Efficient phase-modulated waveform design for active sensing systems

This paper considers the unit energy phase-modulated (PM) waveform design in communications and radar. For a given scenario, the weighted integrated sidelobe level (WISL) of a waveform is often used as a metric to evaluate the performance of a system. The waveform design with the minimization of the WISL as the criteria is a high dimension search problem and the classical solution for the multi-dimension search is the gradient descent method. More over, a recent proposed weighted cyclic algorithm-new (WeCAN) algorithm which is implemented base on the fast Fourier transform (FFT) claimed to be computationally efflient than the gradient descent method. Put aside the computation burden however, the gradient descent method can often produce waveforms with smaller WISL than the WeCAN algorithm. Moreover, in some conditions the WeCAN algorithm can be still time consuming. To overcome these imperfections, we propose a new iterative algorithm for the optimizing problem that is even more efflient than the WeCAN. We compare the computational load of the proposed algorithm with that of the WeCAN by the numbers of their multiplication operations and illustrate the performance of the proposed algorithm via a numbers of numeric simulations.