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.     

Non-Data-Aided Symbol Rate Estimation of Linearly Modulated Signals

The estimation of the symbol rate of a linearly modulated signal is addressed, with special focus on low signal-to-noise ratio (SNR) scenarios. This problem finds application in automatic modulation classification and signal monitoring. A maximum-likelihood (ML) approach is adopted to derive practical estimators, exploiting information on the cyclostationarity of the modulated signal as well as knowledge of the received signaling pulse shape. The structure of the ML estimator suggests a two-step estimation procedure, whereby an initial coarse search determines first a neighborhood from which a subsequent fine search yields the final symbol rate estimate. Links between the ML approach and previous results from the literature in symbol rate estimation are established as well. The proposed scheme is applicable even for small excess bandwidths, at the cost of a higher complexity with respect to simpler estimators known to fail under such conditions.     

Equalization and interference cancellation in linear multiusersystems based on second-order statistics

Potential applications of blind channel identification and equalization in data communication systems have recently been explored. For multiuser systems that are irreducible and column-reduced, second-order statistical methods normally can identify channel dynamics up to a unitary mixing matrix. Additional user separation (equalization) can rely on higher order statistics and other prior information. In this paper, we investigate the equalizability of user signals and the cancellation of unwanted interfering signals based only on second-order output statistics. We show that a user channel can be equalized if it has the longest memory. Furthermore, interfering user signals can be cancelled under a more relaxed multiuser channel condition     

On the design of a novel two-objective harmony search approach for distance- and connectivity-based localization in wireless sensor networks

In several wireless sensor network applications the availability of accurate nodes' location information is essential to make collected data meaningful. In this context, estimating the positions of all unknown-located nodes of the network based on noisy distance-related measurements (usually referred to as localization) generally embodies a non-convex optimization problem, which is further exacerbated by the fact that the network may not be uniquely localizable, especially when its connectivity degree is not sufficiently high. In order to efficiently tackle this problem, we propose a novel two-objective localization approach based on the combination of the harmony search (HS) algorithm and a local search procedure. Moreover, some connectivity-based geometrical constraints are defined and exploited to limit the areas in which sensor nodes can be located. The proposed method is tested with different network configurations and compared, in terms of normalized localization error and three multi-objective quality indicators, with a state-of-the-art metaheuristic localization scheme based on the Pareto archived evolution strategy (PAES). The results show that the proposed approach achieves considerable accuracies and, in the majority of the scenarios, outperforms PAES.     

Second-order statistical properties of nonlinearly distorted phase-shift keyed (PSK) signals

In wireless communication systems operation of the amplifiers near saturation is often required for efficiency reasons, resulting in a nonlinearly distorted signal at the amplifier output. A popular model for the corresponding baseband equivalent nonlinear channel is a truncated Volterra series. By exploiting the bandpass nature of the channel and the statistical properties of phase-shift keyed signals, we show that the different terms in the Volterra series are white and uncorrelated with each other. This result is useful when considering blind equalization approaches for this class of systems.     

Blind input, initial state, and system identification of SIMO Laguerre systems

Laguerre filters have infinite impulse responses (IIRs) but with finite tapped delay-line parameterizations. This paper investigates subspace-based blind identification of Laguerre filter tap coefficients, the internal filter state, and the input, given only noisy observations of the output. This paper deals only with single-input, multiple-output (SIMO) Laguerre models. A state space model for the SIMO Laguerre system is derived from which blind estimation algorithms are developed. As in the finite impulse response (FIR) case, the Laguerre filter taps coefficients can be estimated from the column space of a certain Hankel matrix constructed from noisy output observations, whereas the internal state and input can be estimated from the row space by exploiting state space structure. While not exactly uniquely identifiable, conditions are given for which the tap coefficients, the internal state, and the input can be determined to within a multiplicative scalar factor.     

Blind equalization of nonlinear channels from second-orderstatistics

This paper addresses the blind equalization problem for single-input multiple-output nonlinear channels, based on the second-order statistics (SOS) of the received signal. We consider the class of "linear in the parameters" channels, which can be seen as multiple-input systems in which the additional inputs are nonlinear functions of the signal of interest. These models include (but are not limited to) polynomial approximations of nonlinear systems. Although any SOS-based method can only identify the channel to within a mixing matrix (at best), sufficient conditions are given to ensure that the ambiguity is at a level that still allows for the computation of linear FIR equalizers from the received signal SOS, should such equalizers exist. These conditions involve only statistical characteristics of the input signal and the channel nonlinearities and can therefore be checked a priori. Based on these conditions, blind algorithms are developed for the computation of the linear equalizers. Simulation results show that these algorithms compare favorably with previous deterministic methods     

Exponential asymptotic stability of time-varying inverse predictionerror filters

It is a classical result of linear prediction theory that as long as the minimum prediction error variance is nonzero, the transfer function of the optimum linear prediction error filter for a stationary process is minimum phase, and therefore, its inverse is exponentially stable. Here, extensions of this result to the case of nonstationary processes are investigated. In that context, the filter becomes time-varying, and the concept of “transfer function” ceases to make sense. Nevertheless, we prove that under mild condition on the input process, the inverse system remains exponentially stable. We also consider filters obtained in a deterministic framework and show that if the time-varying coefficients of the predictor are computed by means of the recursive weighted least squares algorithm, then its inverse remains exponentially stable under a similar set of conditions     

An algorithm for unit-norm equation error system identification based on the method of multipliers

It is known that the unit-norm constraint for equation-error based system identification is superior to the monic constraint since it produces consistent estimates for white measurement noise and also presents better approximation properties in reduced-order cases. Here, a new algorithm for unit-norm equation-error adaptive filtering is proposed. This scheme is inspired by the constrained optimization technique known as the method of multipliers. An analysis of stationary points and mean convergence properties is developed.     

Hyperstable adaptive IIR algorithms with polyphase structures:analysis and design

We consider adaptive identification algorithms based on hyperstability concepts with polyphase structures. The SPR condition required for convergence of these schemes can be always met by using a sufficiently high polyphase expansion factor M. The degree of persistent excitation required for parameter convergence is obtained. If some a priori knowledge about the system to identify is available, a compensating filter can be designed to avoid the need for a high M