Combined K-Best sphere decoder based on the channel matrix condition number

It is known that sphere decoding (SD) methods can provide maximum-likelihood (ML) detection over Gaussian MIMO channels with lower complexity than the exhaustive search. Channel matrix condition number represents an important influence on the performance of usual detectors. Throughout this paper, two particular cases of a SD method called K-Best carry out a combined detection in order to reduce the computational complexity with predictable performance degradation. Algorithm selection is based on channel matrix condition number thresholding. K-Best is a suboptimal SD algorithm for finding the ML solution of a detection problem. It is based on a fixed complexity tree search, set by a parameter called k. The proposed receiver makes use of a low value of k while working with well-conditioned channels and switches to a higher value of k whether the channel gets worse. It is also presented practical algorithms for finding the 1-norm condition number of a given channel matrix and the condition number threshold selection. Finally an algorithm variant that switches between an ML SD and a linear detector is also evaluated.