Time-Packing as Enabler of Optical Feeder Link Adaptation in High Throughput Satellite Systems

This paper studies the data rate that a High Throughput Satellite (HTS) system with fully-regenerative payload can achieve when using an intensity modulation/direct detection optical feeder link. A low-order M-ary Pulse Amplitude Modulation (M-PAM) with time-packing is used to modulate the intensity of the laser diode beam, making use of an external Mach-Zehnder modulator. These M-PAM symbols are recovered on-board the satellite with the aid of a photodetector, and are then encapsulated into the 5G radio frame of the access link. The M-PAM modulation order and the overlapping factor of timepacking are jointly selected to tackle the impact of slowly-varying weather conditions. Moreover, the inter-symbol interference that time-packing introduces is mitigated in reception using a Viterbi equalizer. As expected, time-packing enables a finer granularity on the link adaptation capability of the optical feeder link, enabling to adjust its spectral efficiency according to the moderate attenuation that thin cloud layers introduce.


I. INTRODUCTION
High Throughput Satellite (HTS) systems are evolving to enable 5G data services in those remote areas of the globe in which terrestrial mobile access is not available [1]. To support an aggregate data rate of few Terabit-per-second (Tbps), the GEO satellite should utilize a very large number of spotbeams with an aggressive frequency reuse factor in the radio access link (i.e., from the satellite to the user terminals) [2], and possibly optical wireless technology to support a similar point-to-point data rate on the feeder link (i.e., from the gateway to the satellite) [3]. Though there are few approaches to implement the optical feeder link [4], in this paper we focus on the fully regenerative payload case, in which the optical feeder link terminates in the satellite, and the 5G radio frame is generated on-board the satellite [5]. This way, realvalued modulation can be used to transport the payload bits on the optical feeder link, which is compatible with an Intensity Modulation (IM)/Direct Detection (DD) implementation. GEO satellites are located over the equator at a height of about 36 000 km, implying a free-space path loss of 290 dB. In order to close such a demanding link budget, high-power transmitters and high-sensitivity receivers with Erbium-Doped Fibre Amplifiers (EDFA) are needed. In addition, optical telescopes with gains in the order of 100 dBi should be used in both extremes of the optical feeder link [6]. Finally, the impact that bad weather has on the received optical signal must be also taken into account. The power loss that turbulenceinduced fading introduces can be reduced to just few dBs by using multiple optical apertures placed in the same satellite gateway (micro-diversity). However, the only way to tackle the absorption that slowly-moving clouds introduce is by reserving a margin of few-tens-of-dB in the link budget, which implies a waste of resources in presence of clear skies. Unfortunately, since real-valued modulations such as M -PAM are used in the IM/DD optical feeder link, there are limited degrees-offreedom for link adaptation, as the BER of M -PAM grows notably when M 2. Therefore, if time-packing is added on top of the adaptive modulation scheme, the overlapping factor of the M -PAM signal can be used as an additional parameter to adapt the spectral efficiency of the optical feeder link.
Faster-than-Nyquist signaling, also known as time-packing, was proposed in the 1970s as a simple solution to increase the spectral efficiency of a communication channel [7]. More precisely, it was shown that in presence of a binary sequence of Sinc-pulses, a 25%-data-rate-increase is achievable by shrinking the time between adjacent Sinc-pulses to about 80.2% of the Nyquist symbol time. By doing so, the minimum Euclidean distance between received constellation points did not change, enabling a higher data rate without augmenting the communication bandwidth. With the implementation of timepacking, the use of high-order modulations could be avoided; therefore, this signaling is specially appealing for satellite systems with optical feeder link, as the Peak-to-Average Power Ratio (PAPR) of the transmit signal does not grow notably, and thus the power of the non-linear distortion and the signaldependent noise that are added can be kept low [8], [9].
In this paper, we focus on a HTS system with fullyregenerative payload, where the optical feeder link is prepared to tackle the moderate cloud attenuation that slowly-varying weather conditions introduce. In this situation, adaptive modulation with time-packing signaling can be used in transmission to maximize the spectral efficiency of the optical feeder link, and the Inter-Symbol Interference (ISI) that time-packing introduces can be mitigated in reception with the aid of a Viterbi equalizer. Different design parameters are considered in the performance evaluation, such as the overlapping factor, the roll-off factor of the Square-Root Raised-Cosine (SRRC) filters, and the number of states of the Viterbi equalizer that detects the sequence of received symbols on-board the satellite. As expected, the use of time-packing provides additional degrees-of-freedom to implement the adaptation of the optical feeder link, enabling a higher spectral efficiency than the one obtained when using adaptive modulation solely.
The rest of the paper is organized as follows: Section II presents the principles of time-packing and the details of the Viterbi equalizer that needs to be placed in reception. Section III introduces the system model and describes the most important blocks of the optical feeder link, including the IM transmitter, the optical wireless channel, and the DD receiver. The details of the simulation setup, as well as the evaluation of adaptive modulation with time-packing signaling are presented in Section IV. Finally, conclusions are drawn in Section V.

