GCNO: Gramian Chebyshev Neural Operator for Physics-Based Compression of Wireless Channels

Rafid Umayer Murshed; Shahab Hamidi-Rad; Elahe Soltanaghai; Akshay Malhotra

cs.ITAug 19, 2026

GCNO: Gramian Chebyshev Neural Operator for Physics-Based Compression of Wireless Channels

Authors: Rafid Umayer Murshed, Shahab Hamidi-Rad, Elahe Soltanaghai, Akshay Malhotra

Organizations: Department of Computer Science, University of Illinois Urbana-Champaign · InterDigital AI Lab

Abstract

Large antenna arrays allow wireless systems to serve more users and achieve higher data rates, but they also make channel feedback expensive: the receiving device must repeatedly report a large complex-valued channel matrix to the base station. Most neural compressors treat this matrix like an image and replace it with a fixed-length code that only a matched neural decoder can interpret. The message therefore does not adapt to channel complexity, and changing the antenna count typically requires retraining. We ask whether a device can instead report only the few dominant propagation paths underlying each channel. We introduce the Gramian Chebyshev Neural Operator (GCNO), a physics-based, variable-rate compressor that identifies a sample-dependent set of path directions. GCNO uses receive-transmit channel structure to locate paths, a first-order Taylor correction to refine directions that fall between grid points, and least squares to recover their complex strengths. It is trained without path labels, and the base station reconstructs the channel analytically from the transmitted path tuples rather than through a learned decoder. Across three ray-traced environments, GCNO achieves better reconstruction accuracy at the same payload - or lower payload at the same accuracy - than neural feedback baselines, and transfers to unseen antenna counts without retraining.

Figures & tables

Figure 1: Off-grid paths spread their energy across neighboring cells. The map is shown (a) alone and (b) with the underlying paths marked, illustrating why a grid-only description may use several entries for one physical path.

Figure 2: Overview of GCNO compression. The channel and evidence map are encoded jointly; GCNO predicts path scores and off-grid corrections, path selection retains useful directions, and LS recovers their gains. Appendix B provides more detail.

Figure 3: Rate–distortion results on ASU. Median NMSE is shown against (a) unquantized payload and (b) total feedback bits; (c) compares the test-channel error distributions at 16 transmitted values. Lower and farther left is better.

Figure 4: Ablation and Generalization results on ASU. (a) RD after replacing only the GCNO backbone. (b) Generalization of the

32\times 32

-trained model to unseen array sizes without retraining. (c) Selected path counts (Numbers above bars show mean of

4K

) as the target NMSE becomes stricter. (d) Angular error and recall (above markers) versus the number of strong paths.

	Seattle		Dallas
Method	64 bits	16 floats	64 bits	16 floats
TransNet	$-9.71$	$-10.11$	$-6.01$	$-6.22$
StarCANet	$-13.04$	$-13.65$	$-9.35$	$-9.79$
SwinCFNet	$-14.37$	$-14.70$	$-10.71$	$-11.28$
GCNO (Ours)	$\mathbf{-14.93}$	$\mathbf{-18.15}$	$\mathbf{-15.22}$	$\mathbf{-19.23}$

Table 1: Median NMSE (dB; lower is better) vs 3 best baselines. Full Comparison is in Appendix C.

Dataset	Method@16 floats	Median NMSE (dB)	Angular error ( ∘ )
ASU	GCNO (Taylor)	$-20.08$	$0.23\;(0.37)$
ASU	GCNO (no Taylor)	$-3.84$	$2.01\;(2.75)$
Dallas	GCNO (Taylor)	$-19.23$	$0.28\;(0.59)$
Dallas	GCNO (no Taylor)	$-4.14$	$2.17\;(3.66)$
Seattle	GCNO (Taylor)	$-18.15$	$0.23\;(0.46)$
Seattle	GCNO (no Taylor)	$-3.29$	$2.11\;(3.20)$

Table 2: Effect of Taylor refinement, error is median (P75).

Appendix figures & tables19 assets

Supplementary material from the paper’s appendix.

Appendix

Stage	Output shape	Type	Operation	Status
Observed channel	$N_{b}\times 32\times 32$	complex	Physical channel $H$	Input
Channel scale	$N_{b}$	real	$h_{\mathrm{scale}}=\lVert H\rVert_{F}$	Fixed
Normalized channel	$N_{b}\times 32\times 32$	complex	$H/h_{\mathrm{scale}}$	Fixed
Channel-branch input	$N_{b}\times 2\times 32\times 32$	real	Real and imaginary parts of $H_{\mathrm{norm}}$	Fixed
Evidence map	$N_{b}\times 28\times 28$	complex	$C_{ij}=\langle D_{ij},H_{\mathrm{norm}}\rangle_{F}$	Fixed
Evidence-branch input	$N_{b}\times 2\times 28\times 28$	real	Real and imaginary parts of $C$	Fixed

Appendix

Table 3: End-to-end tensor flow for GCNO.

