Fast Beam Alignment for Millimeter Wave Time-Varying Channels Using Sparse Codes

In this paper, a novel beam alignment algorithm based on the sparse graph coding theory is proposed for millimeter wave (mmWave) time-varying channels. Firstly, a pilot design method is introduced to transform the mmWave time-varying beam alignment into a sparse-graph design and detection problem. Inspired by Low-Density-Parity-Check (LDPC) codes and fountain codes, a multi-stage sparse coding method is proposed for the design of the measurement matrix and the theoretical bound of the probability of success is derived to guide the design of the sparse-graph. A beam alignment algorithm is subsequently proposed to detect the beam index and estimate the carrier frequency offset (CFO). Then, the Carmer-Rao Lower Bound (CRLB) is derived. Simulation results demonstrate that the proposed beam alignment algorithm achieves significant performance improvements over the conventional counterparts in both the noiseless and noise cases.