Blind phase recovery in cross QAM communication systems with eighth-order statistics

Gain-Control-Free Near-Efficient Phase Acquisition for QAM Constellations

“…Now, let us consider a magnitude weighed version of (4), namely (5) In (5) we have performed a tomographic projection of the magnitude weighed phase pdf ; we will refer to the function as the magnitude weighed tomographic projection (MWTP) of the magnitude/phase bidimensional pdf . From (5), we recognize that also the MWTP cyclically shifts of under a phase-offset , and that, in presence of additive noise, also the Dirac pulses in (5) become wider pulses whose shape depends on the SNR and the noise pdf; the analytical evaluation of (5) is reported in Appendix A.…”

“…For comparison purposes, also results pertaining to other selected estimators are reported, namely the nonlinear least square (WA03) estimator [11], the concentration ellipse orientation (CEO) estimator [12], and the fourth-order (CW99) estimator [1] for square constellations or the eighth-order (CW01) estimator [5] for cross constellations. In particular, the WA03 estimator is obtained by evaluating the angular coordinate of the sample average of a suitable nonlinear transformation of the received signal samples; it is constellation dependent, and it requires knowledge of both SNR and gain.…”

“…The associate editor coordinating the review of this manuscript and approving it for publication was Dr. Erchin Serpedin. The authors are with the Dipartimento INFOCOM, "Sapienza" Università di Roma, I-00184 Rome, Italy (e-mail: ( values; in [4], this estimator has been shown to be equivalent to the fourth-power estimator of [1]. Several improvements to [1] have been investigated, resorting to eighth-order statistics [5], to data aided estimation [6], and to ML estimation for not equiprobable symbols [7]. In [8], a phase histogram-based estimator has been derived according to a high SNR approximation of the ML criterion.…”

GENp2-1: A Simple Improvement to the Viterbi and Viterbi Monomial-Based Phase Estimators

“…These systems can be grouped into two areas -those that require established gain control and those that do not. The Fourth Power Phase Estimator [1]- [3], which is a special case of the Viterbi and Viterbi (V&V) monomial-based estimators [4], the Eighth-Order Estimator (EOE) [5], the Concentration Ellipse Orientation (CEO) [6], and more recently the iterative methods (DCA-a and DCA-b) of Alvarez-Diaz and Lopez-Valcarce [7] are systems in the latter category. Among the former category are the Reduced-Constellation Fourth Power Estimator [1], the two methods of Georghiades [1] which require finding the mode of the probability density of the phase, the rather complex Minimum Distance Estimator (MDE) [8], the TwoStage Conjugate (2SC) algorithm which according to Rice et al.…”

Carrier phase recovery without pilot sub-carriers in coherent optical OFDM transmission systems

“…The performance of the fourth-power method applied to square QAM constellations is considered acceptable. Alternatives have been devised to improve phase detection for such constellations: the Eighth-Order Estimator (EOE) [3], the Concentration Ellipse Orientation (CEO) [4], and more recently the iterative methods (DCA-a and DCA-b) of Alvarez-Diaz and Lopez-Valcarce [5], Reduced-Constellation Fourth Power Estimator [2], the Two-Stage Conjugate (2SC) algorithm [6], the optimal method, proposed by Wang and Serpedin [7]. Those methods are so complicated for hardware implementation, their increased computational expense prevent their practical adoption even in experiments.…”