Performance bounds for remote estimation with an energy harvesting sensor

Remote estimation with an energy harvesting sensor with a limited data buffer is considered. The sensor node observes an unknown correlated circularly wide-sense stationary (c.w.s.s.) Gaussian field and communicates its observations to a remote fusion center using the energy it harvested. The fusion center employs minimum mean-square error (MMSE) estimation to reconstruct the unknown field. The distortion minimization problem under the online scheme, where the sensor has only access to the statistical information for the future energy packets is considered. We provide performance bounds on the achievable distortion under a slotted block transmission scheme, where at each transmission time slot, the data and the energy buffer is completely emptied. Our bounds provide insight to the trade-off between the buffer sizes and the achievable distortion. These trade-offs illustrate the insensitivity of the performance to the buffer size for signals with low degree of freedom and suggest performance improvements with increasing buffer size for signals with relatively higher degree of freedom.