Accelerated anti-lopsided algorithm for nonnegative least squares

Nguyen, Duy; Ho, Tu Bao

doi:10.1007/s41060-016-0037-7

Cited by 6 publications

(6 citation statements)

References 19 publications

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“…As discussed in [31], NNLS implicitly performs 1 -regularization and promotes the sparsity of the resulting solution provided that the measurement matrix B satisfies the M + -criterion [32], i.e., there exits a vector In terms of numerical implementations, the NNLS can be posed as an unconstrained LS problem over the positive orthant and can be solved by several efficient techniques such as Gradient Projection, Primal-Dual techniques, etc., with an affordable computational complexity [34], generally significantly less than CS algorithms for problems of the same size and sparsity level. We refer to [35,36] for the recent progress on the numerical solution of NNLS and a discussion on other related work in the literature.…”

Section: Path Strength Estimation Via Non-negative Least Squaresmentioning

confidence: 99%

“…In Fig. 9, we illustrate the lower and upper bounds on the achievable ergodic rate (see (36) and (37)) as a function of SNR BBF . While it is clear that the lower bound is interference-limited while the upper bound is not, we notice that the gap between the bounds is quite small in the regime of low pre-beamforming SNR (SNR BBF < 10 dB), which is relevant in mmWave applications.…”

Section: B Effectiveness Of Single-carrier Modulationmentioning

confidence: 99%

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Efficient Beam Alignment for Millimeter Wave Single-Carrier Systems With Hybrid MIMO Transceivers

Song

Haghighatshoar

Caire

2019

IEEE Trans. Wireless Commun.

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Communication at millimeter wave (mmWave) bands is expected to become a key ingredient of next generation (5G) wireless networks. Effective mmWave communications require fast and reliable methods for beamforming at both the User Equipment (UE) and the Base Station (BS) sides, in order to achieve a sufficiently large Signal-to-Noise Ratio (SNR) after beamforming. We refer to the problem of finding a pair of strongly coupled narrow beams at the transmitter and receiver as the Beam Alignment (BA) problem. In this paper, we propose an efficient BA scheme for single-carrier mmWave communications.In the proposed scheme, the BS periodically probes the channel in the downlink via a pre-specified pseudo-random beamforming codebook and pseudo-random spreading codes, letting each UE estimate the Angle-of-Arrival / Angle-of-Departure (AoA-AoD) pair of the multipath channel for which the energy transfer is maximum. We leverage the sparse nature of mmWave channels in the AoA-AoD domain to formulate the BA problem as the estimation of a sparse non-negative vector. Based on the recently developed Non-Negative Least Squares (NNLS) technique, we efficiently find the strongest AoA-AoD pair connecting each UE to the BS. We evaluate the performance of the proposed scheme under a realistic channel model, where the propagation channel consists of a few multipath scattering components each having different delays, AoAs-AoDs, and Doppler shifts. The channel model parameters are consistent with experimental channel measurements. Simulation results indicate that the proposed method is highly robust to fast channel variations caused by the large Doppler spread between the multipath components.Furthermore, we also show that after achieving BA the beamformed channel is essentially frequency-flat, such that single-carrier communication needs no equalization in the time domain.

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Section: Path Strength Estimation Via Non-negative Least Squaresmentioning

confidence: 99%

Section: B Effectiveness Of Single-carrier Modulationmentioning

confidence: 99%

Efficient Beam Alignment for Millimeter Wave Single-Carrier Systems With Hybrid MIMO Transceivers

Song

Haghighatshoar

Caire

2019

IEEE Trans. Wireless Commun.

