195611249
A Novel Decentralized Scheme for Cooperative Compressed Spectrum Sensing in Distributed Networks
Compressed sensing (CS) recently turns out to be an effective approach to alleviate the sampling bottleneck in wideband spectrum sensing. However, the computation overhead incurred by compressed reconstruction is nontrivial, especially in a power-constrained cognitive radio (CR). Moreover, additional information, which is generally unavailable in practice, is needed in conventional CS-based wideband spectrum sensing schemes to improve the reconstruction quality as well as the detection performance. To address these issues, this paper proposes a novel decentralized scheme for cooperative compressed spectrum sensing in distributed CR networks. Our key observation is that the sparse signals are unnecessary to be reconstructed since the task of spectrum sensing is only interested in the spectrum occupancy status. The major novelty of the proposed scheme relates to the use of Karcher mean as a statistic indicating the spectrum occupancy status, thereby eliminating the compressed reconstruction stage and significantly reducing the computational complexity. Considering limited communication resources per CR, a decentralized implementation based on alternating direction method of multipliers is presented to calculate the Karcher mean via one-hop communications only. The superior performance of the proposed scheme is demonstrated by comparing with several existing decentralized schemes in terms of detection performance, communication overhead, and computational complexity.
9056128
NeXt generation/dynamic spectrum access/cognitive radio wireless networks: A survey
Today's wireless networks are characterized by a fixed spectrum assignment policy. However, a large portion of the assigned spectrum is used sporadically and geographical variations in the utilization of assigned spectrum ranges from 15% to 85% with a high variance in time. The limited available spectrum and the inefficiency in the spectrum usage necessitate a new communication paradigm to exploit the existing wireless spectrum opportunistically. This new networking paradigm is referred to as NeXt Generation (xG) Networks as well as Dynamic Spectrum Access (DSA) and cognitive radio networks. The term xG networks is used throughout the paper. The novel functionalities and current research challenges of the xG networks are explained in detail. More specifically, a brief overview of the cognitive radio technology is provided and the xG network architecture is introduced. Moreover, the xG network functions such as spectrum management, spectrum mobility and spectrum sharing are explained in detail. The influence of these functions on the performance of the upper layer protocols such as routing and transport are investigated and open research issues in these areas are also outlined. Finally, the cross-layer design challenges in xG networks are discussed.
3759709
Ten years of research in spectrum sensing and sharing in cognitive radio
Cognitive radio (CR) can successfully deal with the growing demand and scarcity of the wireless spectrum. To exploit limited spectrum efficiently, CR technology allows unlicensed users to access licensed spectrum bands. Since licensed users have priorities to use the bands, the unlicensed users need to continuously monitor the licensed users' activities to avoid interference and collisions. How to obtain reliable results of the licensed users' activities is the main task for spectrum sensing. Based on the sensing results, the unlicensed users should adapt their transmit powers and access strategies to protect the licensed communications. The requirement naturally presents challenges to the implementation of CR. In this article, we provide an overview of recent research achievements of including spectrum sensing, sharing techniques and the applications of CR systems.
8987266
Cooperative spectrum sensing in cognitive radio networks: A survey
Spectrum sensing is a key function of cognitive radio to prevent the harmful interference with licensed users and identify the available spectrum for improving the spectrum's utilization. However, detection performance in practice is often compromised with multipath fading, shadowing and receiver uncertainty issues. To mitigate the impact of these issues, cooperative spectrum sensing has been shown to be an effective method to improve the detection performance by exploiting spatial diversity. While cooperative gain such as improved detection performance and relaxed sensitivity requirement can be obtained, cooperative sensing can incur cooperation overhead. The overhead refers to any extra sensing time, delay, energy, and operations devoted to cooperative sensing and any performance degradation caused by cooperative sensing. In this paper, the state-of-the-art survey of cooperative sensing is provided to address the issues of cooperation method, cooperative gain, and cooperation overhead. Specifically, the cooperation method is analyzed by the fundamental components called the elements of cooperative sensing, including cooperation models, sensing techniques, hypothesis testing, data fusion, control channel and reporting, user selection, and knowledge base. Moreover, the impacting factors of achievable cooperative gain and incurred cooperation overhead are presented. The factors under consideration include sensing time and delay, channel impairments, energy efficiency, cooperation efficiency, mobility, security, and wideband sensing issues. The open research challenges related to each issue in cooperative sensing are also discussed.
