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参考文献也要翻译成中文！An Energy-Efficient Cooperative Algorithm for Data Estimation inWireless Sensor NetworksAbstract – In Wireless Sensor Networks (WSN), nodes operate on batteries and network’s lifetime depends on energy consumption of the nodes. Consider the class of sensor networks where all nodes sense a single phenomenon at different locations and send messages to a Fusion Center (FC) in order to estimate the actual information. In classical systems all data processing tasks are done in the FC and there is no processing or compression before transmission. In the proposed algorithm, network is divided into clusters and data processing is done in two parts. The first part is performed in each cluster at the sensor nodes after local data sharing and the second part will be done at the Fusion Center after receiving all messages from clusters. Local data sharing results in more efficient data transmission in terms of number of bits. We also take advantage of having the same copy of data at all nodes of each cluster and suggest a virtual Multiple-Input Multiple-Output (V-MIMO) architecture for data transmission from clusters to the FC. A Virtual-MIMO network is a set of distributed nodes each having one antenna. By sharing their data among themselves, these nodes turn into a classical MIMO system. In the previously proposed cooperative/virtual MIMO architectures there has not been any data processing or compression in the conference phase. We modify the existing VMIMO algorithms to suit the specific class of sensor networks that is of our concern. We use orthogonal Space-Time Block Codes (STBC) for MIMO part and by simulation show that this algorithm saves considerable energy compared to classical systems.I. INTRODUCTIONA typical Wireless Sensor Network consists of a set of small, low-cost and energy-limited sensor nodes which are deployed in a field in order to observe a phenomenon and transmit it to a Fusion Center (FC). These sensors are deployed close to one another and their readings of the environment are highly correlated. Their objective is to report a descriptive behavior of the environment based on all measurements to the Fusion Center. This diversity in measurement lets the system become more reliable and robust against failure. In general, each node is equipped with a sensing device, a processor and a communication module (which can be either a transmitter or transmitter/receiver).Sensor nodes are equipped with batteries and are supposed to work for a long period of time without battery replacement. Thus, they are limited in energy and one of the most important issues in designing sensor networks will be the energy consumption of the sensor nodes. To deal with this problem, we might either reduce the number of bits to be transmitted by source compression or reduce the required power for transmission by applying advanced transmission techniques while satisfying certain performance requirement.A lot of research has been done in order to take advantage of the correlation among sensors’ data for reducing the number of bits to be transmitted. Some are based on distributed source coding[1]while others use decentralized estimation[2-5]. In [1], authors present an efficient algorithm that applies distributed compression based on Slepian – Wolf[14] encoding technique and use an adaptive signal processing algorithm to track correlation among sensors data. In [2-5] the problem of decentralized estimation in sensor networks has been studied under different constraints. In these algorithms, sensors perform a local quantization on their data considering that their observations are correlated with that of other sensors. They produce a binary message and send it to the FC. FC combines these messages based on the quantization rules used at the sensor nodes and estimates the unknown parameter. Optimal local quantization and final fusion rules are investigated in these works. The distribution of data assumed for sensor observation in these papers has Uniform probability distribution function. In our model we consider Gaussian distribution introduced in [17] for sensor measurements which ismore likely to reality.As an alternative approach, some works have been done using energy-efficient communication techniques such as cooperative/virtual Multiple-Input Multiple-Output (MIMO) transmission in sensor networks [6-11]. In these works, as each sensor is equipped with one antenna, nodes are able to form a virtual MIMO system by performing cooperation with others. In [6] the application of MIMO techniques in sensor networks based on Alamouti[15] space-time block codes was introduced. In [8,9] energy-efficiency of MIMO techniques has been explored analytically and in [7] a combination of distributed signal processing algorithm presented and in [1] cooperative MIMO was studied.In this paper, we consider both techniques of compression and cooperative transmission at the same time. We reduce energy consumption in two ways; 1) processing data in part at the transmitting side, which results in removing redundant information thus having fewer bits to be transmitted and 2) reducing required transmission energy by applying diversity and Space-Time coding. Both of these goals will be achieved by our proposed two-phase algorithm. In our model, the objective is to estimate the unknown parameter which is basically the average of all nodes’ measurements. That is, exact measurements of individual nodes are not important and it is not necessary to spend a lot of energy and bandwidth to transmit all measured data with high precision to the