Efficient Beam Alignment in Millimeter Wave Systems Using Contextual Bandits

In this paper, we investigate the problem of beam alignment in millimeter wave (mmWave) systems, and design an optimal algorithm to reduce the overhead. Specifically, due to directional communications, the transmitter and receiver beams need to be aligned, which incurs high delay overhead since without a priori knowledge of the transmitter/receiver location, the search space spans the entire angular domain. This is further exacerbated under dynamic conditions (e.g., moving vehicles) where the access to the base station (access point) is highly dynamic with intermittent on-off periods, requiring more frequent beam alignment and signal training. To mitigate this issue, we consider an online stochastic optimization formulation where the goal is to maximize the directivity gain (i.e., received energy) of the beam alignment policy within a time period. We exploit the inherent correlation and unimodality properties of the model, and demonstrate that contextual information improves the performance. To this end, we propose an equivalent structured Multi-Armed Bandit model to optimally exploit the exploration-exploitation tradeoff. In contrast to the classical MAB models, the contextual information makes the lower bound on regret (i.e., performance loss compared with an oracle policy) independent of the number of beams. This is a crucial property since the number of all combinations of beam patterns can be large in transceiver antenna arrays, especially in massive MIMO systems. We further provide an asymptotically optimal beam alignment algorithm, and investigate its performance via simulations.Comment: To Appear in IEEE INFOCOM 2018. arXiv admin note: text overlap with arXiv:1611.05724 by other author

Best Arm Identification Based Beam Acquisition in Stationary and Abruptly Changing Environments

We study the initial beam acquisition problem in millimeter wave (mm-wave) networks from the perspective of best arm identification in multi-armed bandits (MABs). For the stationary environment, we propose a novel algorithm called concurrent beam exploration, CBE, in which multiple beams are grouped based on the beam indices and are simultaneously activated to detect the presence of the user. The best beam is then identified using a Hamming decoding strategy. For the case of orthogonal and highly directional thin beams, we characterize the performance of CBE in terms of the probability of missed detection and false alarm in a beam group (BG). Leveraging this, we derive the probability of beam selection error and prove that CBE outperforms the state-of-the-art strategies in this metric. Then, for the abruptly changing environments, e.g., in the case of moving blockages, we characterize the performance of the classical sequential halving (SH) algorithm. In particular, we derive the conditions on the distribution of the change for which the beam selection error is exponentially bounded. In case the change is restricted to a subset of the beams, we devise a strategy called K-sequential halving and exhaustive search, K-SHES, that leads to an improved bound for the beam selection error as compared to SH. This policy is particularly useful when a near-optimal beam becomes optimal during the beam-selection procedure due to abruptly changing channel conditions. Finally, we demonstrate the efficacy of the proposed scheme by employing it in a tandem beam refinement and data transmission scheme

Beam Drift in Millimeter Wave Links: Beamwidth Tradeoffs and Learning Based Optimization

Millimeter wave (mmwave) communications, envisaged for the next generation wireless networks, rely on large antenna arrays and very narrow, high-gain beams. This poses significant challenges to beam alignment between transmitter and receiver, which has attracted considerable research attention. Even when alignment is achieved, the link is subject to beam drift (BD). BD, caused by non-ideal features inherent in practical beams and rapidly changing environments, is referred to as the phenomenon that the center of main-lobe of the used beam deviates from the real dominant channel direction, which further deteriorates the system’s performance. To mitigate the BD effect, in this paper we first theoretically analyze the BD effect on the performance of outage probability as well as effective achievable rate, which takes practical factors (e.g., the rate of change of the environment, beam width, transmit power) into account. Then, different from conventional practice, we propose a novel design philosophy where multi-resolution beams with varying beam widths are used for data transmission while narrow beams are employed for beam training. Finally, we design an efficient learning based algorithm which can adaptively choose an appropriate beam width according to the environment. Simulation results demonstrate the effectiveness and superiority of our proposals

mmWave Beam Alignment using Hierarchical Codebooks and Successive Subtree Elimination

We propose a best arm identification multi-armed bandit algorithm in the fixed-confidence setting for mmWave beam alignment initial access called \ac{SSE}. The algorithm performance approaches that of state-of-the-art Bayesian algorithms at a fraction of the complexity and without requiring channel state information. The algorithm simultaneously exploits the benefits of hierarchical codebooks and the approximate unimodality of rewards to achieve fast beam steering, in a sense that we precisely define to provide fair comparison with existing algorithms. We derive a closed-form sample complexity, which enables tuning of design parameters. We also perform extensive simulations over slow fading channels to demonstrate the appealing performance versus complexity trade-off struck by the algorithm across a wide range of channel condition