.T @ r / h1
|
||||
return e1, e2, Q, t1, M2.T @ r / h2
|
||||
|
||||
# ---------------- V4: quoted constants -----------------------------
|
||||
|
||||
def check(name, ok, detail=""):
|
||||
print(f"[{'PASS' if ok else 'FAIL'}] {name} {detail}")
|
||||
return ok
|
||||
|
||||
|
||||
allok = True
|
||||
|
||||
# ---------------------------------------------------------------- V1
|
||||
devs = []
|
||||
for beta in (0.0, 0.311, 0.6):
|
||||
for snr in (10.0, 20.0, 60.0):
|
||||
sig = 10 ** (-snr / 20.0)
|
||||
mc = 0.0
|
||||
NT = 40
|
||||
for _ in range(NT):
|
||||
e1, _, Q, t1, _ = run_pair(beta, sig)
|
||||
g1 = aware(t1, Q, beta, 1.0, sig * sig, D)
|
||||
mc += float(np.linalg.norm(g1 - e1) ** 2)
|
||||
mc /= NT
|
||||
th = mse_theory(beta, 1.0, (1 - beta**2) + D * sig * sig)
|
||||
devs.append(abs(mc / th - 1))
|
||||
allok &= check("V1 Theorem 1 (h=1)", max(devs) < 0.03,
|
||||
f"max dev {100*max(devs):.2f}%")
|
||||
|
||||
# ---------------------------------------------------------------- V2
|
||||
devs = []
|
||||
sig = 10 ** (-20.0 / 20.0)
|
||||
for beta in (0.311, 0.5):
|
||||
for _ in range(30):
|
||||
h1 = np.exp(1j * rng.uniform(0, 2 * np.pi))
|
||||
h2 = np.exp(1j * rng.uniform(0, 2 * np.pi))
|
||||
e1, e2, Q, t1, t2 = run_pair(beta, sig, h1, h2)
|
||||
c1, c2 = h2 / h1, h1 / h2
|
||||
g1 = aware(t1, Q, beta, c1, sig**2, D)
|
||||
g2 = aware(t2, Q.T, beta, c2, sig**2, D)
|
||||
g = 1 - beta**2
|
||||
th1 = mse_theory(beta, c1, g * abs(c1)**2 + D * sig**2)
|
||||
th2 = mse_theory(beta, c2, g * abs(c2)**2 + D * sig**2)
|
||||
devs.append(abs(np.linalg.norm(g1 - e1)**2 / th1 - 1))
|
||||
devs.append(abs(np.linalg.norm(g2 - e2)**2 / th2 - 1))
|
||||
allok &= check("V2 Theorem 1 (random phases, both users)",
|
||||
float(np.mean(devs)) < 0.05,
|
||||
f"mean dev {100*float(np.mean(devs)):.2f}%")
|
||||
|
||||
# ---------------------------------------------------------------- V3
|
||||
beta = 0.6
|
||||
sig = 1e-3
|
||||
mc_a, mc_b = 0.0, 0.0
|
||||
NT = 40
|
||||
for _ in range(NT):
|
||||
e1, _, Q, t1, _ = run_pair(beta, sig)
|
||||
g1 = aware(t1, Q, beta, 1.0, sig * sig, D)
|
||||
mc_a += float(np.linalg.norm(g1 - e1) ** 2)
|
||||
lam = (1.0 / D) / (2.0 / D + sig * sig)
|
||||
mc_b += float(np.linalg.norm(lam * t1 - e1) ** 2)
|
||||
mc_a /= NT
|
||||
mc_b /= NT
|
||||
fa, fb = math.sqrt(1 - beta**2) / 2, 0.5
|
||||
allok &= check("V3 floors sqrt(g)/2 vs 1/2",
|
||||
abs(mc_a - fa) < 0.02 and abs(mc_b - fb) < 0.02,
|
||||
f"aware {mc_a:.4f}~{fa:.4f}, blind {mc_b:.4f}~{fb:.4f}, "
|
||||
f"ratio {mc_b/mc_a:.3f}~{1/math.sqrt(1-beta**2):.3f}")
|
||||
|
||||
# ---------------------------------------------------------------- V4
|
