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

This paper proposes a novel carrier frequency offset (CFO) estimator for the coherent optical orthogonal frequency-division multiplexing (CO-OFDM) systems using the matched-filter (MF) concept. We consider an OFDM symbol with N sub-carriers 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 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 {2 pi/LNl, 2 pi/LNl + 2 pi/N, ... , 2 pi/LNl + 2 pi(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 2 pi/LNl 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 the 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 the 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 the 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 that the estimation error variance of the DA MF ML algorithm can achieve the Cramer-Rao lower bound in the absence of the laser phase noise.