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

66estimate the covariance matrix. Noise exists at all frequencies and hence, an infinitenumber of degrees of freedom is needed to fully estimate the noise subspace. As thesample support size K increases, R approaches the true covariance matrix R andthe noise eigenvalues in A all converge towards the noise power a -2 .3.2 Beamforming TechniquesA brief review of previous and related work in the field of adaptive processing ofradar will now be presented.3.2.1 Non-Adaptive BeamformerThe non-adaptive beamformer uses the weight vectorwhere s is the presumed steering vector for the target. For a given angle and velocity,s has the form of Equation 3.6 or Equation 3.7. Amplitude tapering windowingfunctions maybe used on the steering vector to lower the sidelobes. When this is done,the width of the mainlobe is increased. The non-adaptive beamformer maximizesthe beamformer's output signal-to-noise ratio in the absence of interferences.3.2.2 Optimum Signal ProcessingBrennan and Reed[46] with Mallet [151147], developed the theory for optimumadaptive arrays which maximizes the probability of detection. It was shown that theoptimal detector for a signal in Gaussian noise is achieved by using a Wiener filterwhen the covariance matrix of the signal is known a priori. The weights of this filterare given by