In smart grid, the local data aggregator of an area collects the total electrical consumption of the area by aggregating the measurements of smart meters (SMs). A great number of schemes based on the cryptography have been proposed to guarantee the privacy of the individual measurements of the SMs. However, the cryptographic systems require the complicated computations and key-management infrastructural support as well as introduce information leaking risks. In this paper, we propose a novel physical channel-based scheme for privacy preservation in data aggregation, which can work without a cryptographic system. The SMs preserve the privacy of the measurements by adding the jamming signals, which are constructed by scaled channels. The jamming signals are designed to be cancelled with each other at the aggregator. Concurrently, our scheme can resist different types of attacks such as eavesdropping, compromising, and differential attacks even in the case that they are colluding. The simulation results show that the mean squared error (MSE) of the total measurements is significantly lower than that of the traditional scheme while the privacy of the individual measurements is high.