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

摘要

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, Q₀, by multiplying an identity matrix by a scalar value and then continues to iterate and compute another value of the matrix, Q_n+1, 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.