Diversity Order of MMSE Single-Carrier Frequency Domain Linear Equalization

In this paper we investigate the diversity order of single-carrier frequency domain equalizers (SC-FDE). Specifically, we look at minimum mean square error (MMSE) linear equalizers utilizing block-transmission and cyclic prefix. It is shown that the diversity order in these systems depends on data transmission rate, channel memory length, as well as transmission block length. Analyses reveal that with memory length v and transmission block length L, for the rates Rleslog L/v full diversity of v+1 is achievable. For higher rates the achievable diversity order is degraded and is equal to [2^-R L]+1. Therefore MMSE SC-FDE has a diversity that varies between 1 and v+1, and achieves full diversity only for a limited range of data rates.