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

by F. Benkhelifa, Z. Rezki, M. Alouini
Conference Proceedings Year: 2014


F. Benkhelifa, Z. Rezki, M. Alouini, On the Low SNR Capacity of MIMO Fading Channels with Imperfect Channel State Information,  in Proceedings IEEE  International Symposium on Mod el­ ing  and  O ptimization in  Mobile,  Ad Hoc and  Wireless N etworks  ( Wi0 pt'2014 ), Hammamet, Tunisia, 12-16 May  2014. 


​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 our work, we mainly focus on the low SNR regime and we show that the capacity scales as (1-α) SNR log(1=SNR), where α is the estimation error variance. This characterization shows the loss of performance due to error estimation over the perfect channel stateinformation at both the transmitter and the receiver. As a by-product of our new analysis, we show that our framework can also be extended to characterize the capacity of MIMO Rician fading channels at low SNR with possibly imperfect CSI-T and CSI-R.


DOI: 10.1109/WIOPT.2014.6850313


CSI-R CSI-T Ergodic capacity MIMO Rayleigh fading channel Rician fading channel channel estimation low SNR