11 research outputs found
Estimation of Sparse MIMO Channels with Common Support
We consider the problem of estimating sparse communication channels in the
MIMO context. In small to medium bandwidth communications, as in the current
standards for OFDM and CDMA communication systems (with bandwidth up to 20
MHz), such channels are individually sparse and at the same time share a common
support set. Since the underlying physical channels are inherently
continuous-time, we propose a parametric sparse estimation technique based on
finite rate of innovation (FRI) principles. Parametric estimation is especially
relevant to MIMO communications as it allows for a robust estimation and
concise description of the channels. The core of the algorithm is a
generalization of conventional spectral estimation methods to multiple input
signals with common support. We show the application of our technique for
channel estimation in OFDM (uniformly/contiguous DFT pilots) and CDMA downlink
(Walsh-Hadamard coded schemes). In the presence of additive white Gaussian
noise, theoretical lower bounds on the estimation of SCS channel parameters in
Rayleigh fading conditions are derived. Finally, an analytical spatial channel
model is derived, and simulations on this model in the OFDM setting show the
symbol error rate (SER) is reduced by a factor 2 (0 dB of SNR) to 5 (high SNR)
compared to standard non-parametric methods - e.g. lowpass interpolation.Comment: 12 pages / 7 figures. Submitted to IEEE Transactions on Communicatio
Grant-Free Massive MTC-Enabled Massive MIMO: A Compressive Sensing Approach
A key challenge of massive MTC (mMTC), is the joint detection of device
activity and decoding of data. The sparse characteristics of mMTC makes
compressed sensing (CS) approaches a promising solution to the device detection
problem. However, utilizing CS-based approaches for device detection along with
channel estimation, and using the acquired estimates for coherent data
transmission is suboptimal, especially when the goal is to convey only a few
bits of data.
First, we focus on the coherent transmission and demonstrate that it is
possible to obtain more accurate channel state information by combining
conventional estimators with CS-based techniques. Moreover, we illustrate that
even simple power control techniques can enhance the device detection
performance in mMTC setups.
Second, we devise a new non-coherent transmission scheme for mMTC and
specifically for grant-free random access. We design an algorithm that jointly
detects device activity along with embedded information bits. The approach
leverages elements from the approximate message passing (AMP) algorithm, and
exploits the structured sparsity introduced by the non-coherent transmission
scheme. Our analysis reveals that the proposed approach has superior
performance compared to application of the original AMP approach.Comment: Submitted to IEEE Transactions on Communication
Hybrid approximate message passing
Gaussian and quadratic approximations of message passing algorithms on graphs have attracted considerable recent attention due to their computational simplicity, analytic tractability, and wide applicability in optimization and statistical inference problems. This paper presents a systematic framework for incorporating such approximate message passing (AMP) methods in general graphical models. The key concept is a partition of dependencies of a general graphical model into strong and weak edges, with the weak edges representing interactions through aggregates of small, linearizable couplings of variables. AMP approximations based on the Central Limit Theorem can be readily applied to aggregates of many weak edges and integrated with standard message passing updates on the strong edges. The resulting algorithm, which we call hybrid generalized approximate message passing (HyGAMP), can yield significantly simpler implementations of sum-product and max-sum loopy belief propagation. By varying the partition of strong and weak edges, a performance--complexity trade-off can be achieved. Group sparsity and multinomial logistic regression problems are studied as examples of the proposed methodology.The work of S. Rangan was supported in part by the National Science Foundation under Grants 1116589, 1302336, and 1547332, and in part by the industrial affiliates of NYU WIRELESS. The work of A. K. Fletcher was supported in part by the National Science Foundation under Grants 1254204 and 1738286 and in part by the Office of Naval Research under Grant N00014-15-1-2677. The work of V. K. Goyal was supported in part by the National Science Foundation under Grant 1422034. The work of E. Byrne and P. Schniter was supported in part by the National Science Foundation under Grant CCF-1527162. (1116589 - National Science Foundation; 1302336 - National Science Foundation; 1547332 - National Science Foundation; 1254204 - National Science Foundation; 1738286 - National Science Foundation; 1422034 - National Science Foundation; CCF-1527162 - National Science Foundation; NYU WIRELESS; N00014-15-1-2677 - Office of Naval Research
Inference in Linear Observations with Multiple Signal Sources: Analysis of Approximate Message Passing and Applications to Unsourced Random Access in Cell-Free Systems
Here we consider a problem of multiple measurement vector (MMV) compressed
sensing with multiple signal sources. The observation model is motivated by the
application of {\em unsourced random access} in wireless cell-free MIMO
(multiple-input-multiple-output) networks. We present a novel (and rigorous)
high-dimensional analysis of the AMP (approximate message passing) algorithm
devised for the model. As the system dimensions in the order, say , tend to infinity, we show that the empirical dynamical order parameters
-- describing the dynamics of the AMP -- converge to deterministic limits
(described by a state-evolution equation) with the convergence rate . Furthermore, we have shown the asymptotic consistency of
the AMP analysis with the replica-symmetric calculation of the static problem.
In addition, we provide some interesting aspects on the unsourced random access
(or initial access) for cell-free systems, which is the application motivating
the algorithm
Efficient High-Dimensional Inference in the Multiple Measurement Vector Problem
In this work, a Bayesian approximate message passing algorithm is proposed
for solving the multiple measurement vector (MMV) problem in compressive
sensing, in which a collection of sparse signal vectors that share a common
support are recovered from undersampled noisy measurements. The algorithm,
AMP-MMV, is capable of exploiting temporal correlations in the amplitudes of
non-zero coefficients, and provides soft estimates of the signal vectors as
well as the underlying support. Central to the proposed approach is an
extension of recently developed approximate message passing techniques to the
amplitude-correlated MMV setting. Aided by these techniques, AMP-MMV offers a
computational complexity that is linear in all problem dimensions. In order to
allow for automatic parameter tuning, an expectation-maximization algorithm
that complements AMP-MMV is described. Finally, a detailed numerical study
demonstrates the power of the proposed approach and its particular suitability
for application to high-dimensional problems.Comment: 28 pages, 9 figure