Performance Of MIMO Channel MAT Program

Transmitter channel state information (CSIT) is crucial for the multiplexing gains offered by advanced interference management techniques such as multiuser multiple-input multiple-output (MIMO) and interference alignment. Most multiuser precoding techniques require accurate channel state information at the transmitter (CSIT) to maintain orthogonality between the users. Such techniques have proven quite fragile in time-varying channels because the CSIT obtained by feedback from the receiversis inherently imperfect due to quantization error and feedback delay. When the feedback delay is large compared to the channel coherence time, such a technique completely fails to achieve any multiplexing gain. An alternative approach recently proposed by Maddah-Ali and Tse (MAT) allows for significant multiplexing gain in the multi-input multi-output (MIMO) broadcast channel (BC) even with CSIT that is "completely stale", i.e., uncorrelated with the current channel state.In this paper, we have a detailed description of this approach, even in this case, the completely stale CSI is still very useful. The details are as follows:1. We show that in an MIMO broadcast channel with M transmit antennas and K receivers each with1receive antenna, when M≥(K,K/1+(1/2)+…+(1/k))(>1) degrees of freedom is achievable even when the feedback channel state is completely independent of the current channel state. But when M<K, MAT scheme is not the optimal scheme, we improve MAT scheme of the M=2, K=3case, then the optimal number of degrees of freedom is achievable.2. With M=K systerm, their scheme claims to lose only a log(K) factor relative to the full K degrees of freedom(DOF) attainable in the MIMO BC with perfect CSIT for large K. However, their result does not consider the cost of the feedback, which is potentially very large in high mobility (short channel coherence time). In this paper, we more closely examine the MAT scheme and compare its maximum net DOF gain to single user transmission and partial CSIT linear precoding. In particular, assuming the channel coherence time is N symbol periods and the feedback delay is Nfa, we show that when N<(1+o(1))KlogK(short coherence time), single user transmission performs best, whereas for N>(1+o(1))(Nfd+K/logK)(1-log-1K)-1(long coherence time), zero-forcing precoding outperforms the other two. The MAT scheme is optimal for intermediate coherence times, which for practical parameter choices is indeed quite a large and significant range, even accounting for the feedback cost.