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Merouane Debbah - One of the best experts on this subject based on the ideXlab platform.
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Linear precoding based on Polynomial Expansion: reducing complexity in massive MIMO
EURASIP Journal on Wireless Communications and Networking, 2016Co-Authors: Axel Mueller, Abla Kammoun, Emil Björnson, Merouane DebbahAbstract:Massive multiple-input multiple-output (MIMO) techniques have the potential to bring tremendous improvements in spectral efficiency to future communication systems. Counterintuitively, the practical issues of having uncertain channel knowledge, high propagation losses, and implementing optimal non-linear precoding are solved more or less automatically by enlarging system dimensions. However, the computational precoding complexity grows with the system dimensions. For example, the close-to-optimal and relatively "antenna-efficient" regularized zero-forcing (RZF) precoding is very complicated to implement in practice, since it requires fast inversions of large matrices in every coherence period. Motivated by the high performance of RZF, we propose to replace the matrix inversion and multiplication by a truncated Polynomial Expansion (TPE), thereby obtaining the new TPE precoding scheme which is more suitable for real-time hardware implementation and significantly reduces the delay to the first transmitted symbol. The degree of the matrix Polynomial can be adapted to the available hardware resources and enables smooth transition between simple maximum ratio transmission and more advanced RZF. By deriving new random matrix results, we obtain a deterministic expression for the asymptotic signal-to-interference-and-noise ratio (SINR) achieved by TPE precoding in massive MIMO systems. Furthermore, we provide a closed-form expression for the Polynomial coefficients that maximizes this SINR. To maintain a fixed per-user rate loss as compared to RZF, the Polynomial degree does not need to scale with the system, but it should be increased with the quality of the channel knowledge and the signal-to-noise ratio.
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Polynomial Expansion of the precoder for power minimization in large-scale MIMO systems
2016 IEEE International Conference on Communications ICC 2016, 2016Co-Authors: Houssem Sifaou, Abla Kammoun, Merouane Debbah, Luca Sanguinetti, Mohamed-slim AlouiniAbstract:This work focuses on the downlink of a single-cell large-scale MIMO system in which the base station equipped with M antennas serves K single-antenna users. In particular, we are interested in reducing the implementation complexity of the optimal linear precoder (OLP) that minimizes the total power consumption while ensuring target user rates. As most precoding schemes, a major difficulty towards the implementation of OLP is that it requires fast inversions of large matrices at every new channel realizations. To overcome this issue, we aim at designing a linear precoding scheme providing the same performance of OLP but with lower complexity. This is achieved by applying the truncated Polynomial Expansion (TPE) concept on a per-user basis. To get a further leap in complexity reduction and allow for closed-form expressions of the per-user weighting coefficients, we resort to the asymptotic regime in which M and K grow large with a bounded ratio. Numerical results are used to show that the proposed TPE precoding scheme achieves the same performance of OLP with a significantly lower implementation complexity.
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linear precoding based on Polynomial Expansion large scale multi cell mimo systems
IEEE Journal of Selected Topics in Signal Processing, 2014Co-Authors: Abla Kammoun, Emil Björnson, Axel H E Muller, Merouane DebbahAbstract:Large-scale MIMO systems can yield a substantial improvements in spectral efficiency for future communication systems. Due to the finer spatial resolution and array gain achieved by a massive number of antennas at the base station, these systems have shown to be robust to inter-user interference and the use of linear precoding appears to be asymptotically optimal. However, from a practical point of view, most precoding schemes exhibit prohibitively high computational complexity as the system dimensions increase. For example, the near-optimal regularized zero forcing (RZF) precoding requires the inversion of a large matrix. To solve this issue, we propose in this paper to approximate the matrix inverse by a truncated Polynomial Expansion (TPE), where the Polynomial coefficients are optimized to maximize the system performance. This technique has been recently applied in single cell scenarios and it was shown that a small number of coefficients is sufficient to reach performance similar to that of RZF, while it was not possible to surpass RZF. In a realistic multi-cell scenario involving large-scale multi-user MIMO systems, the optimization of RZF precoding has, thus far, not been feasible. This is mainly attributed to the high complexity of the scenario and the non-linear impact of the necessary regularizing parameters. On the other hand, the scalar coefficients in TPE precoding give hope for possible throughput optimization. To this end, we exploit random matrix theory to derive a deterministic expression of the asymptotic signal-to-interference-and-noise ratio for each user based on channel statistics. We also provide an optimization algorithm to approximate the coefficients that maximize the network-wide weighted max-min fairness. The optimization weights can be used to mimic the user throughput distribution of RZF precoding. Using simulations, we compare the network throughput of the proposed TPE precoding with that of the suboptimal RZF scheme and show that our scheme can achieve higher throughput using a TPE order of only 5.
