Fundamental Limits of Quantized MIMO ISAC under Gaussian Signaling
Provides fundamental performance limits for quantized MIMO ISAC systems, relevant to system designers seeking to understand trade-offs between communication and sensing under practical hardware constraints.
This paper derives capacity bounds for a quantized MIMO ISAC system with dithered quantization, showing tightness at low SNR and saturation at high SNR due to finite resolution. It also provides a closed-form LMMSE expression under a Kronecker model, revealing saturation at high SNR that worsens with lower spatial combining ratios.
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.