Principles of Modern Radar - Volume 2 1891121537

484 CHAPTER 10 Clutter Suppression Using Space-Time Adaptive ProcessingTwo principal challenges when implementing the space-time processor include computationalloading, which is roughly cubic in the DoFs, and the limited availability ofsuitable training data (homogeneous training vectors of quantity at least twice the processor’sDoFs) to estimate the unknown interference-plus-noise covariance matrix. RD-STAPmethods given in this section address these challenges and are of practical significance.This section also briefly discusses reduced-rank STAP (RR-STAP) [21,22], which is aweight calculation method and can be used with the space-time data or RD-STAP methods.An integrated approach to estimate target angle and Doppler is also given, along withan overview of an end-to-end processing block diagram.10.6.1 Reduced-Dimension STAPIn the previous sections we described STAP as a two-dimensional, adaptive, linear filteroperating on M spatial channels and N pulses. This direct formulation is known as thejoint domain STAP. Critical joint domain STAP limitations include a need for substantialtraining sample support and high computational burden. In accord with the RMB rule,nominal training support is approximately 2NM; since typically 32 ≤ N ≤ 128 and6 ≤ M ≤ 10, training data can easily cover 384 to 2560 bins (for comparison, a typicalCFAR window covers from 30 to 40 bins to avoid variable clutter features). Additionally,computational burden associated with the SMI approach is O(N 3 M 3 ). To overcome theselimitations without affecting the space-time aperture (i.e., without reducing either N orM, thereby affecting the overall coherent gain), researchers have developed a variety ofSTAP techniques based on reducing the processor’s dimensionality without substantiallysacrificing performance. In this section of the paper we specifically focus on introducingthe reader to RD-STAP methods [4,5,23–25].In RD-STAP, typically a linear, frequency domain transformation projects the spacetimedata vector x k into a lower dimensional subspace. The transformed data vector is˜x k = T H x k ; T ∈ C NMxJ (10.89)where J ≪ NM and ˜x k has dimension J × 1. Computational burden associated withmatrix inversion drops from O(N 3 M 3 ) to O(J 3 ), and nominal sample support decreasesfrom 2NM to 2J. For example, the transformation may spatially or temporally beamformthe data; subsequently, taking advantage of the compressed nature of the clutter data inthe frequency domain (see Figure 10-10), the RD-STAP then selects several adjacentfrequency bins near the target angle and Doppler of interest as one approach to implementthe adaptive canceller. In other words, in RD-STAP, the processor aims to cancel cluttersignals in the vicinity of the target space-time response to aggregate the largest detectionperformance benefit. We will consider two illustrative example architectures momentarily.The J × J null-hypothesis covariance matrix corresponding to (10.89) is]˜R k = E[˜x k/H0 ˜x k/H H 0= T H R k T (10.90)Applying the same transformation to the space-time steering vector gives ˜s = T Hs s−t ( f sp , ˜f d ). The corresponding optimal weight vector is ˜w k = ˜β ˜R −1k ˜s, for arbitraryscalar ˜β. The adaptive solution involves calculating ˆ˜R k from (10.71) using the transformedtraining data set { T H } Px m , replacing ˜s with the hypothesized steering vector ṽ, andm=1