Cross Ambiguity Function Shaping of Cognitive MIMO Radar: A Synergistic Approach to Antenna Placement and Waveform Design

The ambiguity function (AF) is a crucial tool in characterizing the range-angle response of a multiple-input multiple-output (MIMO) radar system, which is intricately influenced by the transmit waveforms, receiving filters and also antenna configurations. Notably, the role of antenna configurations is less explored compared to the well-studied areas of waveforms and filters. In this article, we incorporate antenna positions as an additional design parameter alongside waveforms and filters to optimize the AF in a specific range-angle bin. We employ the mainlobe-to-integrated-sidelobe-level-ratio (MISLR) as a quantitative metric to assess the performance. The resulting optimization problem is inherently nonconvex, encompassing binary and unimodular constraints. To address this challenge, we reformulate the problem, enabling an alternating optimization approach for antenna positions and waveforms. Each iteration involves solving a sequence of quadratic constrained quadratic programming problems for the binarily constrained antenna position optimization and updating the waveforms iteratively via an analytical expression. Our simulation results validate the effectiveness of the proposed method as it achieves higher MISLR with the same number of antennas compared to conventional approaches. Moreover, the optimized antenna configurations notably enhance the balance between angular ambiguity and resolution.