Flat Beam Design for Massive MIMO Systems via Riemannian Optimization

Fan, Wenzhe; Zhang, Cheng; Huang, Yongming

doi:10.1109/lwc.2018.2871260

Cited by 34 publications

(15 citation statements)

References 11 publications

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“…These beams are now practically synthesized beams that might have attenuated gain in its passband and some leakage through its transition band and side lobe. In particular, we use the state-of-the-art flat-beam design technique [36] to synthesize the desired Tx and Rx beams, assuming that Tx and Rx is equipped with N T = 64 and N R = 32 antennas, respectively, and the antenna spacing is half of the wave length. Fig.…”

Section: A Multi-path Channel Model and Synthesized Beamsmentioning

confidence: 99%

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Explore and Eliminate: Optimized Two-Stage Search for Millimeter-Wave Beam Alignment

Liu

Hanly

et al. 2019

IEEE Trans. Wireless Commun.

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Swift and accurate alignment of transmitter (Tx) and receiver (Rx) beams is a fundamental design challenge to enable reliable outdoor millimeter-wave communications. In this paper, we propose a new Optimized Two-Stage Search (OTSS) algorithm for Tx-Rx beam alignment via spatial scanning. In contrast to one-shot exhaustive search, OTSS judiciously divides the training energy budget into two stages. In the first stage, OTSS explores and trains all candidate beam pairs and then eliminates a set of less favorable pairs learned from the received signal profile. In the second stage, OTSS takes an extra measurement for each of the survived pairs and combines with the previous measurement to determine the best one. For OTSS, we derive an upper bound on its misalignment probability, under a single-path channel model with training codebooks having an ideal beam pattern. We also characterize the decay rate function of the upper bound with respect to the training budget and further derive the optimal design parameters of OTSS that maximize the decay rate. OTSS is proved to asymptotically outperform state-of-the-art beam alignment algorithms, and is numerically shown to achieve better performance with limited training budget and practically synthesized beams. Index TermsBeam alignment, beam training, exhaustive search, hierarchical search, optimized two-stage search, large deviations techniques, millimeter-wave communications.

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Section: A Multi-path Channel Model and Synthesized Beamsmentioning

confidence: 99%

“…An illustration of 8 candidate beams at Rx synthesized by the state-of-the-art flat-beam design technique[36].…”

mentioning

confidence: 99%

Explore and Eliminate: Optimized Two-Stage Search for Millimeter-Wave Beam Alignment

Liu

Hanly

et al. 2019

IEEE Trans. Wireless Commun.

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“…Riemannian geometry [16] has been recently considered in designing beamforming vectors [17], [18]. Additionally, non-euclidean methods have been utilized in codebook design such as non-conic Riemannian manifolds (i.e, unitary, fixed rank) as in [19], [20].…”

Section: Introductionmentioning

confidence: 99%

Geometric Machine Learning for Channel Covariance Estimation in Vehicular Networks

Nasim,

Ibrahim

2021

Preprint

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Learning the covariance matrices of spatiallycorrelated wireless channels, in millimeter-wave (mmWave) vehicular communication, can be utilized in designing environmentaware beamforming codebooks. Such channel covariance matrices can be represented on non-Euclidean Riemannian manifolds, thanks to their symmetric positive definite (SPD) characteristics. Consequently in this paper, we propose a Riemannian-Geometric machine learning (G-ML) approach for estimating the channel covariance matrices based on unsupervised K-Means model. The proposed K-means algorithm utilizes Log-Euclidean metric (LEM) as the distance measure among channel covariance matrices over the Riemannian manifolds. We show that our proposed K-Means G-ML model can achieve up to 80% less error compared to Euclidean-based K-Means algorithm, which applies clustering on the channel vectors themselves.

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“…We note that Riemannian geometry has been recently considered in designing beamforming vectors (e.g., [10], [11]). Moreover, non-Euclidean methods have been utilized in codebook design such as non-conic Riemannian manifolds (i.e, unitary, fixed rank) as in [12], [13].…”

Section: Introductionmentioning

confidence: 99%

Wireless Link Scheduling via Interference-aware Symmetric Positive Definite Connectivity Manifolds

Ibrahim¹

2021

Preprint

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In this paper, we investigate the fundamental problem of wireless link scheduling in device-to-device (D2D) networks, through the lens of Riemannian geometry. Our goal is to find a novel metric to characterize interference among D2D pairs, which can pave the way towards efficient and fast scheduling algorithms. Towards achieving this goal, we first model the connectivity pattern of each D2D pair, including its interference links, as a positively-shifted Laplacian matrix, which is a symmetric positive definite (SPD) one. Noting that SPD matrices constitute a non-Euclidean manifold, we represent each of the D2D pairs as a point on the SPD (i.e., conic) manifold, which is analyzed via Riemannian geometry. Accordingly we employ Riemannian metrics (e.g., Log-Euclidean metric "LEM"), which are suitable measures of distances on manifolds, to characterize the interference among D2D points on the SPD manifold.To validate the effectiveness of the proposed LEM-based interference measure, we propose a sequential link selection algorithm that schedules D2D pairs in a descending order of their signal-to-noise ratio (SNR), while keeping their LEM distances towards the already-scheduled pairs on the Riemannian manifold to be greater than a certain LEM threshold. Such LEM-based condition is equivalent to limiting the interference from potential D2D pairs to be below certain threshold. We show that the proposed LEM-based scheduling algorithm achieves sum rate of more than 86% of state-of-the-art ones (e.g., FPLinQ [1]), while only requiring spatial locations of D2D pairs, as opposed to requiring full channel state information (CSI).

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Flat Beam Design for Massive MIMO Systems via Riemannian Optimization

Cited by 34 publications

References 11 publications

Explore and Eliminate: Optimized Two-Stage Search for Millimeter-Wave Beam Alignment

Explore and Eliminate: Optimized Two-Stage Search for Millimeter-Wave Beam Alignment

Geometric Machine Learning for Channel Covariance Estimation in Vehicular Networks

Wireless Link Scheduling via Interference-aware Symmetric Positive Definite Connectivity Manifolds

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