Optimal Transmit Strategies for Multi-antenna Systems with Joint Sum and Per-antenna Power Constraints

Sammanfattning: Nowadays, wireless communications have become an essential part of our daily life. During the last decade, both the number of users and their demands for wireless data have tremendously increased. Multi-antenna communication is a promising solution to meet this ever-growing traffic demands. In this dissertation, we study the optimal transmit strategies for multi-antenna systems with advanced power constraints, in particular joint sum and per-antenna power constraints. We focus on three different models including multi-antenna point-to-point channels, wiretap channels and massive multiple-input multiple-output (MIMO) setups. The solutions are provided either in closed-form or efficient iterative algorithms, which are ready to be implemented in practical systems.The first part is concerned with the optimal transmit strategies for point-to-point multiple-input single-output (MISO) and multiple-input multiple-output (MIMO) channels with joint sum and per-antenna power constraints. For the Gaussian MISO channels, a closed-form characterization of an optimal beamforming strategy is derived. It is shown that we can always find an optimal beamforming transmit strategy that allocates the maximal sum power with phases matched to the complex channel coefficients. An interesting property of the optimal power allocation is that whenever the optimal power allocation of the corresponding problem with sum power constraint only exceeds per-antenna power constraints, it is optimal to allocate maximal per-antenna power to those antennas to satisfy the per-antenna power constraints. The remaining power is distributed among the other antennas whose optimal allocation follows from a reduced joint sum and per-antenna power constraints problem with fewer channel coefficients and a reduced sum power constraint. For the Gaussian MIMO channels, it is shown that if an unconstraint optimal power allocation for an antenna exceeds a per-antenna power constraint, then the maximal power for this antenna is used in the constraint optimal transmit strategy. This observation is then used in an iterative algorithm to compute the optimal transmit strategy in closed-form.In the second part of the thesis, we investigate the optimal transmit strategies for Gaussian MISO wiretap channels. Motivated by the fact that the non-secure capacity of the MISO wiretap channels is usually larger than the secrecy capacity, we study the optimal trade-off between those two rates with different power constraint settings, in particular, sum power constraint only, per-antenna power constraints only, and joint sum and per-antenna power constraints. To characterize the boundary of the optimal rate region, which describes the optimal trade-off between non-secure transmission and secrecy rates, related problems to find optimal transmit strategies that maximize the weighted rate sum with different power constraints are derived. Since these problems are not necessarily convex, equivalent problem formulation is used to derive optimal transmit strategies. A closed-formsolution is provided for sum power constraint only problem. Under per-antenna power constraints, necessary conditions to find the optimal power allocation are provided. Sufficient conditions, however, are available for the case of two transmit antennas only. For the special case of parallel channels, the optimal transmit strategies can deduced from an equivalent point-to-point channel problem. In this case, there is no trade-off between secrecy and non-secrecy rate, i.e., there is onlya transmit strategy that maximizes both rates.Finally, the optimal transmit strategies for large-scale MISO and massive MIMO systems with sub-connected hybrid analog-digital beamforming architecture, RF chain and per-antenna power constraints are studied. The system is configured such that each RF chain serves a group of antennas. For the large-scale MISO system, necessary and sufficient conditions to design the optimal digital and analog precoders are provided. It is optimal that the phase at each antenna is matched tothe channel so that we have constructive alignment. Unfortunately, for the massive MIMO system, only necessary conditions are provided. The necessary conditions to design the digital precoder are established based on a generalized water-filling and joint sum and per-antenna optimal power allocation solution, while the analog precoder is based on a per-antenna power allocation solution only. Further, we provide the optimal power allocation for sub-connected setups based on two properties: (i) Each RF chain uses full power and (ii) if the optimal power allocation of the unconstraint problem violates a per-antenna power constraint then it is optimal to allocate the maximal power for that antenna. The results in the dissertation demonstrate that future wireless networks can achieved higher data rates with less power consumption. The designs of optimal transmit strategies provided in this dissertation are valuable for ongoing implementations in future wireless networks. The insights offered through the analysis and design of the optimal transmit strategies in the dissertation also provide the understanding of the optimal power allocation on practical multi-antenna systems.