Majorization and matrix-monotone functions in wireless communications
Foundations and Trends in Communications and Information Theory
Power Control in Wireless Cellular Networks
Foundations and Trends® in Networking
Weighted sum rate optimization for cognitive radio MIMO broadcast channels
IEEE Transactions on Wireless Communications
On power allocation for parallel Gaussian broadcast channels with common information
EURASIP Journal on Wireless Communications and Networking - Special issue on optimization techniques in wireless communications
On Gaussian MIMO BC-MAC duality with multiple transmit covariance constraints
ISIT'09 Proceedings of the 2009 IEEE international conference on Symposium on Information Theory - Volume 4
ISIT'09 Proceedings of the 2009 IEEE international conference on Symposium on Information Theory - Volume 4
Joint downlink transmit and receive beamforming under per-antenna power constraints
ICICS'09 Proceedings of the 7th international conference on Information, communications and signal processing
IEEE Transactions on Signal Processing
Secure transmission with multiple antennas: part II: the MIMOME wiretap channel
IEEE Transactions on Information Theory
Optimal multiuser zero forcing with per-antenna power constraints for network MIMO coordination
EURASIP Journal on Wireless Communications and Networking - Special issue on multimedia communications over next generation wireless networks
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The sum capacity of a Gaussian vector broadcast channel is the saddle point of a minimax Gaussian mutual information expression where the maximization is over the set of transmit covariance matrices subject to a power constraint and the minimization is over the set of noise covariance matrices subject to a diagonal constraint. This sum capacity result has been proved using two different methods, one based on decision-feedback equalization and the other based on a duality between uplink and downlink channels. This paper illustrates the connection between the two approaches by establishing that uplink-downlink duality is equivalent to Lagrangian duality in minimax optimization. This minimax Lagrangian duality relation allows the optimal transmit covariance and the least-favorable-noise covariance matrices in a Gaussian vector broadcast channel to be characterized in terms of the dual variables. In particular, it reveals that the least favorable noise is not unique. Further, the new Lagrangian interpretation of uplink-downlink duality allows the duality relation to be generalized to Gaussian vector broadcast channels with arbitrary linear constraints. However, duality depends critically on the linearity of input constraints. Duality breaks down when the input constraint is an arbitrary convex constraint. This shows that the minimax representation of the broadcast channel sum capacity is more general than the uplink-downlink duality representation