Leonardo Rey Vega

A Nonparametric VSS NLMS Algorithm

The aim of a variable step size normalized least-mean-square (VSS-NLMS) algorithm is to try to solve the conflicting requirement of fast convergence and low misadjustment of the NLMS algorithm. Numerous VSS-NLMS algorithms can be found in the literature with a common point for most of them: they may not work very reliably since they depend on several parameters that are not simple to tune in practice. The objective of this letter is twofold. First, we explain a simple and elegant way to derive VSS-NLMS-type algorithms. Second, a new nonparametric VSS-NLMS is proposed that is easy to control and gives good performances in the context of acoustic echo cancellation

A New Robust Variable Step-Size NLMS Algorithm

A new framework for designing robust adaptive filters is introduced. It is based on the optimization of a certain cost function subject to a time-dependent constraint on the norm of the filter update. Particularly, we present a robust variable step-size NLMS algorithm which optimizes the square of the a posteriori error. We also show the link between the proposed algorithm and another one derived using a robust statistics approach. In addition, a theoretical model for predicting the transient and steady-state behavior and a proof of almost sure filter convergence are provided. The algorithm is then tested in different environments for system identification and acoustic echo cancelation applications.

Variable Explicit Regularization in Affine Projection Algorithm: Robustness Issues and Optimal Choice

A variable regularized affine projection algorithm (VR-APA) is introduced, without requiring the classical step size. Its use is supported from different points of view. First, it has the property of being Hinfin optimal and it satisfies certain error energy bounds. Second, the time-varying regularization parameter is obtained by maximizing the speed of convergence of the algorithm. Although we first derive the VR-APA for a linear time invariant (LTI) system, we show that the same expression holds if we consider a time-varying system following a first-order Markov model. We also find expressions for the power of the steady-state error vector for the VR-APA and the standard APA with no regularization parameter. Particularly, we obtain quite different results with and without using the independence assumption between the a priori error vector and the measurement noise vector. Simulation results are presented to test the performance of the proposed algorithm and to compare it with other schemes under different situations. An important conclusion is that the former independence assumption can lead to very inaccurate steady-state results, especially when high values of the projection order are used

Fast communication: A robust variable step-size affine projection algorithm

We present a robust variable step-size affine projection algorithm (RVSS-APA) using a recently introduced new framework for designing robust adaptive filters. The algorithm is the result of minimizing the square norm of the a posteriori error vector subject to a time-dependent constraint on the norm of the filter update. The RVSS-APA is then successfully tested in different environments for system identification and acoustic echo cancellation applications.

On Fundamental Trade-offs of Device-to-Device Communications in Large Wireless Networks

This paper studies the gains, in terms of served requests, attainable through out-of-band device-to-device (D2D) video exchanges in large cellular networks. A stochastic framework, in which users are clustered to exchange videos, is introduced, considering several aspects of this problem, i.e., the video caching policy, user matching for exchanges, and aspects regarding scheduling and transmissions. A family of admissible protocols is introduced: in each protocol the users are clustered by means of a hard-core point process and, within the clusters, video exchanges take place. Two metrics, quantifying the “local” and “global” fractions of video requests served through D2D are defined, and relevant trade-off regions involving these metrics, as well as quality-of-service constraints, are identified. A simple communication strategy is proposed and analyzed to obtain inner bounds to the trade-off regions and to draw conclusions on the performance attainable through D2D. To this end, the analysis of the time-varying interference that the nodes experience and the tight approximations of its Laplace transform are derived.

A Fast Robust Recursive Least-Squares Algorithm

We present a fast robust recursive least-squares (FRRLS) algorithm based on a recently introduced new framework for designing robust adaptive filters. The algorithm is the result of minimizing a cost function subject to a time-dependent constraint on the norm of the filter update. Although the characteristics of the exact solution to this problem are known, there is no closed-form solution in general. However, the approximate solution we propose is very close to the optimal one. We also present some theoretical results regarding the asymptotic behavior of the algorithm. The FRRLS is then tested in different environments for system identification and acoustic echo cancellation applications.

A Family of Robust Algorithms Exploiting Sparsity in Adaptive Filters

We introduce a new family of algorithms to exploit sparsity in adaptive filters. It is based on a recently introduced new framework for designing robust adaptive filters. It results from minimizing a certain cost function subject to a time-dependent constraint on the norm of the filter update. Although in general this problem does not have a closed-form solution, we propose an approximate one which is very close to the optimal solution. We take a particular algorithm from this family and provide some theoretical results regarding the asymptotic behavior of the algorithm. Finally, we test it in different environments for system identification and acoustic echo cancellation applications.

Cooperative strategies for interference-limited wireless networks

Consider the communication of a single user aided by a nearby relay involved in a large and dense wireless network where the nodes form an homogeneous Poisson point process. We assume that the network is working in the interference-limited regime. In this case the asymptotic error probability is bounded from above by the outage probability experienced by the user. We investigate the outage behavior for the well-known cooperative schemes, namely, decode-and-forward (DF) and compress-and-forward (CF). In this setting, the outage events are induced by both fading and the spatial proximity of neighbor nodes who generate the strongest interference and hence the worst communication case. Upper and lower bounds on the asymptotic error probability which are tight in some cases are derived. It is shown that there exists a clear trade-off between the network density and the benefits of user cooperation. These results are useful to evaluate performance and to optimize relaying schemes in the context of large wireless networks.

Optimum Variable Explicit Regularized Affine Projection Algorithm

A variable regularized affine projection algorithm (VR-APA) is introduced, which does not require the classical step size. Its use is supported from different points of view. First, it has the property of being Hinfin optimal, providing robust behavior against perturbations and model uncertainties. Second, the time varying regularization parameter is obtained by maximizing the speed of convergence of the algorithm. At each time step, it needs knowledge of the power of the estimation error vector, which can be estimated by averaging observable quantities. Although we first derive it for a linear time invariant (LTI) system, we show that the same expression holds if we consider a time varying system following a first order Markov model. Simulation results are presented to test the performance of the proposed algorithm and to compare it with other schemes under different situations

Analysis of a cooperative strategy for a large decentralized wireless network

This paper investigates the benefits of cooperation and proposes a relay activation strategy for a large wireless network with multiple transmitters. In this framework, some nodes cooperate with a nearby node that acts as a relay, using the decode-and-forward protocol, and others use direct transmission. The network is modeled as an independently marked Poisson point process, and the source nodes may choose their relays from the set of inactive nodes. Although cooperation can potentially lead to significant improvements in the performance of a communication pair, relaying causes additional interference in the network, increasing the average noise that other nodes see. We investigate how source nodes should balance cooperation versus interference to obtain reliable transmissions, and for this purpose, we study and optimize a relay activation strategy with respect to the outage probability. Surprisingly, in the high reliability regime, the optimized strategy consists on the activation of all the relays or none at all, depending on network parameters. We provide a simple closed-form expression that indicates when the relays should be active, and we introduce closed-form expressions that quantify the performance gains of this scheme with respect to a network that only uses direct transmission.