Designing Constant Modulus Approximate Binary Phase Waveforms for Multitarget Detection in MIMO Radar Using LSTM Networks

Multiple-input–multiple-output (MIMO) radar can improve target detection capability due to its increased spatial degrees of freedom compared with traditional phased array radar. However, in practical applications, perfectly orthogonal waveforms are virtually unattainable. Thus, the orthogonality among the transmitted waveforms becomes a critical factor for determining the operational state in orthogonal MIMO radar. In typical target detection scenarios characterized by complex environments, the received radar echoes are often superimposed by reflections of multiple distinct objects. Such echo signals inevitably impact the orthogonality performance of nonorthogonal waveforms, thereby affecting the detection performance of the MIMO radar. To address this, this article initially undertakes a rigorous analysis of echo signals for nonorthogonal waveforms under both single-target and multitarget conditions. Subsequently, based on the analytical findings, we propose an objective function for the design of constant modulus code-division multiple access waveforms tailored for multitarget scenarios. This objective function is then employed as a loss function in an unsupervised training scheme using a recurrent neural network with a long short-term memory architecture. Furthermore, we utilize a nonlinear function to discretize the network output, making the output phase coding approximate to binary coding. This makes the resulting phase coding more practically applicable. Finally, normalization is performed on the output amplitude of each matched filter to further enhance waveform orthogonality. Simulation results are provided to demonstrate the performance of the proposed method.