A gradient descent implementation of adaptive pulse compression

Gradient descent is an iterative method of determining the minima or maxima of a function. The algorithm can be used to solve a linear system of equations when the computational cost of a matrix inverse is too expensive for an application. Here, gradient descent is applied to Adaptive Pulse Compression (APC), yielding the GraD-APC algorithm. Specifically, a unit-gain constrained version of GraD-APC with optimal step size is derived for use with frequency modulated (FM) waveforms, particularly for cases in which the waveform time-bandwidth product is large enough to prohibit practical use of the original matrix inverse based APC. The range-profile estimation of GraD-APC is compared to that of fully adaptive APC using both simulated and experimentally measured data.