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

74Figure 4.1 Reduced-rank MVBoutput SINR is given byinserting the expression for the RR-MVB weight vector, thewhere for notational convenience it is assumed that the target power is unity, σs² = 1.The reduced-rank GSC is shown in Figure 4.2. From the figure it is observedthat the output can be expressedwhere w c , the weight vector of the nonadaptive portion, is just the steering vectorw, = S, Wa is the adaptive weight, the matrix U is a full column rank transformation,and A is a transformation that blocks the look direction, As =0. Assuming that Ahas full column rank, and that s is the only vector in the null space of A, thedimensions of A are (N — 1) x N. Consequently, the rank reducing matrix U is(N — 1) x r. Multiple linear constraints can be incorporated in A resulting in a nullspace of dimension equal to the number of constraints. The equivalent GSC weightvector can be written asproblemThe vector w a, is found as the solution to the unconstrained optimization