Transmission analysis for OFDM signals over hybrid RF-optical high-throughput satellite.

In this paper, a theoretical investigation of the performance of a communication scenario where a geostationary-orbit satellite provides radio-frequency broadband access to the users through orthogonal-frequency-division multiplexing technology and has an optical feeder link is presented. The interface between the radio frequency and the optical parts is achieved by using radio-on-fiber technology for optical-electro and electro-optical conversion onboard and no further signal processing is required. The proposed scheme has significant potential, but presents limitations related to the noise. The noise in both forward and reverse links is described, and the system performance for an example scenario with 1280 MHz bandwidth for QPSK, 16QAM, and 64QAM subcarrier modulation is estimated. The obtained results show that under certain conditions regarding link budget and components choice, the proposed solution is feasible.


Introduction
Recently, satellite laser communication technology is gaining popularity by offering reduced system size, weight, and power (SWaP) as well as a wider bandwidth [1][2][3][4]. Together with the significant benefits of the technology though, there are a few drawbacks that limit its implementation to a number of applications. The biggest challenge remains to be the laser beam propagation through the atmosphere that is strongly influenced by the atmospheric turbulence effects and the clouds. Different solutions, such as site diversity, have been considered in order to increase the link availability to the levels of the RF alternatives. Currently, most suitable applications of the technology are high-speed inter-satellite links where atmosphere is absent [5], and LEO-to-ground links that allow small observation satellites to download significant amount of data during a few-minutes pass [4]. The dominating satellite-to-ground/maritime/aircraft broadband access technology is more likely to continue to be based on radio-frequency (RF), especially with the implementation of the Ka-band [6]. However, there are particular scenarios that consider optical feeder link in a GEO satellite [7]. Of high interest is the development of a system with broadband RF access between the user and the satellite that can be based on a GEO satellite with multiple beams in Ka band [6]. In order to release more RF bandwidth to be used for different applications and/or higher data rates, an optical feeder link that is to be used as a backhaul link between the satellite and the fixed base station on the ground is considered. For such high throughput satellites (HTS), employing both RF and optical technologies of critical importance is the RFoptical interface solution.
First, it is possible to use the RF signal as an input for the optical signal modulation (analog signal transmission on the optical channel, known as radio over fiber (RoF)). Such solution is preferred since it will guarantee satellite transparency regardless of the RF modulation. However, according to the signal, the signal-to-noise ratio (SNR) requirements drastically change and the GEO-GND link is often hard to achieve. Using OFDM modulation with multiple slow rate channels may significantly ease the link requirements.
Second, it is possible to sample the analog RF signal and turn it into a digital one with Analog-Digital Converter (ADC). Such solution requires some special devices, such as highspeed ADC and DAC. Also, it would require significant optical bandwidth to transport the RF signal, which is quite inefficient. For example, the bit stream after the ADC will be increased significantly (e.g. for an 8-bit ADC is expected to have 8 times higher data rate and most likely higher order ADC and at least double sampling speed will be necessary. If a 3.2 Gbps RF data rate as in [6] is considered, the required optical downlink is in the order of 20-30 Gbps and that is extremely hard to implement considering the onboard electronics and the link budget limitations, which forms a bottle neck).
Third, it is possible to process the RF signal onboard by using Field Programmable Gate Array (FPGA) or dedicated Integrated Circuit (IC) and transmit it on the optical channel as proposed in [8]. While this method guarantees highest efficiency in terms of used bandwidth and SNR, it requires significant processing power onboard and this would actually form a bottleneck considering the state of the art for onboard equipment.
Following the discussion above, the chosen implementation is based on OFDM as simplest and probably with best performance when HTS with RF-Optical interface are discussed. Of utmost importance in this work is the configuration that implements radio over fiber (RoF) technologies, particularly the Direct Detection Orthogonal Frequency Division Multiplexing (DD-OFDM) technology by feeding the RF signal to a laser diode (LD) or optical modulator (typically Mach-Zehnder Modulator (MZM)) that can convert the RF signal to an optical one and send through an optical channel. For the optical to RF signal conversion, the photodiode (PD) itself converts the received optical power to an electrical (RF) signal. The proposed scenario has a lot of limitations, especially considering the noise in the links. However, it allows for seamless transmission of the data. Furthermore, OFDM is considered instead of Time Division Multiplexing (TDM) so that no further processing at the satellite is to take place and the lower data rates in each subcarrier that are robust to higher levels of noise. However, OFDM implementations are sensitive to Doppler shift and a proper compensation is required. The effect in GEO to ground links is much smaller compared to LEO-to-ground links.
This paper is divided as follows. In Section 2, the hybrid forward (optical uplink from the gateway to the satellite and RF downlink to the user) and return (RF uplink from the user to the satellite and optical downlink to gateway) link are described in detail with the different kinds of noise, present in the channels, including the intermodulation distortion and the scintillation. In Section 3, the theory from Section 2 is implemented into a real system design example to estimate the performance. Finally, the paper concludes in Section 4.

