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Hybrid Beamforming Optimization for MIMO ISAC based on Prior Distribution Information

Yizhuo Wang, Shuowen Zhang

TL;DR

This work addresses joint sensing and communication in a MIMO ISAC system using hybrid analog-digital transceivers, where target pose information is unknown but described by a prior distribution. It develops a PCRB-based framework to quantify sensing accuracy and formulates AO-based hybrid beamforming algorithms that balance PCRB minimization with a required communication rate, covering sensing-only, narrowband ISAC, and OFDM ISAC cases. The paper derives closed-form optimal updates for sensing-focused designs, extends the AO approach to MIMO-ISAC and MIMO-OFDM-ISAC with WMMSE and FPP-SCA techniques, and analyzes the impact of transmitter/receiver RF chains on performance, including a fully-connected receiver extension with a DFT codebook. Numerical results show the proposed designs closely approach fully digital performance with moderate RF counts, and reveal that receiver RF chains have a greater effect on sensing accuracy than transmitter chains, with RF allocation becoming more transmitter-heavy as rate targets rise. The results provide practical guidance for efficient ISAC system design under hardware constraints and prior information availability.

Abstract

This paper considers a multiple-input multiple-output (MIMO) integrated sensing and communication (ISAC) system, where a multi-antenna base station (BS) with transceiver hybrid analog-digital arrays transmits dual-functional signals to communicate with a multi-antenna user and simultaneously sense the unknown and random location information of a target based on the reflected echo signals and the prior distribution information on the target's location. Under transceiver hybrid arrays, we characterize the sensing performance by deriving the posterior Cramér-Rao bound (PCRB) of the mean-squared error which is a function of the transmit hybrid beamforming and receive analog beamforming. We study joint transmit hybrid beamforming and receive analog beamforming optimization to minimize the PCRB subject to a communication rate requirement. We first consider a sensing-only system and derive the optimal solution to each element in the transmit/receive analog beamforming matrices that minimizes the PCRB in closed form. Then, we develop an alternating optimization (AO) based algorithm. Next, we study a narrowband MIMO ISAC system and devise an efficient AO-based hybrid beamforming algorithm by leveraging weighted minimum mean-squared error and feasible point pursuit successive convex approximation methods. Furthermore, we extend the results for narrowband systems to a MIMO orthogonal frequency-division multiplexing (OFDM) ISAC system. Numerical results validate the effectiveness of our proposed hybrid beamforming designs. It is revealed that the number of receive RF chains has more significant impact on the sensing performance than its transmit counterpart. Under a given budget on the total number of transmit/receive RF chains at the BS, the optimal number of transmit RF chains increases as the communication rate target increases due to the non-trivial PCRB-rate trade-off.

Hybrid Beamforming Optimization for MIMO ISAC based on Prior Distribution Information

TL;DR

This work addresses joint sensing and communication in a MIMO ISAC system using hybrid analog-digital transceivers, where target pose information is unknown but described by a prior distribution. It develops a PCRB-based framework to quantify sensing accuracy and formulates AO-based hybrid beamforming algorithms that balance PCRB minimization with a required communication rate, covering sensing-only, narrowband ISAC, and OFDM ISAC cases. The paper derives closed-form optimal updates for sensing-focused designs, extends the AO approach to MIMO-ISAC and MIMO-OFDM-ISAC with WMMSE and FPP-SCA techniques, and analyzes the impact of transmitter/receiver RF chains on performance, including a fully-connected receiver extension with a DFT codebook. Numerical results show the proposed designs closely approach fully digital performance with moderate RF counts, and reveal that receiver RF chains have a greater effect on sensing accuracy than transmitter chains, with RF allocation becoming more transmitter-heavy as rate targets rise. The results provide practical guidance for efficient ISAC system design under hardware constraints and prior information availability.

Abstract

This paper considers a multiple-input multiple-output (MIMO) integrated sensing and communication (ISAC) system, where a multi-antenna base station (BS) with transceiver hybrid analog-digital arrays transmits dual-functional signals to communicate with a multi-antenna user and simultaneously sense the unknown and random location information of a target based on the reflected echo signals and the prior distribution information on the target's location. Under transceiver hybrid arrays, we characterize the sensing performance by deriving the posterior Cramér-Rao bound (PCRB) of the mean-squared error which is a function of the transmit hybrid beamforming and receive analog beamforming. We study joint transmit hybrid beamforming and receive analog beamforming optimization to minimize the PCRB subject to a communication rate requirement. We first consider a sensing-only system and derive the optimal solution to each element in the transmit/receive analog beamforming matrices that minimizes the PCRB in closed form. Then, we develop an alternating optimization (AO) based algorithm. Next, we study a narrowband MIMO ISAC system and devise an efficient AO-based hybrid beamforming algorithm by leveraging weighted minimum mean-squared error and feasible point pursuit successive convex approximation methods. Furthermore, we extend the results for narrowband systems to a MIMO orthogonal frequency-division multiplexing (OFDM) ISAC system. Numerical results validate the effectiveness of our proposed hybrid beamforming designs. It is revealed that the number of receive RF chains has more significant impact on the sensing performance than its transmit counterpart. Under a given budget on the total number of transmit/receive RF chains at the BS, the optimal number of transmit RF chains increases as the communication rate target increases due to the non-trivial PCRB-rate trade-off.

Paper Structure

This paper contains 38 sections, 2 theorems, 52 equations, 14 figures.

Table of Contents

  1. Introduction
  2. System Model
  3. MIMO Communication Model under Hybrid Arrays
  4. MIMO Sensing Model under Hybrid Arrays
  5. Characterization of Sensing Performance under Hybrid Arrays Exploiting Prior Information
  6. Hybrid Beamforming for MIMO Sensing
  7. Problem Formulation
  8. Optimal Solution under Special Array Structures
  9. Case I
  10. Case II
  11. Proposed General AO-based Solution to (P0)
  12. Optimal solution to each element in $\bm{W}_{\mathrm{RF}}^H$
  13. Optimal solution to each element in $\bm{V}_{\mathrm{RF}}$ with $N_{\mathrm{RF},\mathrm{T}}=1$
  14. Overall AO-based algorithm for (P0)
  15. Hybrid Beamforming for MIMO ISAC
  16. ...and 23 more sections

Key Result

Proposition 1

When $N_{\mathrm{RF},\mathrm{T}}\geq 2$, hybrid transmit beamforming with fully-digital receive array can achieve the same PCRB performance as the optimal fully-digital beamforming.

Figures (14)

  • Figure 1: Illustration of MIMO ISAC under hybrid BS transceiver arrays.
  • Figure 2: Convergence behavior of the proposed AO-based algorithms.
  • Figure 3: MIMO sensing performance under different array structures.
  • Figure 4: BS received power pattern over $\theta$ for MIMO sensing.
  • Figure 5: PCRB versus the number of transmit RF chains for MIMO sensing.
  • ...and 9 more figures

Theorems & Definitions (2)

  • Proposition 1
  • Proposition 2