Are all basis updates for lattice-reduction-aided MIMO detection necessary?

The question in the title is relevant when considering lattice-reduction-aided MIMO detectors, which achieve the same diversity as the maximum-likelihood detector while exhibiting lower complexity. In this paper we examine if all basis updates, which account for the largest complexity contribution in the Lenstra, Lenstra, Lovasz lattice reduction algorithm, are necessary for lattice reduction in the context of MIMO detection. We first provide an abstract answer to this question in the form of an idealized experiment that demonstrates the potential for a large reduction in the number of basis updates even when spatial correlation is present. Encouraged by these results, we seek a practical answer to this question by formulating a joint lattice reduction and symbol detection algorithm based on successive interference cancellation. Experimental results of the proposed method demonstrate that on average only 10% to 25% of basis updates are necessary on average depending on the degree of spatial correlation. Therefore, the answer to the question in the title is an encouraging no.