Proposed system design and theoretical model
The considered high-throughput satellite scenario is shown in Fig. 1. The user access remains RF-based while the link between the ground base station and the satellite is optical.

Optical link budget
While RF technology and particularly Ka-band are widely studied and used in satellite communications, laser communications technology is relatively novel and still developing technology with different issues to be considered [1][2][3][4]. Therefore, in the presented analysis the RF links are not described in terms of link budget, but only consider the Carrier to Noise Ratio (CNR) degradation due to the RF Low Noise Amplifiers noise figures and the main accent is on the laser links.
In Table 1, the link budget for both optical uplink and downlink in the case of a GEO satellite is shown. The results are similar to [8], with some important differences.
Optical transmit power in satellite communications is a critical parameter-there are power limitations in the uplink due to eye safety and in the downlink due to the available onboard power. It is important to decrease the power as much as possible, and for this reason a 10 W laser in the uplink and 5 W laser in the downlink have been chosen, which is significantly lower compared to the 50-Watt uplink and 10-Watt downlink optical powers, considered in [8]. For different implementation scenarios, some parameters could drastically change thus allowing further decreasing of the transmit power levels but a more general case has been addressed in this paper. For simplicity some of the losses have been combined (e.g. pointing loss, atmospheric loss, etc.). Onboard the satellite, it is better to have a lower transmit power in order to save resources. The transmit optical power is chosen to be 5 W instead of 10 W, and if the link budget allows, it is highly recommended to decrease further.
There are three possible ways to receive the optical signal -directly concentrating the power over an avalanche photodiode (APD) or similar, coupling the signal into a multimode fiber and later coupling it again to a photodiode, or coupling the signal into a single mode fiber. Due to the atmospheric turbulence [9], the angle of arrival is constantly changing, which leads to beam wandering in the focal plane. One solution is to use a PD with very big size, but due to its capacitance there will be a severe limitation in its bandwidth. Coupling to a multimode fiber is relatively easy considering its big size (around 200 micrometer diameter core), compared to a single mode fiber (below 10 micrometer diameter core). To facilitate the coupling for all the methods, there are several technologies including tip/tilt correction that can compensate relatively fast the beam wandering [10], and adaptive optics (AO [11, 12]) correction, that is widely used in astronomy to correct the beam wavefront aberrations after propagating through the turbulent atmosphere. For this purpose, a row called "Additional gain" was added to bring 0 dB gain in the uplink, but if an AO system is installed in the optical ground station (OGS), that could add a gain of 7 dB [11], or even over 10 dB in the downlink [12]. Such possibility has not been considered in [8]. In this proposal, RoF technology is used. If single mode fiber coupling is required, such coupling of an optical signal after propagation through the atmosphere leads to very high losses L scint [13] and OA is necessary before the PD. To leave space for further link improvement and for easier comparison with direct PD receiver without coupling, the OA gain G OA is set to be equal to the losses due to fiber coupling. Thus, the received optical power in the PD is equal regardless if fiber coupling is used or not.
The provided notations in Table 1 are with capital letters, denoting that the values are in dB/dBm for easier link budget calculation. However, in the following noise analysis the same notations with small letters denote values, used as coefficients for easier noise calculation.

