2.1

Optical channel of propagation

The atmospheric turbulence is modelled by the Hufnagel-Valley profile [16] with an atmospheric turbulence level on ground of 10^-13m^-2/3 and a pseudo wind parameter of 21m/s. The wind is modelled by the Bufton model with an upper layer at 12 448m. The wind speed on ground is set to 10m/s and the upper layer wind speed is 25m/s. Such turbulence representation leads to Fried parameters at 1552nm on the Line of Sight (LoS) given in Table 1.

Table 1:

Fried parameter on LOS

2.2

Scenarii description

For the 10Gbps OOK LEO downlink to a low complexity OGS, we consider a satellite at an altitude of 500km. The total transmitter power is 128.7dBm taking into account transmitter losses, antenna gain and optical amplifier power. The elevation angle of the line sight is 15°. On ground, the telescope diameter is 60cm and an adaptive optic system corrects the collected tip/tilt at a frequency of 1 kHz.

For the 25Gbps OOK LEO downlink to a high complexity OGS we consider a satellite at an altitude of 1200km. The total transmitter power is 130.9dBm taking into account transmitter losses, antenna gain and optical amplifier power. The elevation angle of the line sight is 20°. On ground, the telescope diameter is 60cm and an adaptive optic system corrects up to 12 radial orders at a frequency of 3 kHz [12].

Table 2:

Scenarii description

The power available at the optical receiver without atmospheric turbulence losses and transmitter pointing error is computed in Table 3. The losses due to atmospheric turbulence and to transmitter pointing error are computed separately for the end-to-end simulation.

Table 3:

Link budget without turbulence losses and power losses due to on board optical terminal pointing error

3.1

Transmission chains

Figure 1 depicts the 25Gbits/s OOK high complexity transmission chain. At the transmitter, the laser is externally modulated with a Mach Zehnder Modulator (MZM). Then, an optical booster amplifier amplifies the signal and adds amplified autonomous noise. The channel block applies a static attenuation leading to a given Received Optical Power (ROP) at the input of the receiver based on a Low Noise Optical Amplifier (LNOA). At the PIN photodetection followed by a transimpedance amplifier(TIA), the signal is filtered by an electrical low pass filter (ELPF). The block BER computes the Bit Error Rate.

Figure 1:

25Git/s OOK transmission chain - high complexity

Figure 2 depicts the 10Gbit/s OOK low complexity transmission chain. At the transmitter side, the laser is directly modulated. Then, an optical booster amplifier amplifies the signal and adds amplified autonomous noise. The channel block applies a static attenuation leading to a given Received Optical Power (ROP) at the input of the receiver based on a multimode avalanche photodiode (APD). Background noise (BGNoise) is also considered in the transmission chain.

Figure 2:

10Git/s OOK transmission chain - low complexity

3.2

Noise model

Due to the inaccuracy of well-known noise contribution variances [13] to represent noisy signal distribution at the input of the decoder, we prefer to issue our noise model from Optsim simulation at bit level. For example, Figure 5 depicts the difference between Optsim and a MATLAB model implementing the formulas of [13] for the 25Gbit OOK high complexity transmission chain.

Figure 3:

Comparison of the results between numerical simulation and analytical formulae in OOK for an EDFA based receiver (left) Probability Density Function of the noisy signal depending on the emitted bit ‘1’ or ‘0’ and the ROP| (right) bit error rate function of the received optical power

3.3

Mutual information function of received optical power

Both transmission chains have been characterized with the mutual information [14] that measures the statistical correlation between two random variables, here the send code symbols and the received ones. In the present contribution the mutual information has been noted MI_ECC or MI and is computed according to formula (1) where x and y are respectively the signal sent by the transmitter and y the signal at the entry of the decoder, and p(x) and p(y) are the probability density functions.

The mutual information is an interesting metric for FEC performances comparison as it enables to compare the FER performances of different systems operating on different channel conditions or channel models. It will be used to characterize the MI requirements for a FEC scheme to achieve a targeted FER after interleaving. The MI is also the maximum code rate achievable.

Figure 4 and Figure 5 depict the mutual information at the entry of the decoder MI_ECC function of the ROP at the input of the optical receiver. Figure 4 provides the result for the 10Gbit/s OOK low complexity chain based on an APD receiver. Figure 5 provided the result for the 25Gbit/s OOK high complexity chain based on an EDFA receiver.

