Designing Waveform Sets with Good Correlation and Stopband Properties for MIMO Radar via the Gradient-Based Method

Waveform sets with good correlation and/or stopband properties have received extensive attention and been widely used in multiple-input multiple-output (MIMO) radar. In this paper, we aim at designing unimodular waveform sets with good correlation and stopband properties. To formulate the problem, we construct two criteria to measure the correlation and stopband properties and then establish an unconstrained problem in the frequency domain. After deducing the phase gradient and the step size, an efficient gradient-based algorithm with monotonicity is proposed to minimize the objective function directly. For the design problem without considering the correlation weights, we develop a simplified algorithm, which only requires a few fast Fourier transform (FFT) operations and is more efficient. Because both of the algorithms can be implemented via the FFT operations and the Hadamard product, they are computationally efficient and can be used to design waveform sets with a large waveform number and waveform length. Numerical experiments show that the proposed algorithms can provide better performance than the state-of-the-art algorithms in terms of the computational complexity.