Component	Real parameters
Channel stem, $2\!\rightarrow\!96\!\rightarrow\!48$	4,944
Evidence stem, $2\!\rightarrow\!96\!\rightarrow\!48$	4,944
Fusion stem, $98\!\rightarrow\!96\!\rightarrow\!48$	14,160
GCNO layer 1	18,432
GCNO layer 2	18,432
GCNO layer 3	18,432

Appendix

Table 4: Trainable parameters of the implemented GCNO model.

Setting	Value
Initialization	Random; no checkpoint
Optimizer	Adam
Batch size	128
Adam $(\beta_{1},\beta_{2})$	$(0.9,0.999)$
Adam $\epsilon$	$10^{-8}$
Weight decay	$10^{-6}$

Appendix

Table 5: Optimization settings for the ASU reference run.

Phase	Window	Epochs	LR	$\tau$
Global	$28\times 28$	30	$3{\times}10^{-4}$	0.035
Local 1	21	6	$10^{-4}$	0.08
Local 2	15	6	$10^{-4}$	0.08
Local 3	9	7	$10^{-4}$	0.08
Local 4	5	14	$10^{-4}$	0.08
Local 5	3	8	$10^{-4}$	0.08

Appendix

Table 6: Realized selector-window curriculum.

Target Region	$K_{\max}$	$\Delta_{\min}$	Mean	Median
$-12$ dB	1	Single candidate	4.000	4
$-14$ dB	2	0.012	5.795	4
$-16$ dB	6	0.002	9.527	8
$-18$ dB	6	0.0005	13.889	12
$-20$ dB	7	0.0005	14.372	12

Appendix

Table 7: Adaptive support profiles and realized unquantized payloads.

Requested profile	Mean transmitted bits
48	52.359
64	63.354
96	82.109
128	118.987

Appendix

Table 8: Nominal quantized profiles and measured mean packet lengths on ASU.

Item	Verified value
GPU	NVIDIA H100, 80 GB HBM3
Python	3.11.13
PyTorch	2.11.0+ cu128
CUDA runtime	12.8
NumPy	1.26.4
PyYAML	6.0.3

Appendix

Table 9: Frozen ASU model and software environment.

Quantity	Measurement	Scope
Full training wall time	178.441 s	71 epochs, 5,609 updates, including in-loop validation and normal checkpoint writes
Full-fit throughput	3,978.9 samples/s	Complete synchronized training call
Warmed training step	27.212 ms mean	Batch 128; matched filter, network, soft selection, LS loss, backward pass, clipping, and Adam update
Warmed-step throughput	4,703.8 samples/s	100 CUDA-event measurements after 10 warmups
Training CUDA peak	3.173 GB allocated	Maximum live allocation during the full training call
Inference CUDA peak	0.339 GB allocated	Maximum across network, adaptive selector, exact steering, LS, and complete-encoder scopes

Appendix

Table 10: Isolated H100 compute and memory profile.

Profile	Payload mean/med./P95	Mean	Median	P95	P99	Batch-128 throughput
Low	4.000 / 4 / 4	10.131 ms	9.930 ms	10.666 ms	15.341 ms	7,996.6 samples/s
Mid	8.094 / 8 / 16	15.425 ms	15.027 ms	20.803 ms	26.702 ms	3,042.3 samples/s
High variant	15.297 / 16 / 32	20.690 ms	20.317 ms	31.973 ms	32.480 ms	1,098.3 samples/s
High	15.297 / 16 / 32	23.830 ms	23.390 ms	35.908 ms	36.773 ms	1,055.2 samples/s
Maximum	31.922 / 32 / 32	32.789 ms	32.183 ms	35.053 ms	44.715 ms	1,528.4 samples/s

Appendix

Table 11: End-to-end UE-encoder latency across bundled adaptive operating profiles. Payload entries are measured

4K

distributions.

Figure 5: Complete cross-scene rate–distortion curves. Rows correspond to Seattle, ASU, and Dallas; columns correspond to quantized bits and transmitted real values. This figure extends main-paper Fig. 3 and Table 1 rather than repeating their selected operating points. Lower and farther left is better.

