Beam Training and Tracking With Limited Sampling Sets: Exploiting Environment Priors

In this paper, we propose a new beam training framework to cope with mobility scenarios in millimeter wave communications. When a position of the mobile changes, the basestation needs to perform beam training frequently to track the time-varying channel, which leads to significant training overhead in radio resources. In order to alleviate this problem, we propose a “dedicated beam training” which serves only users under high mobility. Combined with conventional common beam training, the proposed dedicated beam training can allow the high mobility users to acquire channels with a small number of training beams exploiting the location information of the target user. The optimal selection of the training beams is formulated such that the lower bound of the angle of departure (AoD) estimate is minimized over the beam codebook indices given the estimate of the previous AoD state. Our numerical evaluation demonstrates that the proposed beam training scheme can maintain good channel estimation performance with less training overhead than the conventional beam training protocol.

Intelligent reflecting surface (IRS) has emerged as a competitive solution to address blockage issues in millimeter wave (mmWave) and Terahertz (THz) communications due to its capability of reshaping wireless transmission environments. Nevertheless, obtaining the channel state information of IRS-assisted systems is quite challenging because of the passive characteristics of the IRS. In this paper, we consider the problem of beam training/alignment for IRS-assisted downlink mmWave/THz systems, where a multi-antenna base station (BS) with a hybrid structure serves a single-antenna user aided by IRS. By exploiting the inherent sparse structure of the BS-IRS-user cascade channel, the beam training problem is formulated as a joint sparse sensing and phaseless estimation problem, which involves devising a sparse sensing matrix and developing an efficient estimation algorithm to identify the best beam alignment from compressive phaseless measurements. Theoretical analysis reveals that the proposed method can identify the best alignment with only a modest amount of training overhead. Simulation results show that, for both line-of-sight (LOS) and NLOS scenarios, the proposed method obtains a significant performance improvement over existing state-of-art methods. Notably, it can achieve performance close to that of the exhaustive beam search scheme, while reducing the training overhead by 95%.

In millimeter wave communications, beam training is an effective way to achieve beam alignment. Traditional beam training method allocates training resources equally to each beam in the pre-designed beam training codebook. The performance of this method is far from satisfactory, because different beams have different beamforming gain, and thus some beams are relatively more difficult to be distinguished from the optimal beam than the others. In this paper, we pro- pose a new beam training algorithm which adaptively allocates training resources to each beam. Specifically, the proposed algorithm allocates more training symbols to the beams with relatively higher beamforming gain, while uses less resources to distinguish the beams with relatively lower beamforming gain. Through theoretical analysis and numerical simulations, we show that in practical situations the proposed adaptive algorithm asymptotically outperforms the traditional method in terms of beam training accuracy. Moreover, simulations also show that this relative performance behavior holds in non-asymptotic regime.

ABSTRACTThis paper proposes an advanced deep learning framework for efficient beam training in millimeter wave (mmWave) massive multiple‐input multiple‐output (MIMO) systems. To overcome the limitations of conventional beam training approaches such as high overhead, slow adaptation to dynamic environments, and poor scalability, an Improving Signal Coverage in Millimeter Wave Massive MIMO via Efficient Predefined Time Adaptive Neural Network based Beam Training (ISC‐MMIMO‐EPTANN‐BT) model is proposed. The proposed model used deep neural network (DNN) to learn complicated nonlinearities in channel power leakage (CPL) and used an efficient predefined time adaptive neural network (EPTANN) to provide real‐time responsiveness and temporal synchronism in beam training. The parameters of the model are also optimized using fire hawk optimization algorithm (FHOA) to get better convergence speed and signal coverage. The proposed technique is executed in MATLAB. The proposed approach attains better performance under successful rate by significantly less beam training overhead and also increases signal coverage based on simulation results. The proposed ISC‐MMIMO‐EPTANN‐BT method attains 26.15%, 21.08%, and 33.75% higher successful rates and 16.32%, 28.94%, and 20.24% lower normalized mean square error compared with existing methods such as deep learning for beam training in millimeter wave massive MIMO schemes (BT‐MMIMO‐DNN), deep learning for combined feedback and channel prediction in large‐scale MIMO systems (CNN‐JCS‐MMIMO), and triple‐refined hybrid‐field beam training in mmWave extremely large‐scale MIMO (TR‐FBT‐MIMO), respectively. The ISC‐MMIMO‐EPTANN‐BT technique reduced beam training overhead, enhanced signal coverage, and identified a promising candidate for successful beam training in mmWave massive MIMO schemes.

