6,528 research outputs found
Generalized Approximate Message Passing for Massive MIMO mmWave Channel Estimation with Laplacian Prior
This paper tackles the problem of millimeter-Wave (mmWave) channel estimation
in massive MIMO communication systems. A new Bayes-optimal channel estimator is
derived using recent advances in the approximate belief propagation (BP)
Bayesian inference paradigm. By leveraging the inherent sparsity of the mmWave
MIMO channel in the angular domain, we recast the underlying channel estimation
problem into that of reconstructing a compressible signal from a set of noisy
linear measurements. Then, the generalized approximate message passing (GAMP)
algorithm is used to find the entries of the unknown mmWave MIMO channel
matrix. Unlike all the existing works on the same topic, we model the
angular-domain channel coefficients by Laplacian distributed random variables.
Further, we establish the closed-form expressions for the various statistical
quantities that need to be updated iteratively by GAMP. To render the proposed
algorithm fully automated, we also develop an expectation-maximization (EM)
based procedure that can be easily embedded within GAMP's iteration loop in
order to learn all the unknown parameters of the underlying Bayesian inference
problem. Computer simulations show that the proposed combined EM-GAMP algorithm
under a Laplacian prior exhibits improvements both in terms of channel
estimation accuracy, achievable rate, and computational complexity as compared
to the Gaussian mixture prior that has been advocated in the recent literature.
In addition, it is found that the Laplacian prior speeds up the convergence
time of GAMP over the entire signal-to-noise ratio (SNR) range.Comment: 15 pages, 5 figures, Published in IEEE Transactions on Communication
Low-Rank Spatial Channel Estimation for Millimeter Wave Cellular Systems
The tremendous bandwidth available in the millimeter wave (mmW) frequencies
between 30 and 300 GHz have made these bands an attractive candidate for
next-generation cellular systems. However, reliable communication at these
frequencies depends extensively on beamforming with very high-dimensional
antenna arrays. Estimating the channel sufficiently accurately to perform
beamforming can thus be challenging both due to low coherence time and large
number of antennas. Also, the measurements used for channel estimation may need
to be made with analog beamforming where the receiver can "look" in only
direction at a time. This work presents a novel method for estimation of the
receive-side spatial covariance matrix of a channel from a sequence of power
measurements made at different angular directions. The method reduces the
spatial covariance estimation to a matrix completion optimization problem. To
reduce the number of measurements, the optimization can incorporate the
low-rank constraints in the channels that are typical in the mmW setting. The
optimization is convex and fast, iterative methods are presented to solving the
problem. Simulations are presented for both single and multi-path channels
using channel models derived from real measurements in New York City at 28 GHz.Comment: 10 pages, 5 figure
Low Rank Matrix Recovery for Joint Array Self-Calibration and Sparse Model DoA Estimation
In this work, combined calibration and DoA estimation is approached as an
extension of the formulation for the Single Measurement Vector (SMV) model of
self-calibration to the Multiple Measurement Model (MMV) case. By taking
advantage of multiple snapshots, a modified nuclear norm minimization problem
is proposed to recover a low-rank larger dimension matrix. We also give the
definition of a linear operator for the MMV model, and give its corresponding
matrix representation to generate a variant of a convex optimization problem.