Forward link
The forward link scenario is shown in Fig. 2. At the OGS, the signal is being encoded and interleaved for higher resistance to the signal fading due to atmospheric turbulence [9]. Then the signal goes to an OFDM transmitter. The considered subcarrier modulation types are m-QAM. The output of the OFDM transmitter is taken directly to a LD or a MZM to modulate the optical signal, as often implemented in RoF technology [14]. The optical power output from the LD will be [15][16][17]: where p t is the average transmitted optical power, a 3 is the third order nonlinearity coefficient, n m m N = is the optical modulation index (OMI) for the n-th subcarrier (m is the total OMI) assuming that all tones are to be modulated with the same modulation index m n , and s(t) is the signal at the n-th sub-carrier. The received optical power in the satellite photodetector will be: where X quantifies the variation of the signal fading due to atmospheric turbulence transmission effects and its probability density function (PDF) is often defined to be Gamma-Gamma [9], and n FSO characterizes the additive white Gaussian noise (AWGN) and is assumed that it can be filtered in the PD and is not consider in the further analysis. If direct fiber coupling is implemented, due to the angle of arrival change and the wavefront aberrations the beam could not be inserted in the single mode fiber efficiently and losses l scint will be added. After coupling, however, an optical amplifier with gain g OA can be added to amplify the optical signal prior to PD direct detection. The nonlinearity in the LD and MZM will lead to increased noise mainly due to the third order modulation distortion (IMD3), since these components lie very close to the fundamental carriers and cannot be easily removed by RF filtering [15][16][17]. The IMD3 which falls into the n-th subcarrier among equally spaced N carriers can be described as [15][16][17] where I ORX is the current at the photodiode in the satellite, ρ is the photodiode responsitivity, and D 2 and D 3 represent the number of intermodulation distortion products, which influence the desired carrier. As described in [17,18], if the number of subcarriers is over six, D 2 can be neglected. Furthermore, for high number of transmitted carriers, the maximum number of intermodulation products is generated in the center of the band (n = N/2) and [17,18]: (5) Considering the losses in the OGS and the required levels for the optical uplink budget, an optical amplifier (OA) with very high gain is necessary in the optical ground station. Such gain will affect not only the signal but also the noise, adding additional noise due to the amplified spontaneous emission in the amplifier (ASE noise). Similar to the electronic amplifiers, the concept of noise figure can be applied to OA [19], where the noise figure represents the SNR degradation between the input and the output signals of the optical amplifier, and includes the ASE noise. Therefore, the OA noise figure is used in the following analysis instead of the ASE noise itself. The parameter nf TXOA is defined to be the noise figure of the OA in the OGS, and nf RXOA to be the noise figure of the OA in the satellite side. Small letters are used to emphasize that the noise figure values are not in dB thus CNR in = nf*CNR out .
Including the thermal and shot noise in the receiver, the total noise in the PD will be: where, K B is the Boltzmann's constant, T abs is the absolute temperature, q is the electron charge and T s is the OFDM symbol duration. The guard interval is set to zero and thus T s equals to the Fourier analysis window. From here, the carrier to noise and distortion ratio for the n-th sub-carrier CNDR n_ORX = C/N tot can be derived by using Eqs. (5) and (6). The PD current is directly amplified and sent through the satellite RF antenna with no further processing. When received in the ground antenna, the signal is amplified and sent to the OFDM receiver. CNDR FWD will be further decreased because of the noise figures of the RF low noise amplifiers in the satellite and in the user side -nf TXLNA and nf RXLNA .

Reverse link
In the reverse link (Fig. 3) the user ground-to-satellite link is RF-based and it is assumed that the only noise is the thermal noise that will be further increased by the two OA noise figures (nf TXLNA and nf RXLNA ). The received RF signal is directly used to modulate the LD or MZM output and the RIN noise and the third order modulation distortion will be added. At the base station side, the noise on the LD output will be further degraded by the noise figures of the OA in the optical downlink (both on the satellite and on the ground) and the shot noise of the receiver will be added. The total noise for the reverse link will be:

