Beamforming Design For Relay Assisted Millimeter Wave Systems

As a promising technique for the next generation of wireless communications,millimeterwave(mm Wave)communications have drawn extensive interests in the recent years.By utilizing large spectrum bands between 30 GHz and 300 GHz,mm Wave communications are capable of meeting the explosive growth of demanding in spectral efficiency and the connectivity among users.Further,the short wavelengths of mm Wave signals also facilitate the deployment of the massive multiple-input multiple-output(MIMO),which can efficiently improve the reception quality by achieving high antenna gain.On the other hand,as the mm Wave signals undergo severe path loss,penetration loss,and blockage,the applications of mm Wave communications are limited in short-distance transmission.Specially,the non-line-of-sight(NLOS)scenario is a major challenge for mm Wave frequencies,due to the high propagation loss caused by blockage.The most recent research results show that the inherent drawbacks of mm Wave signals in NLOS scenarios can be overcomed by employing relay at mm Wave systems.In relay assisted mm Wave systems,the channels from the source to the relay and from the relay to the destination may be line-of-sight(LOS),which can significantly alleviate the negative impacts of blockage and penetration loss.Further,the massive MIMO can be employed at the source,the relay,and the destination,to compensate the path loss by achieving high antenna gain.Since the antenna gain is realized by the beamforming,the beamforming design is a key issue in the mm Wave relay systems.In this dissertation,the beamforming designs are investigated under several mm Wave communication scenarios.The main contributions of this dissertation are summarized as follows:1)For single-user mm Wave relay systems,the joint source-relay full-digital beamforming design is investigated.This joint beamforming problem is formulated as the maximization of achievable rate under the per-antenna power constraints at the source and the relay.As massive MIMO is employed in the considered mm Wave relay systems,the joint full-digital beamforming problem is a large-scale nonconvex problem.Due to this fact,the beamforming scheme and algorithms are proposed to solve this nonconvex problem as follows.First,the full-digital beamforming design problem is converted to a sparse problem by exploiting the sparse and low-rank structures of mm Wave channels.Second,this sparse problem is reformulated into two SDP subproblems with rank-one constraints,which are still nonconvex.Third,two algorithms are proposed to solve these two nonconvex SDP subproblems,namely,the random vector generation based interior-point method(RVG-IPM)and the lowrank based augmented Lagrangian function(LR-ALF)algorithms.Overall,the original rate maximization problem can be efficiently by iteratively solving these SDP subproblems via the two proposed algorithms.Specially,the proposed LR-ALF algorithm owns much lower computational complexity than the RVG-IPM algorithm due to the following facts: a)the LR-ALF algorithm examines the optimal solution in one-dimensional spatial signal space;b)this algorithm utilizes the sparse characteristics of the formulated problem and the complexity of the algorithm is depending on the number of non-zero elements in the problem;c)there is no additional auxiliary variables in the proposed LR-ALF algorithm.The LR-ALF can efficiently solve the beamforming design problem in mm Wave systems.Finally,the simulation results are presented to demonstrate that: a)both of the algorithms achieve good performances in terms of achievable rate;b)the proposed algorithms both achieve superior performances compared to the existing beamformer design algorithms;c)the LR-ALF algorithm is much faster than the RVG-IPM one with a slight decrease in performance.2)For the single-user mm Wave relay systems,a novel analog-digital hybrid beamforming is designed to reduce the power consumption and device complexity.Since the sub-connected structure can further reduce the hardware complexity and power consumption compared to the full-connected one,the hybrid beamforming is investigated under the sub-connected structures first.The goal of sub-connected hybrid beamforming design is to minimize the mean squared error(MSE)between the transmitted symbols at the source and the received signals at the destination under the power constraints at the source and the relay stations.However,this beamforming problem is highly nonconvex due to the presence of six-order polynomial objective function,six-order polynomial constraints,block-diagonal constraints,and constant-modulus constraints.For this sake,the original nonconvex problem is reformulated into three quadratic subproblems,where one of the subproblems is convex and the other two are nonconvex.Then,two algorithms are proposed,namely,the iterative successive approximation(ISA)algorithm and the phased-MSE(P-MSE)algorithm.The ISA algorithm attains the near-optimal solution of the original problem,while the P-MSE algorithm owns low computational complexity.Specifically,in the proposed ISA algorithm,first,the two nonconvex subproblems are converted to convex ones by the relaxation of the constant-modulus constraints,and then,the three corresponding convex subproblems are solved iteratively.Further,the ISA algorithm can also be extended to solve the hybrid beamforming problem under full-connected structures.It is theoretically proved that the ISA algorithm converges to a Karush-Kuhn-Tucker(KKT)point of the original beamforming problem.In the proposed P-MSE algorithm,the hybrid beamformers are obtained without iteratively computing,indicating that the complexity of P-MSE algorithm is much lower than that of the I-SA algorithm.Simulation results demonstrate that,a)the proposed ISA algorithm achieves superior performance in terms of achievable rate for both full-connected and sub-connected structures;b)the P-MSE algorithm can be applied into sub-connected structures,which is lower in computational complexity with a bit performance degradation.3)For multi-user mm Wave relay systems,the source-relay-users hybrid beamforming design is investigated.The hybrid beamforming problem is formulated as maximizing the sum rate under the power constraints at the source and the relay.The original sum rate maximization problem consists of nonconvex objective and constraint functions,which is difficult to be solved by the existing algorithms.For this sake,the original problem is reformulated as the minimization of the MSE between the received signal of the hybrid and the full-digital beamforming designs.Then,the full-digital beamforming matrices of the source,the relay,and each user are obtained by the well known block diagonalization(BD)approach.Finally,the hybrid beamformings of the source,relay and each user are designed by exploiting compressive sensing techniques.Simulation results confirm that the proposed hybrid beamforming design achieves performance very close to the traditional full-digital one.