308 research outputs found
Subspace Methods for Joint Sparse Recovery
We propose robust and efficient algorithms for the joint sparse recovery
problem in compressed sensing, which simultaneously recover the supports of
jointly sparse signals from their multiple measurement vectors obtained through
a common sensing matrix. In a favorable situation, the unknown matrix, which
consists of the jointly sparse signals, has linearly independent nonzero rows.
In this case, the MUSIC (MUltiple SIgnal Classification) algorithm, originally
proposed by Schmidt for the direction of arrival problem in sensor array
processing and later proposed and analyzed for joint sparse recovery by Feng
and Bresler, provides a guarantee with the minimum number of measurements. We
focus instead on the unfavorable but practically significant case of
rank-defect or ill-conditioning. This situation arises with limited number of
measurement vectors, or with highly correlated signal components. In this case
MUSIC fails, and in practice none of the existing methods can consistently
approach the fundamental limit. We propose subspace-augmented MUSIC (SA-MUSIC),
which improves on MUSIC so that the support is reliably recovered under such
unfavorable conditions. Combined with subspace-based greedy algorithms also
proposed and analyzed in this paper, SA-MUSIC provides a computationally
efficient algorithm with a performance guarantee. The performance guarantees
are given in terms of a version of restricted isometry property. In particular,
we also present a non-asymptotic perturbation analysis of the signal subspace
estimation that has been missing in the previous study of MUSIC.Comment: submitted to IEEE transactions on Information Theory, revised versio
Discrete and Continuous Sparse Recovery Methods and Their Applications
Low dimensional signal processing has drawn an increasingly broad amount of attention in the past decade, because prior information about a low-dimensional space can be exploited to aid in the recovery of the signal of interest. Among all the different forms of low di- mensionality, in this dissertation we focus on the synthesis and analysis models of sparse recovery. This dissertation comprises two major topics. For the first topic, we discuss the synthesis model of sparse recovery and consider the dictionary mismatches in the model. We further introduce a continuous sparse recovery to eliminate the existing off-grid mismatches for DOA estimation. In the second topic, we focus on the analysis model, with an emphasis on efficient algorithms and performance analysis.
In considering the sparse recovery method with structured dictionary mismatches for the synthesis model, we exploit the joint sparsity between the mismatch parameters and original sparse signal. We demonstrate that by exploiting this information, we can obtain a robust reconstruction under mild conditions on the sensing matrix. This model is very useful for
radar and passive array applications. We propose several efficient algorithms to solve the joint sparse recovery problem. Using numerical examples, we demonstrate that our proposed algorithms outperform several methods in the literature. We further extend the mismatch model to a continuous sparse model, using the mathematical theory of super resolution. Statistical analysis shows the robustness of the proposed algorithm. A number-detection algorithm is also proposed for the co-prime arrays. By using numerical examples, we show that continuous sparse recovery further improves the DOA estimation accuracy, over both the joint sparse method and also MUSIC with spatial smoothing.
