Realizable Linear and Decision Feedback Equalizers: Properties and Connections

Recently, there has been renewed interest in the use of infinite impulse response (IIR) linear equalizers (LEs) for digital communication channels as a means for both improving performance and blindly initializing decision feedback structures (DFEs). Theoretical justification for such an approach is usually given assuming unconstrained filters, which are not causal and therefore not implementable in practice. We present an analysis of realizable (i.e., causal, stable, and of finite degree) minimum mean square error (MMSE) equalizers for single-input multiple-output channels, both in the LE and DFE cases, focusing on their structures and filter orders, as well as the connections between them. The DFE resulting from rearranging the MMSE LE within a decision feedback loop is given special attention. It is shown that although this DFE does not in general coincide with the MMSE DFE, it still enjoys certain optimality conditions. The main tools employed are the Wiener theory of minimum variance estimation and Kalman filtering theory, which show interesting properties of the MMSE equalizers not revealed by previous polynomial approaches

A greedy topology design to accelerate consensus in broadcast wireless sensor networks

We present techniques to improve convergence speed of distributed average consensus algorithms in wireless sensor networks by means of topology design. A broadcast network is assumed, so that only the transmit power of each node can be independently controlled, rather than each individual link. Starting with a maximally connected configuration in which all nodes transmit at full power, the proposed methods successively reduce the transmit power of a chosen node in order to remove one and only one link; nodes are greedily selected either in order to yield fastest convergence at each step, or if they have the largest degree in the network. These greedy schemes provide a good complexity-performance tradeoff with respect to full-blown global search methods. As a side benefit, improving the convergence speed also results in savings in energy consumption with respect to the maximally connected setting

Adaptive Lattice IIR Filtering Revisited: Convergence Issues and New Algorithms with Improved Stability Properties

Several algorithms for adaptive IIR filters parameterized in lattice form can be found in the literature. The salient feature of these structures when compared with the direct form is that ensuring stability is extremely easy. On the other hand, while computing the gradient signals that drive the direct form update algorithms is straightforward, it is not so for the lattice algorithms. This has led to simplified lattice algorithms using gradient approximations. Although, in general, these simplified schemes present the same stationary points as the original algorithms, whether this is also true for convergent points has remained an open problem. This also applies to nongradient-based lattice algorithms such as hyperstability based and the Steiglitz--McBride algorithms. Here, we answer this question in the negative, by showing that for several adaptive lattice algorithms, there exist settings in which the stationary point corresponding to identification of the unknown system is not convergent. In addition, new lattice algorithms with improved convergence properties are derived. They are based in the cascade lattice structure, which allows the derivation of sufficient conditions for local stability

A study on the application of different two-objective evolutionary algorithms to the node localization problem in wireless sensor networks

A number of applications of wireless sensor networks require to know the location of the sensor nodes. Typically, however, mainly due to costs and limited capacity of the batteries powering the sensor nodes, only a few nodes of the network, denoted anchor nodes in the literature, are endowed with their exact positions. Thus, given a number of anchor nodes, the problem of estimating the locations of all the nodes of a wireless sensor network has attracted a large interest in the last years. The localization task is based on the estimated distances between pairs of nodes in range of each other and is particularly hard in the most appealing scenario, that is, when the network connectivity is quite low. In a recent paper, we have proposed to tackle the localization problem as a two-objective optimization task with the localization accuracy and the number of connectivity constraints that are not satisfied by the candidate geometry as the two objectives. In this paper, we aim to evaluate the behavior of five state-of-the-art multi-objective evolutionary algorithms (MOEAs) in solving the localization problem on different network topologies. We show that one of these MOEAs, namely PAES, statistically outperforms the others in terms of localization error