In order to mitigate the computational complexity of the approach, singular
value decomposition (SVD) is applied to reduce the problem size. The
performance of the proposed methods are demonstrated by numerical simulations
CSMA using the Bethe Approximation: Scheduling and Utility Maximization
CSMA (Carrier Sense Multiple Access), which resolves contentions over
wireless networks in a fully distributed fashion, has recently gained a lot of
attentions since it has been proved that appropriate control of CSMA parameters
guarantees optimality in terms of stability (i.e., scheduling) and system- wide
utility (i.e., scheduling and congestion control). Most CSMA-based algorithms
rely on the popular MCMC (Markov Chain Monte Carlo) technique, which enables
one to find optimal CSMA parameters through iterative loops of
`simulation-and-update'. However, such a simulation-based approach often
becomes a major cause of exponentially slow convergence, being poorly adaptive
to flow/topology changes. In this paper, we develop distributed iterative
algorithms which produce approximate solutions with convergence in polynomial
time for both stability and utility maximization problems. In particular, for
the stability problem, the proposed distributed algorithm requires, somewhat
surprisingly, only one iteration among links. Our approach is motivated by the
Bethe approximation (introduced by Yedidia, Freeman and Weiss in 2005) allowing
us to express approximate solutions via a certain non-linear system with
polynomial size. Our polynomial convergence guarantee comes from directly
solving the non-linear system in a distributed manner, rather than multiple
simulation-and-update loops in existing algorithms. We provide numerical
results to show that the algorithm produces highly accurate solutions and
converges much faster than the prior ones
Bayesian Optimal Approximate Message Passing to Recover Structured Sparse Signals
We present a novel compressed sensing recovery algorithm - termed Bayesian
Optimal Structured Signal Approximate Message Passing (BOSSAMP) - that jointly
exploits the prior distribution and the structured sparsity of a signal that
shall be recovered from noisy linear measurements. Structured sparsity is
inherent to group sparse and jointly sparse signals. Our algorithm is based on
approximate message passing that poses a low complexity recovery algorithm
whose Bayesian optimal version allows to specify a prior distribution for each
signal component. We utilize this feature in order to establish an
iteration-wise extrinsic group update step, in which likelihood ratios of
neighboring group elements provide soft information about a specific group
element. Doing so, the recovery of structured signals is drastically improved.
We derive the extrinsic group update step for a sparse binary and a sparse
Gaussian signal prior, where the nonzero entries are either one or Gaussian
distributed, respectively. We also explain how BOSSAMP is applicable to
arbitrary sparse signals. Simulations demonstrate that our approach exhibits
superior performance compared to the current state of the art, while it retains
a simple iterative implementation with low computational complexity.Comment: 13 pages, 9 figures, 1 table. Submitted to IEEE Transactions on
Signal Processin
Scaling-up Distributed Processing of Data Streams for Machine Learning
Emerging applications of machine learning in numerous areas involve
continuous gathering of and learning from streams of data. Real-time
incorporation of streaming data into the learned models is essential for
improved inference in these applications. Further, these applications often
involve data that are either inherently gathered at geographically distributed
entities or that are intentionally distributed across multiple machines for
memory, computational, and/or privacy reasons. Training of models in this
distributed, streaming setting requires solving stochastic optimization
problems in a collaborative manner over communication links between the
physical entities. When the streaming data rate is high compared to the
processing capabilities of compute nodes and/or the rate of the communications
links, this poses a challenging question: how can one best leverage the
incoming data for distributed training under constraints on computing
capabilities and/or communications rate? A large body of research has emerged
in recent decades to tackle this and related problems. This paper reviews
recently developed methods that focus on large-scale distributed stochastic
optimization in the compute- and bandwidth-limited regime, with an emphasis on
convergence analysis that explicitly accounts for the mismatch between
computation, communication and streaming rates. In particular, it focuses on
methods that solve: (i) distributed stochastic convex problems, and (ii)
distributed principal component analysis, which is a nonconvex problem with
geometric structure that permits global convergence. For such methods, the
paper discusses recent advances in terms of distributed algorithmic designs
when faced with high-rate streaming data. Further, it reviews guarantees
underlying these methods, which show there exist regimes in which systems can
learn from distributed, streaming data at order-optimal rates.Comment: 45 pages, 9 figures; preprint of a journal paper published in
Proceedings of the IEEE (Special Issue on Optimization for Data-driven
Learning and Control
Super-Resolution Blind Channel-and-Signal Estimation for Massive MIMO with One-Dimensional Antenna Array
In this paper, we study blind channel-and-signal estimation by exploiting the
burst-sparse structure of angular-domain propagation channels in massive MIMO
systems. The state-of-the-art approach utilizes the structured channel sparsity
by sampling the angular-domain channel representation with a uniform
angle-sampling grid, a.k.a. virtual channel representation. However, this
approach is only applicable to uniform linear arrays and may cause a
substantial performance loss due to the mismatch between the virtual
representation and the true angle information. To tackle these challenges, we
propose a sparse channel representation with a super-resolution sampling grid
and a hidden Markovian support. Based on this, we develop a novel approximate
inference based blind estimation algorithm to estimate the channel and the user
signals simultaneously, with emphasis on the adoption of the
expectation-maximization method to learn the angle information. Furthermore, we
demonstrate the low-complexity implementation of our algorithm, making use of
factor graph and message passing principles to compute the marginal posteriors.