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linear precoding based on Polynomial Expansion reducing complexity in massive mimo extended version
2013Co-Authors: Axel H E Muller, Abla Kammoun, Emil Björnson, Merouane DebbahAbstract:Massive multiple-input multiple-output (MIMO) techniques have the potential to bring tremendous improvements in spectral efficiency to future communication systems. Counterintuitively, the practical issues of having uncertain channel knowledge, high propagation losses, and implementing optimal nonlinear precoding are solved more-or-less automatically by enlarging system dimensions. However, the computational precoding complexity grows with the system dimensions. For example, the close-to-optimal regularized zero-forcing (RZF) precoding is very complicated to implement in practice, since it requires fast inversions of large matrices in every coherence period. Motivated by the high performance of RZF, we propose to replace the matrix inversion by a truncated Polynomial Expansion (TPE), thereby obtaining the new TPE precoding scheme which is more suitable for real-time hardware implementation. The degree of the matrix Polynomial can be adapted to the available hardware resources and enables smooth transition between simple maximum ratio transmission (MRT) and more advanced RZF. By deriving new random matrix results, we obtain a deterministic expression for the asymptotic signal-to-interference-andnoise ratio (SINR) achieved by TPE precoding in massive MIMO systems. Furthermore, we provide a closed-form expression for the Polynomial coefficients that maximizes this SINR. To maintain a fixed per-user rate loss as compared to RZF, the Polynomial degree does not need to scale with the system, but it should be increased with the quality of the channel knowledge and the signal-to-noise ratio (SNR).
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linear precoding based on truncated Polynomial Expansion part i large scale single cell systems
2013Co-Authors: Abla Kammoun, Emil Björnson, Axel H E Muller, Merouane DebbahAbstract:Large-scale MIMO systems can yield a substantial improvement in spectral efficiency for future communication systems. Due to the finer spatial resolution achieved by a huge number of antennas at the base stations, these systems have shown to be robust to inter-user interference and the use of linear precoding is asymptotically optimal. However, from a practical point of view, most precoding schemes exhibit prohibitively high computational complexity as the system dimensions increase. For example, the near-optimal regularized zero forcing (RZF) precoding requires the inversion of a large matrix. This motivated our companion paper, where we proposed to solve the issue in singlecell multi-user systems by approximating the matrix inverse by a truncated Polynomial Expansion (TPE), where the Polynomial coefficients are optimized to maximize the system performance. We have shown that the proposed TPE precoding with a small number of coefficients reaches almost the performance of RZF but never exceeds it. In a realistic multi-cell scenario involving large-scale multiuser MIMO systems, the optimization of RZF precoding has thus far not been feasible. This is mainly attributed to the high complexity of the scenario and the non-linear impact of the necessary regularizing parameters. On the other hand, the scalar weights in TPE precoding give hope for possible throughput optimization. Following the same methodology as in the companion paper, we exploit random matrix theory to derive a deterministic expression for the asymptotic signal-to-interference-and-noise ratio (SINR) for each user based on channel statistics. We also provide an optimization algorithm to approximate the weights that maximize the network-wide weighted max-min fairness. The optimization weights can be used to mimic the user throughput distribution of RZF precoding. Using simulations, we compare the network throughput of the proposed TPE precoding with that of the suboptimal RZF scheme and show that our scheme can achieve higher throughput using a TPE order of only 3.
David K Hoffman - One of the best experts on this subject based on the ideXlab platform.
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a general energy separable Polynomial representation of the time independent full green operator with application to time independent wavepacket forms of schrodinger and lippmann schwinger equations
Chemical Physics Letters, 1994Co-Authors: Youhong Huang, Donald J Kouri, David K HoffmanAbstract:Abstract A general, energy-separable Faber Polynomial representation of the full time-independent Green operator is presented. Non-Hermitian Hamiltonians are included, allowing treatment of negative imaginary absorbing potentials. A connection between the Faber Polynomial Expansion and our earlier Chebychev Polynomial Expansion (Chem. Phys. Letters 206 (1993) 96) is established, thereby generalizing the Chebychev Expansion to the complex energy plane. The method is applied to collinear H + H2 reactive scattering.
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orthogonal Polynomial Expansion of the spectral density operator and the calculation of bound state energies and eigenfunctions
Chemical Physics Letters, 1994Co-Authors: Wei Zhu, Youhong Huang, Donald J Kouri, Colston Chandler, David K HoffmanAbstract:Abstract An orthogonal Polynomial Expansion method is presented, and illustrated with calculations, for calculating δ( E – H ), the spectral density operator (SDO), the projection operator that projects out of any L 2 wavepacket the eigenstate (s) of H having energy E . If applied to an L 2 wavepacket which overlaps the interaction, it yields either scattering-type (improper) eigenstates or proper bound eigenstates. For negative energies, the exact SDO yields zero away from an eigenvalue, and yields the energy eigenstate (times a constant) when E equals an eigenvalue. The finite orthogonal Polynomial Expansion of the SDO, acting on an L 2 wavepacket, yields approximately zero for E not equal to an eigenvalue, and becomes nonzero in the neighborhood of an eigenvalue.
