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

subspace is formed using the remaining L r eigenvector. The two matrices areformed as follows:65The interference eigenvalues are used to form an r x r matrix, Air , and the noiseeigenvalues are used to form an (L r) x (L — r) matrix, A ,as follows:Using Qr, Q A r , and 'A, the desired signal free R may be expressedEquation 3.8 is an estimate of the true covariance matrix R. For low rankinterference, R can be decomposed into interference and white noise contributionsas followswhere the diagonal of the r x r matrixconsists of the r principal (largest) eigenvalues of R, the columns of C2r are thecorresponding eigenvectors, o -2 is the variance of the white noise, and the columns ofare the remaining eigenvectors of R. The actual value of r is scenario dependent,but it is upper bounded by r < v — 1, for equidistant sampling in space andtime and for a perfectly calibrated array [17]. The spectral decomposition of Rin Equation 3.16 suggests a decomposition for the estimate R similar to Equation3.15. The noise eigenvalues of the true covariance matrix in Equation 3.16 are allthe same and given by the noise power a. However, the noise eigenvalues obtainedby decomposing the covariance matrix estimate R in Equation 3.15 are going to bespread over a range of power which depending on the sample support size used to