Scaling Laws of Multiple Antenna (Group) Broadcast Channels

Broadcast (or point to multipoint) communication has attracted a lot of research recently. In this talk we consider the scaling laws for two broadcast scenarios.

In the first part of the talk, we consider the effect of spatial correlation between transmit antennas on the sum-rate capacity of the MIMO broadcast channel (i.e., downlink of a cellular system). Specifically, for a system with a large number of users n, we analyze the scaling laws of the sum-rate for the dirty paper coding (DPC) and for different types of beamforming transmission schemes. When the channel is i.i.d., it has been shown that for large number of users n, the sum rate is equal to M*loglog(n) + M*log SNR where M is the number of transmit antennas. When the channel exhibits some spatial correlation with a covariance matrix R, we show that this results in an SNR hit that depends on 1) the multiuser broadcast technique and 2) on the eigenvalues of the correlation matrix R. We quantify this hit for DPC and various beamforming techniques.

In the second part of the talk, we consider the multiple antenna group broadcast channel where a base station is to transmit to a group of users and where the users' pool is divided into K groups, each group of which is interested in common information. Such a situation occurs for example in digital audio and video broadcast where the users are divided into various groups according to the shows they are interested in. We study the scaling laws of the sum-rate in the large number of users and/or large number of antennas regimes.  Intuitively, the group broadcast capacity should decrease with the number of users. We show that in order to achieve a constant rate per user, the number of transmit antennas should scale at least logarithmically with the number of users.

This is a joint work with Masoud Sharif (Boston University), Amir Dana (Qualcomm Corporation), and Babak Hassibi (California Institute of Technology)