II. THEORETICAL BACKGROUND
This section summarizes the key theoretical principles to be taken into account when adding time-packing into the realvalued modulation scheme of our IM/DD optical feeder link.

A. Principle of time-packing
The continuous-time signal that a transmitter with timepacking generates can be written as where k is the position of the data symbol in the input stream {s[k] : k = 1, . . . }, T s is the Nyquist symbol time, g tx (t) is the time response of the transmit pulse-shaping filter, and δ is the overlapping factor used for time-packing. As in conventional communication systems, transmit pulses with response g tx (t) have unit energy and are orthogonal when shifted by integer multiples of T s . However, it is important to note that when using time-packing, the orthogonality property is lost as ∞ −∞ g tx (t)g tx t − n(1 − δ)T s dt = 0 usually holds. Therefore, Inter-Symbol Interference (ISI) is added but, in return, a time-packing signaling rate R s = R s /(1−δ) ≥ R s = 1/T s can be achieved without increasing the communication bandwidth. In brief, time-packing enables a more efficient use of the communication bandwidth at the expenses of adding ISI, which should be mitigated adding complexity in reception.
Let us assume that the continuous-time received signal is r(t) = s(t) + n(t), where n(t) is Additive White Gaussian Noise (AWGN). The sufficient statistics for symbol detection can be obtained after applying Match Filtering (MF) [10], i.e., where g rx (t) = g tx (−t) * and, due to that, which is the so-called Ungerboeck observation model [11]. However, this model is not practical since the ISI in (2) is non-causal and the noise samples η[n] are correlated. In order to circumvent these problems, the signal after MF is passed through a whitening filter [12], which provides where , and η [n] are AWGN samples. This ISI will depend on the modulation, roll-off and overlapping factors that are used. To illustrate this concept, Fig. 1 shows the received samples of a sequence of 2-PAM symbols when using SRRC filters with different roll-off factors ρ and overlapping factors δ. Note that each isolated SRRC pulse spans in time between −50T s and 50T s . As expected, when the overlapping factor δ grows, the duration of the received signal sequence is reduced at the expense of increasing its amplitude variability or, equivalently, the PAPR. Concerning the roll-off factor, it is possible to show that as ρ grows, the energy of the SRRC pulse spreads less and less in time and, consequently, the PAPR is slightly reduced. Fig. 2 shows the PAPR of the transmit signal s(t) when using M -PAM (M = 2, 4, 8) after being sampled at t = kT s for k = 0, . . . , (1 − δ) 100 , assuming that both δ and ρ take different values. As previously mentioned, when comparing the three sub-figures, it is possible to observe that the PAPR grows slightly as ρ decreases. Furthermore, when studying the effect of δ in the PAPR, it is possible to see that in all curves there is an initial part in which the PAPR decreases and, after that, it starts to constantly grow. Leaving aside this low-overlapping-factor region, it is possible to conclude that the overall tendency is that both ISI and PAPR grow as δ is increased and ρ is decreased [13]. Then, if Maximum-Likelihood Sequence Estimation (MLSE) is implemented in reception, the impact of ISI could be mitigated, and the spectral efficiency of the modulation scheme with time-packing will be better than the one with baseline signaling an no time-packing (δ = 0).

