Efficient parallel computation of the estimated covariance matrix

Computation of a signal´s estimated covariance matrix is an important building block in signal processing, e.g., for spectral estimation. It involves a sliding window over an input matrix, and the summation of products to construct any given output-matrix element. Any given product contributes to multiple output elements, thereby complicating parallelization. We present a novel algorithm that attains very high parallelism without repeating multiplications or requiring inter-core synchronization. Key to this is the assignment to each core of distinct diagonal segments of the output matrix, selected such that no multiplications need be repeated, and exploitation of a shared memory (including L1 cache) that obviates the need for a corresponding awkward partitioning of the memory among cores. Implementation on Plurality´s shared memory many-core architecture and, in order to demonstrate additional benefits, also on the x86, reveals linear speedup and a 130-fold power-performance advantage over x86.