On the Sublinear Behavior of MIMO Channel Capacity at Low SNR

We consider wideband wireless communication over a multiple-input, multiple-output (MIMO) Rayleigh fading channel where the transmitter has no channel state information (CSI). We study the channel with perfect receiver CSI (coherent channel) versus the channel with no CSI at the receiver (non-coherent channel). A channel with partial CSI at the receiver has a capacity between the coherent and non-coherent channels and in this paper, we study the two extremes. The capacities of the coherent and non-coherent channels differ in their sublinear term and in [6], Verdú computed the sublinear term of the coherent channel and gave a lower bound for the sublinear term of the noncoherent channel. However, without an upper bound for this term, we cannot quantify the loss in capacity (or increase in bandwidth required) due to lack of receiver CSI. In this paper, we compute an upper bound for the sublinear term of the non-coherent MIMO channel and show that it is approximately O(SNR). We therefore quantify the maximum penalty for not having CSI at the receiver. For the i.i.d. Rayleigh fading channel, we study the effect of the number of receive antennas on the loss in capacity due to not having CSI at the receiver. We show that this loss increases monotonically with the number of receive antennas. Therefore, as the number of receive antennas increases, channel estimation becomes more and more important. This also shows that the capacity increase due to power gain from the additional receive antennas is more if we know the additional paths at the receiver.