645 research outputs found
A Compact Formulation for the Mixed-Norm Minimization Problem
Parameter estimation from multiple measurement vectors (MMVs) is a
fundamental problem in many signal processing applications, e.g., spectral
analysis and direction-of- arrival estimation. Recently, this problem has been
address using prior information in form of a jointly sparse signal structure. A
prominent approach for exploiting joint sparsity considers mixed-norm
minimization in which, however, the problem size grows with the number of
measurements and the desired resolution, respectively. In this work we derive
an equivalent, compact reformulation of the mixed-norm
minimization problem which provides new insights on the relation between
different existing approaches for jointly sparse signal reconstruction. The
reformulation builds upon a compact parameterization, which models the
row-norms of the sparse signal representation as parameters of interest,
resulting in a significant reduction of the MMV problem size. Given the sparse
vector of row-norms, the jointly sparse signal can be computed from the MMVs in
closed form. For the special case of uniform linear sampling, we present an
extension of the compact formulation for gridless parameter estimation by means
of semidefinite programming. Furthermore, we derive in this case from our
compact problem formulation the exact equivalence between the
mixed-norm minimization and the atomic-norm minimization. Additionally, for the
case of irregular sampling or a large number of samples, we present a low
complexity, grid-based implementation based on the coordinate descent method
Augmented Lagrange Based on Modified Covariance Matching Criterion Method for DOA Estimation in Compressed Sensing
A novel direction of arrival (DOA) estimation method in compressed sensing (CS) is presented, in which DOA estimation is considered as the joint sparse recovery from multiple measurement vectors (MMV). The proposed method is obtained by minimizing the modified-based covariance matching criterion, which is acquired by adding penalties according to the regularization method. This minimization problem is shown to be a semidefinite program (SDP) and transformed into a constrained quadratic programming problem for reducing computational complexity which can be solved by the augmented Lagrange method. The proposed method can significantly improve the performance especially in the scenarios with low signal to noise ratio (SNR), small number of snapshots, and closely spaced correlated sources. In addition, the Cramér-Rao bound (CRB) of the proposed method is developed and the performance guarantee is given according to a version of the restricted isometry property (RIP). The effectiveness and satisfactory performance of the proposed method are illustrated by simulation results
Super-resolved localisation in multipath environments
In the last few decades, the localisation problems have been studied extensively. There are still some open issues that remain unresolved. One of the key issues is the efficiency and preciseness of the localisation in presence of non-line-of-sight (NLoS) path. Nevertheless, the NLoS path has a high occurrence in multipath environments, but NLoS bias is viewed as a main factor to severely degrade the localisation performance. The NLoS bias would often result in extra propagation delay and angular bias. Numerous localisation methods have been proposed to deal with NLoS bias in various propagation environments, but they are tailored to some specif ic scenarios due to different prior knowledge requirements, accuracies, computational complexities, and assumptions.
To super-resolve the location of mobile device (MD) without prior knowledge, we address the localisation problem by super-resolution technique due to its favourable features, such as working on continuous parameter space, reducing computational cost and good extensibility. Besides the NLoS bias, we consider an extra array directional error which implies the deviation in the orientation of the array placement. The proposed method is able to estimate the locations of MDs and self-calibrate the array directional errors simultaneously. To achieve joint localisation, we directly map MD locations and array directional error to received signals. Then the group sparsity based optimisation is proposed to exploit the geometric consistency that received paths are originating from common MDs. Note that the super-resolution framework cannot be directly applied to our localisation problems. Because the proposed objective function cannot be efficiently solved by semi-definite programming.
