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 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.