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“…In terms of numerical implementations, the NNLS in (69) can be posed as an unconstrained Least-Squares problem over the positive orthant and can be solved by efficient techniques such as Gradient Projection, Primal-Dual techniques, etc., with an affordable computational complexity [30]. We refer to [31,32] for the recent progress on the numerical solution of NNLS and a discussion on other related work in the literature. Using the estimate s in (69), one can obtain an estimate of the measure µ as in (68) and an estimate of σ dl as in (67) followed by an appropriate truncation.…”

Section: B Interpolation From Ul Covariance Matrixmentioning

confidence: 99%

Multi-Band Covariance Interpolation with Applications in Massive MIMO

Haghighatshoar

Khalilsarai

Caire

2018

2018 IEEE International Symposium on Information Theory (ISIT)

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In this paper, we study the problem of multi-band (frequency-variant) covariance interpolation with a particular emphasis towards massive MIMO applications. In a massive MIMO system, the communication between each BS with M 1 antennas and each single-antenna user occurs through a collection of scatterers in the environment, where the channel vector of each user at BS antennas consists in a weighted linear combination of the array responses of the scatterers, where each scatterer has its own angle of arrival (AoA) and complex channel gain. The array response at a given AoA depends on the wavelength of the incoming planar wave and is naturally frequency dependent. This results in a frequency-dependent distortion where the second order statistics, i.e., the covariance matrix, of the channel vectors varies with frequency. In this paper, we show that although this effect is generally negligible for a small number of antennas M , it results in a considerable distortion of the covariance matrix and especially its dominant signal subspace in the massive MIMO regime where M → ∞, and can generally incur a serious degradation of the performance especially in frequency division duplexing (FDD) massive MIMO systems where the uplink (UL) and the downlink (DL) communication occur over different frequency bands. We propose a novel UL-DL covariance interpolation technique that is able to recover the covariance matrix in the DL from an estimate of the covariance matrix in the UL under a mild reciprocity condition on the angular power spread function (PSF) of the users (this is in contrast with the UL-DL reciprocity of the instantaneous realization of the channel vectors which does not generally hold). We analyze the performance of our proposed scheme mathematically and prove its robustness under a sufficiently large spatial oversampling of the array. We also propose several simple off-the-shelf algorithms for UL-DL covariance interpolation and evaluate their performance via numerical simulations.Index Terms-UL-DL reciprocity, UL-DL reciprocity of the power spectral function, massive MIMO system.

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“…To do so, the following optimization problem was solved where the inequality is considered element-wise. To compute the NNLS coefficients efficiently, we implemented the algorithm described in Nguyen and Ho (2017). We modified the algorithm to be able to perform computations on a matrix of responses instead of on a single vector.…”

Section: Methodsmentioning

confidence: 99%

Reconstructing the regulatory programs underlying the phenotypic plasticity of neural cancers

Larsson

Held

Popova

et al. 2023

Preprint

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Nervous system cancers contain a large spectrum of transcriptional cell states, reflecting processes active during normal development, injury response and growth. However, we lack a good understanding of these states' regulation and pharmacological importance. Here, we describe the integrated reconstruction of such cellular regulatory programs and their therapeutic targets from extensive collections of single-cell RNA sequencing data (scRNA-seq) from both tumors and developing tissues. Our method, termed single-cell Regulatory-driven Clustering (scRegClust), predicts essential kinases and transcription factors in little computational time thanks to a new efficient optimization strategy. Using this method, we analyze scRNA-seq data from both adult and childhood brain cancers to identify transcription factors and kinases that regulate distinct tumor cell states. In adult glioblastoma, our model predicts that blocking the activity of PDGFRA, DDR1, ERBB3 or SOX6, or increasing YBX1-activity, would potentiate temozolomide treatment. We further perform an integrative study of scRNA-seq data from both cancer and the developing brain to uncover the regulation of emerging meta-modules. We find a meta-module regulated by the transcription factors SPI1 and IRF8 and link it to an immune-mediated mesenchymal-like state. Our algorithm is available as an easy-to-use R package and companion visualization tool that help uncover the regulatory programs underlying cell plasticity in cancer and other diseases.

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Accelerated anti-lopsided algorithm for nonnegative least squares

Cited by 6 publications

References 19 publications

Efficient Beam Alignment for Millimeter Wave Single-Carrier Systems With Hybrid MIMO Transceivers

Efficient Beam Alignment for Millimeter Wave Single-Carrier Systems With Hybrid MIMO Transceivers

Multi-Band Covariance Interpolation with Applications in Massive MIMO

Reconstructing the regulatory programs underlying the phenotypic plasticity of neural cancers

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