Miloje S. Radenkovic

Adaptive IIR filtering of nonstationary signals

This paper presents global stability of the adaptive IIR filter in a nonstationary environment. For the estimation of time-varying parameters, the normalized least-mean-square (LMS) algorithm based on the output error method is used. We assume the presence of a possibly colored and nonstationary measurement noise. The global stability analysis is carried out in a deterministic context, and it is shown that the filter output is uniformly bounded for all initial conditions. We then consider the special case when the noise is a martingale difference sequence, and establish the almost sure mean-square performance in a stochastic framework.

Verification of the self-stabilization mechanism in robust stochastic adaptive control using Lyapunov function arguments

The objective of this paper is to propose a new algorithm for self-tuning control in the presence of unmodeled dynamics. The algorithm is a modified version of the well-known stochastic gradient scheme. It is shown (with probability one) that the resulting closed-loop system is globally stable and the mean-square tracking error is proportional to the size of unmodeled dynamics. In the absence of unmodeled dynamics, the algorithm produces the minimum-variance self-timing control. It is analytically verified that the proposed algorithm has self-stabilization property; i.e., possible occurrence of instability results in mean-square bounded signals. Global stability of the adaptive system is achieved without imposing persistency exciting condition on the regressor and positive real assumption on the system noise dynamics.

Robust Multiuser Automatic Modulation Classifier for Multipath Fading Channels

Automatic Modulation Classifier (AMC) is an important component of a Cognitive Radio (CR) architecture that helps in better utilization of the spectrum. AMC in literature is mostly developed for classifying the signal transmitted by a single user. Multiuser AMC, as the name suggests, simultaneously classifies signals transmitted by multiple users. In this paper we propose a fourth order cumulant based multiuser AMC that can perform well even in a multipath fading environment. A recursive blind multiuser channel estimation algorithm, which forms an integral part of the multiuser AMC, is also proposed. Simulation results are provided to illustrate the promising results yielded by the proposed algorithm.

Combined Blind Equalization and Automatic Modulation Classification for Cognitive Radios

Blind equalization and Automatic Modulation Classification (AMC) have been of significant importance for cognitive radios when the receiver has no information about the channel or modulation type. Choosing an appropriate equalizer is difficult in the absence of channel information. In this paper, an AMC based on cyclostationary feature detection and a predictor-based recursive blind equalizer is used in conjunction. The probability of classification of the AMC is used as a metric and fed back to update the blind equalizer order. The equalizer and the AMC enhance the performance of each other. Computer simulations are given to illustrate the concept and yield promising results.

Using Persistent Excitation with Fixed Energy to Stabilize AdaptiveControllers and Obtain Hard Bounds for the Parameter Estimation Error

Two important instability problems in certainty equivalence adaptive control are solved by external excitation. The first instability is parameter drift along an unstable manifold when the excitation level is not high enough. The second instability is numerical and due to a division with zero in the adaptive law. Global methods based on excitation have been developed to solve this problem, but the energy of the excitation has been tuned on-line. The main contribution of the current paper is in showing that the estimator is stabilized when we apply excitation with fixed and finite energy. The level of excitation should be sufficiently high relative to the magnitudes of the external disturbances and the unmodeled dynamics. The approach can be generalized to more complex adaptive laws. This, together with the fact that we obtain hard bounds for the parameter estimation error, opens up for the possibility of designing robust controllers that are adaptive.

Blind Adaptive Equalization of MIMO Systems: New Recursive Algorithms and Convergence Analysis

An adaptive (recursive in time) filtering method is proposed for blind deconvolution of multiple-input multiple-output (MIMO) channels modeled by an autoregressive moving average (ARMA) process. This method consists of two recursive schemes. The adaptive blind identification algorithm estimates the MIMO system impulse response. These estimates are then used in an adaptive Wiener-type filter to extract the instantaneous mixture of input sources. Such a mixture is further processed by a blind source separation algorithm to obtain the individual sources. Only second-order (SOS) statistics are used, and precise knowledge of the system order is not required as long as it is overmodeled. We also present an algorithm for the case of time-varying parameters. It is proved that the developed algorithms are globally convergent with probability one.

On multi-agent self-tuning consensus

This paper considers the consensus problem in complex networks of uncertain discrete time agents. The coupling parameters among agents are locally self tuned by least-mean square (LMS) algorithm, without using any global information. In this process each agent minimizes a local cost function dependent on the error between the agent state and the average of neighbors states. Provided that the network graph is strongly connected, it is shown that for each agent the sequence of coupling parameters is convergent, and all agent states converge toward the same constant value. It is demonstrated that in the face of unknown high-frequency gain, the proposed algorithms generate such coupling parameters so that the overall multi-agent system is marginally stable with only one pole on the unit circle, located at λ = 1 .

Stochastic Adaptive Stabilization via Extremum Seeking in Case of Unknown Control Directions

This technical note presents a novel extremum seeking (ES)-based algorithm for global stabilization of unstable first order linear discrete-time (LDT) stochastic systems with unknown control directions. The probing signal is a martingale difference sequence with a vanishing variance. The controller parameter estimate converges almost surely (a.s.) to the optimizing value. The sample mean-square value of the output converges (a.s.) to the minimal variance.

A Recursive Blind Adaptive Equalizer for IIR Channels with Common Zeros

This paper considers the problem of blind adaptive equalization of infinite impulse response (IIR) channels without requiring the channel diversity condition. That is, the subchannels in the fractionally sampled model can have common factors. We analyze the case of two parallel channels, and develop an equalizer based on IIR prediction of the received signal. The predictor parameters are estimated by using the recursive extended least squares (RELS) algorithm. It is proved that with probability one the adaptive equalizer is globally stable, the parameter estimates are consistent, and the prediction error converges toward a scalar multiple of the input symbol sequence.

Optimality and Almost Sure Convergence of Adaptive IIR Filters with Output Error Recursion

We consider the almost sure convergence of the adaptive IIR filter based on the output error method. It is rigorously shown that the algorithm is globally stable, parameter estimation is consistent, and perfect noise cancellation is achieved in the presence of nonstationary colored noise. Due to the complexity of the analysis, we consider the scalar case, i.e., a one-pole IIR filter.