Optimizing the Number of Feedback Users

In a multiuser broadcast channel with M antennas at the base station and K = M i.i.d. users, multiuser diversity can be exploited by optimally choosing a set of M users to serve simultaneously with linear beamforming. In order to perform the user selection, the base station requires channel state information (CSI) of all K users which is obtained through limited feedback in frequency division duplex (FDD) systems. In this work we assume the feedback consists solely of the channel direction information (CDI) of the users. Although most of the literature assumes a per-user limited feedback, a constraint on the system limited feedback is actually more appropriate. Given a constraint on the total amount of channel uses reserved for the feedback of all the users, we experience a tradeoff between the attainable degree of multiuser diversity and the CDI feedback quality. The optimum number of feedback users are determined based on a closed-form approximation of a lower bound on the sum rate achieved with user selection. It is shown that the optimum number of feedback users increases linearly with the total amount of channel uses reserved for the feedback of all the users.