This paper studies the instantaneous rate maximization and the weighted sum
delay minimization problems over a K-user multicast channel, where multiple
antennas are available at the transmitter as well as at all the receivers.
Motivated by the degree of freedom optimality and the simplicity offered by
linear precoding schemes, we consider the design of linear precoders using the
aforementioned two criteria. We first consider the scenario wherein the linear
precoder can be any complex-valued matrix subject to rank and power
constraints. We propose cyclic alternating ascent based precoder design
algorithms and establish their convergence to respective stationary points.
Simulation results reveal that our proposed algorithms considerably outperform
known competing solutions. We then consider a scenario in which the linear
precoder can be formed by selecting and concatenating precoders from a given
finite codebook of precoding matrices, subject to rank and power constraints.
We show that under this scenario, the instantaneous rate maximization problem
is equivalent to a robust submodular maximization problem which is strongly NP
hard. We propose a deterministic approximation algorithm and show that it
yields a bicriteria approximation. For the weighted sum delay minimization
problem we propose a simple deterministic greedy algorithm, which at each step
entails approximately maximizing a submodular set function subject to multiple
knapsack constraints, and establish its performance guarantee.Comment: 37 pages, 8 figures, submitted to IEEE Trans. Signal Pro