Aitzaz Ahmad

Joint Node Localization and Time-Varying Clock Synchronization in Wireless Sensor Networks

The problems of node localization and clock synchronization in wireless sensor networks are naturally tied from a statistical signal processing perspective. In this work, we consider the joint estimation of an unknown nodes location and clock parameters by incorporating the effect of imperfections in node oscillators, which render a time varying nature to the clock parameters. The data exchange mechanism is based on a two-way message exchange with anchor nodes. In order to alleviate the computational complexity associated with the optimal maximum a-posteriori estimator, two iterative approaches are proposed as simpler alternatives. The first approach utilizes an Expectation-Maximization (EM) based algorithm which iteratively estimates the clock parameters and the location of the unknown node. The EM algorithm is further simplified by a non-linear processing of the data to obtain a closed form solution of the location estimation problem using least squares (LS). The performance of the estimation algorithms is benchmarked by deriving the Hybrid Cramer-Rao lower bound (HCRB) on the mean square error (MSE) of the estimators. The theoretical findings are corroborated by simulation studies which reveal that the LS estimator closely matches the performance of the EM algorithm for small time of arrival measurement noise, and is well suited for implementation in low cost sensor networks.

A Factor Graph Approach to Clock Offset Estimation in Wireless Sensor Networks

The problem of clock offset estimation in a two-way timing message exchange regime is considered when the likelihood function of the observation time stamps is Gaussian, exponential, or log-normally distributed. A parameterized solution to the maximum likelihood (ML) estimation of clock offset is analytically obtained, which differs from the earlier approaches where the likelihood function is maximized graphically. In order to capture the imperfections in node oscillators, which may render a time-varying nature to the clock offset, a novel Bayesian approach to the clock offset estimation is proposed by using a factor graph representation of the posterior density. Message passing using the max-product algorithm yields an exact expression for the Bayesian inference problem. Several lower bounds on the variance of an estimator are derived for arbitrary exponential family distributed likelihood functions which, while serving as stepping stones to benchmark the performance of the proposed clock offset estimators, can be useful in their own right in classical as well Bayesian parameter estimation theory. To corroborate the theoretical findings, extensive simulation results are discussed for classical as well as Bayesian estimators in various scenarios. It is observed that the performance of the proposed estimators is fairly close to the fundamental limits established by the lower bounds.

Network-Wide Clock Synchronization via Message Passing with Exponentially Distributed Link Delays

Clock synchronization has become an indispensable requirement in wireless sensor networks due to its central importance in vital network operations such as data fusion and duty cycling, and has attracted considerable research interest recently. Assuming exponentially distributed random delays in a two-way message exchange mechanism, this work proposes a network-wide clock synchronization algorithm using a factor graph representation of the network. Message passing using the max-product algorithm is adopted to derive the update rules for the proposed iterative procedure. A closed form solution is obtained for each nodes belief about its clock offset at each iteration. Simulation results show that the application of the proposed message passing-based network-wide clock synchronization algorithm provides convergent estimates for both regular cycle-free and random topologies. Moreover, the mean square error (MSE) performance of the proposed algorithm is also compared with the Cramer-Rao bound (CRB) for small example networks, which further highlights the effectiveness of the proposed algorithm.

ROBNCA: robust network component analysis for recovering transcription factor activities

Network component analysis (NCA) is an efficient method of reconstructing the transcription factor activity (TFA), which makes use of the gene expression data and prior information available about transcription factor (TF) - gene regulations. We propose ROBust Network Component Analysis (ROBNCA), a novel iterative algorithm that explicitly models the possible outliers in the microarray data. ROBNCA algorithm provides a closed form solution for estimating the connectivity matrix, which was not available in prior contributions. The ROBNCA algorithm is compared to FastNCA and the Non-iterative NCA (NI-NCA) and is shown to estimate the TF activity profiles as well as the TF-gene control strength matrix with a much higher degree of accuracy than FastNCA and NI-NCA, irrespective of varying noise, and/or amount of outliers in case of synthetic data. The run time of the ROBNCA algorithm is comparable to that of FastNCA, and is hundreds of times faster than NI-NCA.

