The Effect of Training-Based Channel Estimation on the Capacity of Closed-Loop MIMO Systems with Imperfect CSI Feedback

In this paper, we study the influence of training-based channel estimation on the information-theoretic capacity of closed-loop MIMO systems with imperfect channel state information (CSI) feedback. First, a lower bound on capacity is formulated as a function of various parameters such as received signal-to-noise ratio, number of training symbols, feedback delay time, and the feedback noise variance. Next, we maximize the bound by obtaining the optimal allocation of power for training and data along with the optimal training interval. Fair comparison, through simulation, is also made with the maximized capacity of an open-loop MIMO system. An increase in capacity is still observed over the open-loop capacity for low to mid values of SNR. However, as the result of the imperfect feedback, the open-loop system has higher capacity that the closed-loop system for high SNR. This contribution helps sets the scene for looking at the realizable capacity, which involves the details of a specific communication system.