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Nyquist signals with low roll-off factors pose a challenge for non-data-aided blind symbol rate estimation problems in long-haul applications. We adopted the nonlinear least squares (NLS) approach to estimate the symbol rate of low roll-off factor signals. This method tolerates chromatic dispersion and additive Gaussian noise. In addition, this method can operate below two samples per symbol, thus enabling low-power-consumption receivers. Simulation and experimental results show that the mean squared error is below $10^{-4}$ with only 3000 samples needed for polarization-division-multiplexed (PDM) quadrature phase-shift keying (QPSK) or quadrature amplitude modulation (QAM) systems with a roll-off factor below 0.1 for an optical signal-to-noise ratio greater than 12 dB. Compared with the maximum likelihood estimation (MLE) method, our proposed method has a more robust performance under low roll-off factor signals and in low-sampling-rate scenarios. The mean squared error remains the same for a nominal symbol rate (i.e., the ratio of the symbol rate to the sampling rate, also widely known as oversampling rate) ranging from 0.1 to 0.9.

Symbol rate and chromatic dispersion (CD) are very important for optical performance monitoring. The CD, however, hinders the symbol rate detection. In this paper, we proposed a joint estimation of symbol rate and chromatic dispersion. We show that, when the signal conjugates and multiplies with the delayed replica, the spectral line can be restored. The proposed method provides a fast and simple solution for joint estimation as traditional tentative CD scanning is time consuming. The simulation shows that the root-mean-squared error (RMSE) for CD was 39.5 ps/nm and the symbol rate was 2.4 MHz. For the squared-root-raised-cosine (SRRC) pulse shape with a roll-off factor of 0.1, the experimental results show that 25,000 input samples were needed for an error-free estimation. The RMSE is 105.6 ps/nm and 63.5 kHz for CD and symbol rate, respectively.

Abstract Background Preoperatively evaluating the feasibility of safe C2 pedicle screw placement is the key to avoiding iatrogenic vertebral artery injury. However, it has not been verified whether the conventional CT measurements of C2 pediculoisthmic component (PIC) are reliable and accurate, and the results may lack validity. The purpose of this study is to analyze the evaluative performance of conventional CT measurements and to create an accurate predictor of morphometrics of C2 PIC. Methods A total of 304 C2 PICs were measured in 152 consecutive patients who underwent CT examination of the cervical spine between April 2020 and December 2020. We obtained the morphometric parameters of C2 PIC by measuring minimum PIC diameter (MPD) in CT multiplanar reconstruction versus conventional measurements of transverse PIC width (TPW), oblique PIC width (OPW) and definition of high-riding vertebral artery (HRVA). The outer diameter measured less than 4 mm in MPD was regarded as the standard of precluding safe C2 pedicle screw insertion. The evaluative performance of the conventional CT measurements was assessed, and the correlation between conventional CT measurements and measurements in CT multiplanar reconstruction was calculated. Results The parameters in OPW and MPD were measured significantly larger than those in TPW, and the preclusion of C2 pedicle screw placement evaluated from TPW and HRVA was significantly higher than that evaluated from OPW and MPD. The sensitivity of TPW was 93.09%, and the specificity was 79.31%. The sensitivity and specificity of OPW were 97.82% and 82.76%. The sensitivity of HRVA was 88.36%, and the specificity was 96.55%. Strong agreement with the highest correlation coefficient (0.879) and determination coefficient (0.7720) suggested that the outer diameter of OPW could be useful for the precise prediction of MPD. Conclusions CT MPR allows accurate measurement of the narrowest section of the C2 PIC. The outer diameter of OPW could be simply measured and be useful for precise prediction of MPD, which makes C2 pedicle screw placement more safely than the conventional measurement of TPW and HRVA.

Abstract Background 3-D printing technology has a large spectrum of applications in upper cervical spinal surgery, but none have evaluated the radiological analysis of the feasibility of C2 pedicle screw placement. Thus, this study aimed to perform 3.5-mm-diameter C2 pedicle screw placement on models for performance assessment of CTA-based preoperative screw preclusion. Methods We enrolled 152 patients who underwent CTA of the cervical spine between April 2020 and December 2020. Transverse pediculoisthmic width (TPW), oblique pediculoisthmic width (OPW), minimum pediculoisthmic diameter (MPD), internal height, and isthmus height were measured preoperatively. Subsequently, 1:1 3D-printed bone models were created, and a 3.5-mm-diameter C2 pedicle screw was placed on the models. All 3D-printed models underwent postoperative CT multiplanar reconstruction to evaluate the screw trajectory for the performance assessment of CTA-based preoperative screw preclusion. Results The ROC curves of the MPD, TPW, OPW, Internal height and Isthmus height showed that the optimal cutoff values for each of the five groups were measured values of 4.78, 4.44, 4.37, 4.22 and 5.59 mm, respectively. The AUC, sensitivity, and specificity of MPD were 0.992, 95.1% and 100%, respectively. The MPD had higher metrics than the TPW (AUC, 0.949; sensitivity, 87.9%), internal height (AUC, 0.885; sensitivity, 80.8%; specificity, 84.6%), and isthmus height (AUC, 0.941; sensitivity, 87.2%). We found no evidence of a difference between MPD and OPW in terms of the AUC and sensitivity (0.93 and 95.5%, respectively). Conclusions C2 pedicle screw placement on 3D-printed models is useful for performance assessment of CTA-based preoperative screw preclusion. MPD measurement with CTA multiplanar reconstruction showed the best performance for judging acceptable or unacceptable screws. However, the definition of HRVA could be modified by a 4.2 mm-internal height or by measuring only the isthmus height for judging the preclusion of C2 pedicle screw placement.