B. MLSE detection for time-packing signaling
Time-packing increases the data rate of a communication channel with constant bandwidth but, in return, introduces ISI that should be mitigated in reception to keep the Bit Error Rate (BER) low. When the minimization of the BER is the target goal, it is well-known that the optimal solution consists in implementing the MLSE algorithm [10]. However, when looking for a trade-off between BER performance and implementation complexity, Maximum Likelihood (ML) detection methods assisted by channel shortening become more convenient [14], [15]. For this purpose, the selection of the roll-off factor of the SRRC filters (ρ), the overlapping factor of the time packing signaling (δ), and the order of the M -PAM modulation should be done jointly, in order to keep the spectral efficiency of the communication channel as high as possible.
The This huge load can be notably reduced with the aid of the Viterbi algorithm [10], which takes advantage of the trellis structure of the overall communication channel (including the SRRC filters). In this case, the implementation complexity reduces from O(M N ) to O(M LT ), where L T represents the channel memory. Fortunately, the overall channel memory with time-packing is a design parameter that can be controlled using channel shortening techniques [14], increasing the rolloff factor of the SRRC filters, and reducing the overlapping factor [12]. With these modifications, the PAPR in transmission and the energy consumption in reception are reduced but, in return, the spectral efficiency of the communication channel may be impacted if the BER due to residual ISI grows [13].
In this regard, Fig. 3 illustrates the number of M -PAM symbols or channel coefficients L, whose time-packing induced ISI must be mitigated to be within the target SNR gap ∆SNR = 3 dB, with respect to the baseline M -PAM signaling without time-packing when BER = 10 −3 . Studying these figures, it is possible to conclude the number of channel coefficients introducing notable ISI grows with the order of the M -PAM modulation. For example, when ρ = 0.25 and δ = 0.30, the number of coefficients with notable ISI are L T = 3 for 2-PAM, L T = 4 for 4-PAM, and L T = 5 for 8-PAM. Unfortunately, it is not always practical to dimension the Viterbi equalizer for these L T implementation parameters, particularly in presence of high-order M -PAM modulations.
The aim is to achieve a quasi-optimal performance only in the target SNR region of interest, in which the given M -PAM with time-packing signaling would be used. Therefore, we now study the combinations of roll-off factor ρ and overlapping factor δ in which ML-decoding has an acceptable implementation complexity. It is well known that, as channel memory that is considered for ML-decoding grows, the BER tends to the one achieved with the baseline M -PAM signaling without time-packing (i.e., when the ISI power is null). However, our aim is to consider in the ML-decoding only part of the timepacking ISI; due to that, there will be some residual ISI that will make the received Signal-to-Interference-plus-Noise Ratio where L T is the number of ISI symbols considered in the Viterbi Algorithm, N 0 is the noise power, and E{s[n]} is the mathematical expectation of s[n]. By replacing the SNR with the SINR, the following formula for the error probability of the k-th bit of the M -PAM symbol is obtained [16]: where x is the greatest integer less than or equal to x and erfc(x) = 1/ √ 2π The mutual information for M -PAM with time-packing signaling attains the form [17] being N R the number of Monte-Carlo runs. Finally, the capacity for M -PAM with time-packing signaling is given by assuming that the penalization for bandwidth re-growth for using non-Sinc pulse-shaping filters is considered. Based on these previous formulas, the feasible throughput becomes where the Block Length Error Rate (BLER) is computed encapsulating L p bits per data packet, i.e., BLER = 1 − (1 − BER) Lp , and the error control coding rate R c = 1 for simplicity (uncoded case). Based on these theoretical principles, we are now ready to study the performance when time-packet M -PAM is used in an IM/DD optical feeder link.
III. OPTICAL FEEDER LINK WITH TIME-PACKING The simplified system model that corresponds to the optical feeder link of a HTS system with fully regenerative payload is illustrated in Fig. 4. It consists of a multi-level modulator Fig. 4: Block diagram of a HTS system with regenerative payload. Blue blocks identify digital signal processing, whereas orange blocks identify the optical feeder link. Time-packing with overlapping factor δ is used to tackle slowlyvarying power loss that thin clouds/fog introduce (link adaptation).
(e.g., M -PAM) that constructs a real-valued signal, which is used to perform the IM of the Laser Diode (LD) light beam. In practice this is obtained with the aid of an external Mach-Zehnder Modulator (MZM) working at a quadrature bias point. At the receiver side, a Photodetector (PD) is used for the DD of the optical signal that reaches the GEO satellite and, after that, digital signal processing is applied to recover the stream of bits that was transmitted. With this payload data, the radio frame of the access link (e.g., DVB-S2X) is finally constructed on-board the satellite and transmitted to the user terminal on the Radio Frequency band that corresponds.

