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Hybrid Beamforming Design for Integrated Sensing and Communication Exploiting Prior Information

Yizhuo Wang, Shuowen Zhang

TL;DR

This paper analytically proves that hybrid beamforming can achieve the same performance as the optimized digital beamforming as long as the number of radio frequency (RF) chains is larger than 1, and proposes a convex relaxation based algorithm for the hybrid beamforming design with a single RF chain.

Abstract

In this paper, we investigate the hybrid beamforming design for a multiple-input multiple-output (MIMO) integrated sensing and communication (ISAC) system, where a multi-antenna base station (BS) with hybrid analog-digital transmit antenna arrays sends dual-functional signals to communicate with a multi-antenna user and simultaneously sense the location information of a point target based on the reflected echo signals. Specifically, we aim to sense the target's unknown and random angle information by exploiting its prior distribution information, with posterior Cramér-Rao bound (PCRB) employed as the sensing performance metric. First, we consider a sensing-only case and study the hybrid beamforming optimization to minimize the sensing PCRB. We analytically prove that hybrid beamforming can achieve the same performance as the optimized digital beamforming as long as the number of radio frequency (RF) chains is larger than 1. Then, we propose a convex relaxation based algorithm for the hybrid beamforming design with a single RF chain. Next, we study the hybrid beamforming optimization to minimize the PCRB subject to a communication rate target. Due to the intractability of the exact PCRB expression, we replace it with a tight upper bound. Although this problem is still non-convex and challenging to solve, we propose an alternating optimization (AO) algorithm for finding a high-quality suboptimal solution based on the feasible point pursuit successive convex approximation (FPP-SCA) method. Numerical results validate the effectiveness of our proposed hybrid beamforming design.

Hybrid Beamforming Design for Integrated Sensing and Communication Exploiting Prior Information

TL;DR

This paper analytically proves that hybrid beamforming can achieve the same performance as the optimized digital beamforming as long as the number of radio frequency (RF) chains is larger than 1, and proposes a convex relaxation based algorithm for the hybrid beamforming design with a single RF chain.

Abstract

In this paper, we investigate the hybrid beamforming design for a multiple-input multiple-output (MIMO) integrated sensing and communication (ISAC) system, where a multi-antenna base station (BS) with hybrid analog-digital transmit antenna arrays sends dual-functional signals to communicate with a multi-antenna user and simultaneously sense the location information of a point target based on the reflected echo signals. Specifically, we aim to sense the target's unknown and random angle information by exploiting its prior distribution information, with posterior Cramér-Rao bound (PCRB) employed as the sensing performance metric. First, we consider a sensing-only case and study the hybrid beamforming optimization to minimize the sensing PCRB. We analytically prove that hybrid beamforming can achieve the same performance as the optimized digital beamforming as long as the number of radio frequency (RF) chains is larger than 1. Then, we propose a convex relaxation based algorithm for the hybrid beamforming design with a single RF chain. Next, we study the hybrid beamforming optimization to minimize the PCRB subject to a communication rate target. Due to the intractability of the exact PCRB expression, we replace it with a tight upper bound. Although this problem is still non-convex and challenging to solve, we propose an alternating optimization (AO) algorithm for finding a high-quality suboptimal solution based on the feasible point pursuit successive convex approximation (FPP-SCA) method. Numerical results validate the effectiveness of our proposed hybrid beamforming design.
Paper Structure (13 sections, 1 theorem, 19 equations, 4 figures, 1 algorithm)

This paper contains 13 sections, 1 theorem, 19 equations, 4 figures, 1 algorithm.

Table of Contents

  1. Introduction
  2. System Model
  3. Hybrid Beamforming Optimization for PCRB Minimization
  4. Problem Formulation
  5. Proposed Solution to (P1)
  6. Hybrid Beamforming Optimization for PCRB-Rate Trade-Off
  7. Problem Formulation
  8. Proposed Solution to (P2)
  9. Digital Beamformer Optimization
  10. Analog Beamformer Optimization
  11. Complexity Analysis
  12. Numerical Results
  13. Conclusions

Key Result

Proposition 1

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

Figures (4)

  • Figure 1: Illustration of a MIMO ISAC system with hybrid beamforming.
  • Figure 2: Convergence behavior of Algorithm 1.
  • Figure 3: Radiated power pattern and $p_{\Theta}(\theta)$ over different angles.
  • Figure 4: $\mathrm{PCRB}$ versus the communication rate target.

Theorems & Definitions (1)

  • Proposition 1