Transceiver Design with Matrix-Version Water-Filling Solutions under Mixed Power Constraints

In this paper, we investigate the transceiver design under mixed power constraint in which for a given set of antennas, several subsets are constrained by sum power constraints while the other antennas are subject to individual power constraints. This kind of design includes transceiver designs under sum power constraint and per-antenna power constraint as its special cases. In particular, this design is of great importance for distributed antenna systems (DASs) with heterogeneous remote radio heads (RRHs) such as cloud radio access networks (C-RANs). In our work, we try to solve the optimization problem in an analytical way instead of relying on some famous software packages e.g., CVX or SeDuMi. First, the specific formula of the optimal signal covariance matrix has been derived. In order to compute the optimal solutions, both iterative and non-iterative solutions are proposed. The iterative solution achieved a better performance but it suffers several famous weakness such as initial value selection, convergence, etc. To overcome these weakness, a non-iterative solution is given. Interestingly the non-iterative solution can be interpreted as a matrix version water-filling solution extended from the well-known and extensively studied vector version. This solution has a much clear engineering meaning and suitable for practical implementation. Finally, simulation results demonstrate the accuracy of our theoretical results.