Approximate Noise-Whitening in MIMO Detection via Banded-Inverse Extension

In this paper, we propose a novel approximate noise-whitening for multi-input multi-output (MIMO) detection with banded-inverse extension (BIE). If a noise covariance matrix origins from a Gauss-Markov process (GMP), its inverse is banded and the proposal is exact and yields no accuracy-losses. For general matrices to be inverted, the approximation-errors from inversion introduce a mismatched MIMO detection-model, which can cause performance-degradation. Hence, we develop an information-theoretic tool with generalized mutual information (GMI) to evaluate the impacts from approximation-errors on the final achievable rate. We show that the approximate noise-whitening method based on BIE not only minimizes the noise-distortion measured from the Kullback-Leibler (KL) divergence, but also asymptotically maximizes GMI of the MIMO system as signal-to-noise ratio (SNR) increases. Besides, the proposal also provides a unified framework for approximate matrix-inverse with an adjustable band-size that can tune the trade-off between complexity and accuracy.