Design and Analysis of Transmit Beamforming for Millimetre Wave Base Station Discovery

In this paper, we develop an analytical framework for the initial access (a.k.a. Base Station (BS) discovery) in a millimeter-wave (mm-wave) communication system and propose an effective strategy for transmitting the Reference Signals (RSs) used for BS discovery. Specifically, by formulating the problem of BS discovery at User Equipments (UEs) as hypothesis tests, we derive a detector based on the Generalised Likelihood Ratio Test (GLRT) and characterise the statistical behaviour of the detector. The theoretical results obtained allow analysis of the impact of key system parameters on the performance of BS discovery, and show that RS transmission with narrow beams may not be helpful in improving the overall BS discovery performance due to the cost of spatial scanning. Using the method of large deviations, we identify the desirable beam pattern that minimises the average miss-discovery probability of UEs within a targeted detectable region. We then propose to transmit the RS with sequential scanning, using a pre-designed codebook with narrow and/or wide beams to approximate the desirable patterns. The proposed design allows flexible choices of the codebook sizes and the associated beam widths to better approximate the desirable patterns. Numerical results demonstrate the effectiveness of the proposed method.Comment: 30 pages, 13 figures, submitte

Millimeter Wave Beam Alignment: Large Deviations Analysis and Design Insights

In millimeter wave cellular communication, fast and reliable beam alignment via beam training is crucial to harvest sufficient beamforming gain for the subsequent data transmission. In this paper, we establish fundamental limits in beam-alignment performance under both the exhaustive search and the hierarchical search that adopts multi-resolution beamforming codebooks, accounting for time-domain training overhead. Specifically, we derive lower and upper bounds on the probability of misalignment for an arbitrary level in the hierarchical search, based on a single-path channel model. Using the method of large deviations, we characterize the decay rate functions of both bounds and show that the bounds coincide as the training sequence length goes large. We go on to characterize the asymptotic misalignment probability of both the hierarchical and exhaustive search, and show that the latter asymptotically outperforms the former, subject to the same training overhead and codebook resolution. We show via numerical results that this relative performance behavior holds in the non-asymptotic regime. Moreover, the exhaustive search is shown to achieve significantly higher worst-case spectrum efficiency than the hierarchical search, when the pre-beamforming signal-to-noise ratio (SNR) is relatively low. This study hence implies that the exhaustive search is more effective for users situated further from base stations, as they tend to have low SNR.Comment: Author final manuscript, to appear in IEEE Journal on Selected Areas in Communications (JSAC), Special Issue on Millimeter Wave Communications for Future Mobile Networks, 2017 (corresponding author: Min Li