1704522
An Introduction To Compressive Sampling
Conventional approaches to sampling signals or images follow Shannon's theorem: the sampling rate must be at least twice the maximum frequency present in the signal (Nyquist rate). In the field of data conversion, standard analog-to-digital converter (ADC) technology implements the usual quantized Shannon representation - the signal is uniformly sampled at or above the Nyquist rate. This article surveys the theory of compressive sampling, also known as compressed sensing or CS, a novel sensing/sampling paradigm that goes against the common wisdom in data acquisition. CS theory asserts that one can recover certain signals and images from far fewer samples or measurements than traditional methods use.
15068636
Compressed Sensing for Wideband Cognitive Radios
In the emerging paradigm of open spectrum access, cognitive radios dynamically sense the radio-spectrum environment and must rapidly tune their transmitter parameters to efficiently utilize the available spectrum. The unprecedented radio agility envisioned, calls for fast and accurate spectrum sensing over a wide bandwidth, which challenges traditional spectral estimation methods typically operating at or above Nyquist rates. Capitalizing on the sparseness of the signal spectrum in open-access networks, this paper develops compressed sensing techniques tailored for the coarse sensing task of spectrum hole identification. Sub-Nyquist rate samples are utilized to detect and classify frequency bands via a wavelet-based edge detector. Because spectrum location estimation takes priority over fine-scale signal reconstruction, the proposed novel sensing algorithms are robust to noise and can afford reduced sampling rates.
13938868
Compressive wide-band spectrum sensing
We present a compressive wide-band spectrum sensing scheme for cognitive radios. The received analog signal at the cognitive radio sensing receiver is transformed in to a digital signal using an analog-to-information converter. The autocorrelation of this compressed signal is then used to reconstruct an estimate of the signal spectrum. We evaluate the performance of this scheme in terms of the mean squared error of the power spectrum density estimate and the probability of detecting signal occupancy.
866076
Compressive spectrum sensing front-ends for cognitive radios
We propose a novel parallel mixed-signal compressive spectrum sensing architecture for Cognitive Radios (CRs) with a detailed study of the signal modeling. The mixed-signal compressive sensing is realized with a parallel segmented compressive sensing (PSCS) architecture, which not only can filter out all the harmonic spurs that leak from the local random generator, but also provides a tradeoff between the sampling rate and the system complexity such that a practical hardware implementation is possible. We consider application of the architecture to do spectrum estimation, which is the first step for spectrum sensing in CRs. The benefit of prior knowledge about the input signal's structure is explored and it is shown that this can be exploited in the PSCS architecture to greatly reduce the sampling rate.
15401729
Distributed compressive wide-band spectrum sensing
We consider a compressive wide-band spectrum sensing scheme for cognitive radio networks. Each cognitive radio (CR) sensing receiver transforms the received analog signal from the licensed system in to a digital signal using an analog-to-information converter. The autocorrelation of the compressed signal is then collected from each CR at a fusion center. A compressive sampling recovery algorithm that exploits joint sparsity is then employed to reconstruct an estimate of the signal spectrum and used to make a decision on signal occupancy. We compare the performance of this distributed compressive spectrum sensing scheme with a compressive spectrum sensing scheme at a single CR and show the performance gains obtained from spatial diversity.