Figure 4:

MI_ECC function of received optical power - 10Gbit/s OOK – Low complexity

Figure 5:

MI_ECC function of received optical power 25Gbit/s OOK – High complexity

4.1

Considered FEC Codes

Quasi-Cyclic LDPC are a sub-class of structured codes that should achieve performances close to unstructured LDPC codes while being much more convenient for parallel encoder and decoder architecture design.

For the QC LDPC code family, we investigate:

For the DVB-S2 codes, we referred to the ETSI standard [11]. For the Turbo Product Code, BCH component codes are investigated.

In each case, the interleaving size and codes parameters, such length or size of circulants, are carefully selected both (a) to achieve a required FER after deinterleaving and (b) to enable full exploitation of byte-aligned hardware architecture.

Code rates of 1/2, 2/3, 4/5, 9/10 are considered but code rate superior or equal to 4/5 are more interesting to achieve high useful data rate. The code word length is around 16380 bits knowing that greater FEC frames would improve performances and enable higher decoder capacity for a given hardware.

4.2

Decoding algorithm and its parameters

The LDPC codes (IRA, ARJA, FG) and the DVB-S2 codes are decoded thanks to the Normalized Min-Sum (NMS) algorithm [19] with a normalization factor of 0.75 and a number of decoding iteration limited to 10 iterations. This is a major difference with existing solutions: we should rather consider FEC schemes that enable rapid convergence rather than achieving the best threshold to enable high throughput decoders.

The TPC are decoded thanks to the Chase-Pyndiah decoder [10] with 32 test patterns and 8 iterations. The weighting factor α(m) = [0.1 0.1 0.25 0.25 0.5 0.5 0.75 0.75 … 1] and reliability factor β dynamically computed.

4.3

Performances

Figure 6 depicts the Frame Error Rate (FER) function of the Mutual Information (MI) seen at the entry of the decoder.

Figure 6:

Frame Error Rate function of the mutual information of the signal at the entry of the decoder. Blue, red, purple, green curves correspond respectively to code rate around 1/2, 2/3, 4/5, 9/10.

It results that:

5.1

Optical channel

We compute the Received Optical Power (ROP) time series by mixing the atmospheric turbulence attenuation time series computed by ONERA, the power losses time series due to transmitter pointing error computed by Airbus Defence and Space, and the link budget value presented in Table 3. Figure 8 depicts the characteristics of the power losses due to the on-board optical terminal pointing error and the power losses due to atmospheric turbulence considering adaptive optic system on ground. In our references scenarios, the losses due to the impacts of the atmospheric turbulence are predominant.

Note that these losses are slow compared to the optical data rate. As a result an interleaver is mandatory to span the burst of errors and to achieve quasi error free link thanks to the physical layer error correcting code.

Figure 7:

Characteristic of power losses due to the on board optical terminal pointing error | (left) spectrogram, (right) distribution - high complexity scenario

Figure 8:

Characteristic of power losses due to atmospheric turbulence considering adaptive optic system | (left) spectrogram, (right) distribution – high complexity scenario | ONERA time series

5.2

Interleaver sizing

Figure 9 depicts the simulation chain that has been designed to size the duration of the row column interleaver.

Figure 9:

Blocks of the simulation chain

At the transmitter side, the bit generation, the encoder, and the row-column interleaver are joined. Then, the optical channel refers to the two steps:

Then the Log-likelihood ratios (LLRs) are computed under the assumption of equal probability of bit ‘0’, and ‘1’before the de-interleaving process and the decoding process.

Table 4 provides the interleaver duration required for an error free link function of the FEC code rate. For both scenarii, according to simulations, a protection scheme composed of FG LDPC codes with a code rate of 4/5 and an interleaver of 10ms shall achieve error free communication at the considered elevation angles, respectively 15° for the low complexity downlink and 20° for the high complexity downlink.

Table 4:

Interleaver duration function of the scenario and the FEC code rate – value in italic correspond to an estimation due to simulation memory limitation

As soon as the elevation angle increases, the link turns to be error free even before decoding as the link budget is overpowered.

In case the latency of the service is a hard constraint, the FEC code rate might be decrease.