Recently, many researches are focusing on millimeter wave (mmWave) due to its large bandwidth resources. In the next 5G generation, wireless multi-gigabit (WiGig) is developed based on IEEE 802.11ad/ay standards at unlicensed mmWave bands for providing extremely high throughput. However, mmWave has high propagation loss due to high frequency transmission properties. Beamforming (BF) technique is adopted to solve this problem, and therefore, we have to perform beam training before data transmission. In the standard, the conventional method for beam training is exhaustive beam search (EBS) which takes too much time so that the data transmission time will decrease. On the other hand, blocked environments may severely degrade WiGig beam training performance, and most of existing algorithms do not consider this issue. Recently, machine and deep learning have been widely used in the wireless communication field. We propose a learning-based beam training (LBT) to simultaneously learn about wireless environments and beam training candidates. We select simplified neural network (NN) model to achieve lower computation overhead. To further refine learning information, we propose two enhanced algorithm, expanded LBT (LBT-E) and history-aided expanded LBT(LBT-HE). LBT-E aims to tackle unexpected slight deviation and LBT-HE make use of historical information to improve beam matching accuracy with acceptable latency. In our simulation, our proposed learning-based schemes achieve much higher throughput compared to EBS and algorithms in existing literatures.

Simulation of a non-Gaussian stochastic process based on a combined distribution of the UHPM and the GBD

In this paper, we consider the problem of downlink beam training for extremely large-scale millimeter wave (mmWave)/Terahertz (THz) systems, where the far-field assumption which treats wavefronts as planar waves may not hold valid. For such hybrid far/near-field channels, beam training needs to identify the best beam alignment on a two-dimensional angle-range domain. An exhaustive search scheme sequentially scanning the entire angle-range space incurs a high training overhead. To address this issue, in this paper, we propose an efficient hybrid far/near-field beam training method. By utilizing the approximate orthogonality of near-field steering vectors of the same effective distance, we devise a multi-directional beam training sequence which can more efficiently scan the entire angle-range space. Based on the devised beam training sequence, we develop a simple estimation method at the receiver that can simultaneously identify the angle and the range associated with the dominant path. Simulation results show that the proposed method achieves better performance than the exhaustive search scheme, while with a much lower overhead cost. The proposed method also presents a clear advantage over other existing state-of-the-art hybrid far/near-field beam training methods in terms of performance and generality.

The low-frequency and mmWave links usually co-exist in the next generation wireless terminals, where the low-frequency link is always on and the mmWave link becomes active when high rate transmission is required. Since low-frequency and mmWave channels have spatial similarities, it is feasible to utilize low-frequency channel information to reduce the beam training overhead in mmWave communications. In this paper, we propose a deep learning assisted beam prediction scheme using out-of-band information extracted from low-frequency channel state information (CSI). To overcome the inaccuracy in estimating spatial features due to small number of antennas in low-frequency band, deep learning is introduced to extract robust channel features and increase the prediction accuracy. Moreover, dedicated pre-processing algorithm and network architecture are derived to improve the performance. Simulation results demonstrate that the proposed scheme is robust to various CSI matrix sizes and signal-to-noise ratio. By exploiting low-frequency CSI, it could successfully predict the optimal beam direction to facilitate the initial beam training in mmWave communications with over 94% accuracy in line-of-sight scenarios, which can reduce the overhead of beam training significantly.

In order to meet the high data rate requirements of emerging roadway use cases, mmWave vehicular communications will be needed. This work studies the ability of vehicles to communicate with a Roadside Unit (RSU) placed at an intersection. Practical mmWave radios utilize a codebook, a discrete set of analog beams, that is periodically searched during runtime to find the optimal beam to use for each receiver. This search creates overhead as the wireless channel is not used for communication while this beam search is happening. This work focuses on reducing the overhead of beam training by optimizing the site-specific codebook design of a RSU. Owing to the sparsity of the mmWave channel and the user distribution for vehicles, it is found that 85% of beams can be removed from the codebook with zero-impact. By carefully selecting the usage of wide beams the codebook size can be further reduced to just 64 beams while still providing omni-directional coverage for an intersection. Other research thrusts have focused on attempting to augment or remove beam training entirely; however, this necessitates a change to the PHY layer. Codebook optimization achieves approximately 80% of the communications performance that would be achieved if beam training overhead could be completely removed while only requiring a radio configuration update. Thus, this work finds that today’s commercial mmWave radios are sufficient for deployments in RSUs. To validate the proposed codebook optimization algorithm, a detailed mmWave ray tracing framework that encompasses 3D environmental information and material properties of reflectors is developed.

