The Noise Transfer Analysis in Frequency Domain Zero-Forcing Equalization

Frequency domain equalization (FDE), as a linear equalizing method, is widely adopted in many applications with either OFDM or single carrier (SC) modulation. This paper analyzes the the noise transfer effect, a case for noise colorization, after FDE. This process is investigated for CP-OFDM, ZP-OFDM and SC systems where SC is treated as a multi-carrier modulation with the number of subcarriers equal to 1. Based on this analysis and by assuming the de-mapping independence among subcarriers, the average channel capacity for the systems is derived. We have proved that the capacity of the CP-OFDM system is at least equal to that of ZP-OFDM in both low and high SNR scenarios and that the capacity of the SC system is no greater than that of either ZP-OFDM or CP-OFDM systems. In a multi-path channel, if the IDFT size of the OFDM symbol is not equal to the DFT size of the equalizer, the leakage of the enhanced noise in a deeply faded sub-channel will cause the loss of capacity in adjacent sub-channels and the overall average capacity is thus reduced.