1822442
Collaborative Spectrum Sensing from Sparse Observations in Cognitive Radio Networks
Spectrum sensing, which aims at detecting spectrum holes, is the precondition for the implementation of cognitive radio (CR). Collaborative spectrum sensing among the cognitive radio nodes is expected to improve the ability of checking complete spectrum usage. Due to hardware limitations, each cognitive radio node can only sense a relatively narrow band of radio spectrum. Consequently, the available channel sensing information is far from being sufficient for precisely recognizing the wide range of unoccupied channels. Aiming at breaking this bottleneck, we propose to apply matrix completion and joint sparsity recovery to reduce sensing and transmission requirements and improve sensing results. Specifically, equipped with a frequency selective filter, each cognitive radio node senses linear combinations of multiple channel information and reports them to the fusion center, where occupied channels are then decoded from the reports by using novel matrix completion and joint sparsity recovery algorithms. As a result, the number of reports sent from the CRs to the fusion center is significantly reduced. We propose two decoding approaches, one based on matrix completion and the other based on joint sparsity recovery, both of which allow exact recovery from incomplete reports. The numerical results validate the effectiveness and robustness of our approaches. In particular, in small-scale networks, the matrix completion approach achieves exact channel detection with a number of samples no more than 50% of the number of channels in the network, while joint sparsity recovery achieves similar performance in large-scale networks.
11801468
Compressed Wideband Sensing in Cooperative Cognitive Radio Networks
In emerging cognitive radio (CR) networks with spectrum sharing, the first cognitive task preceding any dynamic spectrum access is the sensing and identification of spectral holes in wireless environments. This paper develops a distributed compressed spectrum sensing approach for (ultra-)wideband CR networks. Compressed sensing is performed at local CRs to scan the very wide spectrum at practical signal-acquisition complexity. Meanwhile, spectral estimates from multiple local CR detectors are fused to collect spatial diversity gain, which improves the sensing quality especially under fading channels. New distributed consensus algorithms are developed for collaborative sensing and fusion. Using only one-hop local communications, these distributed algorithms converge fast to the globally optimal solutions even for multi-hop CR networks, at low communication and computation load scalable to the network size.
1162354
Distributed Compressive Spectrum Sensing in Cooperative Multihop Cognitive Networks
In wideband cognitive radio (CR) networks, spectrum sensing is an essential task for enabling dynamic spectrum sharing, but entails several major technical challenges: very high sampling rates required for wideband processing, limited power and computing resources per CR, frequency-selective wireless fading, and interference due to signal leakage from other coexisting CRs. In this paper, a cooperative approach to wideband spectrum sensing is developed to overcome these challenges. To effectively reduce the data acquisition costs, a compressive sampling mechanism is utilized which exploits the signal sparsity induced by network spectrum under-utilization. To collect spatial diversity against wireless fading, multiple CRs collaborate during the sensing task by enforcing consensus among local spectral estimates; accordingly, a decentralized consensus optimization algorithm is derived to attain high sensing performance at a reasonable computational cost and power overhead. To identify spurious spectral estimates due to interfering CRs, the orthogonality between the spectrum of primary users and that of CRs is imposed as constraints for consensus optimization during distributed collaborative sensing. These decentralized techniques are developed for both cases of with and without channel knowledge. Simulations testify the effectiveness of the proposed cooperative sensing approach in multi-hop CR networks.
66047
Compressive detection for wide-band spectrum sensing
In this paper we propose a novel wide-band spectrum sensing scheme using compressive sensing. The wide-band signal is fed into a number of wide-band filters and the outputs of the filters are used to reconstruct the vector of channel energies through the ℓ1 norm minimization. An energy detection is then performed by comparing the obtained vector to a vector of energy thresholds to decide about the occupancy of each channel. Performance of the proposed approach is compared to the current wide-band spectrum sensing algorithms as well as the conventional channel-by-channel scanning method.
414635
Recovery Algorithms for Vector-Valued Data with Joint Sparsity Constraints
Vector-valued data appearing in concrete applications often possess sparse expansions with respect to a preassigned frame for each vector component individually. Additionally, different components may also exhibit common sparsity patterns. Recently, there were introduced sparsity measures that take into account such joint sparsity patterns, promoting coupling of nonvanishing components. These measures are typically constructed as weighted $\ell_1$ norms of componentwise $\ell_q$ norms of frame coefficients. We show how to compute solutions of linear inverse problems with such joint sparsity regularization constraints by fast thresholded Landweber algorithms. Next we discuss the adaptive choice of suitable weights appearing in the definition of sparsity measures. The weights are interpreted as indicators of the sparsity pattern and are iteratively updated after each new application of the thresholded Landweber algorithm. The resulting two-step algorithm is interpreted as a double-minimization scheme for a suitable target functional. We show its $\ell_2$-norm convergence. An implementable version of the algorithm is also formulated, and its norm convergence is proven. Numerical experiments in color image restoration are presented.
