Sparsity Exploitation via Joint Receive Processing and Transmit Beamforming Design for MIMO-OFDM ISAC Systems

Integrated sensing and communication (ISAC) is widely recognized as a pivotal enabling technique for the advancement of future wireless networks. This paper aims to efficiently exploit the inherent sparsity of echo signals for the multi-input-multi-output (MIMO) orthogonal frequency division multiplexing (OFDM) based ISAC system. A novel joint receive echo processing and transmit beamforming design is presented to achieve this goal. Specifically, we first propose a compressive sensing (CS)-assisted estimation approach to facilitate ISAC receive echo processing, which can not only enable accurate recovery of target information, but also allow a substantial reduction in the number of sensing subcarriers to be sampled and processed. Then, based on the proposed CS-assisted processing method, the associated transmit beamforming design is formulated with the objective of maximizing the sum-rate of multiuser communications while satisfying the transmit power budget and ensuring the received signal-to-noise ratio (SNR) for the designated sensing subcarriers. In order to address the formulated non-convex problem involving high-dimensional variables, an effective iterative algorithm employing majorization minimization (MM), fractional programming (FP), and the nonlinear equality alternative direction method of multipliers (neADMM) with closed-form solutions has been developed. Finally, extensive numerical simulations are conducted to verify the effectiveness of the proposed algorithm and the superior performance of the introduced sparsity exploitation strategy.