On Parameter Estimation for Bandlimited Optical Intensity Channels

Abstract

Parameter estimation is of paramount importance in every digital receiver. This is not only true for radio, but also for optical links; otherwise, subsequent processing stages, like detector units or error correction schemes, could not be operated reliably. However, for a bandlimited optical intensity channel, the problem of parameter estimation is strongly related to non-negative pulse shapes satisfying also the Nyquist criterion to keep the detection process as simple as possible. To the best of the author’s knowledge, it is the first time that both topics—parameter estimation on the one hand and bandlimited intensity modulation on the other—are jointly investigated. Since symbol timing and signal amplitude are the parameters of interest in this case, the corresponding Cramer–Rao lower bounds are derived as the theoretical limit of the jitter variance generated by the related estimator algorithms. In this context, a maximum likelihood solution is developed for the recovery of both timing and amplitude. Since this approach requires a receiver matched filter destroying the Nyquist criterion of the non-negative pulse shape, we compare it to a flat receiver filter preserving the required orthogonality property. It turned out that the jitter performance of the matched filter method is close to the Cramer-Rao lower bound in the medium-to-low SNR range, but due to inter-symbol interference effects an error floor emerges at higher SNR values. The flat filter solution avoids this drawback, although the price to be paid is a larger noise level at the filter output, so that a somewhat increased jitter variance is observed.