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 node's 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.

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.

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.

In this paper, a consensus-based clock synchronization algorithm is presented and its resilience to frequency displacement estimation errors as well as communication noise is analyzed. The synchronization-enforcing control that is to be applied to clock periods is derived upon re-casting the consensus problem into a convex optimization problem and solving it in a distributed fashion via alternating direction method of multipliers. Conversely, plain consensus is used for reaching agreement on clock values. The proposed algorithm achieves higher convergence rates and equivalent noise resilience with respect to algorithmic solutions based on the only plain average consensus. The superior clock synchronization performance is corroborated via numerical tests.

In a cooperative multi-cell network the uplink signal coming from each mobile terminal (MT) is simultaneously demodulated by multiple base stations (BSs). Both backhaul capacity and BS processing capabilities limit the number of demodulating BSs. In order to fit the information exchange among BSs to backhaul resources we minimize the average number of demodulating BSs, under a constraint on the average outage probability. The BS selection problem becomes more complicated when error control configurations as automatic repeat request (ARQ) and hybrid ARQ (HARQ) with chase combining or incremental redundancy are considered. Multi-cell processing is implemented both by decoding the packet at each BS and by a joint decoding among BSs. We first derive the outage probability as a function of the number of cooperating BSs and the error control strategy. A heuristic approach for BS selection is then developed, to find at each frame which BSs perform demodulation and share the information in the backhaul. Lastly, we show that backhaul usage can be reduced up to 64% with respect to an unoptimized solution.

In a cooperative multi-cell network we propose to simultaneously demodulate the uplink signal coming from mobile terminals (MTs) with multiple base stations (BSs) for a joint decoding of the data packets. However, limited backhaul capacity and BS demodulation capabilities limits the number of cooperating BSs. In this paper we consider MTs using a hybrid automatic repeat request (HARQ) protocol for error control, as in 3G and 4G cellular systems. In order to limit the exchange of information among BSs we aim at minimizing the number of demodulating BSs at each HARQ retransmission, under a constraint on the outage probability after a pre-set number of retransmissions. A greedy approach is developed for the system using HARQ, which determines at each retransmission which BSs must perform demodulation and share the information in the backhaul. Numerical results compare the performance of the proposed algorithm with existing solutions, showing that backhaul usage can be reduced up to 38% in a usual 3G scenario.