FC. We can move some part of data processing to the sensors side. This can be done by local data sharing among sensors. We divide the network into clusters of ‘m’ members. The number of members in the cluster (m) is both the compression factor in data processing and also the diversity order in virtual-MIMO architecture. The remaining of this paper is organized as following: in section II we introduce our system model and basic assumptions. In section III we propose our collaborative algorithm. In section IV we present the mathematical analysis of the proposed algorithm and in section V we give some numerical simulations. Finally section VI concludes the paper.II. SYSTEM MODELA. Network ModelThe network model that we use is similar to the one presented in [2-5].Our network consists of N distributed Sensor Nodes (SN) and a Fusion Center (FC). Sensors are deployed uniformly in the field, close to one another and each taking observations on an unknown parameter (θ). Fusion Center is located far from the nodes. All nodes observe same phenomenon but with different measurements. These nodes together with the Fusion Center are supposed to find the value of the unknown parameter. Nodes send binary messages to Fusion Center. FC will process the received messages and estimate the unknown value.B. Data ModelIn our formulation we use the data model introduced in[17]. We assume that all sensors observe the same phenomenon (θ) which has Gaussian distribution with variance σx 2. They observe different versions of θ and we model this difference as an additive zero mean Gaussian noisewith variance σn 2. Therefore, sensor observations will be described byn i i θx += （1） Where θ ~ N (0, σx 2) and n i ~ N (0, σn 2) for i = 1, 2, … , N .Based on thisassumption the value of θ can be estimated by taking the numerical average of the nodes observations, i.e.∑==N i i x N 11θ（2）C. Reference System ModelOur reference system consists of N conventional Single Input Single Output (SISO) wireless links, each connecting one of the sensor nodes to the FC. For the reference system we do not consider any communication or cooperation among the sensors. Therefore each sensor quantizes its observation by an L-bit scalar quantizer designed for distribution of θ, generates a message of length L and transmits it directly to the FC. Fusion Center receives all messages and performs the processing, which is calculation of the numerical average of these messages.III. COOPERATIVE DATA PROCESSING ALGORITHMSensor readings are analog quantities. Therefore, each sensor has to compress its data into several bits. For data compression we use L -bit scalar quantizer [12,13].In our algorithm, network is divided into clusters, each cluster having a fixed and pre-defined number of members (m). Members of each cluster are supposed to cooperate with one another in two ways:1. Share, Process and Compress their data2. Cooperatively transmit their processed data using virtual MIMO.IV. ANALYSISThe performance metric considered in our analysis is the total distortion due to compression and errors occurred during transmission. The first distortion is due to finite length quantizer, used in each sensor to represent the analog number by L bits. This distortion depends on the design of quantizer.We consider a Gaussian scalar quantizer which is designed over 105 randomly generated samples. The second distortion is due to errors occurred during transmission through the channel. In our system, this distortion is proportional to the probability of bit error. Since the probability of bit error (Pe) is a function of transmission energy per bit (Eb), total distortion will be a function of Eb. In this section we characterize the transmission and total consumed energy of sensors and find the relationship between distortion and probability of bit error.V. SIMULATION AND NUMERICAL RESULTS To give a numerical example, we assume m = 4 members in each cluster. Therefore our Virtual-MIMO scheme will consist of 4 transmit antennas. We assume that network has N = 32 sensors. Sensor observations are Gaussian with σx2= 1 and are added to a Gaussian noise of σn2= 0.1 .Nodes are deployed uniformly in the field and are 2 meters apart from each other and the Fusion Center is located 100 meters away from the center of the field. The values for circuit parameters are quoted from [6] and are listed in Table I. These parameters depend on the hardware design and technological advances. Fig. 1 illustrates the performance (Distortion) of reference system and proposed two-phase V-MIMO scheme versus transmission energy consumption in logarithmic scale. As shown in the figures, depending on how much precision is needed in the system, we can save energy by applying the proposed algorithm.TABLE IFig. 2 illustrates the Distortion versus total energy consumption of sensor nodes. That is, in this figure we consider both the transmission and circuit energy consumption. The parameters that lead us to these results may be designed to give better performance than presented here. However, from these figures we can conclude that the proposed algorithm outperforms the reference system when we want to have distortion less than 10−3 and it can save energy as high as 10 dB.VI. CONCLUSIONIn this paper we proposed a novel algorithm which takes advantage of cooperation among sensor nodes in two ways: it not only compresses the set of sensor messages at the sensor nodes into one message, appropriate for final estimation but also encodes them into orthogonal space-time symbols which are easy to decode and energy-efficient. 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