Abstract
In order to achieve millimeter wave (mmWave) beam alignment , a class of beam scanning and searching schemes have been extensively studied [1–3]. Recently, to address the problems of the traditional algorithms have a high sample complexity, some adaptive beam scanning approaches utilize the hierarchical beamforming codebook to reduce the training time at the cost of frequent feedback [2]. Then, to eliminate the feedback link, a random beam alignment algorithm is proposed by utilizing the pseudo-random spreading codes [3]. However, it needs a Pseudo-Noise (PN) sequences with sufficient length to ensure the good correlation properties of different beams. Furthermore, in addition to the above disadvantages, most of the existing algorithms require either a separate pilot sequence per user or long beam scanning time when considering mmWave multiuser uplinking systems. To solve the above problems, a novel class of beam alignment algorithms based on the sparse graph coding theory are proposed in this paper. Firstly, we investigate the uplink mmWave beam training structure. Based on the analysis, the mmWave multiuser beam alignment problem is transformed into the sparse-graph design and detection problem. Secondly, a beam alignment algorithm framework based on sparse-graph coding and decoding is proposed. Furthermore , we derive the theoretical bound to chose the optimal parameters of the designed coding matrix. Finally, two beam alignment algorithms are proposed to detect the beam index in different settings. Simulation results confirm that our beam algorithms outperform the conventional beam training methods. Proposed Uplink Beam Training Scheme. This paper considers a typical uplink mmWave MU-MIMO system, where the BS communicates with K UEs simultaneously. Suppose that the BS is equipped with N R antennas and N RF RF chains, while the k-th UE has M T antennas and M RF RF chains. Then, the channel associated with the k-th UE can be given by [4]