Multi-Resolution Codebook Based Beamforming Sequence Design in Millimeter-Wave Systems

Noh, Song; Zoltowski, M.D.; Love, David J.

doi:10.1109/glocom.2015.7417848

Cited by 36 publications

(38 citation statements)

References 22 publications

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“…For BTOI, we find that the BAER decreases exponentially with the SNR 1 In practice, enough power should be allocated during the training stage. The SNR can be increased by sending beams repeatedly [15], [18]. Moreover, simulation result shows that it is also consistent with theoretical BAER under low SNR conditions.…”

Section: Theoretical Analysis Of Btoi Schemesupporting

confidence: 83%

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An Improved Beam Training Scheme Under Hierarchical Codebook

Guan

et al. 2020

IEEE Access

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In millimeter wave (mmWave) communications, the beamforming gains of large-scale antenna arrays are used to combat severe path losses and improve communication link quality. This requires beam training (BT) to determine the optimal beam direction and achieve beam alignment. The hierarchical codebook with multi-resolution training beams is widely used in BT to reduce training overhead. Unfortunately, due to hardware restrictions, the transition area between two adjacent training beams often leads to error propagation in a traditional BT scheme, which limits the accuracy of beam alignment. In this paper, we propose an improved BT scheme under hierarchical codebook. First, we define an index to measure the power difference of the received signals. Once the index is lower than the predefined threshold, the optimal beam direction is considered to be in the transition area, and an extra interval that contains the transition area is proposed for further beam searching. Then, we analyze the optimal threshold and the probability of beam misalignment based on the ideal beam pattern, proving that the error rate exponentially decreases with the signal-to-noise ratio (SNR) under a single-path channel with constant gain. Finally, simulation results demonstrate that the proposed scheme can significantly improve the accuracy of beam alignment and is applicable to most existing beam patterns. INDEX TERMS Hierarchical codebook, millimeter wave, beam training, beam alignment, error propagation, beam alignment error rate.

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Section: Theoretical Analysis Of Btoi Schemesupporting

confidence: 83%

“…The last step uses (23) and omits higher-order terms. According to [18], the BAER can be approximated as s p s (τ ), so we can obtain (15).…”

Section: Appendix C Proof Of Propositionmentioning

confidence: 99%

An Improved Beam Training Scheme Under Hierarchical Codebook

Guan

et al. 2020

IEEE Access

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“…Love are with the School of Electrical and Computer Engineering, Purdue University, West Lafayette, IN 47907, USA (e-mail:songnoh@purdue.edu and {mikedz,djlove}@ecn.purdue.edu). A preliminary version of this work will be presented in [1]. the works in [6]- [9] propose analog beam alignment techniques in which phase shifters or discrete lens arrays are employed.…”

Section: Introductionmentioning

confidence: 99%

Multi-Resolution Codebook and Adaptive Beamforming Sequence Design for Millimeter Wave Beam Alignment

Noh

Zoltowski

Love

2017

IEEE Trans. Wireless Commun.

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233

189

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Abstract-Millimeter wave (mmWave) communication is expected to be widely deployed in fifth generation (5G) wireless networks due to the substantial bandwidth available at mmWave frequencies. To overcome the higher path loss observed at mmWave bands, most prior work focused on the design of directional beamforming using analog and/or hybrid beamforming techniques in largescale multiple-input multiple-output (MIMO) systems. Obtaining potential gains from highly directional beamforming in practical systems hinges on sufficient levels of channel estimation accuracy, where the problem of channel estimation becomes more challenging due to the substantial training overhead needed to sound all directions using a high-resolution narrow beam. In this work, we consider the design of multi-resolution beamforming sequences to enable the system to quickly search out the dominant channel direction for single-path channels. The resulting design generates a multilevel beamforming sequence that strikes a balance between minimizing the training overhead and maximizing beamforming gain, where a subset of multilevel beamforming vectors is chosen adaptively to provide an improved average data rate within a constrained time. We propose an efficient method to design a hierarchical multiresolution codebook utilizing a Butler matrix, a generalized discrete Fourier transform (DFT) matrix implemented using analog RF circuitry. Numerical results show the effectiveness of the proposed algorithm.

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“…Beam sweeping [8][9][10][11][12][13] is an appealing approach for mmWave massive MIMO communications, by which the transmitter radiates multiple beams in different directions to find the best transmission direction through feedback from the receiver side for beamforming of the modulated data sequences. In massive MIMO systems, when the number of antennas increases, the transmitter becomes capable of generating narrow beams that enable so-called pencil beamforming.…”

Section: Introductionmentioning

confidence: 99%

Statistical MIMO beam codebook design for mmWave transmissions

Khormuji

Pitaval

2018

J Wireless Com Network

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We propose a novel method for constructing beam codebooks, i.e., a set of beamforming weights, to be used for beam sweeping and data transmission in mmWave massive MIMO channels. The proposed beam codebooks are designed according to the statistical distribution of the channel's angles of departure in order to efficiently sectorize the angular space covered by the beams. In particular, the cumulative distribution function of these angles is used to sectorize the angular beam space in order to design the beams. We first present a general closed-form construction of beam codebooks for an arbitrary distribution and then tailor the results to the Laplace distribution. We consider both narrow and broad beams. The resulting beams are a priori better adapted to the channel statistics and thus enhance the spectral efficiency of the transmission as compared to the state-of-the-art beam designs. Finally, we investigate the performance of the design and also present some analytical bounds quantifying the inherent loss of a directional beamforming compared to the optimal beamforming with perfect channel state information at the transmitter.

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Multi-Resolution Codebook Based Beamforming Sequence Design in Millimeter-Wave Systems

Cited by 36 publications

References 22 publications

An Improved Beam Training Scheme Under Hierarchical Codebook

An Improved Beam Training Scheme Under Hierarchical Codebook

Multi-Resolution Codebook and Adaptive Beamforming Sequence Design for Millimeter Wave Beam Alignment

Statistical MIMO beam codebook design for mmWave transmissions

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