||||
acc = 0.0
|
||||
for _ in range(NT):
|
||||
e1, _, Q, t1, _ = run_pair(beta, sig)
|
||||
acc += cosim(aware(t1, Q, beta, 1.0, sig * sig, D), e1)
|
||||
acc /= NT
|
||||
pred = math.sqrt(1 - fa)
|
||||
allok &= check("V4 cosine ceiling sqrt(1-MSE)", abs(acc - pred) < 0.01,
|
||||
f"MC {acc:.4f} vs {pred:.4f}")
|
||||
|
||||
# ---------------------------------------------------------------- V5
|
||||
e1, _, Q, t1, _ = run_pair(0.311, 0.1)
|
||||
lam = 0.37 # any scalar
|
||||
allok &= check("V5 blind == MF in cosine",
|
||||
abs(cosim(lam * t1, e1) - cosim(t1, e1)) < 1e-12)
|
||||
|
||||
# ---------------------------------------------------------------- V6
|
||||
k = D / 100.0
|
||||
vals = [mse_theory(b, 1.0, (1 - b * b) + k)
|
||||
for b in np.linspace(0, 0.99, 50)]
|
||||
allok &= check("V6 monotonic decrease in beta",
|
||||
all(x > y for x, y in zip(vals, vals[1:])))
|
||||
|
||||
# ---------------------------------------------------------------- V7
|
||||
ok7 = True
|
||||
worst = 0.0
|
||||
for rho in (1.0, 100.0, 1e4):
|
||||
kk = D / rho
|
||||
coop = math.log2(1 + 4 * rho / D)
|
||||
for b in np.linspace(0, 1.0, 41):
|
||||
m = mse_theory(b, 1.0, (1 - b * b) + kk)
|
||||
T = 2 * math.log2(1 / m)
|
||||
ok7 &= T <= coop + 1e-9
|
||||
worst = max(worst, T - coop)
|
||||
m1 = mse_theory(1.0, 1.0, kk)
|
||||
ok7 &= abs(2 * math.log2(1 / m1) - coop) < 1e-9
|
||||
allok &= check("V7 full-cooperation bound, equality at beta=1", ok7,
|
||||
f"max T-coop {worst:.2e}")
|
||||
|
||||
# ---------------------------------------------------------------- V8
|
||||
ok8 = True
|
||||
for rho in (1.0, 10.0, 100.0, 1e3):
|
||||
kk = D / rho
|
||||
for b in (0.1, 0.311, 0.6, 0.9):
|
||||
g = 1 - b * b
|
||||
m = mse_theory(b, 1.0, g + kk)
|
||||
T = 2 * math.log2(1 / m)
|
||||
mac = math.log2(1 + 2 * rho / D)
|
||||
lhs = g * g * (2 + kk)
|
||||
rhs = 2 * b * b * kk * kk
|
||||
ok8 &= (T <= mac + 1e-9) == (lhs >= rhs - 1e-9)
|
||||
allok &= check("V8 MAC-condition boundary", ok8)
|
||||
|
||||
# ---------------------------------------------------------------- V9
|
||||
beta = 0.311
|
||||
g = 1 - beta**2
|
||||
c1v, c2v = csi1(beta, 1.0 + 0j), csi2(beta, 1.0 + 0j)
|
||||
cbar = (c1v + c2v) / 2
|
||||
ceil1 = 1 / math.sqrt(1 + c1v)
|
||||
rho_f_db = 10 * math.log10(768 * g / c1v)
|
||||
ok = (abs(cbar - 1.2349) < 5e-4 and abs(ceil1 - 0.70) < 5e-3
|
||||
and abs(rho_f_db - 28) < 0.5)
|
||||
report("V4 quoted constants", ok,
|
||||
f"C_SI,1 {c1v:.4f}, C_SI,2 {c2v:.4f}, C-bar {cbar:.4f} "
|
||||
f"(quoted 1.2349), ceiling {ceil1:.4f} (quoted 0.70), "
|
||||
f"rho_f {rho_f_db:.1f} dB (quoted 28)")
|
||||
sig = 10 ** (-20.0 / 20.0)
