A multistage STAP CFAR detection technique

Short Data Record Adaptive Filtering: The Auxiliary-Vector Algorithm

“…Interestingly, the AV estimators w n from n = 4 to 7 outperform in MS-error the best possible DL-SMI estimator ( 3.45). Finally, a finite set of L filter estimators with varying bias-covariance balance can be obtained through the use of the orthogonal multistage filter decomposition procedure in [9,10] (the resulting filters have been also referred to as nested Wiener filters). It can be shown theoretically that the l-stage filter, w l-stage , 0 ≤ l ≤ L − 1, is equivalent to the following structure.…”

“…It can be shown theoretically that the l-stage filter, w l-stage , 0 ≤ l ≤ L − 1, is equivalent to the following structure. First, change the auxiliary-vector generation recursion in (9) or Fig. 2 to impose orthogonality not only with respect to the constraint vector v but also with respect to all previously defined auxiliary vectors y 1 , y 2 , .…”

“…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).…”

“…10, we plot the BER 5 of the AV filter estimators w n 1 (M) and w n 3 (M) as a function of the SNR of the user of interest for data records of size M = 230. The BER curve of the genie-assisted maximum SINR optimum filter choice w n opt (M) as well as the corresponding curves of the ideal MMSE-MVDR filter w MMSE/MVDR , the SMI filter estimator w ∞ (M), the S-T RAKE matched filter (MF) w 0 (M) = v 1 , and the multistage filter [9,10] with the preferred number of stages 6 l = 7 are also included for comparison purposes. We observe that both w n 1 (M) and w n 3 (M) are very close to the genie optimum AV filter estimator choice and outperform significantly the SMI filter estimator, the multistage filter estimator, and the matched filter.…”

“…Starting from the 0-variance, high-bias (for nonwhite inputs) w 0 (M) = (ρ * / v 2 )v estimate, we can go all the way up to the unbiased, yet high-variance for small data record sizes M, w ∞ (M) estimate and anywhere in between, w n (M), 1 ≤ n < ∞. As a result, adaptive filters from this newly developed class can be seen to outperform in expected norm-square estimation error, E{ w(M) − w MMSE/MVDR 2 }, (constraint-) LMS [4], sample matrix inversion (SMI) [5] with or without diagonal loading [6], RLS-type [7,8], and orthogonal multistage decomposition (also called nested Wiener) [9,10] adaptive filter implementations. It is worth mentioning that the familiar trialand-error tuning to problem and data-record-size specifics of the real-valued LMS gain or RLS inverse matrix initialization constant or SMI diagonal loading parameter that plagues field practitioners is now replaced by an integer choice of one of the recursively generated filters.…”