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arxiv: 2606.31301 · v1 · pith:QFLSU3ACnew · submitted 2026-06-30 · 💻 cs.IT · eess.SP· math.IT

Fundamental Limits of Quantized MIMO ISAC under Gaussian Signaling

Hossein Atrsaei , Mireille Sarkiss , Mich\`ele Wigger This is my paper

Pith reviewed 2026-07-01 03:34 UTC · model grok-4.3

classification 💻 cs.IT eess.SPmath.IT
keywords quantized MIMOISACcapacity boundsGaussian signalingeffective noiseLMMSEspatial combiningKronecker model
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The pith

i.i.d. isotropic Gaussian signaling achieves rates close to capacity in quantized MIMO ISAC despite non-Gaussian effective noise.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

This paper examines the capacity of a MIMO integrated sensing and communication system where both receivers use analog spatial combining and scalar subtractive dithered quantization. The quantization creates an additive effective noise that is non-Gaussian. Upper and lower bounds on the capacity are derived, and numerical evaluations show these bounds are close at low SNR but level off at high SNR because of the limited quantization resolution. The work finds that standard i.i.d. isotropic Gaussian signaling performs nearly as well as the capacity despite the non-Gaussian noise. A closed-form expression is also given for the linear minimum mean-squared error estimator under a Kronecker sensing channel model when using Gaussian signals.

Core claim

In a quantized MIMO ISAC system with analog spatial combining and subtractive dithered quantization, upper and lower bounds on capacity are derived under the resulting additive non-Gaussian effective-noise model. Numerical results establish that i.i.d. isotropic Gaussian signaling achieves rates close to these bounds. For the sensing component under a Kronecker channel model, a closed-form LMMSE expression is obtained that saturates at high SNR, with the saturation level rising as the spatial combining ratio falls and occurring even without quantization when the ratio is below one.

What carries the argument

Additive effective-noise representation with non-Gaussian statistics produced by analog spatial combining followed by scalar subtractive dithered quantization, used to obtain capacity bounds and LMMSE expressions.

If this is right

  • Capacity upper and lower bounds are tight at low SNR.
  • Both capacity and LMMSE saturate at high SNR due to finite-resolution quantization.
  • LMMSE saturation level increases as the spatial combining ratio decreases.
  • LMMSE saturation occurs even without quantization when the combining ratio is below one.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • Near-optimality of Gaussian signaling may allow simpler transceiver design in quantized ISAC without needing non-Gaussian codebooks.
  • The saturation behavior implies that increasing transmit power yields diminishing returns once quantization limits are reached.
  • The Kronecker model enables closed-form sensing results, but extensions to other channel models would require numerical evaluation.
  • The closeness result could be tested by comparing Gaussian rates to capacity bounds under varying quantization bit resolutions.

Load-bearing premise

The quantization model with analog spatial combining followed by scalar subtractive dithered quantization leads to an additive effective-noise representation with non-Gaussian noise that is used for the capacity bounds.

What would settle it

A direct computation of mutual information achieved by a non-Gaussian input distribution at moderate SNR, compared against the derived upper bound, would show whether Gaussian signaling rates remain close to capacity.

Figures

Figures reproduced from arXiv: 2606.31301 by Hossein Atrsaei, Mich\`ele Wigger, Mireille Sarkiss.

Figure 1
Figure 1. Figure 1: Subtractive dithered quantizer. covariance matrix is RX = E h 1 T XXH i with the average power constraint Tr(RX) = NtP0. The unquantized received signals at the communication and sensing receivers are Yc = HX + Wc, (1a) Ys = GX + Ws. (1b) Here, H ∈ C Nc×Nt denotes the communication channel, and G ∈ C Ns×Nt denotes the sensing (target-response) channel. The noise matrices have independent circularly symmetr… view at source ↗
Figure 2
Figure 2. Figure 2: Quantized MIMO-ISAC system model. The transmitted random waveform [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: Lower and upper bounds, exact rate, and unquantized no-combiner [PITH_FULL_IMAGE:figures/full_fig_p005_3.png] view at source ↗
Figure 5
Figure 5. Figure 5: compares the Gaussian-signaling LMMSE ϵG with the unquantized distortion obtained with the optimal linear combiner under the Gaussian signaling. In the expression for ϵG in (35), the expectation has no closed form for a general RB. We therefore approximate it by sample￾average approximation (SAA): we draw independent wave￾form samples according to (23), compute the eigenvalues of R 1/2 B X ∗X T (R 1/2 B ) … view at source ↗
read the original abstract

