Design of single user limited feedback systems

The available channel state information (CSI) in a limited feedback system like the frequency division duplex (FDD) downlink is not perfect since it is subject to estimation, quantization and feedback errors, and in addition, can be outdated. Despite the fact that the capacity of limited feedback systems is unknown in general, we derive a novel lower bound on the capacity of single user limited feedback systems with imperfect CSI. Based on this bound, we propose the design of an FDD system by finding the optimum training and number of feedback bits. To this end we also take the FDD uplink into account, since practical FDD systems represent two-way systems. We also provide closed-form approximations for the optimum downlink training, uplink training and number of feedback bits which basically maximize lower bounds on the FDD downlink and uplink capacity with imperfect CSI.