Antonia M Tulino - One of the best experts on this subject based on the ideXlab platform.
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low complexity truncated Polynomial Expansion dl precoders and ul receivers for massive mimo in correlated channels
IEEE Transactions on Wireless Communications, 2019Co-Authors: Andreas Benzin, Giuseppe Caire, Yonatan Shadmi, Antonia M TulinoAbstract:In Time Division Duplex reciprocity-based massive MIMO, it is essential to compute the downlink precoding matrix over all OFDM resource blocks within a small fraction of the uplink-downlink slot duration. Because of this harsh computation latency constraint, early implementations of massive MIMO considered the simple Conjugate Beamforming (ConjBF) precoding method. On the other hand, it is well-known that in the regime of a large but finite number of antennas, the Regularized Zero-Forcing (RZF) precoding is generally much more effective than ConjBF. In order to close the gap between ConjBF and RZF, while meeting the latency constraint, truncated Polynomial Expansion (TPE) methods have been proposed. In this paper, we present a novel TPE method that outperforms previously proposed methods in the non-symmetric case of users with different channel correlations, subject to the condition that the covariance matrices of the user channel vectors can be approximated, for a large number of antennas, by a family of matrices with common eigenvectors. This condition is met, for example, by uniform linear and uniform planar arrays in far-field conditions. The proposed method is computationally simple and lends itself to classical power allocation optimization such as min-sum power and max-min rate . We provide a detailed analysis of the computation latency vs computation resources, specifically targeted to a highly parallel FPGA hardware architecture. We conclude that the proposed TPE method can effectively close the performance gap between ConjBF and RZF with computation latency of less than one LTE OFDM symbol, as assumed in Marzetta’s work on massive MIMO.
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truncated Polynomial Expansion downlink precoders and uplink detectors for massive mimo
arXiv: Information Theory, 2017Co-Authors: Andreas Benzin, Giuseppe Caire, Yonatan Shadmi, Antonia M TulinoAbstract:In TDD reciprocity-based massive MIMO it is essential to be able to compute the downlink precoding matrix over all OFDM resource blocks within a small fraction of the uplink-downlink slot duration. Early implementation of massive MIMO are limited to the simple Conjugate Beamforming (ConjBF) precoding method, because of such computation latency limitation. However, it has been widely demonstrated by theoretical analysis and system simulation that Regularized Zero-Forcing (RZF) precoding is generally much more effective than ConjBF for a large but practical number of transmit antennas. In order to recover a significant fraction of the gap between ConjBF and RZF and yet meeting the very strict computation latency constraints, truncated Polynomial Expansion (TPE) methods have been proposed. In this paper we present a novel TPE method that outperforms all previously proposed methods in the general non-symmetric case of users with arbitrary antenna correlation. In addition, the proposed method is significantly simpler and more flexible than previously proposed methods based on deterministic equivalents and free probability in large random matrix theory. We consider power allocation with our TPE approach, and show that classical system optimization problems such as min-sum power and max-min rate can be easily solved. Furthermore, we provide a detailed computation latency analysis specifically targeted to a highly parallel FPGA hardware architecture.
Carl-fredrik Westin - One of the best experts on this subject based on the ideXlab platform.
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Diffusion tensor image registration using Polynomial Expansion
Physics in medicine and biology, 2013Co-Authors: Yuanjun Wang, Zengai Chen, Shengdong Nie, Carl-fredrik WestinAbstract:In this paper, we present a deformable registration framework for the diffusion tensor image (DTI) using Polynomial Expansion. The use of Polynomial Expansion in image registration has previously been shown to be beneficial due to fast convergence and high accuracy. However, earlier work was developed only for 3D scalar medical image registration. In this work, it is shown how Polynomial Expansion can be applied to DTI registration. A new measurement is proposed for DTI registration evaluation, which seems to be robust and sensitive in evaluating the result of DTI registration. We present the algorithms for DTI registration using Polynomial Expansion by the fractional anisotropy image, and an explicit tensor reorientation strategy is inherent to the registration process. Analytic transforms with high accuracy are derived from Polynomial Expansion and used for transforming the tensor's orientation. Three measurements for DTI registration evaluation are presented and compared in experimental results. The experiments for algorithm validation are designed from simple affine deformation to nonlinear deformation cases, and the algorithms using Polynomial Expansion give a good performance in both cases. Inter-subject DTI registration results are presented showing the utility of the proposed method.
