Multi-Resolution Codebook and Adaptive Beamforming Sequence Design for Millimeter Wave Beam Alignment

Abstract

Abstract-Millimeter wave (mmWave) communication is expected to be widely deployed in fifth generation (5G) wireless networks due to the substantial bandwidth available at mmWave frequencies. To overcome the higher path loss observed at mmWave bands, most prior work focused on the design of directional beamforming using analog and/or hybrid beamforming techniques in largescale multiple-input multiple-output (MIMO) systems. Obtaining potential gains from highly directional beamforming in practical systems hinges on sufficient levels of channel estimation accuracy, where the problem of channel estimation becomes more challenging due to the substantial training overhead needed to sound all directions using a high-resolution narrow beam. In this work, we consider the design of multi-resolution beamforming sequences to enable the system to quickly search out the dominant channel direction for single-path channels. The resulting design generates a multilevel beamforming sequence that strikes a balance between minimizing the training overhead and maximizing beamforming gain, where a subset of multilevel beamforming vectors is chosen adaptively to provide an improved average data rate within a constrained time. We propose an efficient method to design a hierarchical multiresolution codebook utilizing a Butler matrix, a generalized discrete Fourier transform (DFT) matrix implemented using analog RF circuitry. Numerical results show the effectiveness of the proposed algorithm.

Beam selection for performance-complexity optimization in high-dimensional MIMO systems

“…Previous approaches to reducing complexity, such as antenna selection, suffer from significant performance degradation [9]. Recent optimal approaches to BS have used strategies such as brute force optimization [10], sparse reconstruction [11], and iterative precoding using a hierarchical codebook [12], [13]. Although [10]- [13] present effective classifiers, they suffer from high computational complexity and training overhead.…”

Spectrum Sharing Backhaul Satellite-Terrestrial Systems via Analog Beamforming

“…Considering the SDR relaxation in (14) with the corresponding phase-only set of constraints (17d) and V ⋆ not being rank one, the Gaussian randomization technique computes a vector Gaussian random variable with zero mean and covariance matrix V ⋆ . With this variable, v rand , the system designer has to obtain a feasible solution of (17). This feasible solution is imposed by the phase-only restrictions which require that the randomization is transformed into…”

“…By iterative solving (32) and updating z (k) max with the eigenvector associated with the largest eigenvalue of the previous optimization solution, we can obtain an objective value solution of the optimization problem (17). As for general methods dealing with non-convex problems, the performance of the obtained solution depends on the proper election of Z (0) and the value of µ (k) .…”

“…where V * is the SDR solution of (17). The figure of merit of Loss Tx describes how close the relaxation technique approximates to the upper bound solution of V * .…”

“…Despite the recent works on phase-only beamforming [15]- [17], little is known about interference mitigation techniques using this multiantenna configuration. To the best of authors knowledge, the work in [18] is the first one considering interference mitigation via phase-only beamforming.…”