Symbol and bit error probability (SEP, BEP)
The SEP per subcarrier P s,n for the received M-QAM OFDM signal, where M = 2 k and k is even number, is given by [15,16] where 2 R σ is the Rytov variance [20]. By using a bigger receiver aperture, aperture averaging effect that leads to lower scintillation index values is observed [20,21]. That improves the BEP performance of the system, as shown in the next Section. Following the analysis in [16], the final formula for SEP when Gamma-Gamma PDF is considered for the fading due to scintillation can be provided but instead of the noise in [16], Eq. (10), the corresponding CNDR for the forward and reverse links based on the noise Eqs. (7) and (8) is the MeijerG function.
If Gray-coded mapping is used the average BEP will be [16]: When the number of subcarriers is large, the total average BEP over the entire OFDM band can be delivered based on the law of large numbers [16]:

Results and discussion
For the system characteristics estimation, an OFDM signal that combines multiple 40 MHz WiFi channels with 128 sub-carriers, each with 800 nm guard interval (25%), that results in OFDM symbol duration of 4 μs, was considered. Since the OFDM signal employs IFFT that requires subcarrier number N = 2 n , it is assumed that 32 × 40 MHz channels are covering 1280 MHz bandwidth. As defined by the 802.11n standard for a single spatial stream, the possible M-QAM modulations with the corresponding coding rates and user speeds are shown in Table 2. As mentioned in Section 2, the coding is necessary for error correction mainly due to atmospheric turbulence.
The parameters used in the analysis are listed in Table 3.

Optimal CNDR selection
CNDR is dependent mainly on the OMI and the received optical power. In Figs. 4(a) and 4(b), the relationship between CNDR and the OMI and received power respectively for the forward and the reverse link are shown. The case of an LD with RIN = −135 dB/Hz on the transmitter side and fiber coupling and OA in the receiver side was chosen. It can be observed that the strong dependence on the OMI while increasing the received power after a given level leads to no significant improvement. Due to the noise differences, the CNDR in the reverse link is noticeably much higher and it changes much faster. For optimal OMI that leads to maximal CNDR in both forward and reverse link, the value of 0.29 is chosen and Figs. 5(a) and 5(b) show the relationships between CNDR and the received power for the optimal OMI = 0.29, respectively for the forward and reverse link.
There are four different cases -LD with RIN = −135 dB/Hz with fiber coupling or direct PD detection, LD with RIN = −150 dB/Hz with direct PD detection and MZM with IMD3 and RIN noise reduction through different techniques (e.g. parallel schemes) [22]. For the MZM case, RIN = −150 dB/Hz and IMD3 is reduced with 20 dB. The significant effect of lower RIN/IMD3 on the forward link by using MZM instead of LD intensity modulation can be observed. Compared to the scenario with direct fiber coupling and LD with RIN = −135 dB/Hz, according to the received power using MZM modulator can lead to 15 dB higher CNDR when direct fiber coupling is used and about 20 dB higher CNDR when direct PD detection is used. Also, it can be seen that the removal of the OA when no fiber coupling takes place leads to about 5 dB CNDR improvement. Choosing an LD with lower RIN noise can also significantly improve the CNDR. For example, RIN noise of −150 dB/Hz instead of −135 dB/Hz leads to about 7 dB higher CNDR. While the reverse link CNDR is strongly dependent on the received optical power, it is not significantly affected by the optical modulation type (LD or MZM) and the different parameters of the considered cases. As a general conclusion for lower received power, it is considered that it is better to use a system with no direct fiber coupling since that leads to about 5 dB higher CNDR. It is important to note that the amplifier noise figures would generally be lower than the ones considered (4.77 dB), which will further improve the CNDR.
Further analysis of the effect of the number of channels on the CNDR is performed, since it directly affects the OMI per channel. The results are shown in Table 4. The current choice of 4096 is somehow optimal with 1 dB loss compared to a system with 8192 channels.