A. Intensity modulation of optical carrier at ground station
The continuous-time signal that modulates the intensity of the LD beam was presented in (1). Then, the driving voltage of the external MZM is given by where V B and V π are the bias and half-wavelength voltages of the MZM, β is the intensity modulation index, and is the normalized continuous-time M -PAM signal with unitary Root Mean Square (RMS) amplitude. We note that the specific choice of β controls the range in which the MZM regularly works. Deep intensity modulation indexes (i.e., large β) increase the power on the optical feeder link sidebands but, at the same time, increment the non-linear distortion power on the electrical signal that is recovered on-board the satellite. The relation between the driving voltage v mzm (t) and the optical field at the MZM output E o (t) is given by [18] where P o,ld is the mean optical power of the LD that feeds the MZM and ω o is the angular frequency of the unmodulated optical carrier that is transmitted with the optical sidebands. Then, the instantaneous value that the optical intensity modulated signal takes at the output of the MZM becomes When the quadrature bias point V B = (3V π )/2 is used, where the latter approximation is due to sin (x) ≈ x for small x. In this situation, the effect that the MZM non-linear distortion has on the optical feeder link can be neglected.

B. Optical wireless channel modeling
The Free Space Loss (FSL) represents the largest power loss in the optical feeder link, and is given by where d fso is the range and λ is the wavelength that the optical feeder link utilizes. Besides the FSL, additional losses may be experienced when the optical signal propagates through the low layers of the atmosphere, particularly in case of bad weather conditions in which visibility is reduced. It is important to note that atmospheric losses L o,atm can be as low as few dBs in presence of Fog and Cirriform clouds, few tens of dBs in case of Stratocumulus and Altostratus, and from few hundreds to few thousand dBs in presense of Cumulonimbus. As expected, L o,atm for cloudy weather will depend on the thickness and density of water droplets that clouds contain [19]. Though communication is not possible in presence heavy Cumuloninbus, our aim it to use time-packing as enabler of better link adaptation granularity, such that the throughput of the optical feeder link is optimized assuming partly cloudy weather in which L o,atm is few tens of dBs. Finally, the atmospheric turbulence is caused by the mixing of warm and cold air on the different layers of the atmosphere. Turbulence generates small variations on the refractive index of the signal path, inducing a fluctuation on the received optical intensity that is known as Scintillation. In case of weak turbulence, the statistics of the received intensity modulated signal can be approximated with a Log-Normal distribution. Similarly, the exponential distribution can be used to model this turbulence-induced fading in case of strong turbulence, whereas the Gamma-Gamma distribution models this effect very well in a wider range of turbulence conditions. Although these stochastic models have been widely studied in the literature, transmit diversity techniques are needed to mitigate the impact of turbulence (e.g., multiple optical apertures). This is because the coherence time of the turbulence-induced fading states is much shorter than the propagation time of the optical signal from the ground station to the GEO satellite. To tackle this, few dBs of the optical feeder link budget are reserved as system losses to include the turbulence effect.

C. Direct Detection of the optical signal onboard the satellite
The optical signal that illuminates the sensitive area of the PD in the satellite generates an electrical current that equals where T o = 2π/ω o is the period of the optical carrier, µ [A/W] is the PD responsivity, G o,tx and G o,rx are the optical gains of the transmit and receive telescopes, respectively, G o,edfa is the gain of the Erbium-Doped Fiber Amplifier (EDFA), and L o,sys contemplates the system losses in the optical feeder link. Note that the current in (20) can be divided into two terms, where the DC component is given by and remains fixed regardless of β, whereas the AC component depends on the intensity modulation index and attains the form The SNR of the electrical signal that is direct-detected by the PD on-board the GEO satellite becomes E{|n includes the contribution of all noise sources in the optical feeder link, namely the shot noise sources, thermal noise, Relative Intensity Noise (RIN) of LD, and beat noise [20]. Note that shot noise term includes the contribution of the received optical signal, the Amplified Spontaneous Emission (ASE) noise, background optical noise and the dark current noise, whereas the beat noise term accounts the effect of combining the received optical signal with the ASE noise. When the received optical power is between −90 and −20 dBW, it can be shown that the beat noise between received optical signal and ASE noise dominates the SNR performance of the optical feeder link [21]. In this situation, we have that where B o and B e are the bandwidth of the optical signal and the electrical signal at the input and output of the PD, respectively, whereas I ase = µ G o,edfa P ase is the DC component generated by the ASE noise when P ase = ρ ase B o is the equivalent noise power of the EDFA before amplification. Table I summarizes the parameters of the optical feeder link, including the optical gains and optical losses [22], and the different sources of optical noise [21]. Unless stated otherwise, the effect of any other parameter that is not listed in this table is assumed negligible (e.g., specific PD non-idealities and optical wireless channel impairments).