|
||||
H = np.array([[1.0]])
|
||||
while H.shape[0] < D:
|
||||
H = np.block([[H, H], [H, -H]])
|
||||
H /= math.sqrt(D)
|
||||
mc, th = 0.0, 0.0
|
||||
for _ in range(30):
|
||||
e1, e2 = embed_pair(D, beta)
|
||||
D1 = np.sign(rng.standard_normal(D))
|
||||
D2 = np.sign(rng.standard_normal(D))
|
||||
W1, W2 = H * D1[None, :], H * D2[None, :]
|
||||
r = W1 @ e1 + W2 @ e2 + sig * cnoise(D)
|
||||
t1 = W1.T @ r
|
||||
q = D1 * D2
|
||||
a = 1.0 + beta * q
|
||||
rho = g / D + sig * sig
|
||||
w1 = (a / (a * a / D + rho)) * t1 / D
|
||||
mc += float(np.linalg.norm(w1 - e1) ** 2)
|
||||
th += float(np.mean((g + D * sig**2) / (a * a + g + D * sig**2)))
|
||||
allok &= check("V9 WH exact finite-d closed form",
|
||||
abs(mc / th - 1) < 0.03, f"dev {100*abs(mc/th-1):.2f}%")
|
||||
|
||||
# ---------------- V5: SINR = 1/MSE ---------------------------------
|
||||
rho = 10 ** (15 / 10)
|
||||
eta = 1 / (512 / (rho * g) + c1v)
|
||||
mse = 512 / (rho * g) + c1v
|
||||
report("V5 SINR corollary", abs(eta * mse - 1) < 1e-12,
|
||||
f"eta*MSE = {eta*mse:.6f}")
|
||||
|
||||
# ---------------- V6: C_SI >= 1 and proof identities ---------------
|
||||
ok = True
|
||||
worst = 1e9
|
||||
for b in np.linspace(0.0, 0.99, 200):
|
||||
gg = 1 - b**2
|
||||
lhs1 = gg * csi1(b, 1.0 + 0j)
|
||||
lhs2 = gg * csi2(b, 1.0 + 0j)
|
||||
if abs(lhs1 - (gg + 4 * b**4)) > 1e-12: ok = False
|
||||
if abs(lhs2 - (1 + 3 * b**2)) > 1e-12: ok = False
|
||||
worst = min(worst, csi1(b, 1.0 + 0j), csi2(b, 1.0 + 0j))
|
||||
report("V6 C_SI >= 1 + proof identities", ok and worst >= 1 - 1e-12,
|
||||
f"min C_SI over beta grid = {worst:.6f}")
|
||||
|
||||
# ---------------- V7: MAC consistency on a grid --------------------
|
||||
def T_edma(b, r_, d_):
|
||||
gg = 1 - b**2
|
||||
cb = (csi1(b, 1 + 0j) + csi2(b, 1 + 0j)) / 2
|
||||
return 2 * np.log2(1 + 1 / (d_ / (r_ * gg) + cb))
|
||||
|
||||
ok = True
|
||||
for b in np.linspace(0, 0.95, 40):
|
||||
for rdb in np.linspace(-10, 60, 60):
|
||||
r_ = 10 ** (rdb / 10)
|
||||
gg = 1 - b**2
|
||||
mid = np.log2(1 + 2 * r_ * gg / 512)
|
||||
cmac = np.log2(1 + 2 * r_ / 512)
|
||||
if T_edma(b, r_, 512) > mid + 1e-12 or mid > cmac + 1e-12:
|
||||
ok = False
|
||||
report("V7 MAC consistency grid", ok, "T_EDMA <= log2(1+2 rho g/d) <= C_MAC")
|
||||
|
||||
# ---------------- V8: wideband limit -------------------------------
|
||||
b = 0.311
|
||||
r_ = 1e-6 * 512
|
||||
lim = T_edma(b, r_, 512) / np.log2(1 + 2 * r_ / 512)
|
||||
report("V8 wideband limit", abs(lim - (1 - b**2)) < 1e-3,
|
||||
f"T/C_MAC at rho/d=1e-6: {lim:.5f} vs gamma {1-b**2:.5f}")
|
||||
|
||||
# ---------------- V9: beta* crossover roots ------------------------
|
