Natural Expression of the Best-Match Search Godard Clock-Tone Algorithm for Blind Chromatic Dispersion Estimation in Digital Coherent Receivers

Anatomy of a Digital Coherent Receiver

“…Diverse variants of this procedure, each using a different metric, have been shown so far. A criterion derived from constant modulus algorithm (CMA) is used in [10], [11], delay-tap sampling estimator [12], [13], autocorrelation of signal power waveform [14], [15], clock tone search [16]- [18], Gardner time error detector variance [19]. Recently, another technique has been demonstrated, where the sweep over CD values is performed automatically when applying FFT on the autocorrelation of discrete spectrum [20].…”

Analogue‐to‐digital converter phase insensitive dispersion search method with large search step size for low computational cost

“…Though a good performance is obtained, its high computational complexity prohibits its real application. Instead, several other CD estimation methods have been proposed in recent works with both data‐aided method [12, 13] and blind estimation [14–25]. The coefficients from a converged TDE are used for CD estimation in [14, 15], but both the convergence speed and the CD estimation range are limited by the size of the TDE.…”

“…Best‐match search type of CD estimation algorithms with different metrics have been proposed as another type of blind CD estimation method [9, 19–25]. The possible metrics include error criterion derived from Godard's constant modulus algorithm [9], frequency‐domain (FD) cost function for minimum search [19], time domain (TD) timing error‐based metric [20] and peak‐to‐average‐power ratio‐based metric [21].…”

“…To solve the problem of high computational cost of the CD search method, Malouin et al [24] proposed an efficient one‐step way to compute the FD cost functions of [23] using fast Fourier transform (FFT). The FFT‐based cost function computation method is later extended to the case of different receiver analogue‐to‐digital converter (ADC) sampling rate other than twice the symbol rate in [25].…”

Efficient and low-complexity chromatic dispersion estimation in coherent optical systems

“…On the other hand, blind methods based on the received signal (or signal modifications) autocorrelation functions [3][4][5] (directly related to the clock tone quality) completely fail in Nyquist systems with a roll-off factor (ROF) equal to 0. Additionally, none of these algorithms can work in faster than Nyquist systems (FTN) [6] that has become very attractive in strongly bandlimited systems applications. In case of fast start-up, hardware complexity becomes a critical issue for algorithms presented in [4][5] which also do not distinguish the sign of CD.…”