5880859
Theoretical and Empirical Results for Recovery From Multiple Measurements
The joint-sparse recovery problem aims to recover, from sets of compressed measurements, unknown sparse matrices with nonzero entries restricted to a subset of rows. This is an extension of the single-measurement-vector (SMV) problem widely studied in compressed sensing. We study the recovery properties of two algorithms for problems with noiseless data and exact-sparse representation. First, we show that recovery using sum-of-norm minimization cannot exceed the uniform-recovery rate of sequential SMV using l 1 minimization, and that there are problems that can be solved with one approach, but not the other. Second, we study the performance of the ReMBo algorithm (M. Mishali and Y. Eldar, ¿Reduce and boost: Recovering arbitrary sets of jointly sparse vectors,¿ IEEE Trans. Signal Process., vol. 56, no. 10, 4692-4702, Oct. 2008) in combination with l 1 minimization, and show how recovery improves as more measurements are taken. From this analysis, it follows that having more measurements than the number of linearly independent nonzero rows does not improve the potential theoretical recovery rate.
51789432
Distributed Optimization and Statistical Learning via the Alternating Direction Method of Multipliers
Many problems of recent interest in statistics and machine learning can be posed in the framework of convex optimization. Due to the explosion in size and complexity of modern datasets, it is increasingly important to be able to solve problems with a very large number of features or training examples. As a result, both the decentralized collection or storage of these datasets as well as accompanying distributed solution methods are either necessary or at least highly desirable. In this review, we argue that the alternating direction method of multipliers is well suited to distributed convex optimization, and in particular to large-scale problems arising in statistics, machine learning, and related areas. The method was developed in the 1970s, with roots in the 1950s, and is equivalent or closely related to many other algorithms, such as dual decomposition, the method of multipliers, Douglas–Rachford splitting, Spingarn's method of partial inverses, Dykstra's alternating projections, Bregman iterative algorithms for l1 problems, proximal methods, and others. After briefly surveying the theory and history of the algorithm, we discuss applications to a wide variety of statistical and machine learning problems of recent interest, including the lasso, sparse logistic regression, basis pursuit, covariance selection, support vector machines, and many others. We also discuss general distributed optimization, extensions to the nonconvex setting, and efficient implementation, including some details on distributed MPI and Hadoop MapReduce implementations.
5642927
On the Linear Convergence of the ADMM in Decentralized Consensus Optimization
In decentralized consensus optimization, a connected network of agents collaboratively minimize the sum of their local objective functions over a common decision variable, where their information exchange is restricted between the neighbors. To this end, one can first obtain a problem reformulation and then apply the alternating direction method of multipliers (ADMM). The method applies iterative computation at the individual agents and information exchange between the neighbors. This approach has been observed to converge quickly and deemed powerful. This paper establishes its linear convergence rate for the decentralized consensus optimization problem with strongly convex local objective functions. The theoretical convergence rate is explicitly given in terms of the network topology, the properties of local objective functions, and the algorithm parameter. This result is not only a performance guarantee but also a guideline toward accelerating the ADMM convergence.
2066416
Distributed average consensus with least-mean-square deviation
We consider a stochastic model for distributed average consensus, which arises in applications such as load balancing for parallel processors, distributed coordination of mobile autonomous agents, and network synchronization. In this model, each node updates its local variable with a weighted average of its neighbors' values, and each new value is corrupted by an additive noise with zero mean. The quality of consensus can be measured by the total mean-square deviation of the individual variables from their average, which converges to a steady-state value. We consider the problem of finding the (symmetric) edge weights that result in the least mean-square deviation in steady state. We show that this problem can be cast as a convex optimization problem, so the global solution can be found efficiently. We describe some computational methods for solving this problem, and compare the weights and the mean-square deviations obtained by this method and several other weight design methods.