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Random ISAC Signals Deserve Dedicated Precoding

Shihang Lu, Fan Liu, Fuwang Dong, Yifeng Xiong, Jie Xu, Ya-Feng Liu, Shi Jin

TL;DR

This work tackles the challenge that ISAC signals are inherently random and can degrade sensing performance. It introduces the ergodic LMMSE (ELMMSE) to capture sensing errors averaged over random Gaussian ISAC signals and develops two dedicated precoding schemes: data-dependent (DDP) and data-independent (DIP). It provides a closed-form, per-realization solution for sensing-only DDP, a stochastic-gradient-based DIP, and a high-SNR analysis revealing eigenstructure alignment with the sensing channel covariance. The ISAC extension uses a penalty-based alternating optimization (AO) and a stochastic-gradient AO (SGP-AO) to satisfy communication-rate constraints while minimizing ELMMSE, with high-SNR approximations offering computationally efficient alternatives. Numerical results show substantial gains of DDP and DIP over conventional deterministic-signal designs, confirming that random ISAC signals deserve dedicated precoding design for improved sensing and communication performance, especially under short frame lengths.

Abstract

Radar systems typically employ well-designed deterministic signals for target sensing, while integrated sensing and communications (ISAC) systems have to adopt random signals to convey useful information. This paper analyzes the sensing and ISAC performance relying on random signaling in a multi-antenna system. Towards this end, we define a new sensing performance metric, namely, ergodic linear minimum mean square error (ELMMSE), which characterizes the estimation error averaged over random ISAC signals. Then, we investigate a data-dependent precoding (DDP) scheme to minimize the ELMMSE in sensing-only scenarios, which attains the optimized performance at the cost of high implementation overhead. To reduce the cost, we present an alternative data-independent precoding (DIP) scheme by stochastic gradient projection (SGP). Moreover, we shed light on the optimal structures of both sensing-only DDP and DIP precoders. As a further step, we extend the proposed DDP and DIP approaches to ISAC scenarios, which are solved via a tailored penalty-based alternating optimization algorithm. Our numerical results demonstrate that the proposed DDP and DIP methods achieve substantial performance gains over conventional ISAC signaling schemes that treat the signal sample covariance matrix as deterministic, which proves that random ISAC signals deserve dedicated precoding designs.

Random ISAC Signals Deserve Dedicated Precoding

TL;DR

This work tackles the challenge that ISAC signals are inherently random and can degrade sensing performance. It introduces the ergodic LMMSE (ELMMSE) to capture sensing errors averaged over random Gaussian ISAC signals and develops two dedicated precoding schemes: data-dependent (DDP) and data-independent (DIP). It provides a closed-form, per-realization solution for sensing-only DDP, a stochastic-gradient-based DIP, and a high-SNR analysis revealing eigenstructure alignment with the sensing channel covariance. The ISAC extension uses a penalty-based alternating optimization (AO) and a stochastic-gradient AO (SGP-AO) to satisfy communication-rate constraints while minimizing ELMMSE, with high-SNR approximations offering computationally efficient alternatives. Numerical results show substantial gains of DDP and DIP over conventional deterministic-signal designs, confirming that random ISAC signals deserve dedicated precoding design for improved sensing and communication performance, especially under short frame lengths.

Abstract

Radar systems typically employ well-designed deterministic signals for target sensing, while integrated sensing and communications (ISAC) systems have to adopt random signals to convey useful information. This paper analyzes the sensing and ISAC performance relying on random signaling in a multi-antenna system. Towards this end, we define a new sensing performance metric, namely, ergodic linear minimum mean square error (ELMMSE), which characterizes the estimation error averaged over random ISAC signals. Then, we investigate a data-dependent precoding (DDP) scheme to minimize the ELMMSE in sensing-only scenarios, which attains the optimized performance at the cost of high implementation overhead. To reduce the cost, we present an alternative data-independent precoding (DIP) scheme by stochastic gradient projection (SGP). Moreover, we shed light on the optimal structures of both sensing-only DDP and DIP precoders. As a further step, we extend the proposed DDP and DIP approaches to ISAC scenarios, which are solved via a tailored penalty-based alternating optimization algorithm. Our numerical results demonstrate that the proposed DDP and DIP methods achieve substantial performance gains over conventional ISAC signaling schemes that treat the signal sample covariance matrix as deterministic, which proves that random ISAC signals deserve dedicated precoding designs.
Paper Structure (21 sections, 69 equations, 12 figures, 1 table, 4 algorithms)

This paper contains 21 sections, 69 equations, 12 figures, 1 table, 4 algorithms.

Table of Contents

  1. Introduction
  2. System Model
  3. Sensing with Deterministic Training Signals
  4. Sensing with Random Signals
  5. ISAC Precoding with Gaussian Signals
  6. Sensing-Only Precoding with Gaussian Signals
  7. DDP: A Closed-Form Solution
  8. DIP: An SGP-Based Precoding Method
  9. DIP in the High-SNR Regime
  10. ISAC Precoding with Gaussian Signals
  11. DDP for ISAC: A Penalty-Based AO Method
  12. DIP for ISAC: A Penalty-Based SGP-AO Method
  13. DIP for ISAC in the High-SNR Regime
  14. Simulation Results
  15. Convergence Examples
  16. ...and 6 more sections

Figures (12)

  • Figure 1: The approximation error of \ref{['SampleMatrix_Appro']} versus the frame length.
  • Figure 2: The frame-length-asymptotic performance of Gaussian signals is assessed under the conditions of $N_T = N_R = 32$. The total transmit power is fixed at $16$ dBm, ensuring that the factor of impacting the sensing performance is solely the frame length $L$.
  • Figure 3: Normalized ELMMSE and its asymptotic formulation \ref{['ELMMSE_HSNR_Appro']} versus transmit SNR.
  • Figure 4: The convergence performance of the proposed MB-SGP algorithm and the proposed SGP algorithm versus different SNR settings.
  • Figure 5: iteration number and normalized ELMMSE performance of using MB-SGP and SGP algorithms versus different SNR settings.
  • ...and 7 more figures