We study a quantized multiple-input multiple-output (MIMO) integrated sensing and communication (ISAC) system in which the communication and sensing receivers each apply analog spatial combining followed by scalar subtractive dithered quantization. This quantization model leads to an additive effective-noise representation with non-Gaussian noise. We derive upper and lower bounds on the capacity of this channel. Numerical results show that these bounds are tight at low signal-to-noise ratios (SNR) and saturate at high SNR due to finite-resolution quantization. They also show that, despite the effective noise being non-Gaussian, independent and identically distributed (i.i.d.) isotropic Gaussian signaling achieves rates close to capacity. Focusing on i.i.d. Gaussian signaling, this paper also presents a closed-form expression for the linear minimum mean-squared error (LMMSE) achieved under a Kronecker sensing-channel model. Numerical results show that the LMMSE also saturates at high SNR, where the saturation level increases as the spatial combining ratio decreases, and for combining ratios below one, saturation occurs even without quantization.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

0 major / 2 minor

Summary. The manuscript studies quantized MIMO ISAC systems in which communication and sensing receivers apply analog spatial combining followed by scalar subtractive dithered quantization, yielding an additive effective-noise model with non-Gaussian noise. Upper and lower bounds on the capacity of this channel are derived. Numerical results indicate that the bounds are tight at low SNR and both saturate at high SNR due to finite-resolution quantization. The work further shows that i.i.d. isotropic Gaussian signaling achieves rates close to the upper bound despite the non-Gaussian noise, and supplies a closed-form LMMSE expression under the Kronecker sensing-channel model whose saturation level increases as the spatial combining ratio decreases.

Significance. If the derived bounds and the numerical tightness hold, the results establish concrete fundamental limits for quantized MIMO ISAC and demonstrate the near-optimality of Gaussian inputs for this non-Gaussian effective channel. The closed-form LMMSE expression under the Kronecker model is a useful analytical tool for sensing performance evaluation. The observed saturation behavior quantifies how quantization and combining ratio constrain high-SNR operation.

minor comments (2)
  1. [Abstract] The abstract states that the bounds are tight at low SNR and saturate at high SNR, but the main text should explicitly identify the SNR regimes, antenna dimensions, and quantization bit depths used in the numerical evaluation so that the tightness claim can be reproduced.
  2. The closed-form LMMSE expression is presented for the Kronecker model; a brief derivation outline or reference to the key matrix inversion step would improve readability for readers focused on the sensing metric.

Simulated Author's Rebuttal

0 responses · 0 unresolved

We thank the referee for the positive summary, recognition of the significance of the derived bounds and closed-form LMMSE, and the recommendation for minor revision. No specific major comments were provided in the report.

Circularity Check

0 steps flagged

No significant circularity in derivation chain

full rationale

The paper derives capacity upper and lower bounds for the effective channel after analog combining and subtractive dithered scalar quantization, which produces an additive non-Gaussian noise term by the standard dither construction. The closed-form LMMSE under the Kronecker sensing model follows directly from the stated linear model and Gaussian signaling assumption. No steps reduce by construction to fitted parameters, self-definitions, or load-bearing self-citations; the numerical closeness of Gaussian rates to the bounds is an empirical observation, not a definitional identity. The derivation chain is self-contained against the given channel and quantization model.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

Based solely on the abstract, the paper relies on standard information-theoretic channel models and quantization assumptions without introducing new free parameters or invented entities.

axioms (1)
  • standard math Standard information-theoretic assumptions for deriving capacity bounds on channels with additive effective noise
    Invoked to obtain upper and lower bounds on capacity of the quantized MIMO ISAC channel.

pith-pipeline@v0.9.1-grok · 5721 in / 1197 out tokens · 50201 ms · 2026-07-01T03:34:37.201087+00:00 · methodology

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Reference graph

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