End-to-End Communication Rate Maximization in MIMO ISAC Multi-Hop Wireless Networks

Abstract

Integrated sensing and communication (ISAC) in multi-hop wireless networks represents a transformative solution for enabling next-generation Internet-of-things (IoT) applications, addressing critical challenges such as spectrum scarcity and limited coverage. By leveraging shared resources and multi-antenna techniques, this architecture simultaneously supports high-quality end-to-end communication and accurate environmental sensing, thus a methodical exploration of the trade-offs between these two functionalities is required. To achieve this goal, this paper focuses on maximizing the end-to-end communication rate while ensuring the overall sensing performance in multiple-input multiple-output (MIMO) ISAC multi-hop wireless networks. In particular, a joint optimization problem for routing strategy and transmit covariance matrix design is formulated, which is, however, highly non-convex and challenging to solve directly. To tackle this problem with implicit routing variables, we first transform it into an equivalent but more tractable mixed-integer nonlinear programming (MINLP) problem through a series of equivalent transformations. Then, instead of relying on computationally expensive exhaustive search methods, we propose an efficient (centralized) algorithm based on generalized Benders decomposition (GBD), which can obtain the optimal solution of the MINLP problem with much lower complexity as compared to the exhaustive search method. Moreover, to further alleviate the communication overhead and computational complexity of solving the MINLP problem in a centralized manner, we also develop a low-complexity distributed algorithm that integrates the alternating direction method of multipliers (ADMM), the penalty method and the successive convex approximation (SCA) method. Finally, numerical results demonstrate that: 1) the centralized algorithm is able to achieve the optimal performance obtained by the exhaustive search method, while the low-complexity distributed algorithm attains near-optimal performance; 2) as the sum-CRB threshold is relaxed from 0.041 to 0.055, the average end-to-end achievable rate of both proposed algorithms increases from approximately 14 to 24.5 bps/Hz. Moreover, compared with the greedy and random routing baselines, the distributed algorithm achieves rate improvements of about 43%–69% and 32%–40%, respectively.