BEP Analysis
The BEP of the uncoded signal is calculated using Eqs. (12)- (14) for several different casesno turbulence, weak turbulence and strong turbulence. Considering the aperture averaging effect, the chosen values for the scintillation index for weak turbulence is 2 (D 0.2 m) 0.047 I σ = = and for strong turbulence is 2 (D 0.2 m) 0.316 The dependence of BEP on CNDR for QPSK ( Fig. 6(a)), 16QAM (Fig. 6(b)) and 64QAM (Fig. 6(c)) is shown for two different scenarios -no turbulence to strong turbulence condition defining a range of possible turbulence conditions. Assuming BER = 10 −3 to be enough for errorless transmission of the coded signal, it can be observed that the required CNDR for the proposed system to operate under all atmospheric conditions is 21.8 dB for QPSK, 28.2 dB for 16QAM and 33.8 dB for 64QAM. Considering the CNDR results from Figs. 5(a) and 5(b) and their dependence on the received power, the CNDR for the different cases can be listed in Table 5. The link budget in Table 1 assumes fiber coupling and includes 10 dB coupling loss due to scintillation and 12 dB OA gain. For the cases with no fiber coupling we assume losses due to scintillation of 3 dB and lack of OA gain, which results in 9 dB less received power. The values in Table 5 show the significant effect of the link budget on the link throughput. Under the proposed link budget only fiber coupling solutions can transport the OFDM signal with different success. Considering the CNDR to received power ratio on Figs. 5(a) and 5(b), there are several solutions to improve the system throughput.
In the forward link, the transmit power of the OGS can be increased to the levels of [8]. This would secure up to 7 dB higher received power and the CNDR will vary in the order of 21 dB to 37 dB thus allowing 64QAM for the fiber coupling with OA implementations and QPSK for the other cases. However, the implementation of a fiber coupled LD with −135 dB/Hz RIN noise, would not be able to support higher order modulation than QPSK regardless of the received power level. Higher gains (over 30 dB) for the OA are possible and this could significantly relax the system requirements (e.g. OGS transmit power). Another possibility is to increase the receiving aperture size, which would lead to higher levels of received power and stronger aperture averaging effect, resulting in smaller power fluctuations due to turbulence. However, apart from the increased size and weight, such solution would make direct fiber coupling harder increasing the coupling loss. As a conclusion, an optical source with low RIN noise is critical.
In the reverse link, the considered link budget provides CNDR that for the fiber coupling scenarios is enough to transmit 16QAM signal, even under strong turbulence. Nevertheless, the optical downlink provides further possibilities for improvement and 64QAM transmission. Bigger aperture size (typically in the range of 40 cm to 60 cm) would significantly increase the received power level, respectively the system CNDR, and decrease the power fluctuations due to aperture averaging that would further decrease the required CNDR for the desired BEP. Furthermore, AO system could be integrated in the OGS side. The considered AO gain was set to be 12 dB, but much higher gain is possible [12]. All these improvements allow to decrease the satellite OA gain directly leading to a better SWaP or consideration of higher orders of modulation or simpler implementations.
Finally, while feeder link is supposed to be available 24/7, due to the atmospheric conditions (e.g. clouds, rain, sandstorm, etc.) in practice, the availability of satellite to ground laser links is expected to be quite low. As mentioned earlier, site diversity is a typical solution for this problem. The technology relies on the deployment of multiple OGS stations around the Globe with uncorrelated weather conditions and relatively high availability in terms of sunny days/hours per year. Thus, if there is rain at one site, there is high probability that another OGS has clear sky and handover can take place [23]. The handover decisions can be improved to consider not only the weather conditions, but also the seeing parameters (atmospheric turbulence conditions) allowing further improvement of the system.

Conclusion
A network with broadband user access to a satellite and an optical feeder link has been presented. Compared to alternative solutions, the proposed design onboard the satellite is very simple and requires no data processing. Both forward and reverse links have been analyzed and the close-form equations for the total noise in the system were provided. Based on the theoretical equations different optical modulation solutions (LD, MZM) of the proposed system have been evaluated for a given OFDM signal and three different subcarrier modulations -QPSK, 16QAM and 64QAM. The results show the design considerations and strict limitations in the forward link and possible solutions to allow higher order modulation schemes to be used. The proposed reverse link allows much easier implementation even under the shown link budget, which allows further design optimization (e.g. lower transmit power on the satellite side). The chosen parameters are not optimal to allow future system performance improvement.
As a general conclusion, while in terms of CNDR versus received power performance the fiber coupling implementations show worse results, the link budget limitations clearly make other choices hard to implement efficiently and in terms of throughput fiber coupling with OA prior to signal detection would be a preferred choice.
This work could be used as a reference for future design of hybrid satellite networks with broadband RF user access network and optical feeder link employing the proposed plain design with no processing onboard.