The RF-Chain Limited MIMO System: Part II Case Study of V-BLAST and GMD

In Part I of this paper, we have established the fundamental D-M tradeoff of a RF-chain limited MIMO system as a function of transmitting antenna number Mt, receiving antenna number Mr, and N , min(Lt, Lr) where Lt and Lr are the numbers of the RF-chains at the transmitter and receiver respectively. Here we continue the investigation by studying two interesting schemes, i.e., the vertical bell-labs layered space time (V-BLAST) and the geometric mean decomposition (GMD) transceiver design, both applied to a RF-chain limited MIMO system with optimal antenna selection (AS). The V-BLAST scheme is popular in that it can achieve high spectral efficiency with simple scalar coding/decoding. However, it is also known to have maximal diversity gain only Mr − Mt + 1 when applied to a full Mr × Mt system. In this paper, we show that with optimal antenna selection, the diversity gain of V-BLAST can be greatly improved i.e., it can achieve the D-M tradeoff dvb,p(r) = (Mr − N + 1)(Mt − N + 1)(1 − r N ). Due to the analogy between the V-BLAST scheme in a MIMO channel and the successive interference cancellation (SIC) detector in a multi-access channel (MAC), our result sheds lights on the benefits of opportunistic communications facilitated by finite rate feedback. The GMD scheme has the same receiver as V-BLAST. However, it exploits the channel state information at transmitter (CSIT) to perform some channel-dependent unitary precoding. We derive the D-M tradeoff of the GMD scheme applied to the RF-Chain limited system. The GMD scheme is shown to be significantly better than the V-BLAST, although it is still D-M tradeoff suboptimal in general.