Coding to reduce the interference to carrier ratio of OFDM signals

In this paper, we propose a simple approach to reduce the sensitivity of OFDM system to the carrier frequency offset (CFO). The main idea is to choose a well-known channel code and to rotate each coordinate by a fixed phase shift such that the maximum inter-carrier interference (ICI) taken over all sub-carriers is minimized. This approach is based on a geometric interpretation of the peak interference to carrier ratio (PICR) of OFDM signals. Simulation results show that a reduction in PICR of 7 dB can be easily achieved. Furthermore, we addressed the fundamental limit of the proposed technique by providing both an exact and an approximate lower bound of PICR of phase-shifted binary codes. The bounds are applied to some codes: non-redundant binary code, BCH codes, and Reed-Muller codes. Simulation results demonstrated that phase-shift designs approach lower bounds and are resilient to CFO change.