  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.
