Distortion-Rate Bounds for Distributed Estimation Using Wireless Sensor Networks

We deal with centralized and distributed rate-constrained estimation of random signal vectors performed using a network of wireless sensors (encoders) communicating with a fusion center (decoder). For this context, we determine lower and upper bounds on the corresponding distortion-rate (D-R) function. The nonachievable lower bound is obtained by considering centralized estimation with a single-sensor which has all observation data available, and by determining the associated D-R function in closedform. Interestingly, this D-R function can be achieved using an estimate first compress afterwards (EC) approach, where the sensor (i) forms the minimum mean-square error (MMSE) estimate for the signal of interest; and (ii) optimally (in the MSE sense) compresses and transmits it to the FC that reconstructs it. We further derive a novel alternating scheme to numerically determine an achievable upper bound of the D-R function for general distributed estimation using multiple sensors. The proposed algorithm tackles an analytically intractable minimization problem, while it accounts for sensor data correlations. The obtained upper bound is tighter than the one determined by having each sensor performing MSE optimal encoding independently of the others. Numerical examples indicate that the algorithm performs well and yields D-R upper bounds which are relatively tight with respect to analytical alternatives obtained without taking into account the cross-correlations among sensor data.