In distributed communication networks, the signal received at the destination is characterized by unknown multiple carrier frequency offsets (MCFOs) and improper channel state information (CSI). The knowledge of offsets and channel gains are required for coherent deployment of distributed systems. Hence, joint training sequence (TS) design method is proposed for joint estimation of MCFOs and channel estimation over spatially correlated channel. Thus, the present invention provides a method of providing joint estimation for distributed communication systems with multiple antennas at the nodes over spatial correlated channels. The designed optimal training sequences are short length and spectrally efficient. The designed training sequence produces zero cross-correlation, facilitating channel estimation without matrix inversion, significantly lowers the complexity of the estimation algorithm.