On the Low SNR Capacity of MIMO Fading Channels With Imperfect Channel State Information

The capacity of multiple-input multiple-output (MIMO) Rayleigh fading channels with full knowledge of channel state information (CSI) at both the transmitter and the receiver (CSI-TR) has been shown recently to scale at low signal-to-noise ratio (SNR) essentially as SNR log(1/SNR), independently of the number of transmit and receive antennas. In this paper, we investigate the ergodic capacity of MIMO Rayleigh fading channel with estimated channel state information at the transmitter (CSI-T) and possibly imperfect channel state information at the receiver (CSI-R). Our framework can be seen as a generalization of previous works as it can capture the perfect CSI-TR as a special case when the estimation error variance goes to zero. In this paper, we mainly focus on the low SNR regime, and we show that the capacity scales as $(1-\alpha)$ SNR log(1/SNR), where $\alpha$ is the estimation error variance. This characterization shows the loss of performance due to error estimation over the perfect channel state information at both the transmitter and the receiver. As a by-product of our new analysis, we show that our framework can be also extended to characterize the capacity of MIMO Rician fading channels at low SNR with possibly imperfect CSI-T and CSI-R.

I. Introduction

MULTIPLE-INPUT MULTIPLE-OUTPUT (MIMO) systems have captured in the last two decades great interest as they have been shown to provide an increased spectral efficiency compared to the conventional wireless systems [1]– [17]. For an independent and identically distributed (i.i.d.) Rayleigh fading channel, the capacity scales linearly times compared to single-input single-output (SISO), where is the number of transmit antennas and is the number of receive antennas with perfect Channel State Information (CSI) at high signal-to-noise ratio (SNR) [1]– [3]. When perfect CSI is available at both the transmitter and at the receiver (CSI-TR), the capacity of MIMO channels is well known and has been widely studied in [1], [7], [18], [19].