Method and apparatus for determining an inverse square root of a given positive-definite hermitian matrix

Abstract

Generally, a method and apparatus are provided for computing a matrix inverse square root of a given positive-definite Hermitian matrix, K. The disclosed technique for computing an inverse square root of a matrix may be implemented, for example, by the noise whitener of a MIMO receiver. Conventional noise whitening algorithms whiten a non-white vector, X, by applying a matrix, Q, to X, such that the resulting vector, Y, equal to Q·X, is a white vector. Thus, the noise whitening algorithms attempt to identify a matrix, Q, that when multiplied by the non-white vector, will convert the vector to a white vector. The disclosed iterative algorithm determines the matrix, Q, given the covariance matrix, K. The disclosed matrix inverse square root determination process initially establishes an initial matrix, Q, by multiplying an identity matrix by a scalar value and then continues to iterate and compute another value of the matrix, Q, until a convergence threshold is satisfied. The disclosed iterative algorithm only requires multiplication and addition operations and allows incremental updates when the covariance matrix, K, changes.