Worst case robust downlink beamforming on the Riemannian manifold

Ciochina, Dana; Pesavento, Marius; Wong, K.M.

doi:10.1109/icassp.2013.6638369

Cited by 6 publications

(12 citation statements)

References 27 publications

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“…Using (15), problem (14) can be rewritten in the following way: min w wR w subject to w a − 1 2 = 2 w w.…”

Section: Robust Clms Algorithm Based On Worst-case Sinr Maximizationmentioning

confidence: 99%

“…In more recent years, some new robust adaptive beamforming approaches have been proposed [13][14][15][16][17]. The problem of finding a weight vector maximizes the worst-case SINR over the uncertainty model.…”

Section: Introductionmentioning

confidence: 99%

“…In [14], a robust downlink beamforming optimization algorithm is proposed for secondary multicast transmission in a multipleinput multiple-output (MIMO) spectrum sharing cognitive radio (CR) network. Recognizing that all channel covariance matrices form a Riemannian manifold, Ciochina et al propose worst-case robust downlink beamforming on the Riemannian manifold in order to model the set of mismatched channel covariance matrices for which robustness shall be guaranteed [15]. In [16], a robust beamforming scheme is proposed for the multiantenna nonregenerative cognitive relay network where the multiantenna relay with imperfect channel state information (CSI) helps the communication of single-antenna secondary users (SUs).…”

Section: Introductionmentioning

confidence: 99%

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Robust Recursive Algorithm under Uncertainties via Worst-Case SINR Maximization

Song

Wang

et al. 2015

Journal of Electrical and Computer Engineering

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The performance of traditional constrained-LMS (CLMS) algorithm is known to degrade seriously in the presence of small training data size and mismatches between the assumed array response and the true array response. In this paper, we develop a robust constrained-LMS (RCLMS) algorithm based on worst-case SINR maximization. Our algorithm belongs to the class of diagonal loading techniques, in which the diagonal loading factor is obtained in a simple form and it decreases the computation cost. The updated weight vector is derived by the descent gradient method and Lagrange multiplier method. It demonstrates that our proposed recursive algorithm provides excellent robustness against signal steering vector mismatches and the small training data size and, has fast convergence rate, and makes the mean output array signal-to-interference-plus-noise ratio (SINR) consistently close to the optimal one. Some simulation results are presented to compare the performance of our robust algorithm with the traditional CLMS algorithm.

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“…Using (15), problem (14) can be rewritten in the following way: min w wR w subject to w a − 1 2 = 2 w w.…”

Section: Robust Clms Algorithm Based On Worst-case Sinr Maximizationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Robust Recursive Algorithm under Uncertainties via Worst-Case SINR Maximization

Song

Wang

et al. 2015

Journal of Electrical and Computer Engineering

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“…29,30 Compared to the mentioned works, other works consider the imperfect covariance-based CSI. [31][32][33][34][35][36][37] The worst-case robust beamforming designs have been investigated in which the error of covariance matrices are assumed to be upper bounded by a specified constant. [31][32][33] Furthermore, the statistical approaches are taken into account.…”

Section: Introductionmentioning

confidence: 99%

Max–min fair robust beamforming design for underlay device‐to‐device communications in cellular networks

Alibeigi

Taherpour

Rahmani

2021

Int J Communication

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This paper investigates the robust downlink beamforming designs based on max-min fairness and base station (BS) power consumption constraint for device-to-device (D2D) communications underlaying cellular network, under the assumption of imperfect channel state information (CSI) at the BS. Our objective is to maximize the minimum signal-to-interference-plus-noise ratio (SINR) or non-outage probability of users while guaranteeing that the consumed power at the BS is less than a threshold. In particular, three max-min fairness scenarios are considered. In the first scenario, the worst-case SINR of cellular users (CUs) is maximized where the D2D SINR is guaranteed to be above a specified predetermined threshold. In the second scenario, we extend the first scenario and maximized D2D SINR while maximizing CUs' SINR. In these two scenarios, it is assumed that the errors are upper bounded in their Frobenius norms. In the third scenario, the minimum non-outage probability of users is maximized, while a probabilistic model is considered for the uncertainty of channel covariance matrices. Although such optimization problems are not convex, the semidefinite relaxation (SDR) approach is used to obtain the optimal beamforming matrix, which always complies the rank-one constraint. Simulation results show that significant improvement in terms of minimum SINR of CUs, the minimum non-outage probability of CUs, and the probability of feasibility and the fairness index can be achieved with our proposed algorithms in comparison with other beamforming schemes. K E Y W O R D Sdevice-to-device communications, imperfect channel state information, max-min fairness, robust beamforming

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“…On the other hand, d R 1 and d R 2 are newly developed [8] and have not been widely used yet. However, since it is much easier to manipulate in mathmatics, d R 2 has been employed in robust beamforming and signal detection recently with very encouraging results [23], [24], [25].…”

Section: Riemannian Distance D Rmentioning

confidence: 99%

Mean and Median of PSD Matrices on a Riemannian Manifold: Application to Detection of Narrow-Band Sonar Signals

Wong

Zhang

Liang

et al. 2017

IEEE Trans. Signal Process.

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We investigate the employment of power spectral density (PSD) matrix, which is constructed by the received signals in a multi-sensor system and contains additional cross-correlation information, as a feature in signal processing. Since the PSD matrices are structurally constrained, they form a manifold in signal space. The commonly used Euclidean distance (ED) to measure the distance between two such matrices are not informative or accurate. Riemannian distances (RD), which measure distances along the surface of the manifold, should be employed to give more meaningful measurements. Furthermore, the principle that the geodesics on the manifold can be lifted to an isometric Euclidean space is emphasized since any processing involving the optimization of the geodesics can be lifted to the isometric Euclidean space and be carried out in terms of the equivalent Euclidean metric. Application of this principle is illustrated by having efficient algorithms locating the mean and median of the PSD matrices on the manifold developed. These concepts are then applied to the detection of narrow-band sonar signals from which the decision rule is set up by translating the measure reference. In order to further enhance the detecton performance, an algorithm is developed for obtaining the optimum weighting matrix which can better classify the signal from noise. The experimental results show that the performance by the PSD matrices being the detection feature is very encouraging.iv

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Worst case robust downlink beamforming on the Riemannian manifold

Cited by 6 publications

References 27 publications

Robust Recursive Algorithm under Uncertainties via Worst-Case SINR Maximization

Robust Recursive Algorithm under Uncertainties via Worst-Case SINR Maximization

Max–min fair robust beamforming design for underlay device‐to‐device communications in cellular networks

Mean and Median of PSD Matrices on a Riemannian Manifold: Application to Detection of Narrow-Band Sonar Signals

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