We consider the distributed estimation of an unknown vector signal in a resource constrained sensor network with a fusion center. Due to power and bandwidth limitations, each sensor compresses its data in order to minimize the amount of information that needs to be communicated to the fusion center. In this context, we study the linear decentralized estimation of the source vector, where each sensor linearly encodes its observations and the fusion center also applies a linear mapping to estimate the unknown vector signal based on the received messages. We adopt the mean squared error (MSE) as the performance criterion. When the channels between sensors and the fusion center are orthogonal, it has been shown previously that the complexity of designing the optimal encoding matrices is NP-hard in general. In this paper, we study the optimal linear decentralized estimation when the multiple access channel (MAC) is coherent. For the case when the source and observations are scalars, we derive the optimal power scheduling via convex optimization and show that it admits a simple distributed implementation. Simulations show that the proposed power scheduling improves the MSE performance by a large margin when compared to the uniform power scheduling. We also show that under a finite network power budget, the asymptotic MSE performance (when the total number of sensors is large) critically depends on the multiple access scheme. For the case when the source and observations are vectors, we study the optimal linear decentralized estimation under both bandwidth and power constraints. We show that when the MAC between sensors and the fusion center is noiseless, the resulting problem has a closed-form solution (which is in sharp contrast to the orthogonal MAC case), while in the noisy MAC case, the problem can be efficiently solved by semidefinite programming (SDP).
Bibliographical noteFunding Information:
Manuscript received December 10, 2006; revised June 4, 2007. The associate editor coordinating the review of this manuscript and approving it for publication was Dr. Aleksandar Dogandzic. The work of J.-J. Xiao and Z.-Q. Luo was supported in part by the National Science Foundation by Grant DMS-0610037, and by the USDOD ARMY by Grant W911NF-05-1-0567. The work of S. Cui was supported in part by the University of Arizona Foundation. The work of A. J. Goldsmith was supported in part by the National Science Foundation by Grant CCR-0325639-001. This work was presented in part at the IEEE Global Conference on Communications, San Francisco, CA, November 2006.
- Convex optimization
- Distributed estimation
- Energy efficiency
- Linear source-channel coding
- Multiple access channel (MAC)