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.

Publication:

IEEE Transactions on Signal Processing (Volume: 72) 12 July 2024 

http://dx.doi.org/10.1109/TSP.2024.3427373

Author:

Shihang Lu

School of System Design and Intelligent Manufacturing (SDIM), Southern University of Science and Technology, Shenzhen 518055, China

Email: lush2021@mail. sustech.edu.cn

Fuwang Dong

School of System Design and Intelligent Manufacturing (SDIM), Southern University of Science and Technology, Shenzhen 518055, China

Email: dongfw@sustech.edu.cn

Fan Liu 

National Mobile Communications Research Laboratory, Southeast University, Nanjing 210096, China

Email: f.liu@ieee.org

Shi Jin

National Mobile Communications Research Laboratory, Southeast University, Nanjing 210096, China

Email: jinshi@seu.edu.cn

Yifeng Xiong

School of Information and Communication Engineering, Beijing University of Posts and Telecommunications, Beijing 100876, China

Email: yifengxiong@bupt.edu.cn

Jie Xu

School of Science and Engineering (SSE) and the Future Network of Intelligence Institute (FNii), The Chinese University of Hong Kong (Shenzhen), Shenzhen 518172, China

Email:xujie@cuhk.edu.cn

Ya-Feng Liu

State Key Laboratory of Scientific and Engineering Computing, Institute of Computational Mathematics and Scientific/ Engineering Computing, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100190, China

Email:yafliu@ lsec.cc.ac.cn