Multiuser Downlink Beamforming Techniques forCognitive Radio Networks

Spectrum expansion and a significant network densification are key elements in meeting the ever increasing demands in data rates and traffic loads of future communication systems. In this context, cognitive radio (CR) techniques, which sense and opportunistically use spectrum resources, as well as beamforming methods, which increase spectral efficiency by exploiting spatial dimensions, are particularly promising. Thus, the scope of this thesis is to propose efficient downlink (DL) beamforming and power allocation schemes, in a CR framework. The methods developed here, can be further applied to various practical scenarios such as hierarchical multi-tier, heterogenous or dense networks. In this work, the particular CR underlay paradigm is considered, according to which, secondary users (SUs) opportunistically use the spectrum held by primary users (PUs), without disturbing the operation of the latter. Developing beamforming algorithms, in this scenario, requires that channel state information (CSI) from both SUs and PUs is required at the BS. Since in CR networks PUs have typically limited or no cooperation with the SUs, we particularly focus on designing beamforming schemes based on statistical CSI, which can be obtained with limited or no feedback. To further meet the energy efficiency requirements, the proposed beamforming designs aim to minimize the transmitted power at the BS, which serves SUs at their desired Quality-of-Service (QoS), in form of Signal-to-interference-plus-noise (SINR), while respecting the interference requirements of the primary network. In the first stage, this problem is considered under the assumption of perfect CSI of both SUs and PUs. The difficulty of this problem consists on one hand, in its non-convexity and, on the other hand, in the fact that the beamformers are coupled in all constraints. State-of-the-art approaches are based on convex approximations, given by semidefinite relaxation (SDR) methods, and suffer from large computational complexity per iteration, as well as the drawback that optimal beamformers cannot always be retrieved from the obtained solutions. The approach, proposed in this thesis, aims to overcome these limitations by exploiting the structure of the problem. We show that the original downlink problem can be equivalently represented in a so called ’virtual’ uplink domain (VUL), where the beamformers and powers are allocated, such that uplink SINR constraints of the SUs are satisfied, while both SUs and PUs transmit to the BS. The resulting VUL problem has a simpler structure than the original formulation, as the beamformers are decoupled in the SINR constraints. This allows us to develop algorithms, which solve the original problem, with significantly less computational complexity than the state-of-the-art methods. The rigurous analysis of the Lagrange duality, performed next, exposes scenarios, in which the equivalence between VUL and DL problems can be theroretically proven and shows the relation between the obtained powers in the VUL domain and the optimal Lagrange multipliers, corresponding to the original problem. We further use the duality results and the intuition of the VUL reformulation, in the extended problem of joint admission control and beamforming. The aim of this is to find a maximal set of SUs, which can be jointly served, as well as the corresponding beamforming and power allocation. Our approach uses Lagrange duality, to detect infeasible cases and the intuition of the VUL reformulation to decide upon the users, which have the largest contribution to the infeasibiity of the problem. With these elements, we construct a deflation based algorithm for the joint beamforming and admission control problem, which benefits from low complexity, yet close to optimal perfomance. To make the method also suitable for dense networks, with a large number of SUs and PUs, a cluster aided approach is further proposed and consists in grouping users, based on their long term spatial signatures. The information in the clusters serves as an initial indication of the SUs which cannot be simultaneously served and the PUs which pose similar interference constraints to the BS. Thus, the cluster information can be used to significantly reduce the dimension of the problem in scenarios with large number of SUs and PUs, and this fact is further validated by extensive simulations. In the second part of this thesis, the practical case of imperfect covariance based CSI, available at the transmitter, is considered. To account for the uncertainty in the channel knowledge, a worst case approach is taken, in which the SINR and the interference constraints are considered for all CSI mismatches in a predefined set One important factor, which influences the performance of the worst case beamforming approach is a proper choice of the the defined uncertainty set, to accurately model the possible uncertainties in the CSI. In this thesis, we show that recently derived Riemannian distances are better suited to measure the mismatches in the statistical CSI than the commonly used Frobenius norms, as they better capture the properties of the covariance matrices, than the latter. Therefore, we formulate a novel worst case robust beamforming problem, in which the uncertainty set is bounded based on these measures and for this, we derive a convex approximation, to which a solution can be efficiently found in polynomial time. Theoretical and numerical results confirm the significantly better performance of our proposed methods, as compared to the state-of-the-art methods, in which Frobenius norms are used to bound the mismatches. The consistently better results of the designs utilizing Riemannian distances also manifest in scenarios with large number of users, where admission control techniques must supplement the beamforming design with imperfect CSI. Both benchmark methods as well as low complexity techniques, developed in this thesis to solve this problem, show that designs based on Riemannian distance outperform their competitors, in both required transmit power as well as number of users, which can be simultaneously served.