A deterministic lower bound for the radius in sphere decoding search

In this paper we examine the problem of MIMO detection with sphere decoding (SD) methods. These methods obtain the Maximum Likelihood solution in a reasonable time, through restriction of the space search to an hypersphere of a given radius, with center in the received signal. The performance of the sphere decoding algorithms will be acceptable only if the initial radius estimate is close to the final, optimal radius. Here we give a nontrivial lower bound for the radius, based only on the received signal and on the channel matrix, being then a purely deterministic estimate. This lower bound can be successfully integrated in some SD algorithms, providing a substantial decrease of the computational cost of the search.