Cost Function Analysis for FD-MC-CDMA Blind Frequency Offset Estimation in High Speed Aerial Communication

FD-MC-CDMA is an attractive candidate for next generation high speed aerial vehicle communication for its high spectrum efficiency and excellent BER performance. Similar to other multi-carrier transmission technologies, FD-MC-CDMA suffers significant performance degradation resulting from intercarrier interference (ICI) in high mobility environments. Particularly, because the ICI is observed from all other subcarriers, the benefit of decomposing subcarriers into non-contiguous sets diminishes. In our previous work, a parallel processing based blind frequency offset estimation and ICI cancellation method to significantly improve the BER performance in high mobility environments has been proposed. However, the proposed blind frequency offset estimation and ICI cancellation scheme relies on the assumption that there will be one global minimum to the cost function that is generated from the Euclidean distances between the true received signal vector and synthesized signal vectors. In this paper, we theoretically analyze the cost function in this blind estimation and cancellation algorithm and verify this assumption. Furthermore, by thoroughly examining the cost function in various scenarios, we also prove that this cost function is actually statistically symmetric. This cost function analysis not only help us understand the underlying principle of the effectiveness of the proposed blind frequency offset estimation and ICI cancellation scheme, it points to more sophisticated high efficiency algorithms which can significantly reduce the computational complexity.