On using the logarithmic number system for finite wordlength matrix inversion

Matrix inversion is a key operation in for instance adaptive filters and MIMO communication system receivers. For ill-conditioned channel matrices long wordlengths are required for fixed-point implementation of matrix inversion. In this work, the wordlength/error trade-offs for matrix inversion using different algorithms with fixed-point and logarithmic number systems (LNS) are considered. LNS provides higher resolution for small numbers and a larger dynamic range. Also, it will alter the cost of the basic operations in the algorithms. The results show that also the wordlength required to achieve a comparable error differ significantly between different algorithms and for most algorithms is reduced for LNS compared to fixed-point.