Reducing the Computational Complexity for BLAST by Using a Novel Fast Algorithm to Compute an Initial Square-Root Matrix

We propose a fast algorithm to compute an initial triangular square-root of the estimation error covariance matrix for BLAST, which are then applied to develop a square-root algorithm for BLAST. The speedups of our square-root BLAST algorithm over the previous square-root BLAST algorithm in the number of multiplications and additions are 3.78-5.8 and 3.95-5 respectively, and the ratios between the computational complexity of our BLAST algorithm and that of the linear MMSE detection algorithm in the number of multiplications and additions are 1.10-0.71 and 0.90-0.71 respectively, which means that for the first time, the nonlinear MMSE BLAST detector with successive interference cancellation can have even lower complexity than the linear MMSE detector. Moreover, our BLAST algorithm is also numerically stable and hardware friendly, since it uses unitary transformations to avoid the matrix inversions, and gets the initial square-root which is equivalent to a Cholesky factor of the estimation error covariance matrix.