[Paper Review] Optimal Transmit Beamforming for Integrated Sensing and Communication

Haocheng Hua, Jie Xu+1 more|arXiv (Cornell University)|Apr 24, 2021

Radar Systems and Signal ProcessingEngineering46 references33 citations

TL;DR

The paper designs downlink ISAC transmit beamforming at a multi-antenna base station by jointly optimizing information and dedicated radar signals under SINR and power constraints, introducing a new minimum weighted beampattern gain criterion and two receiver types with SDR-based globally optimal solutions.

ABSTRACT

This paper studies the transmit beamforming in a downlink integrated sensing and communication (ISAC) system, where a base station (BS) equipped with a uniform linear array (ULA) sends combined information-bearing and dedicated radar signals to simultaneously perform downlink multiuser communication and radar target sensing. Under this setup, we maximize the radar sensing performance (in terms of minimizing the beampattern matching errors or maximizing the minimum weighted beampattern gains), subject to the communication users' minimum signal-to-interference-plus-noise ratio (SINR) requirements and the BS's transmit power constraints. In particular, we consider two types of communication receivers, namely Type-I and Type-II receivers, which do not have and do have the capability of cancelling the interference from the {\emph{a-priori}} known dedicated radar signals, respectively. Under both Type-I and Type-II receivers, the beampattern matching and minimum weighted beampattern gain maximization problems are globally optimally solved via applying the semidefinite relaxation (SDR) technique together with the rigorous proof of the tightness of SDR for both Type-I and Type-II receivers under the two design criteria. It is shown that at the optimality, radar signals are not required with Type-I receivers under some specific conditions, while radar signals are always needed to enhance the performance with Type-II receivers. Numerical results show that the minimum weighted beampattern gain maximization leads to significantly higher beampattern gains at the worst-case sensing angles with a much lower computational complexity than the beampattern matching design. We show that by exploiting the capability of canceling the interference caused by the radar signals, the case with Type-II receivers results in better sensing performance than that with Type-I receivers and other conventional designs.

Motivation & Objective

• Motivate the integration of sensing and communication in downlink wireless systems using multi-antenna beamforming.
• Jointly optimize information-bearing signals and a dedicated radar signal to enhance sensing while meeting per-user SINR requirements.
• Compare two sensing design criteria and two receiver types, and establish conditions under which SDR yields globally optimal solutions.
• Show the benefits of dedicated radar signals for ISAC and analyze when they are unnecessary under LOS conditions.

Proposed method

• Model the BS with a uniform linear array transmitting information signals to K users and a dedicated radar signal with covariance Rd.
• Formulate two non-convex optimization problems: beampattern matching (P1) and minimum weighted beampattern gain maximization (P2) under SINR constraints and power limit.
• Introduce T_k = t_k t_k^H to enable semidefinite relaxation (SDR) and reformulate as (P1.1) and (P2.1).
• Prove SDR tightness via Propositions showing rank-one optimality for all T_k and Rd, eliminating the need for Gaussian randomization.
• Define Type-I receivers that cannot cancel radar interference and Type-II receivers that can cancel pre-known radar signals, and derive corresponding SINR expressions.
• Compare with a benchmark design without radar signals to illustrate performance gains from dedicated radar signals.

Experimental results

Research questions

• RQ1 Can SDR provide globally optimal solutions to the non-convex beampattern design problems with dedicated radar signals present?
• RQ2 How do Type-I and Type-II receivers differ in achievable ISAC performance under beampattern matching and minimum weighted beampattern gain designs?
• RQ3 Does incorporating dedicated radar signals consistently improve sensing beampatterns under SINR constraints, and under which channel conditions might they be unnecessary?
• RQ4 How does the minimum weighted beampattern gain maximization design compare to traditional beampattern matching in terms of sensing performance and computational complexity?
• RQ5 What are the fundamental performance relationships among the four designs (P1 vs P2 with Type-I vs Type-II receivers) and the design without radar signals?

Key findings

• The SDRs for the four problems are proven tight, yielding globally optimal rank-one solutions.
• Dedicated radar signals generally improve ISAC performance across designs and receiver types by exploiting full spatial DoF.
• For Type-II receivers, radar interference cancellation yields better sensing performance than Type-I receivers and conventional designs.
• The minimum weighted beampattern gain maximization design yields stronger beampattern gains at interested angles and lower computational complexity than beampattern matching.
• In LOS scenarios for Type-I receivers, dedicated radar signals may be unnecessary, highlighting design dependent on channel conditions.
• Numerical results show the minimum weighted design outperforms beampattern matching in both sensing quality and speed of computation.