Typical strategies focus on reducing adverse effect due to the NLoS bias by separating line-of-sight (LoS)/NLoS path or mitigating NLoS effect. The LoS path is well studied for localisation and multiple methods have been proposed in the literature. However, the number of LoS paths are typically limited and the effect of NLoS bias may not always be reduced completely. As a long-standing issue, the suitable solution of using NLoS path is still an open topic for research. Instead of dealing with NLoS bias, we present a novel localisation method that exploits both LoS and NLoS paths in the same manner. The unique feature is avoiding hard decisions on separating LoS and NLoS paths and hence relevant possible error. A grid-free sparse inverse problem is formulated for localisation which avoids error propagation between multiple stages, handles multipath in a unified way, and guarantees a global convergence. Extensive localisation experiments on different propagation environments and localisation systems are presented to illustrate the high performance of the proposed algorithm compared with theoretical analysis. In one of the case studies, single antenna access points (APs) can locate a single antenna MD even when all paths between them are NLoS, which according to the authors’ knowledge is the first time in the literature.Open Acces
A survey on 5G massive MIMO Localization
Massive antenna arrays can be used to meet the requirements of 5G, by exploiting different spatial signatures of users. This same property can also be harnessed to determine the locations of those users. In order to perform massive MIMO localization, refined channel estimation routines and localization methods have been developed. This paper provides a brief overview of this emerging field
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Structured Sub-Nyquist Sampling with Applications in Compressive Toeplitz Covariance Estimation, Super-Resolution and Phase Retrieval
Sub-Nyquist sampling has received a huge amount of interest in the past decade. In classical compressed sensing theory, if the measurement procedure satisfies a particular condition known as Restricted Isometry Property (RIP), we can achieve stable recovery of signals of low-dimensional intrinsic structures with an order-wise optimal sample size. Such low-dimensional structures include sparse and low rank for both vector and matrix cases. The main drawback of conventional compressed sensing theory is that random measurements are required to ensure the RIP property. However, in many applications such as imaging and array signal processing, applying independent random measurements may not be practical as the systems are deterministic. Moreover, random measurements based compressed sensing always exploits convex programs for signal recovery even in the noiseless case, and solving those programs is computationally intensive if the ambient dimension is large, especially in the matrix case. The main contribution of this dissertation is that we propose a deterministic sub-Nyquist sampling framework for compressing the structured signal and come up with computationally efficient algorithms. Besides widely studied sparse and low-rank structures, we particularly focus on the cases that the signals of interest are stationary or the measurements are of Fourier type. The key difference between our work from classical compressed sensing theory is that we explicitly exploit the second-order statistics of the signals, and study the equivalent quadratic measurement model in the correlation domain. The essential observation made in this dissertation is that a difference/sum coarray structure will arise from the quadratic model if the measurements are of Fourier type. With these observations, we are able to achieve a better compression rate for covariance estimation, identify more sources in array signal processing or recover the signals of larger sparsity. In this dissertation, we will first study the problem of Toeplitz covariance estimation. In particular, we will show how to achieve an order-wise optimal compression rate using the idea of sparse arrays in both general and low-rank cases. Then, an analysis framework of super-resolution with positivity constraint is established. We will present fundamental robustness guarantees, efficient algorithms and applications in practices. Next, we will study the problem of phase-retrieval for which we successfully apply the sparse array ideas by fully exploiting the quadratic measurement model. We achieve near-optimal sample complexity for both sparse and general cases with practical Fourier measurements and provide efficient and deterministic recovery algorithms. In the end, we will further elaborate on the essential role of non-negative constraint in underdetermined inverse problems. In particular, we will analyze the nonlinear co-array interpolation problem and develop a universal upper bound of the interpolation error. Bilinear problem with non-negative constraint will be considered next and the exact characterization of the ambiguous solutions will be established for the first time in literature. At last, we will show how to apply the nested array idea to solve real problems such as Kriging. Using spatial correlation information, we are able to have a stable estimate of the field of interest with fewer sensors than classic methodologies. Extensive numerical experiments are implemented to demonstrate our theoretical claims
Optimization methods for active and passive localization
Active and passive localization employing widely distributed sensors is a problem of interest in various fields. In active localization, such as in MIMO radar, transmitters emit signals that are reflected by the targets and collected by the receive sensors, whereas, in passive localization the sensors collect the signals emitted by the sources themselves. This dissertation studies optimization methods for high precision active and passive localization.
