Design of Discrete-Phase Orthogonal Waveforms for Cognitive MIMO Systems

The design of discrete phase-coded orthogonal waveforms is a critical issue in cognitive multiple-input multiple-output (MIMO) radar and communication systems. Typically, existing methods usually only optimize integrated sidelobe level (ISL) metric without acceptable time. To address this issue, we propose a method that considers nearly all metrics while maintaining short computation time even for long sequences. We model the problem as an optimization of a discrete phase matrix, aiming to design orthogonal waveforms by minimizing the weighted sum of peak sidelobe level (PSL) and ISL. Since the non-smooth non-convex nature of the PSL and discrete phases, this problem is challenging to solve. Among existing methods, the block coordinate descent (BCD) method can be used to address it, but it often incurs significant computational costs. We notice that nonlinear activation functions can approximate quantization functions, and that deep learning (DL) networks are effective in solving certain non-convex optimization problems. Therefore, we combine a nonlinear smoothing function and deep residual network (ResNet) to construct the soft quantization network (SQN) to solve this problem. Specifically, we incorporate a soft quantization layer in the SQN to simulate the effect of hard quantization, ultimately discretizing the approximate discrete phase sequence. Simulation results demonstrate that our proposed method generates waveforms with better orthogonality and lower computational cost compared to BCD.