Waveform Design With Unit Modulus and Spectral Shape Constraints via Lagrange Programming Neural Network

To maximize the transmitted power available in active sensing, the probing waveform should be of constant modulus. On the other hand, in order to adapt to the increasingly crowed radio frequency spectrum and prevent mutual interferences, there are also requirements in the waveform spectral shape. That is to say, the waveform must fulfill constraints in both time and frequency domains. In this work, designing these waveforms is formulated as a nonlinear constrained optimization problem. By introducing auxiliary variable neurons and Lagrange neurons, we solve it using the Lagrange programming neural network. We also analyze the local stability conditions of the dynamic neuron model. Simulation results show that our proposed algorithm is a competitive alternative for waveform design with unit modulus and arbitrary spectral shapes.