In this paper, we consider how to improve the performance of distributed estimation over a diffusion network in order to estimate the unknown parameter of interest from noisy measurements. Specifically, the distributed blind equalization based on the single-input multiple-output channel model over a wireless sensor network (WSN) is discussed in this paper. We propose a new combination weight rule that the weight of each sensor node is assigned by the signal power of the sensor (received) signal instead of only the degree of each sensor node. We assume that each channel from the common transmitter to the sensor nodes in the WSN is common and that noises, the variances of which are different, are included at each channel. The average mean square error and symbol error rate performance characteristics of the distributed blind equalization are investigated. Simulations show that a significant performance improvement is obtained by employing the proposed combination weight rule compared with using conventional combination weight rules.