BD-IRS Aided Uplink ISAC Exploiting Prior Information: SDMA or TDMA?

In this paper, we study a beyond diagonal intelligent reflecting surface (BD-IRS) aided uplink integrated sensing and communication (ISAC) system with device-based sensing. Specifically, we aim to estimate the unknown and random location of an active target based on its uplink probing signals sent to a multi-antenna base station (BS) and the known prior distribution information of the target's location; meanwhile, multiple communication users send uplink signals to the BS, which results in mutual interference between sensing and communication. We first characterize the sensing performance by deriving the posterior Cramér-Rao bound (PCRB) of the sensing mean-squared error (MSE) when prior information is exploited. Then, we formulate a BD-IRS reflection matrix optimization problem to maximize the minimum expected achievable rate among multiple users over the random target location, subject to a constraint on the PCRB as well as the lossless and reciprocal constraints on the BD-IRS reflection matrix. The formulated problem is non-convex and challenging to solve. To tackle this problem, we propose a penalty dual decomposition (PDD) based algorithm which can find a highquality suboptimal solution with polynomial-time complexity. In addition, we propose and optimize a time-division multiple access (TDMA) based scheme to remove the sensing-communication mutual interference. Numerical results verify the effectiveness of the proposed BD-IRS reflection design and provide useful design insights, such as the optimal choice of multiple access scheme.