This paper presents a rigorous but tractable study of sparsity. We postulate a definition of sparsity that is as broad as possible, so that it generates all the various measures that are useful in practice, but narrow enough that the fundamental properties of generalized sparsity still hold. As we work through the various ways of demonstrating the advantageous properties of sparsity, we illustrate its meaning from geometrical and operational perspectives. Thereafter, we construct specific measures of sparsity which are successfully qualified in complexity analysis and sparse optimization scenarios. Overall, our main objective is to construct measures of sparsity that will facilitate and enhance the design of the next innovative sensing technologies.

Compression of electrocardiograms (ECG) in wireless environments, with diagnostic quality, has shown limited potential. This lack of quality preservation, using Wavelet Transform (WT), is due to the fact that the multiple levels of detail that can be achieved in the time domain are not exploited. In the present work, we propose to fully exploit the wavelet capability to operate at different levels of signal detail at different time scales. WT with an appropriate Compressed Sensing (CS) matrix is used in the electrode nodes of body sensor networks to encode and compress the ECG. Then, the signal is reconstructed using a basis pursuit denoise algorithm. Preservation of the diagnostic quality by means of standardized metrics is then tested for multiple wavelet bases and levels. High quality ECGs from 50 healthy patients are used to statistically show that diagnostic quality preservation is possible even at high compression rates. In these cases suitable ECG wavelets are required.

Heavy-tailed distributions are present in the characterization of different modern systems such as high-resolution imaging, cloud computing, and cognitive radio networks. Commonly, the cumulants of these distributions cannot be defined from a certain order, and this restricts the applicability of traditional methods. To fill this gap, the present letter extends the traditional Edgeworth and Cornish-Fisher expansions, which are based on the cumulants, to analogous asymptotic expansions based on the log-cumulants. The proposed expansions inherit the capability of log-cumulants to characterize heavy-tailed distributions and parallel traditional expansions. Thus, they are readily implemented. Interestingly, the proposed expansions are applicable for light-tailed distributions as well.

The Method of Moments (MoM) and Method of Log-cumulants (MoLC) estimate the distribution parameters in terms of First Kind Statistics (FKS) and Second Kind Statistics (SKS), respectively. Although SKS offer a suitable framework to analyze heavy-tailed (and asymmetric) distributions, which are commonly-found in aggregate interference modeling, statistical methods developed within this framework has been understudied. For networks following point processes of varying regularity, this paper evaluates the MoM and MoLC methods to estimate the distribution parameters of interference under Rayleigh fading and log-normal shadowing. The results confirm that the gamma and log-normal models offer accurate approximations only when the interference does not present a heavy-tail. For heavy-tailed interference, the MoLC allows an accurate and fast estimation for the α-stable model.

In this paper, we propose the use of an ad-hoc wireless network formed by a fraction of the passing vehicles (sensor vehicles) to periodically recover their positions and speeds. A static roadside unit (RSU) gathers data from passing sensor vehicles. Finally, the speed/position information or space-time velocity (STV) field is then reconstructed in a data fusion center with simple interpolation techniques. We use widely accepted theoretical traffic models (i.e., car-following, multilane, and overtake-enabled models) to replicate the nonlinear characteristics of the STV field in representative situations (congested, free, and transitional traffic). To obtain realistic packet losses, we simulate the multihop ad-hoc wireless network with an IEEE 802.11p PHY layer. We conclude that: 1) for relevant configurations of both sensor vehicle and RSU densities, the wireless multihop channel performance does not critically affect the STV reconstruction error, 2) the system performance is marginally affected by transmission errors for realistic traffic conditions, 3) the STV field can be recovered with minimal mean absolute error for a very small fraction of sensor vehicles (FSV) ≈ 9%, and 4) for that FSV value, the probability that at least one sensor vehicle transits the spatiotemporal regions that contribute the most to reduce the STV reconstruction error sharply tends to 1. Thus, a random and sparse selection of wireless sensor vehicles, in realistic traffic conditions, is sufficient to get an accurate reconstruction of the STV field.

Self-organizing algorithms (SOAs) for wireless sensor networks (WSNs) usually seek to increase the lifetime, to minimize unnecessary transmissions or to maximize the transport capacity. The goal left out in the design of this type of algorithms is the capability of the WSN to ensure an accurate reconstruction of the sensed field while maintaining the self-organization. In this work, we formulate a general framework where the data from the resulting clusters ensures the well-posedness of the signal processing problem in the cluster. We develop the second-order data-coupled clustering (SODCC) algorithm and the distributed compressive-projections principal component analysis (D-CPPCA) algorithm, that use second-order statistics. The condition to form a cluster is that D-CPCCA does not fail to resolve the Principal Components in any given cluster. We show that SODCC is scalable and has similar or better message complexity than other well-known SOAs. We validate these results with extensive computer simulations using an actual LS-WSN. We also show that the performance of SODCC is, comparative to other state-of-the-art SOAs, better at any compression rate and needs no prior adjustment of any parameter. Finally, we show that SODCC compares well to other energy efficient clustering algorithms in terms of energy consumption while excelling in data reconstruction Average SNR.