Method	Trainable parameters
CsiNet	302,956
CRNet	450,150
CLNet	449,270
TransNet	1,026,224
MNet	445,200
CSITransformer	563,520

Appendix

Table 12: Trainable parameter counts for representative instantiated models.

Method	Mean values	NMSE (dB)
Grid-OMP @ 4 values	4.000	$-2.607$
Grid-OMP @ 8 values	8.000	$-3.791$
Grid-OMP @ 16 values	14.949	$-4.582$
Grid-OMP @ 32 values	32.000	$-5.152$
GCNO ( $K=4$ )	16.000	$\mathbf{-16.511}$

Appendix

Table 13: Grid-OMP operating points and a fixed-four-path GCNO control.

Environment	4 values	8 values	32 values
ASU	10.729	13.649	20.439
Dallas	6.628	13.672	17.732
Seattle	10.819	12.176	18.529

Appendix

Table 14: NMSE improvement from Taylor refinement beyond the 16-value result in main-paper Table 2. Positive values favor Taylor refinement.

Figure 6: Post-hoc multipath fidelity. Strong-path F1 measures joint support recovery, while median joint effective-angle error measures directional accuracy. Higher is better for F1 and lower is better for angular error.

Target shape	Forward scale	Forward AA	Reverse scale	Reverse AA	Payload	Compression
$16\times 16$	$1/2$	No	$2$	Both dimensions	16	$32\times$
$16\times 32$	$1/\sqrt{2}$	No	$\sqrt{2}$	Receive dimension	16	$64\times$
$32\times 16$	$1/\sqrt{2}$	No	$\sqrt{2}$	Transmit dimension	16	$64\times$
$24\times 24$	$3/4$	No	$4/3$	Both dimensions	16	$72\times$
$32\times 32$	$1$	Exact identity	$1$	Exact identity	16	$128\times$
$32\times 64$	$\sqrt{2}$	Transmit dimension	$1/\sqrt{2}$	No	16	$256\times$

Appendix

Table 15: Deterministic input/output adapter used for every frozen neural baseline in main-paper Fig. 4(b). AA denotes antialiasing. The latent payload remains 16 real values for every array shape.

Source $\rightarrow$ target	GCNO	SwinCFNet	StarCANet
Dallas $\rightarrow$ Seattle	$\mathbf{-14.203}$	$-14.037$	$-11.799$
Dallas $\rightarrow$ ASU	$\mathbf{-14.815}$	$-10.490$	$-9.747$
Seattle $\rightarrow$ Dallas	$\mathbf{-14.197}$	$-7.146$	$-6.572$
Seattle $\rightarrow$ ASU	$\mathbf{-15.191}$	$-9.560$	$-9.522$
ASU $\rightarrow$ Dallas	$\mathbf{-15.401}$	$-6.962$	$-6.308$
ASU $\rightarrow$ Seattle	$\mathbf{-15.821}$	$-12.932$	$-11.092$

Appendix

Table 16: Cross-scene median NMSE (dB) at the nominal 16-value operating point. Lower is better.

One stream
Method	0 dB	10 dB	20 dB	30 dB
GCNO	$\mathbf{0.9411}$	$\mathbf{3.3452}$	$\mathbf{6.5319}$	$\mathbf{9.8395}$
StarCANet	0.9204	3.2864	6.4447	9.7381
SwinCFNet	0.9212	3.2875	6.4488	9.7480
Perfect CSI	0.9428	3.3488	6.5360	9.8437
Two streams

Appendix

Table 17: Mean spectral efficiency (bit/s/Hz). Bold marks the strongest compressed method; perfect CSI is a dense reference.

Payload	Seed 43	Seed 44	Seed 45	$\mu\pm\sigma$
8	$-15.5861$	$-15.0772$	$-15.1942$	$-15.2858\pm 0.2666$
16	$-18.6382$	$-17.1041$	$-17.6077$	$-17.7833\pm 0.7820$
32	$-22.4733$	$-20.3709$	$-19.9455$	$-20.9299\pm 1.3534$

Appendix

Table 18: GCNO seed-level median NMSE across three seeds. All values are in dB.

Target	Comparator	Best NMSE	$\min\Delta$
8	SwinCFNet	$-14.4309$	$+0.6463$
8	StarCANet	$-12.0964$	$+2.9808$
16	SwinCFNet	$-14.7013$	$+2.4028$
16	StarCANet	$-14.0868$	$+3.0173$
32	SwinCFNet	$-15.7820$	$+4.1635$
32	StarCANet	$-14.7140$	$+5.2315$

Appendix

Table 19: Baseline-favorable best-seed results at each target payload. All values are in dB.

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