Millimeter wave (mmWave) provides extremely high throughput owing to their high bandwidth utilization over higher frequencies. To compensate for the severe loss and attenuation, beamforming training is used to determine the optimal beam direction and thereby improve directional transmission power. However, the training overhead will be significantly increased with narrower beams, particularly under conventional exhaustive schemes. Therefore, we propose a learning-based adjustable beam number training (LABNT) scheme to intelligently and flexibly select beam training candidates considering different user mobility and hybrid line-of-sight (LOS) and non-line-of-sight (NLOS) scenarios. In LABNT, several deep learning networks are parallelly constructed and connected to a reinforcement learning network to determine training candidates dynamically based on performance rewards. A novel enhanced feature selection method, that is, uniformly distributed mutual information, is developed based on the correlation of historical results to select the beam inputs for each deep learning network. In simulations, the proposed LABNT outperforms other existing schemes in terms of beam alignment accuracy, training latency, and system throughput. Moreover, following the IEEE 802.11ad/ay protocols, we implement realistic mmWave beamforming training on a programmable hardware platform with integrated 60 GHz wireless-gigabit (WiGig) transceiver devices. The experimental results on the WiGig platform demonstrate that the proposed LABNT scheme can achieve real-time performance with approximately Gbps transmission throughput and millisecond-level training overhead.

Enabling highly-mobile millimeter wave (mmWave) and terahertz (THz) wireless communication applications requires overcoming the critical challenges associated with the large antenna arrays deployed at these systems. In particular, adjusting the narrow beams of these antenna arrays typically incurs high beam training overhead that scales with the number of antennas. To address these challenges, this paper proposes a multi-modal machine learning based approach that leverages positional and visual (camera) data collected from the wireless communication environment for fast beam prediction. The developed framework has been tested on a real-world vehicular dataset comprising practical GPS, camera, and mmWave beam training data. The results show the proposed approach achieves more than 75% top-1 beam prediction accuracy and close to 100% top-3≈beam prediction accuracy in realistic communication scenarios.

Previous article Next article Second-Order Markov and Reciprocal Stationary Gaussian ProcessesR. N. MiroshinR. N. Miroshinhttps://doi.org/10.1137/1124099PDFBibTexSections ToolsAdd to favoritesExport CitationTrack CitationsEmail SectionsAbout[1] S. N. Bernshtei˘n, On the dependencies among random variablesCollected Works, Vol. IV, Nauka, Moscow, 1964, 235–254, (In Russian.) Google Scholar[2] J. L. Doob, Stochastic processes, John Wiley & Sons Inc., New York, 1953viii+654 MR0058896 0053.26802 Google Scholar[3] Benton Jamison, Reciprocal processes: The stationary Gaussian case, Ann. Math. Statist., 41 (1970), 1624–1630 MR0267637 0248.60030 CrossrefGoogle Scholar[4] I. I. Gikhman and , A. V. Skorokhod, The Theory of Stochastic Processes, Vol. I, Springer-Verlag, New York, 1974 CrossrefGoogle Scholar[5] E. Kamke, Differentialgleichungen. Lösungsmethoden and Lösungen, Vol. 1, Chelsea, New York, 1974 Google Scholar[6] E. Wong, Some results concerning the zero-crossings of Gaussian noise, SIAM J. Appl. Math., 14 (1966), 1246–1254 10.1137/0114099 MR0207059 0147.15905 LinkGoogle Scholar[7] E. Wong, The distribution of intervals between zeros for a stationary Gaussian process, SIAM J. Appl. Math., 18 (1970), 67–73 10.1137/0118008 MR0256456 0221.60024 LinkGoogle Scholar[8] R. N. Miroshin, Convergence of Rice and Longuet-Higgins series for a Wong process, Theory Prob. Applications, 21 (1976), 863–866 10.1137/1121103 0374.60049 LinkGoogle Scholar[9] R. N. Miroshin, Asymptotics of the second factorial moment of the number of upward crossings of the line $kt+a$ by a Gaussian stationary process, Vestnik Leningrad. Univ., 23 (1968), 109–120 MR0235612 0165.52602 Google Scholar[10] M. Krein, Sur le problème du prolongement des fonctions hermitiennes positives et continues, C. R. (Doklady) Acad. Sci. URSS (N.S.), 26 (1940), 17–22 MR0004333 0022.35302 Google Scholar Previous article Next article FiguresRelatedReferencesCited byDetails Characterization of Multivariate Stationary Gaussian Reciprocal DiffusionsJournal of Multivariate Analysis, Vol. 62, No. 1 Cross Ref Gaussian reciprocal diffusions and positive definite sturm-liouville operators4 April 2007 | Stochastics and Stochastic Reports, Vol. 55, No. 3-4 Cross Ref Gaussian reciprocal processes revisitedStatistics & Probability Letters, Vol. 12, No. 4 Cross Ref Reciprocal covariance solutions of some matrix differential equationsStochastic Processes and their Applications, Vol. 37, No. 1 Cross Ref Characterization and Classification of Gaussian Second Order Reciprocal Processes Cross Ref Gaussian reciprocal processes and self-adjoint stochastic differential equations of second order2 May 2007 | Stochastics and Stochastic Reports, Vol. 34, No. 1-2 Cross Ref Reciprocal diffusions and stochastic differential equations of second order ∗Stochastics, Vol. 24, No. 4 Cross Ref Multivariate reciprocal stationary Gaussian processesJournal of Multivariate Analysis, Vol. 23, No. 1 Cross Ref On Miroshin’s Second-Order Reciprocal ProcessesJulia Abrahams3 August 2006 | SIAM Journal on Applied Mathematics, Vol. 44, No. 1AbstractPDF (316 KB)The Use of Rice SeriesR. N. Miroshin28 July 2006 | Theory of Probability & Its Applications, Vol. 28, No. 4AbstractPDF (1011 KB)The zero-crossing problem for some nonstationary Gaussian processes (Corresp.)IEEE Transactions on Information Theory, Vol. 28, No. 4 Cross Ref Convergence of Longuet-Higgins Series for Stationary Gaussian Markov Processes of First OrderR. N. Miroshin17 July 2006 | Theory of Probability & Its Applications, Vol. 26, No. 1AbstractPDF (1546 KB) Volume 24, Issue 4| 1980Theory of Probability & Its Applications History Submitted:11 July 1977Published online:17 July 2006 InformationCopyright © Society for Industrial and Applied MathematicsPDF Download Article & Publication DataArticle DOI:10.1137/1124099Article page range:pp. 845-852ISSN (print):0040-585XISSN (online):1095-7219Publisher:Society for Industrial and Applied Mathematics

