On the relation between ordering metrics for ZF and MMSE successive detection in MIMO systems

Multiple-input multiple-output (MIMO) systems can improve the spectral efficiency of a wireless link, by transmitting several data streams simultaneously from different transmit antennas. However, at the receiver, multi-stream detection is needed for extracting the transmitted data streams from the received signals. This letter considers ordered successive detection (OSD) for multi-stream detection. OSD consists of several stages, and at each stage only one data stream is chosen to be detected among the remaining streams according to a specified ordering metric. OSD has been formulated using both the zero forcing (ZF) and minimum mean square error (MMSE) criteria. This letter clarifies the reason behind the superiority of OSD using the MMSE criterion to OSD using the ZF criterion through the investigation of the relation between their ordering metrics. For uncorrelated MIMO channels, we show that both ordering metrics yield the same performance for OSD using either ZF or MMSE criterion. Accordingly, the superiority of OSD using the MMSE criterion to OSD using the ZF criterion is clarified to be a direct result of the inherent superiority of MMSE nulling to ZF nulling, and to be independent of the ordering operation. Performance comparisons of OSD and maximum likelihood detection are also given for modulation schemes of different sizes.