Carrier Frequency Offset Estimation for CO-OFDM: The Matched Filter Approach

Abstract-This paper proposes a novel carrier frequency offset (CFO) estimator for coherent optical orthogonal frequency division multiplexing (CO-OFDM) systems using the matched filter (MF) concept. We consider an OFDM symbol with N subcarriers so that the receiver takes N time-samples of the received noisy CO-OFDM signal. Our idea is to first append these N received samples with (L − 1)N zeros at the end to get a sequence of LN time-samples. By taking the discrete Fourier transform (DFT) of these LN samples, we compute the spectrum of the CO-OFDM symbol at LN discrete frequency points. We think of this spectrum as being made up of L
sets of N points each, each set consisting of the frequency points {2π LN l, 2π LN l + 2π N , · · · , 2π LN l + 2π(N−1) N }, for each value of l, where l = 0, 1, · · · , L − 1. Each set of N points for one value of l can be considered as the spectrum of the CO-OFDM symbol corresponding to one hypothesized value 2π LN l of the CFO. The receiver can now obtain the maximum likelihood (ML) CFO estimate by determining the hypothesized value that best matches the spectrum of the CO-OFDM symbol received from the channel. In the case of data-aided (DA) ML estimation, we treat the OFDM symbol as a pilot symbol in which we know the data in all the subcarriers, and this pilot symbol is used as the reference signal for the MF. In the case of blind (BL) ML estimation, the data in all the subcarriers are unknown, and the receiver uses an OFDM symbol with no data modulation in all the subcarriers as the reference signal. After making the ML decision of the hypothesized value of CFO, a fine search will be carried out to determine the actual value more accurately. It turns out only one step is necessary to locate the actual value of CFO. The DA MF ML algorithm can achieve full-range (integral and fractional part) CFO estimation with high accuracy, while the BL MF ML algorithm has low computational complexity but focuses on fractional CFO estimation only. We discuss the complexity and performance of this MF ML algorithm, and present simulation results to demonstrate the estimation error variance for 16-PSK/QAM modulations. The simulation results show the estimation error variance of DA MF ML algorithm can achieve the Cramer-Rao lower bound in the absence of laser phase noise.