KiHoLee
8f26bf9bc9
Every OMA reference takes the L/16 combining gain so the comparison stays resource matched, four hardcoded copies of the configuration are replaced by MAIN_D or the main curve, and stage_J's K-by-L Gaussian draw becomes its exact scalar Beta equivalent.
107 lines
3.5 KiB
Python
107 lines
3.5 KiB
Python
# -*- coding: utf-8 -*-
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"""Does an orthogonal unit codebook recover the shortfall?
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diag_interference shows the gap to the single-user M-ary bound is not
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multi-user interference but the geometry of the trained unit codebook,
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whose Gram matrix carries a large root-mean-square off-diagonal where an
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orthogonal set would carry zero. Vu <= L admits an exactly orthogonal
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set, so this measures what installing one buys.
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Two orthogonal sets are tried, because the choice is not free. The
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Walsh-Hadamard set collides with the keys: the rows are closed under the
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elementwise product, so masking a Hadamard codeword by a Hadamard key
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returns another Hadamard codeword and every user ends up with the same
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candidate set. A random orthogonal set carries no such group structure,
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and masking by a unit-modulus key preserves its orthogonality exactly.
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"""
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import sys
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from pathlib import Path
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import torch
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sys.path.insert(0, str(Path(__file__).resolve().parent))
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import sse_lib as L
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from sse_lib import DEVICE, SSE
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from exp_full import hadamard, base_keys, oma_ser_keylen, MAIN_D
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from diag_interference import ser
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SNR = [0.0, 10.0, 20.0]
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FRAMES = 400_000
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def fixed_model(B, P=4, vu=16, d=64, U=4):
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L.set_seed(1)
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m = SSE(P=P, vu=vu, d=d, users=U).to(DEVICE)
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with torch.no_grad():
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m.B.copy_(B.to(DEVICE))
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m.W.copy_(base_keys(U, d // P).to(DEVICE))
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m.calibrate_power()
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return m
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def hadamard_book(vu=16, Lp=MAIN_D // 4):
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B = torch.zeros(vu, Lp)
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B[:, :vu] = torch.tensor(hadamard(vu).copy(), dtype=torch.float32)
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return B
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def random_ortho_book(vu=16, Lp=MAIN_D // 4, seed=7):
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g = torch.Generator().manual_seed(seed)
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A = torch.randn(Lp, Lp, generator=g)
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Q, _ = torch.linalg.qr(A)
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return Q[:vu].contiguous()
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def report(name, m):
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with torch.no_grad():
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Bn = m.unit_codebook()
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G = Bn @ Bn.T
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off = (G - torch.diag(torch.diag(G))).abs().max()
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row = [name, "%.2e" % off]
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for s in SNR:
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row.append("%.4f" % ser(m, s, FRAMES))
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print("%-22s %-10s %-9s %-9s %-9s" % tuple(row))
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def main():
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print("%-22s %-10s %-9s %-9s %-9s"
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% ("unit codebook", "max|off|", "0 dB", "10 dB", "20 dB"))
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report("Walsh-Hadamard", fixed_model(hadamard_book()))
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report("random orthogonal", fixed_model(random_ortho_book()))
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from exp_full import main_model
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report("trained", main_model())
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Lp = MAIN_D // 4
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print("%-22s %-10s %-9s %-9s %-9s"
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% ("OMA, resource matched", "-",
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"%.4f" % oma_ser_keylen(Lp, 0.0),
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"%.4f" % oma_ser_keylen(Lp, 10.0),
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"%.4f" % oma_ser_keylen(Lp, 20.0)))
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def solo_check():
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"""Splitting each candidate set from the superposition it must live
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in. Orthogonal codewords are ideal for one user alone and are what
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the single-user bound assumes, but the masked sets of different users
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are then far from orthogonal to each other."""
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print()
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print("%-22s %-12s %-12s" % ("unit codebook", "solo 10 dB", "4-user 10 dB"))
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for name, B in (("random orthogonal", random_ortho_book()),
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("trained (retrain)", None)):
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if B is None:
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from exp_full import main_model
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m = main_model()
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else:
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m = fixed_model(B)
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print("%-22s %-12.4f %-12.4f"
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% (name, ser(m, 10.0, FRAMES, solo=True),
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ser(m, 10.0, FRAMES, solo=False)))
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print("(solo isolates the candidate set from the superposition)")
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if __name__ == "__main__":
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main()
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solo_check()
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