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WBIR - Multi-modal image registration using Polynomial Expansion and mutual information
Biomedical Image Registration, 2012Co-Authors: Daniel Forsberg, Gunnar Farneback, Hans Knutsson, Carl-fredrik WestinAbstract:The use of Polynomial Expansion in image registration has previously been shown to be beneficial due to fast convergence and high accuracy. However, earlier work has only been for mono-modal image registration. In this work, it is shown how Polynomial Expansion and mutual information can be linked to achieve multi-modal image registration. The proposed method is evaluated using MRI data and shown to have a satisfactory accuracy while not increasing the computation time significantly.
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Multi-affine registration using local Polynomial Expansion
Journal of Zhejiang University SCIENCE C, 2010Co-Authors: Yuanjun Wang, Gunnar Farneback, Carl-fredrik WestinAbstract:In this paper, we present a non-linear (multi-affine) registration algorithm based on a local Polynomial Expansion model. We generalize previous work using a quadratic Polynomial Expansion model. Local affine models are estimated using this generalized model analytically and iteratively, and combined to a deformable registration algorithm. Experiments show that the affine parameter calculations derived from this quadratic model are more accurate than using a linear model. Experiments further indicate that the multi-affine deformable registration method can handle complex non-linear deformation fields necessary for deformable registration, and a faster convergent rate is verified from our comparison experiment.
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affine and deformable registration based on Polynomial Expansion
Medical Image Computing and Computer-Assisted Intervention, 2006Co-Authors: Gunnar Farneback, Carl-fredrik WestinAbstract:This paper presents a registration framework based on the Polynomial Expansion transform. The idea of Polynomial Expansion is that the image is locally approximated by Polynomials at each pixel. Starting with observations of how the coefficients of ideal linear and quadratic Polynomials change under translation and affine transformation, algorithms are developed to estimate translation and compute affine and deformable registration between a fixed and a moving image, from the Polynomial Expansion coefficients. All algorithms can be used for signals of any dimensionality. The algorithms are evaluated on medical data.
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MICCAI (1) - Affine and deformable registration based on Polynomial Expansion
Medical image computing and computer-assisted intervention : MICCAI ... International Conference on Medical Image Computing and Computer-Assisted Inte, 2006Co-Authors: Gunnar Farneback, Carl-fredrik WestinAbstract:This paper presents a registration framework based on the Polynomial Expansion transform. The idea of Polynomial Expansion is that the image is locally approximated by Polynomials at each pixel. Starting with observations of how the coefficients of ideal linear and quadratic Polynomials change under translation and affine transformation, algorithms are developed to estimate translation and compute affine and deformable registration between a fixed and a moving image, from the Polynomial Expansion coefficients. All algorithms can be used for signals of any dimensionality. The algorithms are evaluated on medical data.
Youhong Huang - One of the best experts on this subject based on the ideXlab platform.
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a general energy separable Polynomial representation of the time independent full green operator with application to time independent wavepacket forms of schrodinger and lippmann schwinger equations
Chemical Physics Letters, 1994Co-Authors: Youhong Huang, Donald J Kouri, David K HoffmanAbstract:Abstract A general, energy-separable Faber Polynomial representation of the full time-independent Green operator is presented. Non-Hermitian Hamiltonians are included, allowing treatment of negative imaginary absorbing potentials. A connection between the Faber Polynomial Expansion and our earlier Chebychev Polynomial Expansion (Chem. Phys. Letters 206 (1993) 96) is established, thereby generalizing the Chebychev Expansion to the complex energy plane. The method is applied to collinear H + H2 reactive scattering.
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orthogonal Polynomial Expansion of the spectral density operator and the calculation of bound state energies and eigenfunctions
Chemical Physics Letters, 1994Co-Authors: Wei Zhu, Youhong Huang, Donald J Kouri, Colston Chandler, David K HoffmanAbstract:Abstract An orthogonal Polynomial Expansion method is presented, and illustrated with calculations, for calculating δ( E – H ), the spectral density operator (SDO), the projection operator that projects out of any L 2 wavepacket the eigenstate (s) of H having energy E . If applied to an L 2 wavepacket which overlaps the interaction, it yields either scattering-type (improper) eigenstates or proper bound eigenstates. For negative energies, the exact SDO yields zero away from an eigenvalue, and yields the energy eigenstate (times a constant) when E equals an eigenvalue. The finite orthogonal Polynomial Expansion of the SDO, acting on an L 2 wavepacket, yields approximately zero for E not equal to an eigenvalue, and becomes nonzero in the neighborhood of an eigenvalue.