Piecewise Constant Doppler Algorithm: Performance Analysis, Further Simplification, and Motion Compensation

The piecewise constant Doppler (PCD) algorithm is a novel radar imaging process recently proposed for the generalized continuous-wave synthetic aperture radar (GCW-SAR). This article presents a detailed theoretical analysis on the PCD algorithm's performance and proposes a further complexity-reduced PCD algorithm with motion compensation (MOCO) suitable for practical applications. First, the difference between conventional SAR imaging and PCD imaging, i.e., the zeroth-order versus the first-order slant range approximation, is revealed. Exact ambiguity function expressions of the PCD imaging in range and azimuth directions, respectively, are then derived. An error function of the PCD imaging as compared with the ideal matched filtering method is further defined and shown to be a function of an image quality factor, which can be used to quantify the PCD imaging performance. Finally, a faster and more flexible imaging process, called decimated PCD algorithm, is proposed, by which the image azimuth spacing can be easily extended, and hence, the computational complexity can be significantly reduced. The decimated PCD implementation incorporated with the MOCO is developed for practical GCW-SAR applications, and its imaging error lower-bounded by the PCD imaging error function is analyzed accordingly. Simulation and experimental results validate the theoretical analysis of the PCD imaging and show that the decimated PCD algorithm can achieve a high imaging quality at low cost.