||||
def beta_star(rdb, d_=512):
|
||||
r_ = 10 ** (rdb / 10)
|
||||
T_oma = 2 * np.log2(1 + r_ / (2 * d_))
|
||||
return brentq(lambda b: T_edma(b, r_, d_) - T_oma, 0.3, 0.9)
|
||||
|
||||
b10, b20 = beta_star(10), beta_star(20)
|
||||
report("V9 beta* crossover", abs(b10 - 0.700) < 5e-3
|
||||
and abs(b20 - 0.590) < 5e-3,
|
||||
f"10 dB: {b10:.3f} (quoted 0.700), 20 dB: {b20:.3f} (quoted 0.590)")
|
||||
|
||||
# ---------------- V10: rho_c iff-condition + value -----------------
|
||||
b = 0.311
|
||||
gg = 1 - b**2
|
||||
cb = (csi1(b, 1 + 0j) + csi2(b, 1 + 0j)) / 2
|
||||
rho_c = 512 * (2 - 1 / gg) / cb
|
||||
rho_c_db = 10 * math.log10(rho_c)
|
||||
eps = 1e-4
|
||||
below = T_edma(b, rho_c * (1 - eps), 512) \
|
||||
- 2 * np.log2(1 + rho_c * (1 - eps) / 1024)
|
||||
above = T_edma(b, rho_c * (1 + eps), 512) \
|
||||
- 2 * np.log2(1 + rho_c * (1 + eps) / 1024)
|
||||
report("V10 rho_c crossover", below > 0 > above
|
||||
and abs(rho_c_db - 25.7) < 0.1,
|
||||
f"rho_c {rho_c_db:.2f} dB (quoted 25.7), sign flip verified")
|
||||
|
||||
# ---------------- V11: idealized-MAC crossing ----------------------
|
||||
rho_x = 2 * b**2 * 512 / gg**2
|
||||
f = lambda r_: 2 * np.log2(1 + r_ * gg / 512) - np.log2(1 + 2 * r_ / 512)
|
||||
root = brentq(f, 10.0, 1e4)
|
||||
report("V11 idealized crossing", abs(root / rho_x - 1) < 1e-6
|
||||
and abs(10 * math.log10(root) - 21) < 0.3,
|
||||
f"root {10*math.log10(root):.2f} dB, formula 2b^2d/g^2 "
|
||||
f"{10*math.log10(rho_x):.2f} dB (quoted ~21)")
|
||||
|
||||
# ---------------- V12: mismatch identity + bound value -------------
|
||||
b, delta = 0.3, 0.06
|
||||
bh = b + delta
|
||||
hr = 1.0 + 0j
|
||||
e1, e2 = pair(64, b)
|
||||
t1 = e1 + b * hr * e2 # expected-Gram surrogate outputs
|
||||
t2v_ = e2 + b * np.conj(hr) * e1
|
||||
g1 = (t1 - bh * hr * t2v_) / (1 - bh**2)
|
||||
lhs = g1 - e1
|
||||
rhs = delta / (1 - bh**2) * (bh * e1 - hr * e2)
|
||||
dev = np.linalg.norm(lhs - rhs)
|
||||
bound = delta**2 * (abs(bh) + abs(hr))**2 / (1 - bh**2)**2
|
||||
report("V12 mismatch identity", dev < 1e-12
|
||||
and abs(bound - 8.8e-3) < 2e-4,
|
||||
f"identity dev {dev:.1e}, bound {bound:.4f} (quoted 8.8e-3)")
|
||||
|
||||
# ---------------- V13: CSI-direction invariance --------------------
|
||||
d = 256
|
||||
b = 0.311
|
||||
g = 1 - b**2
|
||||
e1, e2 = pair(d, b)
|
||||
U1, U2 = haar(d), haar(d)
|
||||
M1, M2 = U1, b * U1 + math.sqrt(g) * U2
|
||||
h1, h2 = 0.7 - 0.4j, -0.2 + 1.1j
|
||||
n = (rng.standard_normal(d) + 1j * rng.standard_normal(d)) / math.sqrt(2)
|
||||
r = h1 * (M1 @ e1) + h2 * (M2 @ e2) + 0.1 * n
|
||||
truec = (M1.T @ r / h1 - b * (h2 / h1) * (M2.T @ r / h2)) / g
