Random Unitary Beamforming with Partial Feedback for MISO Downlink Transmission Using Multiuser Diversity

In this paper, we study the problem of downlink transmission in multiple-input-single-output (MISO) wireless communication systems using multiuser diversity. There are $M$ antennas at the base station (BS) and $K$ single-antenna receivers. The performance of multiuser diversity depends on the number of users that have independent channel realizations. It is well known that increasing the number of users improves the performance at the expense of increasing feedback that is proportional to the number of users. For sufficiently large $K$, the capacity scales like $M\log \log K$. When $K$ is large, increasing feedback limits practical applications of the multiuser diversity. Our approach is to reduce the feedback by selecting a threshold for the $\ell _{\infty}$-norm of the normalized cross-correlation $(\Vert {\bf z}_{k}\Vert _{\infty })$ between the users' channel and the beamforming matrix based on the random unitary beamforming. The average amount of feedback per time slot is $d$ real numbers and $d$ integers which does not change with $K$. To improve fairness, an equal ratio scheduling algorithm which could serve the users with different rate requirements is developed. Monte Carlo simulation results is provided to verify the performance of the proposed algorithm.