In the case of active localization, multiple transmit elements illuminate the targets from different directions. The signals emitted by the transmitters may differ in power and bandwidth. Such resources are often limited and distributed uniformly among the transmitters. However, previous studies based on the well known Cramer-Rao lower bound have shown that the localization accuracy depends on the locations of the transmitters as well as the individual channel gains between different transmitters, targets and receivers. Thus, it is natural to ask whether localization accuracy may be improved by judiciously allocating such limited resources among the transmitters. Using the Cr´amer-Rao lower bound for target localization of multiple targets as a figure of merit, approximate solutions are proposed to the problems of optimal power, optimal bandwidth and optimal joint power and bandwidth allocation. These solutions are computed by minimizing a sequence of convex problems. The quality of these solutions is assessed through extensive numerical simulations and with the help of a lower-bound that certifies their optimality. Simulation results reveal that bandwidth allocation policies have a stronger impact on performance than power.
Passive localization of radio frequency sources over multipath channels is a difficult problem arising in applications such as outdoor or indoor geolocation. Common approaches that combine ad-hoc methods for multipath mitigation with indirect localization relying on intermediary parameters such as time-of-arrivals, time difference of arrivals or received signal strengths, are unsatisfactory. This dissertation models the localization of known waveforms over unknown multipath channels in a sparse framework, and develops a direct approach in which multiple sources are localized jointly, directly from observations obtained at distributed sources. The proposed approach exploits channel properties that enable to distinguish line-of-sight (LOS) from non-LOS signal paths. Theoretical guarantees are established for correct recovery of the sources’ locations by atomic norm minimization. A second-order-cone-based algorithm is developed to produce the optimal atomic decomposition, and it is shown to produce high accuracy location estimates over complex scenes, in which sources are subject to diverse multipath conditions, including lack of LOS
On Random Sampling for Compliance Monitoring in Opportunistic Spectrum Access Networks
In the expanding spectrum marketplace, there has been a long term evolution towards more market€“oriented mechanisms, such as Opportunistic Spectrum Access (OSA), enabled through Cognitive Radio (CR) technology. However, the potential of CR technologies to revolutionize wireless communications, also introduces challenges based upon the potentially non€“deterministic CR behaviour in the Electrospace. While establishing and enforcing compliance to spectrum etiquette rules are essential to realization of successful OSA networks in the future, there has only been recent increased research activity into enforcement. This dissertation presents novel work on the spectrum monitoring aspect, which is crucial to effective enforcement of OSA. An overview of the challenges faced by current compliance monitoring methods is first presented. A framework is then proposed for the use of random spectral sampling techniques to reduce data collection complexity in wideband sensing scenarios. This approach is recommended as an alternative to Compressed Sensing (CS) techniques for wideband spectral occupancy estimation, which may be difficult to utilize in many practical congested scenarios where compliance monitoring is required. Next, a low€“cost computational approach to online randomized temporal sensing deployment is presented for characterization of temporal spectrum occupancy in cognitive radio scenarios. The random sensing approach is demonstrated and its performance is compared to CS€“based approach for occupancy estimation. A novel frame€“based sampling inversion technique is then presented for cases when it is necessary to track the temporal behaviour of individual CRs or CR networks. Parameters from randomly sampled Physical Layer Convergence Protocol (PLCP) data frames are used to reconstruct occupancy statistics, taking account of missed frames due to sampling design, sensor limitations and frame errors. Finally, investigations into the use of distributed and mobile spectrum sensing to collect spatial diversity to improve the above techniques are presented, for several common monitoring tasks in spectrum enforcement. Specifically, focus is upon techniques for achieving consensus in dynamic topologies such as in mobile sensing scenarios
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