An Optimum Signal Detection Approach to the Joint ML Estimation of Timing Offset, Carrier Frequency and Phase Offset for Coherent Optical OFDM
An Optimum Signal Detection Approach to the Joint ML Estimation of Timing Offset, Carrier Frequency and Phase Offset for Coherent Optical OFDM
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DOI：
10.1109/jlt.2020.3042546
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发表时间：
2021-03
影响因子：
4.7
通讯作者：
Xinwei Du;Tianyu Song;Yan Li;Mingwei Wu;P. Kam
中科院分区：
文献类型：
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作者：
Xinwei Du;Tianyu Song;Yan Li;Mingwei Wu;P. Kam
相干正交频分复用（OFDM）是当前和未来几代无线和光通信的主要数字调制技术之一。准确的同步是实现可靠OFDM接收机的主要障碍。基于最大似然（ML）信号检测理论，提出了一种相干光OFDM（CO-OFDM）系统定时偏移（TO）、载波频偏（CFO）和载波相位偏移（CPO）的联合最大似然（ML）估计方法。我们的方法从概念上开始，首先计算原始OFDM频谱的$L $副本的想法，其中$L $是2的幂，并假设足够大。这是通过将$（L-1）N $个零填充到$N $个接收到的噪声OFDM样本的末尾来完成的，其中$N $是OFDM子载波的数量。通过计算这些$LN $时间样本的$LN $点离散傅里叶变换（DFT），我们得到原始OFDM频谱的DFT的$L $个副本，其中每个副本对应于CFO的一个假设值的DFT，并且可能的CFO值的集合是$\lbrace l/L\rbrace_{l = 0}^{L-1}$。我们通过选择与原始OFDM频谱具有最小欧几里得距离的副本来选择最可能的副本，这导致在频域中以盲或数据辅助方式进行匹配滤波（MF）操作。基于此MF概念，我们为每个CFO的假设值开发了TO和CPO的联合ML估计。这里的新颖之处在于，通过时域或频域方法，将TO和CPO有效地估计为在噪声中观察到的复正弦曲线的频率和相位。由此产生的联合CFO，CPO，和TO估计比现有的估计，在概念上和实现简单。一个更简单的顺序的方法，我们首先决定的CFO，然后进行联合TO和CPO估计也提出了。这种顺序的方法相比，最佳的联合方法的性能损失是小的，在高信号噪声比（SNR）。我们通过模拟获得我们所有的估计器的性能，并表明它们与现有的知名估计器相比，表现更好。最后，我们推导出我们的估计器的性能的Cramér-Rao下界（CRLB），并通过模拟表明，我们的估计器为高信噪比达到这些性能下界。
Coherent orthogonal frequency-division multiplexing (OFDM) is one of the prime digital modulation techniques for present and future generations of wireless and optical communications. Accurate synchronization is the main obstacle to the implementation of a reliable OFDM receiver. We propose here a joint maximum likelihood (ML) estimator for the timing offset (TO), carrier frequency offset (CFO), and carrier phase offset (CPO) for coherent optical OFDM (CO-OFDM) motivated by the theory of ML signal detection. Our approach starts conceptually with the idea of first computing $L$ replicas of the original OFDM spectrum, where $L$ is a power of two and is assumed sufficiently large. This is done by padding $(L-1)N$ zeros to the end of the $N$ received noisy OFDM samples, where $N$ is the number of OFDM subcarriers. By computing the $LN$-point discrete Fourier transform (DFT) of these $LN$ time samples, we get $L$ replicas of the DFT of the original OFDM spectrum, where each replica corresponds to the DFT for one hypothesized value of the CFO and the set of possible CFO values is $\lbrace l/L\rbrace _{l=0}^{L-1}$. We select the most probable replica by choosing the one that is at the minimum Euclidean distance from the original OFDM spectrum, which leads to a matched-filtering (MF) operation in the frequency domain in either a blind or a data-aided manner. Building on this MF concept, we then develop a joint ML estimator of the TO and CPO for each hypothesized value of the CFO. The novelty here is that the TO and the CPO are estimated efficiently as the frequency and phase of a complex sinusoid observed in noise, via either a time-domain or a frequency-domain approach. The resulting joint CFO, CPO, and TO estimator is simpler than existing estimators, both conceptually and in implementation. A much simpler sequential approach in which we first decide on the CFO and then perform a joint TO and CPO estimation is also proposed. The performance loss of this sequential approach compared to the optimum joint approach is small at high signal-to-noise ratio (SNR). We obtain the performance of all our estimators via simulations, and show that they perform better when compared with the existing well-known estimators. Finally, we derive the Cramér–Rao lower bounds (CRLB) on the performance of our estimators, and show via simulations that our estimators for high SNR attain these performance lower bounds.