Blind signal separation using BATCH and adaptive multilinear regression

This research deals with bilinear and trilinear regression problems arising in the context of blind digital signal separation in communications, and clutter mitigation/target Doppler estimation in radar. The emphasis is on the development of novel algorithms that build on multilinear regression ideas.; In the first part of this work, the problem of blindly separating co-channel digital transmissions received at an antenna array is considered. This is a basic problem in Space-Division Multiple Access (SDMA) that also arises under disguise in related contexts, e.g., CDMA multiuser detection. When little or nothing can be assumed about the mixing matrix, signal separation may be achieved by exploiting structural properties of the transmitted signals, e.g., finite alphabet or coding constraints. We propose a monotonically convergent and computationally efficient iterative least squares (ILS) blind separation algorithm based on an optimal scaling Lemma. The signal estimation step of the proposed algorithm is reminiscent of Successive Interference Cancellation (SIC) ideas. In many cases of practical interest, the proposed SIC-ILS algorithm provides a better performance/complexity tradeoff than competing ILS algorithms, namely iterative least squares with enumeration (ILSE) and iterative least squares with projection (ILSP). In particular, in the fully blind case with well-conditioned data and moderate SNR, or the semi-blind case (wherein limited training is available), SIC-ILS attains the bit error rate performance of ILSE at the complexity cost of ILSP. Coupled with blind algebraic digital signal separation methods like binary ACMA, SIC-ILS offers a computationally inexpensive true LS refinement option.; In the second part of this work, blind clutter mitigation and target Doppler estimation for airborne radar is considered. In radar systems that employ a uniform linear antenna array clutter statistics are quasi-stationary across range, and this can be exploited to derive Space-Time Adaptive Processing (STAP) algorithms that build on Wiener filtering ideas. Circular arrays offer several advantages over linear arrays, but invalidate the clutter quasi-stationarity assumption due to elevation dependence. Building on PARAllel FACtor (PARAFAC) analysis ideas, a new deterministic blind STAP algorithm is proposed that capitalizes on PARAFAC uniqueness properties to directly estimate the clutter's spatio-temporal profiles in the vicinity of a range gate of interest, thereby allowing effective clutter mitigation and target Doppler estimation. The proposed PARAFAC STAP shows very promising performance down to very low target to clutter ratios (−40dB), outperforming existing algorithms like PRSTAP. An adaptive implementation of PARAFAC STAP has also been developed, and it naturally suggests several interesting possibilities for further work in adaptive multilinear regression, which is of much broader interest than the application scope considered so far.