Abstract—In this paper, we consider distributed estimation of

a noise-corrupted deterministic parameter in energy-constrained

wireless sensor networks from energy-distortion perspective.

Given a total energy budget allowable to be used by all sensors,

there exists a tradeoff between the subset of active sensors and

the energy used by each active sensor in order to minimize the

estimation MSE. To determine the optimal quantization bit rate

and transmission energy of each sensor, a concept of equivalent

unit-energy MSE function is introduced. Based on this

concept, an optimal energy-constrained distributed estimation

algorithm for homogeneous sensor networks and a quasi-optimal

energy-constrained distributed estimation algorithm for heterogeneous

sensor networks are proposed. Moreover, the theoretical

energy-distortion performance bound for distributed estimation

is addressed and it is shown that the proposed algorithm is

quasi-optimal within a factor 2 of the theoretical lower bound.