Gaussian Processes (GPs) are widely-used tools in spatial statistics and machine learning and the formulae for the mean function and covariance kernel of a GP [Formula: see text] that is the image of another GP [Formula: see text] under a linear transformation [Formula: see text] acting on the sample paths of [Formula: see text] are well known, almost to the point of being folklore. However, these formulae are often used without rigorous attention to technical details, particularly when [Formula: see text] is an unbounded operator such as a differential operator, which is common in many modern applications. This note provides a self-contained proof of the claimed formulae for the case of a closed, densely-defined operator [Formula: see text] acting on the sample paths of a square-integrable (not necessarily Gaussian) stochastic process. Our proof technique relies upon Hille’s theorem for the Bochner integral of a Banach-valued random variable.

Reconfigurable intelligent surfaces (RISs) play a vital role in future wireless systems with the capability of enhancing propagation environments by intelligently reflecting the signals toward the target receivers. However, optimal tuning of the phase shifters at the RIS is challenging due to the passive nature of reflective elements and the high complexity of acquiring channel state information (CSI). Furthermore, the joint active beamforming and RIS reflection beam design is a tedious task due to the high computational complexity and the dynamic nature of the wireless environment. Today’s cellular networks establish data transmission by relying on pre-defined generic beamforming codebooks, which are neither site-specific nor adaptive to the changes in the wireless environment. Moreover, identifying the best beam is typically performed using an exhaustive search approach that prohibits the use of large codebook sizes due to the resulting high beam training overhead. Depending merely on the binary received signal strength, this work develops a multi-agent deep reinforcement learning (MA-DRL) framework that jointly designs the active and the passive reflection beam codebooks for the BS and the RIS, reflectively. To accelerate learning convergence and reduce the search space, the proposed model divides the RIS into multiple partitions and associates beam patterns to the surrounding environments with low computational complexity. Moreover, a hierarchical beam training solution is proposed to further reduce the beam training overhead of the single-beam training approach. Simulation results show that the proposed MA-DRL approach can provide a 97% beam training overhead reduction over the discrete Fourier transform (DFT) codebook.

Reconfigurable intelligent surface (RIS) has emerged as a competitive solution to the blocking problem in millimeter wave (mmWave) communications. However, due to the passive nature of the RIS, obtaining channel state information (CSI) for RIS-assisted mmWave communication systems is rather difficult. Considering that the currently available RIS hardware cannot arbitrarily switch between the active (reflection with configurable phase response) and deactivate (absorption) modes, we suggest a new beam training method for RIS-assisted mmWave communication systems in this study. First, a predefined hierarchical codebook is created using the pattern synthesis method. Then, we provide a novel hierarchical beam training method using two multi-mainlobe codewords in each layer of the hierarchical codebook for beam sweeping. Combining the results of the beam identification in all the layers will yield the ultimate ideal beam direction. Theoretical analyses demonstrate that the suggested approach can effectively reduce training overhead while ensuring successful beam alignment. Simulation results show that the practical codebook can be created successfully, and the suggested method can achieve accurate beam alignment with reduced training overhead.