Design and Optimization of Finite Alphabet Waveforms for Multiple-Antenna Radar Covariance Matching

Abstract

The beampattern of an MIMO radar depends on the covariance matrix of its transmitted waveforms. Although this matrix can be easily realized using waveforms with large alphabets and a high peak-to-average power ratio (PAPR), such waveforms require significant storage and are difficult to transmit within the limited linear range of power amplifiers. Designing finite-alphabet waveforms with unity PAPR, such as BPSK, is therefore a challenging yet important task, as they reduce storage requirements and satisfy hardware constraints. Although extensive research has addressed this problem, existing approaches lack theoretical insight into performance limits, and the resulting solutions are often suboptimal. This work introduces a novel formulation for binary waveform design based on constrained matrix decomposition that outperforms existing methods. The proposed approach exploits a recently introduced property of beampattern-invariant covariance matrices, which provides additional degrees of freedom and enables faster convergence. From a theoretical perspective, we investigate the feasibility of generating a given covariance matrix using binary waveforms. We prove that the covariance matrix of an autoregressive process is always feasible, and we propose methods to assess feasibility in general. For infeasible cases, we introduce a beampattern adjustment procedure. Finally, we demonstrate the advantages of binary waveforms through several application scenarios.