Numerical results show that our proposed method significantly reduces the
estimation error compared to the state-of-the-art approach under various
settings, which verifies the efficiency and robustness of our method.Comment: 16 pages, 10 figure
Sparse Bayesian learning with uncertainty models and multiple dictionaries
Sparse Bayesian learning (SBL) has emerged as a fast and competitive method
to perform sparse processing. The SBL algorithm, which is developed using a
Bayesian framework, approximately solves a non-convex optimization problem
using fixed point updates. It provides comparable performance and is
significantly faster than convex optimization techniques used in sparse
processing. We propose a signal model which accounts for dictionary mismatch
and the presence of errors in the weight vector at low signal-to-noise ratios.
A fixed point update equation is derived which incorporates the statistics of
mismatch and weight errors. We also process observations from multiple
dictionaries. Noise variances are estimated using stochastic maximum
likelihood. The derived update equations are studied quantitatively using
beamforming simulations applied to direction-of-arrival (DoA). Performance of
SBL using single- and multi-frequency observations, and in the presence of
aliasing, is evaluated. SwellEx-96 experimental data demonstrates qualitatively
the advantages of SBL.Comment: 11 pages, 8 figure
Compressed Sensing for Wireless Communications : Useful Tips and Tricks
As a paradigm to recover the sparse signal from a small set of linear
measurements, compressed sensing (CS) has stimulated a great deal of interest
in recent years. In order to apply the CS techniques to wireless communication
systems, there are a number of things to know and also several issues to be
considered. However, it is not easy to come up with simple and easy answers to
the issues raised while carrying out research on CS. The main purpose of this
paper is to provide essential knowledge and useful tips that wireless
communication researchers need to know when designing CS-based wireless
systems. First, we present an overview of the CS technique, including basic
setup, sparse recovery algorithm, and performance guarantee. Then, we describe
three distinct subproblems of CS, viz., sparse estimation, support
identification, and sparse detection, with various wireless communication
applications. We also address main issues encountered in the design of CS-based
wireless communication systems. These include potentials and limitations of CS
techniques, useful tips that one should be aware of, subtle points that one
should pay attention to, and some prior knowledge to achieve better
performance. Our hope is that this article will be a useful guide for wireless
communication researchers and even non-experts to grasp the gist of CS
techniques
An Approximate Message Passing Framework for Side Information
Approximate message passing (AMP) methods have gained recent traction in
sparse signal recovery. Additional information about the signal, or \emph{side
information} (SI), is commonly available and can aid in efficient signal
recovery. This work presents an AMP-based framework that exploits SI and can be
readily implemented in various settings for which the SI results in separable
distributions. To illustrate the simplicity and applicability of our approach,
this framework is applied to a Bernoulli-Gaussian (BG) model and a time-varying
birth-death-drift (BDD) signal model, motivated by applications in channel
estimation. We develop a suite of algorithms, called AMP-SI, and derive
denoisers for the BDD and BG models. Numerical evidence demonstrating the
advantages of our approach are presented alongside empirical evidence of the
accuracy of a proposed state evolution
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