In millimeter wave （mmWave） massive multiple-input multiple-output （MIMO） systems, because of the high hardware cost and high power consumption, the traditional fully digital beamforming （DBF） cannot be implemented easily. Meanwhile, analog beamforming which is implemented with phase shifters has high availability but suffers poor performance. Considering the advantages of above two, a potential solution is to design an appropriate hybrid analog and digital beamforming structure, where the available iterative optimization algorithm can get performance close to fully digital processing, but solving this sparse optimization problem faces with a high computational complexity. The key challenge of seeking out hybrid beamforming （HBF） matrices lies in leveraging the trade-off between the spectral efficiency performance and the computational complexity. In this paper, we propose an asymptotically unitary hybrid precoding （AUHP） algorithm based on antenna array response （AAR） properties to solve the HBF optimization problem. Firstly, we get the optimal orthogonal analog and digital beamforming matrices relying on the channel＇s path gain in absolute value by taking into account that the AAR matrices are asymptotically unitary. Then, an improved simultaneously orthogonal matching pursuit （SOMP） algorithm based on recursion is adopted to refine the hybrid combining. Numerical results demonstrate that our proposed AUHP algorithm enables a lower computational complexity with negligible spectral efficiency performance degradation.
In order to achieve accurate recovery signals under the underdetermined circumstance in a comparatively short time,an algorithm based on plane pursuit(PP) is proposed. The proposed algorithm selects the atoms according to the correlation between received signals and hyper planes, which are composed by column vectors of the mixing matrix, and uses these atoms to recover source signals. Simulation results demonstrate that the PP algorithm has low complexity and higher accuracy as compared with basic pursuit(BP), orthogonal matching pursuit(OMP), and adaptive sparsity matching pursuit(ASMP) algorithms.
Due to the high cost and power consumption of the radio frequency（RF） chains, it is difficult to implement the full digital beamforming in millimeter-wave（mm Wave） multiple-input multiple-output（MIMO） systems. Fortunately, the hybrid beamforming（HBF） is proposed to overcome these limitations by splitting the beamforming process between the analog and digital domains. In recent works, most HBF schemes improve the spectral efficiency based on greedy algorithms. However, the iterative process in greedy algorithms leads to high computational complexity. In this paper, a new method is proposed to achieve a reasonable compromise between complexity and performance. The novel algorithm utilizes the low-complexity Gram-Schmidt method to orthogonalize the candidate vectors. With the orthogonal candidate matrix, the slow greedy algorithm is avoided. Thus, the RF vectors are found simultaneously without any iteration. Additionally, the phase extraction is applied to satisfy the element-wise constant-magnitude constraint on the RF matrix. Simulation results demonstrate that the new HBF algorithm can make substantial improvements in complexity while maintaining good performance.
Hybrid beamforming（ HBF） technology becomes one of the key technologies in the millimeter wave（ mm Wave）mobile backhaul systems,for its lower complexity and low power consumption compared to full digital beamforming（ DBF）. Two structures of HBF exist in the mm Wave mobile backhaul system,namely,the fully connected structures（ FCS） and partially connected structures（ PCS）. However,the existing methods cannot be applied to both structures. Moreover,the ideal phase shifter is considered in some current HBF methods,which is not realistic. In this paper,a HBF algorithm for both structures based on the discrete phase shifters is proposed in the mm Wave mobile backhaul systems. By using the principle of alternating minimization,the optimization problem of HBF is decomposed into a DBF optimization problem and an analog beamforming（ ABF） optimization problem.Then the least square（ LS） method is enabled to solve the optimization model of DBF. In addition,the achievable data rate for both structures with closed-form expression which can be used to convert the optimization model into a single-stream beamforming optimization model with per antenna power constraint is derived. Therefore,the ABF is easily solved. Simulation results show that the performance of the proposed HBF method can approach the full DBF by using a lower resolution phase shifter.
We propose a novel source recovery algorithm for underdetermined blind source separation, which can result in better accuracy and lower computational cost. On the basis of the model of underdetermined blind source separation, the artificial neural network with single-layer perceptron is introduced into the proposed algorithm. Source signals are regarded as the weight vector of single-layer perceptron, and approximate ι~0-norm is taken into account for output error decision rule of the perceptron, which leads to the sparse recovery. Then the procedure of source recovery is adjusting the weight vector of the perceptron. What's more, the optimal learning factor is calculated and a descent sequence of smoothed parameter is used during iteration, which improves the performance and significantly decreases computational complexity of the proposed algorithm. The simulation results reveal that the algorithm proposed can recover the source signal with high precision, while it requires lower computational cost.