|
||||
csif = (M1 - b * M2).T @ r / (h1 * g)
|
||||
dev1 = np.abs(truec - csif).max()
|
||||
h1w = h1 * (1.5 * np.exp(0.8j)) # badly wrong estimate
|
||||
wrong = (M1 - b * M2).T @ r / (h1w * g)
|
||||
c_true = abs(np.vdot(truec, e1)) / (np.linalg.norm(truec))
|
||||
c_wrong = abs(np.vdot(wrong, e1)) / (np.linalg.norm(wrong))
|
||||
report("V13 CSI invariance", dev1 < 1e-12 and abs(c_true - c_wrong) < 1e-12,
|
||||
f"csi-free identity dev {dev1:.1e}, |cos| unchanged "
|
||||
f"({c_true:.6f} vs {c_wrong:.6f})")
|
||||
|
||||
# ---------------- V14: cross-moment lemma --------------------------
|
||||
d = 256
|
||||
b = 0.311
|
||||
sig2 = 0.5
|
||||
acc = 0.0
|
||||
NT = 4000
|
||||
U1, U2 = haar(d), haar(d)
|
||||
M1, M2 = U1, b * U1 + math.sqrt(1 - b**2) * U2
|
||||
for _ in range(NT):
|
||||
n = math.sqrt(sig2) * (rng.standard_normal(d)
|
||||
+ 1j * rng.standard_normal(d)) / math.sqrt(2)
|
||||
acc += np.real(np.conj(n) @ (M1 @ (M2.T @ n)))
|
||||
acc /= NT
|
||||
th = sig2 * b * d
|
||||
report("V14 cross-moment lemma", abs(acc / th - 1) < 0.05,
|
||||
f"MC {acc:.3f} vs sigma^2 beta d {th:.3f} "
|
||||
f"({100*abs(acc/th-1):.1f}%)")
|
||||
|
||||
# ---------------- V15: [B^-1]_uu Sherman-Morrison ------------------
|
||||
ok = True
|
||||
for U in range(2, 7):
|
||||
for b in (0.1, 0.311, 0.6):
|
||||
B = (1 - b) * np.eye(U) + b * np.ones((U, U))
|
||||
num = 1 + (U - 2) * b
|
||||
den = (1 - b) * (1 + (U - 1) * b)
|
||||
if abs(np.linalg.inv(B)[0, 0] - num / den) > 1e-12:
|
||||
ok = False
|
||||
report("V15 [B^-1]_uu formula", ok, "U=2..6, beta grid, exact")
|
||||
|
||||
# ---------------- V16: multi-user C_SI^(U) -------------------------
|
||||
d = 512
|
||||
b = 0.311
|
||||
g = 1 - b**2
|
||||
cb = (csi1(b, 1 + 0j) + csi2(b, 1 + 0j)) / 2
|
||||
for U in (3, 4):
|
||||
B = (1 - b) * np.eye(U) + b * np.ones((U, U))
|
||||
Binv = np.linalg.inv(B)
|
||||
es = []
|
||||
e1 = unit(rng.standard_normal(d))
|
||||
for u in range(U):
|
||||
if u == 0:
|
||||
es.append(e1)
|
||||
# ---------------------------------------------------------------- V10
|
||||
beta = 0.3
|
||||
sig = 10 ** (-20.0 / 20.0)
|
||||
base, d1, d2 = 0.0, 0.0, 0.0
|
||||
for _ in range(30):
|
||||
e1, _, Q, t1, _ = run_pair(beta, sig)
|
||||
for bh, tag in ((beta, "b"), (beta + 0.2, "1"), (beta + 0.4, "2")):
|
||||
g1 = aware(t1, Q, bh, 1.0, sig * sig, D)
|
||||
m = float(np.linalg.norm(g1 - e1) ** 2)
|
||||
if tag == "b":
|
||||
base += m
|
||||
elif tag == "1":
|
||||
d1 += m
|
||||
else:
|
||||
w = rng.standard_normal(d)
|
||||
w = unit(w - (w @ e1) * e1)
|
||||
es.append(b * e1 + math.sqrt(g) * w)
|
||||
mse = 0.0
|
||||
NT = 60
|
