Low Complexity Iterative Algorithm for Finding the MIMO-OFDM Broadcast Channel Sum Capacity

This paper provides a novel low complexity and provably convergent algorithm to find the sum capacity for vector Gaussian broadcast channels. We formulate the problem in the context of a MIMO-OFDM system and discuss the simplifications provided by the block diagonal channel structure. The algorithm also provides the optimum set of covariance matrices for the dual multiple access channel, from which the transmit covariance matrices for the broadcast channel are easy to compute. The key idea of the algorithm is to iteratively maximize the sum capacity for randomly selected pairs of users whilst considering the other users' signals as noise. The proposed algorithm can be considered dual to the iterative water filling (IWF) algorithm used to maximize the sum capacity for the multiple access channel with individual power constraints, but unlike the recently proposed sum power constraint IWF, our proposed algorithm has lower complexity and does not require additional precautions to ensure the convergence. We have proved analytically that the proposed algorithm is convergent in probability and the computer simulations clearly show that the proposed algorithm converges faster than other known algorithms. Index Terms—Broadcast channels, MIMO systems, orthogonal frequency division multiplexing, iterative water-filling.