Amir Rastegarnia

Vahid Vadidpour, Amir Rastegarnia, Azam Khalili et al.

Partial diffusion scheme is an effective method for reducing computational load and power consumption in adaptive network implementation. The Information is exchanged among the nodes, usually over noisy links. In this paper, we consider a general version of partial-diffusion least-mean-square (PDLMS) algorithm in the presence of various sources of imperfect information exchanges. Like the established PDLMS, we consider two different schemes to select the entries, sequential and stochastic, for transmission at each iteration. Our objective is to analyze the aggregate effect of these perturbations on general PDLMS strategies. Simulation results demonstrate that considering noisy link assumption adds a new complexity to the related optimization problem and the trade-off between communication cost and estimation performance in comparison to ideal case becomes unbalanced.

Vahid Vahidpour, Amir Rastegarnia, Azam Khalili et al.

Partial diffusion-based recursive least squares (PDRLS) is an effective method for reducing computational load and power consumption in adaptive network implementation. In this method, each node shares a part of its intermediate estimate vector with its neighbors at each iteration. PDRLS algorithm reduces the internode communications relative to the full-diffusion RLS algorithm. This selection of estimate entries becomes more appealing when the information fuse over noisy links. In this paper, we study the steady-state performance of PDRLS algorithm in presence of noisy links and investigate its convergence in both mean and mean-square senses. We also derive a theoretical expression for its steady-state meansquare deviation (MSD). The simulation results illustrate that the stability conditions for PDRLS under noisy links are not sufficient to guarantee its convergence. Strictly speaking, considering nonideal links condition adds a new complexity to the estimation problem for which the PDRLS algorithm becomes unstable and do not converge for any value of the forgetting factor.

Azam Khalili, Amir Rastegarnia

In this paper we study the impact of network size on the performance of incremental least mean square (ILMS) adaptive networks. Specifically, we consider two ILMS networks with different number of nodes and compare their performance in two different cases including (i) ideal links and (ii) noisy links. We show that when the links between nodes are ideal, increasing the network size improves the steady-state error. On the other hand, in the presence of noisy links, we see different behavior and the ILMS adaptive network with more nodes necessarily has not better steady-state performance. Simulation results are also provided to illustrate the discussions.

Vahid Vahidpour, Amir Rastegarnia, Azam Khalili et al.

In conventional distributed Kalman filtering, employing diffusion strategies, each node transmits its state estimate to all its direct neighbors in each iteration. In this paper we propose a partial diffusion Kalman filter (PDKF) for state estimation of linear dynamic systems. In the PDKF algorithm every node (agent) is allowed to share only a subset of its intermediate estimate vectors at each iteration among its neighbors, which reduces the amount of internode communications. We study the stability of the PDKF algorithm where our analysis reveals that the algorithm is stable and convergent in both mean and mean-square senses. We also investigate the steady-state mean-square deviation (MSD) of the PDKF algorithm and derive a closed-form expression that describes how the algorithm performs at the steady-state. Experimental results validate the effectiveness of PDKF algorithm and demonstrate that the proposed algorithm provides a trade-off between communication cost and estimation performance that is extremely profitable.

Amir Rastegarnia, Azam Khalili, Md Kafiul Islam

In this letter we focus on designing self-organizing diffusion mobile adaptive networks where the individual agents are allowed to move in pursuit of an objective (target). The well-known Adapt-then-Combine (ATC) algorithm is already available in the literature as a useful distributed diffusion-based adaptive learning network. However, in the ATC diffusion algorithm, fixed step sizes are used in the update equations for velocity vectors and location vectors. When the nodes are too far away from the target, such strategies may require large number of iterations to reach the target. To address this issue, in this paper we suggest two modifications on the ATC mobile adaptive network to improve its performance. The proposed modifications include (i) distance-based variable step size adjustment at diffusion algorithms to update velocity vectors and location vectors (ii) to use a selective cooperation, by choosing the best nodes at each iteration to reduce the number of communications. The performance of the proposed algorithm is evaluated by simulation tests where the obtained results show the superior performance of the proposed algorithm in comparison with the available ATC mobile adaptive network.

Azam Khalili, Amir Rastegarnia

We study the effect of fading in the communication channels between sensor nodes on the performance of the incremental least mean square (ILMS) algorithm, and derive steady state performance metrics, including the mean-square deviation (MSD), excess mean-square error (EMSE) and meansquare error (MSE). We obtain conditions for mean convergence of the ILMS algorithm, and show that in the presence of fading channels, the ILMS algorithm is asymptotically biased. Furthermore, the dynamic range for mean stability depends only on the mean channel gain, and under simplifying technical assumptions, we show that the MSD, EMSE and MSE are non-decreasing functions of the channel gain variances, with mean-square convergence to the steady states possible only if the channel gain variances are limited. We derive sufficient conditions to ensure mean-square convergence, and verify our results through simulations.

Azam Khalili, Amir Rastegarnia

We study the effect of fading in the communication channels between nodes on the performance of the incremental least mean square (ILMS) algorithm. We derive steady-state performance metrics, including the mean-square deviation (MSD), excess mean-square error (EMSE), and mean-square error (MSE). We obtain the sufficient conditions to ensure mean-square convergence, and verify our results through simulations. Simulation results show that our theoretical analysis closely matches the actual steady state performance.

Wael M. Bazzi, Amir Rastegarnia, Azam Khalili

In this paper we consider the issue of reliability of measurements in distributed adaptive estimation problem. To this aim, we assume a sensor network with different observation noise variance among the sensors and propose new estimation method based on incremental distributed least mean-square (IDLMS) algorithm. The proposed method contains two phases: I) Estimation of each sensors observation noise variance, and II) Estimation of the desired parameter using the estimated observation variances. To deal with the reliability of measurements, in the second phase of the proposed algorithm, the step-size parameter is adjusted for each sensor according to its observation noise variance. As our simulation results show, the proposed algorithm considerably improves the performance of the IDLMS algorithm in the same condition.

Azam Khalili, Wael M. Bazzi, Amir Rastegarnia

This paper considers the problem of distributed estimation in an incremental network when the measurements taken by the node follow a widely linear model. The proposed algorithm which we refer to it as incremental augmented affine projection algorithm (incAAPA) utilizes the full second order statistical information in the complex domain. Moreover, it exploits spatio-temporal diversity to improve the estimation performance. We derive steady-state performance metric of the incAAPA in terms of the mean-square deviation (MSD). We further derive sufficient conditions to ensure mean-square convergence. Our analysis illustrate that the proposed algorithm is able to process both second order circular (proper) and noncircular (improper) signals. The validity of the theoretical results and the good performance of the proposed algorithm are demonstrated by several computer simulations.