In this paper, we design and analyze pilot-assisted Distributed Co-Phasing (DCP) schemes for information fusion in a wireless sensor network. First, using a cutoff rate analysis, we show that higher order constellations significantly improve the throughput performance of DCP in comparison with the binary constellation considered in past work. However, using a higher order constellation in the DCP setting requires estimation of the composite channel from the sensors at the Fusion Center (FC), which is not available in current DCP schemes. We propose two blind algorithms for channel estimation, namely, a power method and a modified K-means algorithm. In particular, the latter is computationally efficient and converges significantly faster and more accurately than the conventional K-means algorithm. We derive closed-form expressions for the probability of symbol error and study the performance of DCP both analytically and through simulations. Our simulation results show that even at moderate to low SNRs, the modified K-means algorithm achieves a probability of error comparable to that achievable with a perfect channel estimate at the FC. The proposed DCP and blind channel estimation schemes are thus a promising technique for energy-efficient data fusion in wireless sensor networks.