The Diversity-Multiplexing Tradeoff of RF Chain Limited MIMO System with Antenna Selection: Part I Theoretical Framework

The large gain promised by the multi-input multi-output (MIMO) technology comes with a cost. In particular multiple analog radio frequency (RF) chains, which are expensive and power consuming, are required at both the transmitter and receiver sides. On the other hand, the antennas connecting to the RF chains are less expensive. Hence one engineering compromise is to implement more antennas than RF chains and to use only a subset of them based on some antenna selection (AS) algorithm. An interesting question therefore arises: given a RF chain limited MIMO system, what is the fundamental performance gain by adding more antennas. In this two-part paper, we answer this question by using the diversity-multiplexing (D-M) gain tradeoff metric. Consider a Rayleigh fading channel with Mt antennas and Lt (Lt ≤ Mt) RF chains at the transmitter while Mr antennas and Lr (Lr ≤ Mr) RF chains at the receiver. We obtain the fundamental D-M tradeoff as a function of Mt, Mr, and min(Lr, Lt). Referring to the special case where Lt = Mt and Lr = Mr as the RF unlimited system (or full system) and RF limited system (or pruned system) otherwise, we prove that the pruned system with optimal channel-dependent AS has the same D-M tradeoff as the full system if the multiplexing gain is less than some integer threshold P , while it suffers from some diversity gain loss for multiplexing gains larger than P . In particular, if min(Lr, Lt) = K , min(Mr,Mt), then P = K, i.e. the D-M tradeoffs of the pruned system and the full system are the same. Moreover, this result can be extended to more general fading channels such as Nakagami channel. A fast and D-M tradeoff-optimal AS algorithm is proposed as a byproduct of our analysis. Index Terms MIMO, antenna selection, diversity gain, spatial multiplexing gain, tradeoff, outage probability. This work is supported in part by NSF Grants CCF-0423842 and CCF-0434410. The authors are with the Department of Electrical and Computer Engineering, University of Colorado, Boulder, CO 80309-0425 USA (e-mail: [email protected]; [email protected].) The material of this paper was presented in Asilomar Conference on Signals, Systems, and Computers 2006, IEEE International Conference on Communications 2007, and IEEE International Symposium on Information Theory 2007.