""" Simulations for the EDMA TVT manuscript (v2 design). ======================================================= 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): t1 = (I + beta*c1*Q) e1 + sqrt(g)*c1*Q w + n_t, Q = M1^T M2, 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 = +beta Fixed seed 2026. CSVs -> ../data, PDFs -> ../fig. """ from __future__ import annotations import csv import math from pathlib import Path import numpy as np import matplotlib matplotlib.use("Agg") import matplotlib.pyplot as plt ROOT = Path(__file__).resolve().parents[1] CSV_DIR = ROOT / "data"; CSV_DIR.mkdir(exist_ok=True) FIG_DIR = ROOT / "fig"; FIG_DIR.mkdir(exist_ok=True) plt.rcParams.update({ "font.family": "serif", "font.serif": ["DejaVu Serif", "Times New Roman"], "font.size": 9, "axes.labelsize": 9, "axes.titlesize": 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) # 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) def save_fig(fig, name): p = FIG_DIR / f"{name}.pdf" fig.subplots_adjust(**AXES_RECT) fig.savefig(p) plt.close(fig) print(f"[OK] wrote {p}") 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}") # ------------------------------------------------------------------ # Core constructions # ------------------------------------------------------------------ def haar(d): G = rng.standard_normal((d, d)) Q, R = np.linalg.qr(G) return Q * np.sign(np.diag(R)) def unit(v): return v / np.linalg.norm(v) def embed_pair(d, beta): """e1, e2 real unit vectors with = +beta.""" e1 = unit(rng.standard_normal(d)) w = rng.standard_normal(d) w = unit(w - (w @ e1) * e1) e2 = beta * e1 + math.sqrt(1.0 - beta**2) * w return e1, e2 def rayleigh(n=1): return (rng.standard_normal(n) + 1j * rng.standard_normal(n)) / math.sqrt(2) 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 (both users, random phases) # ------------------------------------------------------------------ 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: 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 = 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}" f" (max dev {dev:.2f}%)") rows.append([beta, r1, r2, dev]) write_csv("theorem_check", ["beta", "user1_mc_over_theory", "user2_mc_over_theory", "max_dev_pct"], rows) print(f" worst-case deviation {worst:.2f}%") return worst # ------------------------------------------------------------------ # 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=120): print("\n=== E1: finite-d validation, aware vs blind floor ===") g = 1.0 - beta**2 fig, ax = plt.subplots() colors = {256: "C0", 768: "C3"} rows = [] for d in dims: mc = np.zeros(len(snr_db)) for _ in range(ntr): e1, e2 = embed_pair(d, beta) M1, M2 = haar(d), haar(d) Q = M1.T @ M2 r0 = (M1 @ e1) + (M2 @ e2) n = cnoise(d) for k, s in enumerate(snr_db): sig = 10 ** (-s / 20.0) 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 = 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"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, 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("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="upper right", ncol=1) save_fig(fig, "fig_floor") 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))") # ------------------------------------------------------------------ # E7 : effective-rate figures (eta = 1/MSE - 1) # ------------------------------------------------------------------ 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)) 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: effective-rate comparison ===") snr_db = np.arange(0, 41, 0.5) rho = 10 ** (snr_db / 10.0) 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, 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("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, "fig_rate_corrected") 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", "blind", "oma", "genie", "mac"], rows) i20 = list(snr_db).index(20.0) 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: 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([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(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], 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.legend(loc="upper left") save_fig(fig, "fig_beta_sweep_corrected") write_csv("beta_sweep_corrected", ["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, "E7a": E7_rates, } for name, fn in ALL.items(): if not todo or name in todo: fn() print("\nAll requested simulations complete.")