The optimal configuration for a Large Scale Wireless Sensor Networks (LS-WSN) is the one that minimizes the sampling rate, the CPU time and the channel accesses (thus maximizing the network lifetime), with a controlled distortion in the recovered data. Initial deployments of LS-WSN are usually not able to adapt to changing environments and rarely take into account either the spatial or temporal nature of the sensed variables, both techniques that optimize the network operation. In this work we propose the use of Self-Organized Distributed Compressive Projection (SODCP) in order to let the nodes to form clusters in a distributed and data-driven way, exploiting the spatial correlation of the sensed data. We compare the performance of this innovative technique, using actual data from the LUCE LS-WSN, with two different baselines: Centralized Compressive Projection (CCP) and Distributed Compressive Projection (DCP). The former uses no clustering, whereas the latter makes use of an a priori clustering that favors proximity and balances the number of nodes in each cluster. We show that SODCP outperforms DCP (in terms of Signal-to-Noise vs. Compression Rate). We also show that the performance of SODCP converges to that of CCP for relatively high compression rates of 55%.

In this work we present a Wireless Sensor Network (WSN) system designed for the on-board determination of human gait entropy. The usage of nonlinear entropy-based metrics has proven to be a useful tool for analyzing the complexity of biological systems. The final goal of entropy calculation in this type of biological system is to identify possible causes of future injuries (in order to improve aging) and the early injury detection (ideal for elite athletes). Existing systems for human gait analysis are limited to traditional data gathering, e.g. continuous measurement and wireless transmission to a Data Fusion Center (DFC), due to the computational burden of entropy calculation. In addition, actual systems are likely to interfere the natural movement due to their cumbersome nature. The WSN presented here uses four sensor nodes, located in both ankles and hip sides, and are equipped with triaxial accelerometers. We propose the use of low-complexity algorithms in order to perform onboard entropy determination prior to wireless transmission. The proposed system can be used to reliably determine long-term human gait entropy.

This paper addresses the problem of finding an analytical expression for the end-to-end Average Bit Error Rate (ABER) in multihop Decode-and-Forward(DAF) routes within the context of wireless networks. We provide an analytical recursive expression for the most generic case of any number of hops and any single-hop ABER for every hop in the route. Then, we solve the recursive relationship in two scenarios to obtain simple expressions for the end-to-end ABER, namely: (a) The simplest case, where all the relay channels have identical statistical behaviour; (b) The most general case, where every relay channel has a different statistical behaviour. Along with the theoretical proofs, we test our results against simulations. We then use the previous results to obtain closed analytical expressions for the end-to-end ABER considering DAF relays over Nakagami-m fading channels and with various modulation schemes. We compare these results with the corresponding expressions for Amplify-and-Forward (AAF) and, after corroborating the theoretical results with simulations, we conclude that DAF strategy is more advantageous than the AAF over Nakagami-m fading channels as both the number of relays and m-index increase.

When a terminal is recruited to cooperate with other neighboring terminals, its channel state and carrier frequency offset (CFO) may be unknown to the destination. Under these circumstances, this paper considers the use of distributed double-differential (DD) modulation, which simplifies receiver implementation because it by-passes channel and CFO estimation. Two double-differential codecs are proposed transmitting: i) across orthogonal channels using time-division multiplexing, achieving rate and error performance similar to that of co-located multi-antenna DD systems; or ii) simultaneously, benefiting from the distinct CFOs across terminals and bypassing the need of ordering protocols. Both (i)-(ii) approaches are considered in adaptive- and selective-relaying cooperation protocols demonstrating that maximum spatial diversity is achievable. Simulations corroborate the theoretical error performance claims.

In this paper, we explore the significance of second- and higher-order statistics learning in communication systems. The final goal in spread-spectrum communication systems is to receive a signal of interest completely free from interference caused by other concurrent signals. To achieve this end, we exploit the structure of the interference by designing second-order statistics detectors, such as the minimum square error, in conjunction with higher-order statistics (HOS) techniques, such as the blind source separation (BSS). This hybrid higher-order statistics (HyHOS) approach enables us to alleviate BSS algorithms of one of their main problems, that is, their sensitiveness to high levels of noise. In addition, we benefit from remarkable properties of BSS in learning such as fast learning (superefficiency) and independence of the initial settings of the problem (equivariance). We successfully applied the results of this approach to the design of multiuser detectors in code-division multiple access channels.

In this paper, novel structures for dynamic removal of multiuser interference are proposed. The natural gradient (NG) is used either to compute whitening matrices in linear blind minimum MSE or to develop new structures. As a result, we propose a family of centralized and non-centralized multiuser detectors (MUDs). The NG provides the MUDs with the equivariant and superfficiency properties, making them near-far resistant by construction and their convergence optimal. Moreover, the complexity of these structures is significantly reduced. These novel solutions are successfully applied to the multiuser synchronous CDMA channel.

A new method for low-complexity multiuser detection (MUD) based in the fast subspace decomposition (FSD) is proposed. The use of FSD allows the estimation of the number of users along with the multiuser detection on line. This leads to a fast multiuser estimation-detection scheme with ultra-low complexity. Furthermore, the method is proved to be strongly consistent and blind. This is applied here to the MMSE. Results included show the MMSE performance at a fraction of the computational cost reported until now. The use for UMTS-TDD receivers is also proposed.