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Intelligent Beam Prediction and Tracking

Christos Masouros1, Jianjun Zhang2, and Yongming Huang3

1Department of Electronic & Electrical Engineering, University College London, London, UK

2College of Computer Science and Technology, Nanjing University of Aeronautics and Astronautics, Nanjing, China

3National Mobile Communications Research Laboratory, Southeast University, Nanjing, China

CHAPTER MENU

1. Introduction
2. Challenge of Beam Prediction Modeling in Wireless Communications
3. Prior Identification – Perspective of Function Space
4. Methodology from Stochastic Process
5. Stochastic Continuity – Beam Index Difference
6. Stochastic Smoothness – Hybrid Data-induced Kalman Filtering
7. Beam Width Optimization
8. Numerical Results
9. Conclusion

1.1 Introduction

Because of abundant spectrum resources at high-frequency band, that enable to achieve ultrahigh-speed data transmission (DT), high-frequency communications, e.g., millimeter wave or even Terahertz communications, have attracted extensive interest from academia, industry, and government [1]. For high-frequency communications, the transmitter and/or receiver are often equipped with large-scale antenna arrays, i.e., massive multiple-input multiple-output (MIMO), to achieve high array gains to overcome signal attenuation of high-frequency band. However, the use of pencil-like highly directional beams makes channel state information (CSI) acquisition via beam alignment (BA) very challenging. First, acquiring CSI in a mobile network is particularly challenging since the wireless channel often varies rapidly. Second, in contrast to the fully digital transceiver, where the pilot transmission scheme can be utilized to acquire CSI [2, 3], channel estimation is more complicated in the hybrid antenna array architecture, which has been used widely in practice, because we cannot extract the actual received signals on all antennas simultaneously. Last but not the least, the large dimension of massive MIMO inevitably results in large and even unaffordable pilot overhead, even if the pilot transmission-based method can be used.

To tackle this challenging issue, the two-step precoding and combining based scheme is widely used in practical systems, e.g., standardized in IEEE 802.11ad/802.15.3c [4, 5]. Let , , and represent the precoding matrix, channel matrix, and combing matrix, respectively. The precoding (combining) matrix is assumed to be decomposed as (), where and ( and ) denote the analog and digital parts, respectively. To reduce the dimension of the CSI estimate problem, beam training is first performed between the transmitter and receiver to obtain the analog precoder and combiner . Then, the effective or equivalent channel can be estimated, based on which the digital parts, i.e., the precoder and combiner , can be designed in the analog domain via a variety of methods, e.g., the heuristic methods or optimization-based algorithms [6–8]. Note that since the size of the effective channel matrix is much smaller than that of the original channel matrix , the pilot overhead in the second step is relatively low. It is observed that the remaining difficulty lies in how to design an efficient beam training scheme to find the optimal and .1

Initially, beam training (also referred to as beam sounding) is implemented via the exhaustive and hierarchical search [5, 9, 10]. Compared to the exhaustive search, whose sounding overhead is with denoting the size of the training codebook, the sounding overhead of the hierarchical search is for the typical binary tree search-based implementation, which is smaller than that of the exhaustive search scheme. For this reason, along with the advantage of easy implementation, the hierarchical search-based scheme has been adopted in several IEEE standards, such as IEEE 802.15.3c and IEEE 802.11aj. Note the performance of the hierarchical search-based algorithms heavily depends on the codebook used. In fact, besides the demand for multi resolution, namely, various widths of main lobes, other properties, such as flat main lobe and side lobe, narrow transition band, and high-power efficiency of power amplifier, are also very important and should be well addressed [9, 11]. In general, the research on hierarchical search often boils down to sounding codebook design [5, 9–14].

The advantage of the exhaustive or hierarchical search-based methods is that they can be applied to an arbitrary scenario because they are nonadaptive methods and thus independent of external environments. However, the beam sounding overhead is almost always very large, especially for a large-scale antenna array and/or a rapidly changing environment. In fact, on the one hand, as the scale of the antenna array increases, the beam width decreases accordingly, which thus increases the sounding overhead. On the contrary other hand, the coherence time or period becomes shorter in a rapidly fluctuating environment. Hence, much of the precious time resource is spent on beam sounding, and the proportion of time resources used for DT is very small. This phenomenon is particularly pronounced for the highly varying communication scenarios, e.g., unmanned aerial vehicle (UAV) communication.

To avoid frequent searches, beam tracking is invoked to reduce the sounding overhead. The complete process of BA operation in a relatively long time consists of two phases. First, initial BA is performed in the first stage to find the optimal beam or beam pair via the exhaustive or hierarchical search, which involves a large beam sounding overhead, as mentioned before. Then, the beam tracking technique is invoked in the second phase to enable efficient search. Compared to the initial BA, the number of beams used for tracking is relatively small, e.g., maybe only one beam is used for sounding. Note that if the tracking fails, which is inevitable, the initial BA operation is invoked again to reinitialize the beam tracking.

The key to beam tracking is beam prediction, i.e., to predict a beam subspace that contains the real beam. In practice, two types of metrics are closely related to beam prediction. The first one is the success rate and prediction efficiency, i.e., the beam subspace predicted should contain the real optimal beam, and meanwhile, the beam subspace should be as small as possible. The second one is the complexities of beam prediction, including both sample complexity and inference complexity. To balance these indicators, various methods have been proposed, the core of which is to exploit temporal and spatial correlations of wireless channels. The most important step toward beam prediction is to construct an appropriate prediction model. Overall, there are mainly two ways to construct a prediction model, i.e., the traditional manual fashion and the recent automatic fashion. The classical and representative manual method to construct a prediction model is the Kalman filtering- or Bayesian filtering-based Beam prediction and tracking (BPT) algorithms [15–22]. Machine learning (ML) methods are used to automatically construct prediction models, typically, in the data-driven manner [23–29].

The Kalman filtering and Bayesian filtering methods address the issue of prediction model construction by building a dynamical model that characterizes the underlying physical system. Specifically, two stochastic differential equations (SDEs), referred to as state-space and measurement equations in literature, are first established. As long as the two SDEs are available, the well-known Kalman filter or Bayesian filter can be invoked to perform real-time inference or prediction. For example, both the extended Kalman filter- and Bayesian filter-based beam tracking algorithms are proposed in Liu et al. [15] and Yuan et al. [18] for the dual-functional radar and communication systems. For the distributed millimeter-wave massive MIMO problem, a monopulse beam tracking method based on the unscented Kalman filter is designed in [21], which shows to achieve good robustness as well as generalization ability.

An important and appealing advantage of the Kalman filtering based methods is that they have low computational complexity. In particular, the scaling of computational complexity for the Kalman filter is linear (where is the number of samples), as opposed to the cubic scaling for Gaussian process (GP) regression-based BPT algorithms. Note that this advantage is attributed to the fact that the underlying state-space system model is exploited. However, since the prediction model is obtained via manual derivation manner, it may fail in complicated scenarios or environments. To tackle this issue, recently a novel hybrid model and data-driven-based approach, referred to as hybrid data-induced Kalman filtering (HDIKF), has been proposed by Zhang et al. [30, 31].

In contrast to the Kalman filtering-based designs, ML typically addresses the issue of prediction modeling by employing the data-driven mode. In fact, it is well known that a powerful ability of ML is that it can automatically extract meaningful patterns and further derive directly an appropriate model from the observed data. According to the underlying ML theory and methods, the ML-based beam prediction methods fall into two categories, i.e., the (deep) reinforcement learning...