We consider the distributed estimation of a random vector signal in a power constraint wireless sensor network (WSN) that follows a multiple-input and multiple-output (MIMO) coherent multiple access channel model. We design linear coding matrices based on linear minimum mean-square error (LMMSE) fusion rule that accommodates spatial correlated data. We obtain a closed-form solution that follows a water-filling strategy. We also derive a lower bound to this model. Simulation results show that when the data is more correlated, the distortion in terms of mean-square error (MSE) degrades. By taking into account the effects of correlation, observation, and channel matrices, the proposed method performs better than equal power method. 1. Introduction The wireless sensor network (WSN) is a potential technology in many application areas including environmental monitoring, health, security and surveillance, and robotic exploration [1]. WSNs have many interested issues, one of them is distributed estimation. In the distributed estimation scenario, sensors observe phenomena from the target(s) and transmit to a fusion center (FC). Received signal at FC is estimated using an estimation technique. Distributed estimation by considering power consumption has attracted much attention in [2–7]. Because the sensors deployed in a certain region are difficult to change the batteries, the low power consumption is important to guarantee a lifetime of the sensors. The distributed estimation is also applied on the orthogonal multiple access channel (MAC) model [4, 6, 8] and the coherent MAC model [2, 5] that considers single-input single-output (SISO). To save energy, multiple-input and multiple-output (MIMO) system has been analyzed by involving signaling overhead [9], in which the MIMO system can offer substantial energy savings in WSN. Cooperative MIMO with data aggregation also has been investigated in [10, 11]. In practical scenario, if the targets or the sensors are close to each other, the data will be potentially correlated. Such a problem has been investigated in [3, 6, 12, 13]. In this paper, we consider multiple targets that are spatially distributed. The targets are observed by multiple sensors that apply an analog forwarding scheme. This scheme will multiply the observed data with a designed coding matrix in each sensor, which results in encoded messages. The encoded messages from the sensors are transmitted to the FC over a coherent MAC. The channel follows MIMO model that has multiple antenna at transmitter and at receiver. At the FC, the received signals are
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