A general solution to the maximization of the multidimensional generalized Rayleigh quotient used in linear discriminant analysis for signal classification

Prieto, Rodolfo

doi:10.1109/icassp.2003.1201642

Cited by 33 publications

(20 citation statements)

References 2 publications

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“…The ratio in Equation 4 is a generalized Rayleigh quotient [13] whose maximum can be found through a generalized eigen decomposition of the matrices X'X and (X-QX)'(X-QX) . This results into two matrices W ,…”

Section: Methodsmentioning

confidence: 99%

Phase synchrony analysis for SSVEP-based BCIs

Zhu

Garcia-Molina

Mihajlović

et al. 2010

2010 2nd International Conference on Computer Engineering and Technology

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Brain-computer interfaces (BCI) based on SteadyState Visual Evoked Potential (SSVEP) can provide higher throughput than other BCI modalities. For the sake of safety and comfort, the frequencies of the stimulus should be higher than 30 Hz. However, only a limited number of these frequencies can elicit SSVEPs that are strong enough for BCI purposes. In order to increase the number of available stimuli, the SSVEP phase can be taken into account. In this study, we used phase synchrony analysis to extract the phase difference between SSVEP and stimuli as a feature to identify a subject's intention. This analysis can mitigate the adverse effect brought by the phase deviation that may occur in the stimuli. Furthermore, the classification accuracy when using a single lead signal (Oz-Cz) is compared to a spatial filtered signal. The result shows that the phase synchrony analysis can effectively extract the phase difference and that spatial filtering can significantly increase the classification accuracy. Keywords-brain computer interface (BCI); steady state visual evoked potential (SSVEP); Hilbert transform; phase synchrony; spatial filtering. I.V2-329 978-1-4244-6349-7/10/$26.00 c 2010 IEEE

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Section: Methodsmentioning

confidence: 99%

Phase synchrony analysis for SSVEP-based BCIs

Zhu

Garcia-Molina

Mihajlović

et al. 2010

2010 2nd International Conference on Computer Engineering and Technology

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“…The maximization of equation (15) can now be immediately recognized as Generalized Rayleigh Quotient maximization problem [24] in absence of constraint ū k = 1 for which the optimum solution is given by the largest generalized eigenvector of the matrix pair (Ĥ k ,Ŵ k ). Furthermore, in [25], the optimal solution is still given by the largest eigenvalue of W −1 k ·Ĥ k , also under desired constraint ū k = 1, thus…”

Section: B Beamformer Optimization Under Fixed Powermentioning

confidence: 99%

Transmission strategies under imperfect instantaneous CSIT

Malla

Abreu

2015

2015 IEEE Wireless Communications and Networking Conference (WCNC)

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We propose a simple solution based on PerronFrobenius theorem and uplink-downlink duality to the longstanding problem of transmission strategies: maximize the minimum SINR or minimize the transmit power. In contrary of using perfect and instantaneous CSIT (requires higher overhead and backhauling), or using only average CSIT, e.g. channel covariance which suffers from quality fluctuations; we account for imperfect instantaneous CSIT. The solution emerges from the observation that the crux of the robustness problem is the construction of SINR estimates itself. We provide a MLE-based estimate which being sub-optimal and failing to incorporate the channel estimation error, we reinforce it by biasing the estimate, which not only achieves smaller error but is strictly conservative as well. We also consider both transmission strategy problems, and show that the biased estimates are not only robust compared to traditional unbiased estimates, but also substantially outperform the probabilistic method with Bernstein-type relaxation proposed in [1].

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“…which holds a generalized RQ structure, such that the optimal solution to u k is obtained by [26] Computev k ∀k from equation (14).…”

Section: ) Design Of Rx Combiner U K ∀Kmentioning

confidence: 99%

Full-Duplex Transmission Optimization for Bi-directional MIMO links with QoS Guarantees

Iimori

Abreu

Alexandropoulos

2018

2018 IEEE Global Conference on Signal and Information Processing (GlobalSIP)

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We consider a bi-directional Full-Duplex (FD) Multiple-Input Multiple-Output (MIMO) communication system in which nodes are capable of performing transitter (TX)-Receiver (RX) digital precoding/combining and multi-tap analog cancellation, and have individual Signal-to-Interference-plusnoise Ratio (SINR) requirements. We present an iterative algorithm for the TX powers minimization that includes closedform expressions for the TX/RX digital beamformers at each algorithmic iteration step. Our representative simulation results demonstrate that the proposed algorithm can reduce residual Self-Interference (SI) due to FD operation to below −110dB, which is the typical noise floor level for wireless communications. In addition, our design outperforms relevant recent solutions proposed for 2-user MIMO systems (the so called MIMO X channel) in terms of both power efficiency and computational complexity.

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A general solution to the maximization of the multidimensional generalized Rayleigh quotient used in linear discriminant analysis for signal classification

Cited by 33 publications

References 2 publications

Phase synchrony analysis for SSVEP-based BCIs

Phase synchrony analysis for SSVEP-based BCIs

Transmission strategies under imperfect instantaneous CSIT

Full-Duplex Transmission Optimization for Bi-directional MIMO links with QoS Guarantees

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