Scale effect analysis of early-termination fixed-complexity sphere detector

In this paper, we show that the early-termination fixed-complexity sphere detector (ET-FSD) has a scale effect when being employed in multi-antenna systems that have to detect signals of multiple users under the constraint of sum complexity. The so-called scale effect stands for a kind of effect in which the complexity per user can be reduced as the number of users increases without loss of diversity order. The main contributions of this study are as follows: (1) we establish a mathematical model based on the large deviation principle to apply the concept of scale effect to ET-FSD; (2) we prove the existence of the scale effect of ET-FSD in a multi-user scenario; and (3) we demonstrate that within multi-user systems, the scale effect can be exploited to realize ET-FSD that has the optimal performance in the point view of diversity order under polynomial complexity constraint per user.