We investigate the properties of data collection in wireless sensor networks, in terms of both capacity and power allocation strategy. We consider a scenario in which a number of sensors observe a target being estimated at fusion center (FC) using minimum mean-square error (MMSE) estimator. Based on the relationship between mutual information and MMSE (I-MMSE), the capacity of data collection in coherent and orthogonal multiple access channel (MAC) models is derived. Considering power constraint, the capacity is derived under two scenarios: equal power allocation and optimal power allocation of both models. We provide the upper bound of capacity as a benchmark. In particular, we show that the capacity of data collection scales as Θ((1/2)log ) when the number of sensors L grows to infinity. We show through simulation results that for both coherent and orthogonal MAC models, the capacity of the optimal power is larger than that of the equal power. We also show that the capacity of coherent MAC is larger than that of orthogonal MAC, particularly when the number of sensors L is large and the total power P is fixed. 1. Introduction Wireless sensor networks (WSNs) consisting of a large number of nodes are usually deployed in a large region for many applications, such as surveillance, security, and environmental monitoring. The goal of a sensor network is often to deliver the sensing data from all sensors to a fusion center (FC) and then conduct further analysis at the FC. Thus, data collection is important in sensor network applications [1]. Theoretical measure that captures the limits of collection processing in sensor network is the capacity of data collection. Capacity of data collection reflects how fast FC can collect sensing data from all sensors [2]. Understanding the capacity of the network is important for network designers in a feasibility of a large scale network deployment [3], particularly, to improve the performance of WSNs [1]. Furthermore, such understanding is essential in the development of efficient protocols [4]. Capacity limits of data collection in wireless sensor networks have been studied in the literature [1–10]. In [4, 5], they introduced the transport capacity of many-to-one in dense sensor networks. The authors in [6, 7] investigated the capacity of data collection with complex physical layer techniques. The capacity that involves multiple selected sources and destination has been studied in [8]. The capacity of data collection of single and multisinks (FC) is investigated [9]. In [2], the authors derive capacity of data collection
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