Signal-to-noise ratio (SNR) estimation for linearly modulated signals is addressed in this letter, focusing on envelope-based estimators, which are robust to carrier offsets and phase jitter, and on the challenging case of nonconstant modulus constellations. For comparison purposes, the true Cramer-Rao lower bound is numerically evaluated, obtaining an analytical expression in closed form for the asymptotic case of high SNR values, which quantifies the performance loss with respect to coherent estimation. As the maximum-likelihood algorithm is too complex for practical implementation, an expectation-maximization (EM) approach is proposed, achieving a good tradeoff between complexity and performance for medium-to-high SNRs. Finally, a hybrid scheme based on EM and moments-based estimates is suggested, which performs close to the theoretical limit over a wide SNR range.

Subcarrier free-space optical (FSO) systems using coherent recovery techniques at the receiver have acquired growing research interest in recent times. However, their optimal performance is diminished by the non-perfect synchronization of carrier frequency and phase, which is mainly due to phase noise problems. Moreover, turbulence and pointing error effects further deteriorate the overall performance. However, relay transmission schemes can extend the coverage distance and offer substantial improvements over fading conditions. In this respect, we consider a serially relayed network using decode-and-forward relays, and investigate its performance by means of average symbol error probability and mean outage duration. Turbulence is modeled by the recently unified M(alaga) distribution, which constitutes a very general statistical model that accurately describes the irradiance fluctuations from weak-to-strong turbulence conditions. Additionally, the presence of non-zero boresight pointing errors due to misalignment between the transmitter–receiver pair is considered, while the effect of phase noise is specified by a Tikhonov distribution. A comparison between single line-of-sight and serially relayed FSO configurations is provided as well. Novel approximated mathematical expressions are deduced, which are proved to be accurate enough over a wide range of turbulence strengths and signal-to-noise values. Finally, proper numerical results are presented and validated by Monte Carlo simulations.

Terrestrial free‐space optical (FSO) communication systems with subcarrier intensity modulation have experienced a particular research attention in the recent past. However, their performance strongly degrades in the presence of atmospheric turbulence, pointing errors, and phase noise impairments. In order to overcome these limitations, the authors consider a receiver diversity scheme of a typical subcarrier phase‐shift keying (PSK) system and investigate the performance by means of the average symbol error probability (ASEP). They assume a wide range of turbulence conditions, non‐zero boresight pointing errors, and phase noise strengths described through the gamma‐gamma, Beckmann, and Tikhonov distributions, respectively. Novel approximate ASEP expressions are derived for single‐input single‐output and single‐input multiple‐output (SIMO) configurations. Appropriate numerical results are depicted and validated by Monte Carlo simulations.

The research area of optical wireless communication links has attracted significant interest over the last years due to the significant advantages offered by this kind of technology. However, the performance of FSO communication systems depends strongly on the effects, which are related to the atmosphere along the propagation path such FSO links are using. More specifically, the weather conditions and atmospheric turbulence effects can deteriorate considerably the performance characteristics. In this work, we are studying the joint influence of atmospheric turbulence and time jitter effects on the average BER of an FSO link by presenting a new approach for various modulation schemes. Thus new closed-form mathematical expressions are derived for accurate estimation of the BER performance of the optical wireless communication systems. Finally, using the obtained expressions and typical parameter values for FSO links, the numerical results are presented and then verified through Monte Carlo simulations.

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.

Assuming the symbol timing to be established, blind estimation of the signal-to-noise ratio (SNR), based on second-and fourth-order moments of the envelope such that the knowledge of the carrier phase becomes obsolete, is well documented in the technical literature. However, to the best of the authors' knowledge, nothing is reported in this respect if the symbol timing is not available or reliable enough, as it might easily happen in practice. Motivated by this background, a moment-based SNR estimator is developed when both timing and carrier phase are unknown. Applied to narrowband signals as they are accessible at the output of the matched receiver filter, the derivation of the algorithm turns out to be fairly intricate from the analytical point of view although the final result is surprisingly simple, i. e., apart from some constants depending on modulation scheme and pulse shape, it is formally not much different from the relationship with perfect symbol timing recovery.