The RF-chain limited mimo system- part I: optimum diversity-multiplexing tradeoff

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 M_t) antennas and L_t (L_t les M_t) RF chains at the transmitter while M_r antennas and L_r (L_r les M_r) RF chains at the receiver. We obtain the fundamental D-M tradeoff as a function of M_t, M_r, and min(L_r, L_t). Referring to the special case where L_t = M_t) and L_r = M_r 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(L_r, L_t) = K = min(M_r, M_t), 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.