Spatial multiplex in downlink multiuser multiple-antenna wireless environments

The paper studies the optimal spatial multiplexing scheme in a downlink multiple-antenna environment with perfect transmitter and receiver channel knowledge. Using recent results on the sum capacity of the Gaussian vector broadcast channel, the optimal number of precoded data streams in a downlink channel is characterized. The main result is the following: the sum-capacity achieving transmission strategy in a random downlink channel with n transmit antennas at the base-station and K receivers each equipped with m antennas involves between n and 1/2 n(n+1) data streams in total, with each user receiving between m and 1/2 m(m+1) data streams. This gives a dimension counting interpretation for multiuser diversity. In particular, it shows that the throughput maximizing transmission strategy in a downlink channel with n transmit antennas should involve between n and 1/2 n(n+1) active users at any time.