A Fast Eigen Solution for Homogeneous Quadratic Minimization with at most Three Constraints

We propose an eigenvalue based technique to solve the Homogeneous Quadratic Constrained Quadratic Programming problem (HQCQP) with at most 3 constraints which arise in many signal processing problems. Semi-Definite Relaxation (SDR) is the only known approach and is computationally intensive. We study the performance of the proposed fast eigen approach through simulations in the context of MIMO relays and show that the solution converges to the solution obtained using the SDR approach with significant reduction in complexity.Comment: 15 pages, The same content without appendices is accepted and is to be published in IEEE Signal Processing Letter

Relay Hybrid Precoding Design in Millimeter-Wave Massive MIMO Systems

This paper investigates the relay hybrid precoding design in millimeter-wave (mmWave) massive MIMO systems. The optimal design of the relay hybrid precoding is highly nonconvex, due to the six-order polynomial objective function, sixorder polynomial constraint, and constant-modulus constraints. To efficiently solve this challenging non-convex problem, we first reformulate it into three quadratic subproblems, where one of the subproblems is convex and the other two are non-convex. Then, we propose an iterative successive approximation (ISA) algorithm to attain the high-approximate optimal solution to the original problem. Specifically, in the proposed ISA algorithm, we first convert the two non-convex subproblems to convex ones by the relaxation of the constant-modulus constraints, and then we solve the three corresponding convex subproblems iteratively. We theoretically prove that the ISA algorithm converges to a KarushKuhn-Tucker (KKT) point of the original problem. Simulation results demonstrate that the proposed ISA algorithm achieves good performance in terms of achievable rate in both fullconnected and sub-connected relay hybrid precoding systems

Multi-antenna relay network beamforming design for multiuser peer-to-peer communications.

In this work, we consider a multi-user peer-to-peer relay network with multiple multiantenna relays which employ amplify-and-forward relaying protocol. Assuming distributed relay beamforming strategy, we investigate the design of each relay processing matrix to minimize the per-antenna relay power usage for given users??? Signal-to-Noise Ratio (SNR) targets. As the problem is NP-hard, we develop an approximate solution through the Lagrange dual domain. Through a sequence of transformations, we obtain a semi-closed form solution which can be determined by solving an efficient semi-definite programming problem. We also consider the semi-definite relaxation (SDR) approach. Compared with this SDR approach, the proposed solution has significantly lower computational complexity. The benefit of such a solution is apparent when the optimal solution can be obtained by both approaches. When the solution is suboptimal, simulations show that the SDR approach has better performance. Thus, we propose a combined method of the two approaches to trade-off performance and complexity. Simulations showed the effectiveness of such a combined method. In the next step, we change the previous objective and constraints to turn the optimization problem into a total power minimization problem for the relay network. We use an approximation by solving this problem in the Lagrange dual domain, and we finally obtain a semi-closed form solution through the dual approach. The use of the SDR approach to solve this problem is also discussed. After analysis, we find the two methods have an advantage over different aspects, thus we propose a combined method for this problem. We eventually compare the two combined methods to see the performance difference in the per-antenna power case and the total relay power case, and discuss reasons for this difference

Adaptive Beamforming for Distributed Relay Networks

Tremendous research work has been put into the realm of distributed relay networks, for its distinct advantages in exploiting spatial diversity, reducing the deployment cost and mitigating the effect of fading in wireless transmission without the multi-antenna requirement on the relay nodes. In typical relay networks, data transmission between a source and a destination is assisted by relay nodes with various relaying protocols. In this thesis, we investigate how to adaptively select the relay weights to meet specific interference suppressing requirements of the network. The thesis makes original contributions by proposing a filter-and-forward (FF) relay scheme in cognitive radio networks and an iterative algorithm based transceiver beamforming scheme for multi-pair relay networks. In the firstly proposed scheme, the relay nodes are adapted to deal with the inter-symbol-interference (ISI) that is introduced in the frequency-selective channel environment and the leakage interference introduced to the primary user. Our proposed scheme uses FF relay beamforming at the relay nodes to combat the frequency selective channel, and our scheme also aims to maximize the received SINR at the secondary destination, while suppressing the interference introduced to the primary user (PU). This scheme is further extended to accommodate a relay nodes output power constraint. Under certain criteria, the extended scheme can be transformed into two sub-schemes with lower computational complexity, where their closed-form solutions are derived. The probability that we can perform these transformations is also tested, which reveals under what circumstances our second scheme can be solved more easily. Then, we propose an iterative transceiver beamforming scheme for the multi-pair distributed relay networks. In our scheme, we consider multi-antenna users in one user group communicating with their partners in the other user group via distributed single-antenna relay nodes. We employ transceiver beamformers at the user nodes, and through our proposed iterative algorithm the relay nodes and user nodes can be coordinatively adapted to suppress the inter-pair-interference (IPI) while maximize the desired signal power. We also divide the rather difficult transceiver beamforming problem into three sub-problems, each of which can be solved with sub-optimal solutions. The transmit beamforming vectors, distributed relay coefficients and the receive beamforming vectors are obtained by iteratively solving these three sub-problems, each having a closed-form solution. The tasks of maximizing desired signal power, and reducing inter-pair interference (IPI) and noise are thus allocated to different iteration steps. By this arrangement, the transmit and receiver beamformers of each user are responsible for improving its own performance and the distributed relay nodes can be employed with simple amplify-and-forward(AF) protocols and only forward the received signal with proper scalar. This iterative relay beamforming scheme is further extended by distributing the computation tasks among each user and relay node, through which high computational efficiency can be ensured while extra overhead of bandwidth is need for sharing beamforming vector updates during the iteration steps. Furthermore, with respect to the channel uncertainty, two more relay strategies are proposed considering two different requirements from the communication network: sum relay output power and individual relay output power. At last, the application of the iterative relay beamforming method in cognitive radio networks is studied, where multiple pairs of users are considered as secondary users (SUs), and the designed transmit beamforming vector, relay beamforming vector and receive beamforming vector together guarantee that the inner interference of their transmissions is well suppressed while the interference introduced by them to the PU is restricted under a predefined threshold