Multipath Matching Pursuit Research Articles

Phase retrieval for signals with block sparsity using BOMP: Algorithms and recovery guarantees

Phase retrieval (PR) from the magnitude-only measurements is a challenging problem that has attracted researchers in many scientific fields regarding the loss of phase information. However, PR for a block-sparse signal with non-zero elements present in several blocks has only a few appropriate methods that are not desirable in large-scale problems. This paper focuses on improving the adaptive capacity of PR of block sparsity for large-scale cases. Two practical greedy PR algorithms are proposed. The first is based on block orthogonal matching pursuit (BOMP) called BOMP-coordinate descent (CD). The other one invokes a tree search strategy of multipath matching pursuit (MMP), termed BMMP-CD, to promote the chance to the optimum. Theoretical conditions of BOMP-CD and BMMP-CD to select the correct index show the advantages of the proposed algorithms. Simulations show that the BOMP-CD is faster, while the recovery probability of BMMP-CD surpasses the compared counterparts.

CS-Based Near-Optimal MUD for Uplink Grant-Free NOMA

In order to furnish connectivity to an incredible number of devices and to satisfy the capacity demands, non-orthogonal multiple access (NOMA) is considered as a hopeful solution for future 5G. Moreover, grant-free transmission is substantially expected in the uplink NOMA to minimize the latency time and detection overhead. However, multi-user detection (MUD) without user-activity information in uplink grant-free NOMA is hard in practice. In this paper, by benefit from the user-activity sparsity existing in uplink grant-free NOMA, the multipath matching pursuit (MMP) is used for user-activity detection, and then message passing algorithm (MPA) can be efficiently applied for active users’ data detection. Simulation results show that the proposed MMP-MAP MUD with acceptable complexity can achieve better performance than conventional solutions. Also, the MMP-MAP detector reaches the performance obtained by the MPA detector with perfect user-activity information once the level of signal-to-noise ratio exceed 11 dB.

Multipath least squares algorithm and analysis

One important task in signal processing is to construct effective algorithms to reconstruct sparse signals from an underdetermined system of linear equations. In this paper, we propose a new sparse recovery algorithm called multipath least squares (MLS), which investigates multiple promising candidates per step and parallels the multipath matching pursuit (MMP) algorithm in this aspect. The performance of the MLS algorithm is evaluated through the ability of signal recovery. Specifically, a recovery guarantee based on the restricted isometry property (RIP) is established for MLS that ensures its exact recovery of any K-sparse signal x from the measurements y=Ax. It is also shown that this sufficient condition is nearly sharp by providing a counterexample such that the algorithm may fail to recover some K-sparse signal. Moreover, the recovery guarantee of the MLS algorithm is also provided for the case of noisy measurements. Finally, numerical experiments are conducted to demonstrate the validity and priority of the proposed algorithm.

RIP‐based analysis of multipath matching pursuit in noisy case

To increase the possibility of choosing the true support of a sparse signal, multipath matching pursuit (MMP) algorithm generates multiple promising candidates of the support set by tree-searching structure. This Letter proposes the restricted isometry property-based conditions under which at least one candidate of MMP contains the true support set in cases of l 2 and l ∞ bounded noises. Comparison with the existing result is also presented.

MMP-DCD-CV based sparse channel estimation algorithm for underwater acoustic transform domain communication system

In this paper, we propose a computationally efficient multipath matching pursuit (MMP) channel estimation algorithm for underwater acoustic (UWA) transform domain communication systems (TDCSs). The algorithm, referred to as the MMP-DCD-CV algorithm, is based on the dichotomous coordinate descent (DCD) iterations and cross validation (CV). The MMP-DCD-CV sparse channel estimator in each iteration searches for multiple promising path candidates most relevant to a residual vector and chooses the best candidate. The DCD iterations are used to solve the corresponding least squares problem with low complexity and numerical stability. The CV provides a stopping criterion of the algorithm without a priori information on the channel sparsity and noise level and examines whether the algorithm overfits its data, thus improving the estimation accuracy. The performance of the proposed algorithm is evaluated under simulated sparse UWA channels. The numerical results show that the algorithm achieves better performance than the original MMP algorithm, has lower complexity, and does not require prior knowledge on the channel sparsity and noise level. We also propose an UWA TDCS with sparse channel estimation based on the proposed MMP-DCD-CV algorithm. The proposed UWA communication system is tested by the Waymark simulator, providing the virtual signal transmission in the UWA channel, with a measured Sound Speed Profile and bathymetry. Numerical results demonstrate that the UWA TDCS with the proposed sparse channel estimator offers considerable improvement in system performance compared to other TDCS schemes.

Regularized Multipath Matching Pursuit for Sparse Channel Estimation in Millimeter Wave Massive MIMO System

Sparse channel estimation is investigated for millimeter wave massive MIMO systems, where a base station equipped with a uniform planar array serves several single-antenna users. At first, the 2-D multiuser channel estimation is formulated as several sparse recovery problems. Then a regularized multipath matching pursuit (RMMP) algorithm is proposed for sparse channel estimation. Compared to the existing multipath matching pursuit (MMP) algorithm, a regularization step is introduced in RMMP to screen the candidate paths, which can reduce the computational complexity as well as the storage overhead. Simulation results show that the proposed RMMP algorithm outperforms the existing orthogonal matching pursuit and orthogonal least squares algorithms. In particular, RMMP has the same sparse channel estimation performance as MMP while the computational complexity of the former is much lower than the latter.

