SPOC: An Innovative Beamforming Method

We recently introduced SPOC (Spatial Processing: Optimized and Constrained) [1] as an innovative replacement for the spatial spectrum estimation traditionally done by beamformers. This work extends the method described in [1] by improving the formalism and presenting results with at-sea sonar data. Beamforming has traditionally been performed by conventional (CBF) or adaptive (ABF) processing. These both provide estimates of spatial spectrum in a given time interval (snapshot). A trade-off between detection and resolution governs CBF performance. ABF offers improvement by lessening the effects of interfering signals at each beam. This is done with an estimated covariance matrix which involves a trade-off in selecting the averaging interval. Long averaging times produce better estimates of the true covariance, but shorter intervals decrease the harmful impact of target dynamics. SPOC produces spatial spectrum estimates without using covariances. It considers an array of N sensors and a finite but large number of sources of energy L (L>>N) spanning the entire Direction of Arrival (DOA) space (–1≤cosθ≤1). SPOC is a constrained optimization approach to estimating the signals at each of the L DOAs (or "beams"). The complex-valued signals are constrained so that the superposition of the weighted steering vectors at each DOA plus the estimated noise equals the measured data. Many sets of signals generally satisfy the constraint so the minimum-energy set of signals is chosen. Mathematical details will appear in the full-length paper. As a preliminary demonstration of performance improvement over ABF, we compared APB-98 passive sonar data (system ABF) versus the same data processed using SPOC. The processing was done on every frequency bin at the system resolution and broadband processing done on both using the same standard "SPED CS" algorithm [2]. The passive broadband grams demonstrate that more contacts are visible with SPOC processing than with ABF. [1] R. Bethel, B. Shapo, and H. Van Trees, "Single Snapshot Spatial Processing: Optimized and Constrained," Sensor Array and Multichannel Signal Processing Workshop 2002 (SAM 2002) Proceedings, pp. 508–512. [2] M. Bono, R. Bethel, P. McCarty, and B. Shapo, "Subband Energy Detection Methods in Passive Array Processing," MIT Lincoln Laboratory ASAP Workshop Proceedings, 2001.