Neural Network-Inspired Phase-Coded Waveform Design for MIMO Radar Based on Gradient Descent

Peak sidelobe level (PSL) stands as a critical performance metric in the design of multiple-input multiple-output (MIMO) radar waveforms. However, optimizing PSL is a challenging task due to its high dimensionality and nonconvex nature. Traditional optimization algorithms often require sophisticated techniques with high computation complexity while the resulting PSL is relatively high. Drawing inspiration from neural network optimization, this article presents an efficient approach that employs gradient descent (GD) to design low sidelobe phase-coded waveforms for MIMO radar. This is accomplished by smoothing the PSL's maximum function with a Log-Sum-Exp (LSE) function, which serves as the objective function for the waveform design problem. Specifically, the new LSE function controls the degree of approximation to the maximum function, preventing numerical overflow and maintaining computational accuracy. The ensuing unconstrained approximate minimization problem is amenable to GD optimization. Besides the new LSE objective function, another key contribution lies in combining GD with neural network optimization, resulting in a significantly faster optimization process compared to traditional methods. Utilizing neural network frameworks, the GD algorithm benefits from automatic differentiation and GPU acceleration, enabling efficient optimization of large waveform sets. Extensive numerical studies demonstrate that the proposed method can design waveform sets with low PSL or weighted PSL effectively, which can be closer to the Welch bound as compared to conventional approaches.