IV. PERFORMANCE EVALUATION
According to these values, mean received optical power is Larger intensity modulation indexes β could be used without increasing the MZM non-linear distortion notably, provided that Digital Pre-Distortion compensation is implemented in transmission [20]. However, in this paper we assume that the dynamic range of the input signal is set low enough, such that the MZM works on its linear region most of the time. Fig. 5 shows the BER as function of the received SINR for different M -PAM modulation schemes, roll-off factors ρ, overlapping factor δ. Two implementation complexities for the ML decoder have been considered, namely N s = 512/1024 states (moderate Trellis) and 4096 states (demanding Trellis). When comparing these curves, it is possible to see that in case of 2-PAM and 4-PAM, most of the roll-off factors and overlapping factors that have been evaluated provide a similar BER to the one attainable when time-packing is not used (lower bound in absence of ISI, when δ = 0). However, in case of 8-PAM, the BER performance degrades notably, particularly when ρ = 0.15 (lowest roll-off factor), δ = 0.3 (highest overlapping factor), and N s = 512 (moderate implementation complexity). This is because 8-PAM is the largest order modulation under evaluation and, due to that, the Trellis states are only enough to tackle the ISI generated by few adjacent symbols (i.e., short channel memory). Due to this, the residual ISI is high, and the BER performance is notably penalized. However, as the roll-off factor increases, the energy of SRRC pulses concentrates on fewer channel coefficients and, due to that, the BER performance is closer to the one attainable when the ISI due to time-packing is completely suppressed.
Finally, Fig. 6 illustrates the throughput as function of the cloud attenuation, normalized by the communication bandwidth, that M -PAM with time-packing is able to achieve when the roll-off factor is ρ = 0.25. For each modulation scheme, three different overlapping factors are considered, namely: δ = 0 (no overlapping), δ = 0.15 (low overlapping), and δ = 0.3 (medium overlapping). Moreover, the number of bits that are encapsulated per data packet is L p = 2536. We note that this packet length is aligned with the maximum Transport Block Size (TBS) from the PUSCH of NB-IoT radio technology standard [23]. Based on this curve, it is possible to see that 2-PAM with δ = 0.3 is the most convenient signaling for a cloud attenuation between 19 and 11 dB. However, as we reduce the cloud attenuation, then 4-PAM with different overlapping factors gives the best throughput for cloud attenuation between 11 and 4 dB, whereas 8-PAM with different overlapping factors is the best choice when cloud attenuation is lower than 4 dB. To sum up, the use of M -PAM with time-packing enables a finer granularity when designing the link adaptation mechanism of the optical feeder link.

V. CONCLUSION
In this paper, we made a comprehensive analysis of the throughput that is achievable when M -PAM with time-packing is used to modulate in intensity the optical feeder link of a HTS system with fully-regenerative payload. The ISI that timepacking introduces was tackled on-board the GEO satellite, with the aid of a Viterbi equalizer that managed to mitigate the impact of ISI for most transmission schemes under analysis. Based on these results, it was possible to show that M -PAM with time-packing is a good solution to increase the granularity of link adaptation for IM/DD optical links, where the use of real-valued modulations limits notably the available transmission schemes when time-packing is not used. Thanks to this approach, the slowly-varying attenuation that thin cloud layers introduce can be addressed by changing the modulation order M and the overlapping factor δ of the waveform that modulates the intensity of the optical feeder link. Therefore, it is possible to conclude that time-packing signaling is an appealing solution to implementing the optical feeder link of HTS system, designed to provide global 5G/5G+ connectivity.