Energy-Efficient Quantization for Parameter Estimation in Inhomogeneous WSNs Sahar Movaghati and Masoud Ardakani Department of Electrical and Computer Engineering, University of Alberta, CANADA Abstract—The estimation of an unknown parameter using distributed measurements is an essential problem in many wireless sensor network (WSN) applications. In a WSN, the shortage of resources, specially the energy in the sensors, acts as a constraint on the design of estimation algorithms. The existing studies on this problem have developed algorithms that try to limit the total energy in the whole network, yet not considering each sensor’s energy consumption individually. We develop an estimation algorithm for inhomogeneous environments considering the transmission load of individual sensors. I. I NTRODUCTION Wireless sensor networks (WSNs) consist of small sensors which cooperate to monitor physical properties of an environ- ment. WSNs are deployed in many applications that involve distributed estimation, distributed detection and localization. The problem of distributed parameter estimation in WSNs is defined as estimating an unknown parameter from noisy local measurements gathered at each sensor. In such problems, we look for distributed algorithms that can produce a high-quality estimation of the unknown, at the fusion center (FC). Sensors’ limited energy is a constraint which necessitates the use of energy-efficient algorithms in order to keep sensors’ lifetime as long as possible. To address this restriction, many studies are focused on reducing the number of transmitted bits from the sensors to the FC via quantization. For example, [1]–[12] suggest efficient quantization rules for sensors’ local measurement data. In quantization algorithms studied in [9]– [12], sensors with higher SNR, i.e. better measurement quality, quantize their measurements into more number of bits com- pared to sensors with lower SNR. This approach is efficient in terms of the total energy consumed in the whole network, but it may not be the best solution when the main constraint is the limited energy available at each individual sensor. To further reduce the energy usage and provide equal energy usage at all sensors, various authors consider estimation algorithms based on a single-bit transmission from each sensor. [12] and [13] use a single common threshold for all the sensors to generate binary observations. To increase the estimation accuracy, [4] and [8] let sensors generate their bit according to different quantization thresholds in the domain of the param- eter. [7] adjusts the thresholds of the sensors dynamically to achieve a better performance. However, none of these studies are optimized for inhomogeneous networks where nonidenti- cal sensor-to-target distances, or varying sensor measurement qualities cause different SNR among the sensors. In this paper, we suggest an energy-efficient quantization algorithm for parameter estimation in inhomogeneous WSNs. Our algorithm benefits from high-precision quantization; how- ever, with high probability, each sensor sends only one bit to the FC. Thus, it guarantees longer lifetime for individual sensors compared to [10] and [11]. Using the knowledge of sensors’ SNR, our main insight is to have the lower-SNR sensors send the lower precision bits and relieve the higher- SNR sensors of the redundant burden. We will also suggest a modification to our algorithm that improves the performance by letting the better sensors occasionally send one extra bit. Analytical formulations for the performance of our algorithm are derived and confirmed with simulation results. II. PROBLEM DESCRIPTION Assume a network of N sensors and a FC with two- directional communication links to all sensors, which coop- erate to estimate an unknown parameter X. When only the occurrence range of the unknown parameter is known, it is reasonable to assume a uniform distribution for X in its range [-V,V ] 1 . Each sensor n; 1 ≤ n ≤ N , gathers a measurement Y n of X which is corrupted by additive Gaussian noise, i.e., Y n = X + w n (1) Here w n ∼N (0,σ 2 n ) is the measurement noise at sensor n whose variance σ 2 n depends on the sensor’s measurement quality or SNR. The measurement noise variance of all sensors is known at the FC and for two sensors n and m, n = m, w n and w m are independent. We quantize Y n into 2 B levels as q n = Q(Y n ) (2) where Q(·) represents the quantization rule. Consequently, q n can be represented by B bits. To minimize the energy consumption at the sensors, we limit each sensor to sending only one of these B bits to the FC. To facilitate this solution, the FC considers B sensors and depending on the SNR of these sensors asks each one for one bit of q n . After receiving B bits, the FC obtains ˆ X, an estimate of X. The estimation error is due to both quantization noise and possible bit errors resulted from measurement noise at the sensors. The communication channel between each sensor and the FC is assumed error free. 1 Equations and results of this paper are obtained assuming uniform distribu- tion for X. Our proposed algorithm can be applied for any other distributions. 978-1-4244-9268-8/11/$26.00 ©2011 IEEE This full text paper was peer reviewed at the direction of IEEE Communications Society subject matter experts for publication in the IEEE Globecom 2011 proceedings.