Principles of Modern Radar - Volume 2 1891121537

456 CHAPTER 10 Clutter Suppression Using Space-Time Adaptive Processingis actually a weight calculation method, it is compatible with reduced-dimension STAP.Post-Doppler, reduced-dimension STAP, as described herein, is especially attractive forimplementation.The last sections of this chapter consider a practical, end-to-end detection architectureincorporating STAP. Angle-Doppler estimation is discussed in this context. Some important,real-world issues concerning covariance matrix estimation challenges are given in thefinal section: we briefly define and discuss the implications of heterogeneous (culturallyvarying) and nonstationary (sensor-induced, angle-Doppler varying) clutter.10.1.3 Key Points• STAP is an adaptive implementation of an optimal, space-time filter.• The STAP weight vector has two key components. The first is an inverse of the unknown,interference covariance matrix containing information on clutter and jamming thatdegrade detection performance; the inverse mitigates their influence. The second is thespace-time steering vector used to integrate energy from a specified angle of arrival andDoppler frequency.• The STAP uses training data to estimate unknown, second-order interference statisticsto calculate the unknown weight vector.• Due to computational loading and limited training data, reduced-dimension STAP is apractical approach suited to real-world implementation.• A number of practical matters require careful consideration when implementing STAP,including methods to mitigate heterogeneous and nonstationary clutter.10.1.4 Notation and OperationsIn general, a boldface, lowercase variable indicates a vector quantity; a boldface, uppercasevariable indicates a matrix; and a variable with a caret is an estimate. Superscripts T orH applied to a vector or matrix denote the transpose or Hermitian (conjugate) transposeoperations.The notation a ∼ CN(μ a ,R a ) indicates that a is complex normal (Gaussian) withmean μ a and covariance matrix R a . The notation x ∈ C mx1 indicates x is an element of theset of complex vectors of dimension m× 1, while X ∈ C mxn indicates a matrix belongingto the set of complex matrices of dimension m × n. Also, [x] m or x m is the m-th elementof x,[X] m,n or X m,n is the m − n-th element of X,x k or X k represent the k-th realization ofthe given vector or matrix, and x k (n) is the n-th sample of the k-th realization (e.g., x k (n)might represent the vector of voltages measured at M antenna elements for the k-th rangeand n-th pulse). Also, {x m } P m=1 is the collection of column vectors, x 1, x 2 ,...,x P .The following linear algebraic operations are used: inner product, outer product,Kronecker (tensor) product, and Schur (Hadamard) product. The inner product describesthe output of a finite impulse reponse (FIR) filter. Given the weight vector w ∈ C Px1 anddata vector x ∈ C Px1 , the inner product defines the peak output of a P-tap FIR filter⎡ ⎤x 1w H x = [ w1 ∗ w2 ∗ ··· w ∗ ]x 2P ⎢ ⎥⎣ . ⎦ =x PP∑[w] ∗ m [x] m (10.2)m=1