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.

翻译：集成感知与通信（ISAC）被广泛认为是推动未来无线网络发展的关键使能技术。本文旨在高效利用基于多输入多输出（MIMO）正交频分复用（OFDM）的ISAC系统中回波信号的固有稀疏性。为此，提出了一种新型联合接收回波处理与发射波束成形设计方案。具体而言，首先提出一种压缩感知（CS）辅助的估计方法以优化ISAC接收回波处理，该方法不仅能实现目标信息的精确恢复，还可大幅减少需要采样和处理的感知子载波数量。基于所提出的CS辅助处理方法，进一步将关联的发射波束成形设计建模为优化问题，目标是在满足发射功率预算并确保指定感知子载波接收信噪比（SNR）的条件下，最大化多用户通信的总速率。为求解涉及高维变量的非凸问题，开发了一种融合优化最小化（MM）、分式规划（FP）及具有闭式解的非线性等式交替方向乘子法（neADMM）的高效迭代算法。最后，通过大量数值仿真验证了所提算法的有效性及所引入稀疏性利用策略的优越性能。