High-SNR analysis of MIMO linear precoders

For linear MIMO precoders, the diversity is an important parameter affecting broad tradeoffs in system design, however, the diversity of many MIMO precoders has not been available in the open literature. This paper analyzes the diversity of the following MIMO precoders: the zero-forcing (ZF), regularized ZF, matched filtering and Wiener filtering. Several interesting properties of these precoders are revealed by this analysis. It is shown that regularized ZF (RZF) and the matched filter (MF) exhibit two-mode diversity: full diversity at low rates R and error floor at high rates. The rate threshold of this two-mode behavior is analytically determined. The Wiener precoder is also shown to produce a diversity that depends on the spectral efficiency and can be as small as one and as large as the product of the number of transmit and receive antennas.