||||
for _ in range(NT):
|
||||
Us = [haar(d) for _ in range(U)]
|
||||
Ms = [Us[0]]
|
||||
for u in range(1, U):
|
||||
Ms.append(b * Us[0] + math.sqrt(g) * Us[u])
|
||||
r = sum(Ms[u] @ es[u] for u in range(U)) # h_u = 1
|
||||
t = np.stack([Ms[u].T @ r for u in range(U)])
|
||||
rec = np.einsum("uv,vd->ud", Binv, t)
|
||||
mse += np.linalg.norm(rec[0] - es[0])**2
|
||||
mse /= NT
|
||||
ratio = mse / ((U - 1) * cb)
|
||||
report(f"V16 C_SI^(U) additivity (U={U})", abs(ratio - 1) < 0.10,
|
||||
f"noise-free MSE {mse:.3f} vs (U-1)C-bar "
|
||||
f"{(U-1)*cb:.3f} (ratio {ratio:.3f})")
|
||||
d2 += m
|
||||
base /= 30; d1 /= 30; d2 /= 30
|
||||
r_quad = (d2 - base) / max(d1 - base, 1e-12)
|
||||
allok &= check("V10 quadratic mismatch (delta doubling ~ 4x)",
|
||||
2.5 < r_quad < 6.5,
|
||||
f"MSE(+0)={base:.4f} MSE(+0.2)={d1:.4f} "
|
||||
f"MSE(+0.4)={d2:.4f} ratio {r_quad:.2f}")
|
||||
|
||||
# ---------------- V17: Walsh-Hadamard masks ------------------------
|
||||
d = 256
|
||||
H = hadamard(d) / math.sqrt(d)
|
||||
b = 0.311
|
||||
acc = np.zeros((d, d))
|
||||
NT = 400
|
||||
for _ in range(NT):
|
||||
D1 = np.diag(rng.choice([-1.0, 1.0], d))
|
||||
D2 = np.diag(rng.choice([-1.0, 1.0], d))
|
||||
W1 = H @ D1
|
||||
W2 = b * W1 + math.sqrt(1 - b**2) * H @ D2
|
||||
acc += W1.T @ W2 / NT
|
||||
orth = np.abs((H @ np.diag(rng.choice([-1.0, 1.0], d))).T
|
||||
@ (H @ np.diag(rng.choice([-1.0, 1.0], d)))
|
||||
@ np.ones(d) / d).max()
|
||||
diag_dev = abs(np.diag(acc).mean() - b)
|
||||
off = np.abs(acc - np.diag(np.diag(acc))).mean()
|
||||
report("V17 WH masks", diag_dev < 0.02 and off < 0.01,
|
||||
f"E[cross-Gram] diag {np.diag(acc).mean():.4f} vs beta {b}, "
|
||||
f"mean |off-diag| {off:.4f}")
|
||||
# ---------------------------------------------------------------- V11
|
||||
beta = 0.311
|
||||
g = 1 - beta**2
|
||||
mc = 0.0
|
||||
for _ in range(30):
|
||||
e1, e2 = embed_pair(D, beta)
|
||||
U1, U2 = haar(D), haar(D)
|
||||
M1, M2 = U1, beta * U1 + math.sqrt(g) * U2
|
||||
r = M1 @ e1 + M2 @ e2 # noise-free -> floor
|
||||
t1 = M1.T @ r
|
||||
t2 = M2.T @ r
|
||||
g1 = (t1 - beta * t2) / g
|
||||
mc += float(np.linalg.norm(g1 - e1) ** 2)
|
||||
mc /= 30
|
||||
th = 1 + 4 * beta**4 / g
|
||||
allok &= check("V11 correlated-mask floor 1+4b^4/g",
|
||||
abs(mc / th - 1) < 0.05,
|
||||
f"MC {mc:.4f} vs {th:.4f}; aware floor "
|
||||
f"{math.sqrt(g)/2:.4f} (dominated)")
|
||||
|
||||
print()
|
||||
print("=" * 60)
|
||||
print(f"RESULT: {'ALL PASS' if not FAIL else 'FAILURES: ' + ', '.join(FAIL)}")
|
||||
print("\nALL CHECKS PASSED" if allok else "\nSOME CHECKS FAILED")
|
||||
|
||||
Reference in New Issue
Block a user