Joint node localization and time-varying clock synchronization in wireless sensor networks

The problems of node localization and clock synchronization in wireless sensor networks are naturally tied from a statistical signal processing perspective. In this work, we consider the joint estimation of an unknown nodes location and clock parameters by incorporating the effect of imperfections in node oscillators, which render a time varying nature to the clock parameters. The data exchange mechanism is based on a two-way message exchange with anchor nodes. In order to alleviate the computational complexity associated with the optimal maximum a-posteriori estimator, two iterative approaches are proposed as simpler alternatives. The first approach utilizes an Expectation-Maximization (EM) based algorithm which iteratively estimates the clock parameters and the location of the unknown node. The EM algorithm is further simplified by a non-linear processing of the data to obtain a closed form solution of the location estimation problem using least squares (LS). The performance of the estimation algorithms is benchmarked by deriving the Hybrid Cramer-Rao lower bound (HCRB) on the mean square error (MSE) of the estimators. The theoretical findings are corroborated by simulation studies which reveal that the LS estimator closely matches the performance of the EM algorithm for small time of arrival measurement noise, and is well suited for implementation in low cost sensor networks.

Time-varying clock offset estimation in two-way timing message exchange in wireless sensor networks using factor graphs

The problem of clock offset estimation in a two-way timing exchange regime is considered when the likelihood function of the observation time stamps is exponentially distributed. In order to capture the imperfections in node oscillators, which render a time-varying nature to the clock offset, a novel Bayesian approach to the clock offset estimation is proposed using a factor graph representation of the posterior density. Message passing using the max-product algorithm yields a closed form expression for the Bayesian inference problem.

On Clock Offset Estimation in Wireless Sensor Networks with Weibull Distributed Network Delays

We consider the problem of Maximum Likelihood (ML) estimation of clock parameters in a two-way timing exchange scenario where the random delays assume a Weibull distribution, which represents a more generalized model. The ML estimate of the clock offset for the case of exponential distribution was obtained earlier. Moreover, it was reported that when the fixed delay is known, MLE is not unique. We determine the uniformly minimum variance unbiased (UMVU) estimators for exponential distribution under such a scenario and produce biased estimators having lower MSE than UMVU for all values of clock offset. We then consider the case when shape parameter is greater than one and reduce the corresponding optimization problems to their equivalent convex forms, thus guaranteeing convergence to a global minimum.

Joint clock offset and skew estimation for inactive nodes in Wireless Sensor Networks

We incorporate the clock skew in the message exchange mechanism of [3], without which the clock synchronization problem remains practically unsolved. For the offset-only case, we determine the ML estimators through a simple application of convex optimization, alleviating the need for the graphical search mentioned in [3]. We also propose estimators that outperform the ML estimators in terms of MSE. For the joint estimation of clock offset and skew, we show that the likelihood maximization can be equivalently represented as a linear program and can be solved efficiently by any gradient descent method.

LTE codebook capacity loss for single-cell multi-user MIMO channels

Multi-user downlink MIMO communication has the potential to increase throughput using efficient beamforming. However, the precoding criteria assume perfect knowledge of the beamforming matrices at the base station (BS). This requires a user to transmit its complete channel information to the BS, a task that entails significant overhead. Limited feedback precoding, a part of LTE standardization now, needs only limited information be fed back to the BS. This paper studies the capacity loss incurred by using LTE codebooks, under different power allocation schemes with varying degrees of optimality. The sub-optimal power allocation schemes also ensure a better throughput-fairness trade-off. It is observed that using LTE codebooks results in a significant loss and that there is a need to develop codebooks which offer better adaptation to channel variations.

A Closed-Form Solution for Transcription Factor Activity Estimation Using Network Component Analysis

Non-iterative network component analysis (NINCA), proposed by Jacklin at.al, employs convex optimization methods to estimate the transcription factor control strengths and transcription factor activities. While NINCA provides good estimation accuracy and higher consistency, the costly optimization routine used therein renders a high computational complexity. This correspondence presents a closed form solution to estimate the connectivity matrix which is tens of times faster, and provides similar accuracy and consistency, thus making the closed form NINCA (CFNINCA) algorithm useful for large data sets encountered in practice. The proposed solution is assessed for accuracy and consistency using synthetic and yeast cell cycle data sets by comparing with the existing state-of-the-art algorithms. The robustness of the algorithm to the possible inaccuracies in prior information is also analyzed and it is observed that CFNINCA and NINCA are much more robust to erroneous prior information as compared to FastNCA.