An Accelerated MMP With a Pruning Tree Strategy

Multipath matching pursuit (MMP) has been developed to solve the sparse signal recovery problems in compressed sensing, which can generate recovery error less than the traditional orthogonal matching pursuit type algorithms in terms of mean square error. However, the computational burden of MMP is seriously heavy, and limits itself in applications, finding the need to be improved urgently. To lighten the burden, in this paper, an accelerated version of the MMP is proposed based on pruning tree strategy for sparse signal recovery, that attempts to reduce some of the paths in subsequent searching. By this strategy, an accelerated MMP is established in the scenarios where the MMP works. It retains the desirable performance as MMP and can shorten the running time. We demonstrate the acceleration ability of the proposed algorithm with almost the same accuracy of the original MMP, for the reconstruction of both synthetic data and images.

On the Fundamental Limit of Multipath Matching Pursuit

Multipath matching pursuit (MMP) is a recent extension of the orthogonal matching pursuit algorithm that recovers sparse signals with a tree-searching strategy. In this paper, we present a new analysis for the MMP algorithm using the restricted isometry property. Our result shows that if the sampling matrix $\mathbf {A} \in \mathbb {R}^{m \times n}$ satisfies the RIP of order $K + L$ with isometry constant $ \delta _{K+L} then the MMP accurately recovers any $K$ -sparse signal $\mathbf {x} \in \mathbf {R}^n$ from the samples $\mathbf {y}=\mathbf {A}\mathbf {x}$ , where $L$ is the number of child paths for each candidate of the algorithm. Moreover, through a counterexample, we show that the proposed bound is optimal in that the MMP algorithm may fail under $\delta _{K+L} = \sqrt{\frac{L}{{K} + {L}}}.$

Improved RIP-based performance guarantees for multipath matching pursuit

The multipath matching pursuit (MMP) is a generalization of the orthogonal matching pursuit (OMP), which generates multiple child paths for every candidate in each iteration and selects the candidate having the minimal residual as the final support set when iteration ends. In this paper we analyze its performance in both noiseless and noisy cases. The restricted isometry property (RIP)-based condition of MMP that ensures accurate recovery of sparse signals in the noiseless case is derived by using a simple technique. The performance guarantees of the MMP for support recovery in noisy cases are also discussed. It is shown that under certain conditions on the RIP and minimum magnitude of nonzero components of the sparse signal, the MMP will exactly recover the true support of the sparse signal in cases of bounded noises and recover the true support with a high probability in the case of Gaussian noise. Our bounds on the RIP improve the existing results.

Sufficient condition analysis of multipath matching pursuit

This Letter presents a sufficient condition under which the multipath matching pursuit (MMP) algorithm recovers sparse signals perfectly in compressive sensing problems. The derived sufficient condition is much more relaxed than the existing one.

Fast sparsity adaptive multipath matching pursuit for compressed sensing problems

The high computational complexity of tree-based multipath search approaches makes putting them into practical use difficult. However, reselection of candidate atoms could make the search path more accurate and efficient. We propose a multipath greedy approach called fast sparsity adaptive multipath matching pursuit (fast SAMMP), which performs a sparsity adaptive tree search to find the sparsest solution with better performances. Each tree branch acquires K atoms, and fast SAMMP reselects the best K atoms among 2K atoms. Fast SAMMP adopts sparsity adaptive techniques that allow more practical applications for the algorithm. We demonstrated the reconstruction performances of the proposed fast scheme on both synthetically generated one-dimensional signals and two-dimensional images using Gaussian observation matrices. The experimental results indicate that fast SAMMP achieves less reconstruction time and a much higher exact recovery ratio compared with conventional algorithms.

Sparse Detection With Integer Constraint Using Multipath Matching Pursuit

In this paper, we consider a detection problem of the underdetermined system when the input vector is sparse and its elements are chosen from a set of finite alphabets. This scenario is popular and embraces many of current and future wireless communication systems. We show that a simple modification of multipath matching pursuit (MMP), recently proposed parallel greedy search algorithm, is effective in recovering the discrete and sparse input signals. We also show that the addition of cross validation (CV) to the MMP algorithm is effective in identifying the sparsity level of input vector.

Multipath Matching Pursuit

In this paper, we propose an algorithm referred to as multipath matching pursuit (MMP) that investigates multiple promising candidates to recover sparse signals from compressed measurements. Our method is inspired by the fact that the problem to find the candidate that minimizes the residual is readily modeled as a combinatoric tree search problem and the greedy search strategy is a good fit for solving this problem. In the empirical results as well as the restricted isometry property-based performance guarantee, we show that the proposed MMP algorithm is effective in reconstructing original sparse signals for both noiseless and noisy scenarios.