FEQ for OFDM systems with insufficient CP

In orthogonal frequency division multiplexing (OFDM) systems, when the length of the cyclic prefix (CP) is shorter than the channel length, the orthogonality between sub-channels is lost because of the intersymbol interference (ISI) and interchannel interference (ICI). In this case, the one-tap frequency domain equalizer can't be used any more. A time-domain equalizer (TEQ) is usually used in the receiver to reduce the duration of the overall response of the transmission system, and therefore minimize the ISI and ICI. However, the optimum design of TEQ turns out to be a very difficult task. In this paper, we propose a frequency domain equalizer (FEQ) for OFDM systems with insufficient CP, by making use of the presence of null side sub-carriers and the redundancy of CP. The equalizer has a sparse matrix structure and thus a low computational complexity. Theoretical analysis and simulation results show that it can efficiently remove ISI and ICI caused by insufficient CP and recover the transmitted data. Moreover, we derive the condition for the existence and uniqueness of FEQ, i.e., the combined length of CP and null sub-carriers is not shorter than the channel order. This means that the insufficiency of CP in time domain can be compensated by the redundancy of the null side sub-carriers in frequency domain.