Joint domain space-time adaptive processing with small training data sets

Short Data Record Adaptive Filtering: The Auxiliary-Vector Algorithm

“…are all constrained to be orthogonal to v, orthogonality among the auxiliary vectors is not imposed [20,21]. This is in sharp contrast to previous work that involved filtering with up to L − 1 orthogonal to each other and to v vectors [22][23][24], where L is the data input vector dimension. We observe, however, that successive auxiliary vectors generated by the above recursive conditional optimization procedures (8)- (10) …”

“…Details are given below. 3 Therefore, the multistage filter in [9,10] is identical to the filter w B as it appears in [22][23][24]. The multistage decomposition algorithm is a computationally efficient procedure for the calculation of this filter tailored to the particular structure of B H RB (tridiagonal matrix).…”

“…where p m is given by (23). The estimatorsσ 2 1 (n) andσ 2 2 (n) exhibit the following properties: (i) They are both biased and (ii)σ 2 2 (n) exhibits smaller MSE from the true value thanσ 2 1 (n).…”

Adaptive Antenna Array Receivers for Spread-Spectrum Signals in Non-Gaussian Noise

“…In [29] a maximum crosscorrelation criterion is proposed and q is selected as the vector that maximizes the magnitude of the cross-correlation (MCC) between the output of the constraint-vector (x) processed data and the auxiliary-vector (q) processed data. In [30][31][32] the AV method is generalized to processing with multiple auxiliary vectors that, together with the corresponding scalars, are obtained through conditional statistical optimization. The overall filter w is now approximated by w…”

“…. , µ d requires an explicit or implicit matrix inversion operation and is also investigated in [30][31][32]. In fact, the filter produced by unconditional vector optimization of the AV weights can be shown theoretically to be identical to the orthogonal multistage decomposition filter in [33].…”