In the second topic, we visit the corresponding analysis model of sparse recovery. Instead of assuming a sparse decomposition of the original signal, the analysis model focuses on the existence of a linear transformation which can make the original signal sparse. In this work we use a monotone version of the fast iterative shrinkage- thresholding algorithm (MFISTA) to yield efficient algorithms to solve the sparse recovery. We examine two widely used relaxation techniques, namely smoothing and decomposition, to relax the optimization. We show that although these two techniques are equivalent in their objective functions, the smoothing technique converges faster than the decomposition technique. We also compute the performance guarantee for the analysis model when a LASSO type of reconstruction is performed. By using numerical examples, we are able to show that the proposed algorithm is more efficient than other state of the art algorithms
Compressive Sensing-Based Grant-Free Massive Access for 6G Massive Communication
The advent of the sixth-generation (6G) of wireless communications has given
rise to the necessity to connect vast quantities of heterogeneous wireless
devices, which requires advanced system capabilities far beyond existing
network architectures. In particular, such massive communication has been
recognized as a prime driver that can empower the 6G vision of future
ubiquitous connectivity, supporting Internet of Human-Machine-Things for which
massive access is critical. This paper surveys the most recent advances toward
massive access in both academic and industry communities, focusing primarily on
the promising compressive sensing-based grant-free massive access paradigm. We
first specify the limitations of existing random access schemes and reveal that
the practical implementation of massive communication relies on a dramatically
different random access paradigm from the current ones mainly designed for
human-centric communications. Then, a compressive sensing-based grant-free
massive access roadmap is presented, where the evolutions from single-antenna
to large-scale antenna array-based base stations, from single-station to
cooperative massive multiple-input multiple-output systems, and from unsourced
to sourced random access scenarios are detailed. Finally, we discuss the key
challenges and open issues to shed light on the potential future research
directions of grant-free massive access.Comment: Accepted by IEEE IoT Journa
Structured Compressed Sensing: From Theory to Applications
Compressed sensing (CS) is an emerging field that has attracted considerable
research interest over the past few years. Previous review articles in CS limit
their scope to standard discrete-to-discrete measurement architectures using
matrices of randomized nature and signal models based on standard sparsity. In
recent years, CS has worked its way into several new application areas. This,
in turn, necessitates a fresh look on many of the basics of CS. The random
matrix measurement operator must be replaced by more structured sensing
architectures that correspond to the characteristics of feasible acquisition
hardware. The standard sparsity prior has to be extended to include a much
richer class of signals and to encode broader data models, including
continuous-time signals. In our overview, the theme is exploiting signal and
measurement structure in compressive sensing. The prime focus is bridging
theory and practice; that is, to pinpoint the potential of structured CS
strategies to emerge from the math to the hardware. Our summary highlights new
directions as well as relations to more traditional CS, with the hope of
serving both as a review to practitioners wanting to join this emerging field,
and as a reference for researchers that attempts to put some of the existing
ideas in perspective of practical applications.Comment: To appear as an overview paper in IEEE Transactions on Signal
Processin
Thirty Years of Machine Learning: The Road to Pareto-Optimal Wireless Networks
Future wireless networks have a substantial potential in terms of supporting
a broad range of complex compelling applications both in military and civilian
fields, where the users are able to enjoy high-rate, low-latency, low-cost and
reliable information services. Achieving this ambitious goal requires new radio
techniques for adaptive learning and intelligent decision making because of the
complex heterogeneous nature of the network structures and wireless services.
Machine learning (ML) algorithms have great success in supporting big data
analytics, efficient parameter estimation and interactive decision making.
Hence, in this article, we review the thirty-year history of ML by elaborating
on supervised learning, unsupervised learning, reinforcement learning and deep
learning. Furthermore, we investigate their employment in the compelling
applications of wireless networks, including heterogeneous networks (HetNets),
cognitive radios (CR), Internet of things (IoT), machine to machine networks
(M2M), and so on. This article aims for assisting the readers in clarifying the
motivation and methodology of the various ML algorithms, so as to invoke them
for hitherto unexplored services as well as scenarios of future wireless
networks.Comment: 46 pages, 22 fig
Low-Complexity Direction-of-Arrival Estimation Based on Wideband Co-Prime Arrays
A class of low-complexity compressive sensing-based direction-of-arrival (DOA) estimation methods for wideband co-prime arrays is proposed. It is based on a recently proposed narrowband estimation method, where a virtual array model is generated by directly vectorizing the covariance matrix and then using a sparse signal recovery method to obtain the estimation result. As there are a large number of redundant entries in both the auto-correlation and cross-correlation matrices of the two sub-arrays, they can be combined together to form a model with a significantly reduced dimension, thereby leading to a solution with much lower computational complexity without sacrificing performance. A further reduction in complexity is achieved by removing noise power estimation from the formulation. Then, the two proposed low-complexity methods are extended to the wideband realm utilizing a group sparsity based signal reconstruction method. A particular advantage of group sparsity is that it allows a much larger unit inter-element spacing than the standard co-prime array and therefore leads to further improved performance
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