Space/time/frequency methods in adaptive radar - New Jersey ...

CHAPTER 3SPACE-TIME ADAPTIVE PROCESSING SIGNAL ENVIRONMENTThis chapter serves as a brief review of related work. It also presents the definitionsand mathematical model of the signals used throughout the remainder of thechapters. The Sample Matrix Inversion (SMI), Generalized sidelobe canceler (GSC),Eigencanceler, and fixed transforms are all introduced. Target cancellation occurswhen the target signal is present during training, when the estimation of the noisecovariance matrix occurs and also when there are calibration errors. Conceptsrelated to this topic are also introduced.3.1 Signal ModelConsider a space-time array with v antennas uniformly spaced and a transmissionof a coherent burst of K, pulses at a constant pulse repetition frequency (PRF). Thetime over which n returns are collected is referred to as the coherent pulse interval(CPI) (Figure 3.1). Data is collected from a 3D data cube which consists of theantenna elements, pulses of the CPI, and range returns as shown in Figure 3.2. Thedetermination as to whether a target is present at a range of interest is the goal of thesignal processing. To that end, an N v x n snapshot consisting of the 2D data sliceat the range of interest, is processed to yield a decision statistic, which subsequentlyis compared to a threshold. Processing is carried out in the N dimensional signalspace resulting from stacking the snapshot column-wise. Radar detection is a binaryhypothesis problem, where hypothesis H o corresponds to target absence and H 1corresponds to target presence. Under hypothesis Ho , the N x 1 received vector xconsists only of clutter c and noise v contributions:60