MIMO Radar Unimodular Waveform Design With Learned Complex Circle Manifold Network

Waveform design with constant modulus constraint (CMC) is of great importance in multiple-input–multiple-output radar systems. Both the relaxations in model-based waveform design methods and data limitation in data-driven deep neural networks (DNNs) methods could result in performance degradation. Nevertheless, these two types of methods have their unique advantages. This motivates us to develop a model-based learned complex circle manifold network (LCCM-Net) method without relaxation, by exploiting the advantages of both gradient descent models over CCM and DNNs with limited data for learning. More concretely, in this article, we propose to formulate the waveform design problem as an unconstrained quadratic fractional problem on the CCM. To solve the resultant problem, the gradient descent algorithm is unfolded as the network layer over the CCM, and the step sizes are adaptively learned. Furthermore, for discrete phases adopted in practical systems, we develop a quantized LCCM-Net, where a low-resolution nonuniform quantizer is designed to quantize the phase. This quantizer relies on a uniquely designed soft staircase function, which incorporates learnable parameters that allow it to adaptively fine tune the decision region. The performance superiority of the proposed method is evidenced by comparing with the existing methods.