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.

Efficient estimation and synchronisation of transmission parameters is key for any satellite receiver, which is especially true for the recovery of carrier frequency and symbol timing. In this respect, a joint feedback solution has been analysed and tested in some recent work conducted by the authors. However, it turned out that the capture range of the carrier frequency is limited by the selected roll‐off factor (excess bandwidth), which means that the synchroniser would not work properly for extremely bandwidth‐efficient transmission schemes. This motivated them to modify the feedback structure by introducing a different filter operated in parallel to the receiver matched filter. In the sequel, it could be verified by analytical and simulation results that the initial frequency offset synchronised successfully can reach up to ±50% of the symbol rate irrespective of the selected modulation scheme, the roll‐off factor, the signal‐to‐noise ratio value and the timing offset the satellite link is operated with. On top of that, a non‐linear modification of the timing error detector has been investigated in detail, since the output of the conventional solution is nullified in case of extremely small excess bandwidths.

Assuming a land‐mobile satellite link with negligible multipath and shadowing effects, the corresponding channel model is adequately described by a correlated Rician distribution. In this context, the estimation of carrier and channel parameters has been investigated in some earlier work by means of an algorithmic approach primarily based on heuristic considerations. In the current study, the authors will review the results obtained so far from a maximum‐likelihood (ML) point of view. A major output of the analysis is that the simple ad‐hoc framework achieved previously is indeed an ML solution, when the impairments introduced by Rician fading are spectrally flat and strictly band limited.

In a recent study, the error performance of pulse-position modulation (PPM) schemes has been investigated for a terrestrial free-space optical (FSO) link, which was assumed to be impaired by both turbulent atmosphere and pointing errors. Only for the binary case a closed-form solution was achievable, whereas for non-binary conditions just an approximate relationship could be given. The key point in this respect was the approximation of the complementary error function so that the two-fold integral, otherwise required in this context, ended up in a closed form. In the current contribution, the problem is tackled by an additive combination of exponentials whose coefficients are optimised in the least-square sense. It turns out that second-order approximations are a good compromise between accuracy and computational complexity.

Signal processing in satellite applications is usually performed either on-ground or on-board, i.e. at the gateway station or in the payload. Within the framework of the European Space Agency (ESA) SatNEx III study, a hybrid approach has been considered by splitting the processing between the satellite and the gateway, aiming to strike a better balance between performance and payload complexity. The design of a high-capacity multi-beam system has been carried out, to assess the potential applicability of a hybrid space-ground processing architecture (Digisat) for satellite broadband systems; this is achieved via hybrid space-ground beamforming, MIMO and MIMO-MUD, Precoding, as well as Digital Feeder link techniques.

In recent studies, the average capacity for optimal rate adaptation (ORA) of free-space optical channels in turbulent atmosphere has been derived in closed form, mainly based on the application of Meijer's G-function. To this end, the channel was assumed to be memoryless, stationary and ergodic, with independent and identically distributed fading statistics. It was also assumed that scintillations follow a gamma–gamma distribution so as to appropriately describe moderate-to-strong turbulence conditions. In the current contribution, the author will extend this work in two aspects: (i) using the properties of Meijer's G-function, it is shown that the average capacity provides also a closed-form solution for adaptation policies other than ORA, namely optimal power and rate adaptation, channel inversion with fixed rate and truncated channel inversion with fixed rate; (ii) if the additional loss caused by a misalignment between transmitter and receiver (pointing error) is taken into account, it is demonstrated that the developed analytical framework applies straightforwardly.

In this comment, it is shown that the semi-numerical algorithm for computation of the ergodic channel capacity, which has been suggested in the paper cited by the headline above, can be replaced by a closed-form solution - either based on generalized hypergeometric functions or, in a more concise and elegant approach, on Meijer's G-function.

We consider the problem of joint non-data-aided (NDA) estimation of carrier frequency and phase offsets, together with that of signal and noise powers, obtained from the baud-rate samples of a linearly modulated signal distorted by Gaussian noise. The Crame¿r-Rao lower bound (CRLB) is derived, for quadrature-symmetric constellations showing that the carrier parameters are decoupled from signal and noise powers. Furthermore, a joint NDA maximum-likelihood estimator is developed, based on the application of the expectation-maximization algorithm, which exhibits a jitter performance close to the CRLB for a wide SNR range.

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.

For free-space optical (FSO) links in turbulent atmosphere modeled by gamma-gamma distributions, an approximation of the pairwise error probability (PEP) was derived for on-off keying in a recently published paper. It has been assumed that the channel state is perfectly known to the receiver and that the fading samples are independent and identically distributed. Based on these conditions, we show in this letter that the approximation can be replaced by a closed-form solution, disregarding a finite-limit integral which forms also part of the approximation in the reference paper. The PEP is then used to evaluate the union upper bound for convolutional codes with Viterbi decoding. Finally, in order to identify the potential of powerful error correction algorithms, like turbo codes as most prominent example in this respect, the lower bound of the error probability is given via the converse of Shannon's coding theorem.

Powerful parameter estimators exhibit a jitter variance which is fairly close to the Cramer-Rao lower bound (CRLB) as the theoretical limit. In contrast to symbol timing and carrier frequency/phase, not very much information is available from the open literature with respect to the signal-to-noise ratio (SNR), i. e., the CRLB has been reported only for the data- aided case and some simple M-PSK examples for non-data-aided estimation of the SNR. Motivated by this background, an efficient algorithm is presented which applies to any M-ary one/two- dimensional modulation scheme with axis/halfplane symmetry and a channel distorted by additive white Gaussian noise. Finally, the performance of different SNR estimators is compared to the derived bound.

In a recent paper, the modified Gardner detector has been proposed for advanced symbol-timing recovery of M-ary phase-shift keying signals. Compared with the original algorithm, the self-noise jitter can be considerably reduced for highly bandlimited systems and smaller values of M. In this letter, a completely different approach is investigated, which improves the self-noise performance for larger values of M, as well