3.1

Link budget and link margin

The link budget is a useful tool that can be used to predict the channel performance of optical communication systems, since it provides a key to system design and component selection.^{12, 13} The link budget represents the relationship between the transmitting power P_Tx and the optical power received at the input of the optical detector, P_Rx and can be estimated by using the link equation:

where we assume circular T_x and R_x apertures.

is the antenna gain T_x,

is the free-space loss and

is the antenna gain R_x, where D_Tx is the T_x telescope diameter, λ is the wavelength of the laser, z is the link distance and D_Rx is the R_x telescope diameter.

is the T_x mispointing loss, where θ_mp is the T_x angular mispointing and θ_w is the T_x angular waist radius. τ_Tx is the T_x transmission loss with typical values between 0.7 – 1.0, τ_Atm is the atmospheric loss with typical values between 0.6 – 0.9 and τ_Rx is the R_x transmission loss with typical values of 0.2 – 0.7.

The link margin (LM), which is calculated as the ratio of the received optical power P_Rx to the detector sensitivity DS for a specific data rate and BER, is defined as is defined as

Typically, for a reliable link it should be LM > 2.¹² LM is a useful parameter to consider for the design of a suitable optical link between a LEO satellite and an OGS; additionally, both the Bit-Error Rate (BER) and the channel capacity should be analyzed to evaluate the optical channel quality in the presence of the atmospheric turbulence. In this paper, we analyze the performance of the optical link with respect to the LM.

Table 1:

Optical link model parameters

3.2

Numerical results and discussion

In the following we study the effect of various parameters in the link margin as described by eq. (1). In more detail, we first investigate the impact of the T_x angle of misalignment θ_mp on the link margin and then study the relation between link margin and the diameter of the receiver telescope, the transmit power and the detector sensitivity for three different θ_mp angles.

In our study, we numerically analyze the performance of the optical communication link between an OGS with a LEO satellite (∼ 560 km, orbital velocity of 7.5 km/sec). In our simulations, we consider a T_x telescope diameter of 1 inch while for the R_x OGS downlink we use the typical values of the Skinakas Observatory, which is equipped with an optical telescope of 1.3 m diameter and is located at an altitude of 1760 m. A detailed list of the optical link model parametersused in our numerical simulations are shown in Table 1.

Fig.(3) shows the numerical results on the effect of various parameters in the LM. Despite the fact that, with respect to the RF case, we can achieve higher data rate with lower size and mass, space links face several challenges, such as pointing errors. Compared to RF, and in order to maximize the received power, optical beams are extremely narrow, posing tight requirements in terms of pointing accuracy. As a consequence, the mispointing between the transmit and the receiver antennas cannot be neglected. The link margin as a function of the transmitter T_x misspointing angle θ_mp is shown in Fig. (3a). The calculations are performed assuming an 1 inch R_x telescope diameter, while the black dashed line depicts the lower limit where the optical link is reliable. As we can clearly observe, we can have a reliable optical link for a T_x misspointing up to 65 μrad.

Figure 3:

Numerical results on the effect of various parameters in the link margin.

Another fundamental design parameter of the optical link is the diameter of the transmitter’s telescope. In Fig.(3b) we show the effect of the T_x telescope diameter on the link margin for three different T_x misalignment angles θ_mp. While for no misalignment, θ_mp = 0, we can have a reliable link for a T_x telescope diameter of more than 0.5 m, a small misalignment of θ_mp = 10 μrad drops this value to ∼ 20 cm. Furthermore, for a larger misalignment, θ_mp = 64 μrad, we can have a reliable link for a T_x telescope diameter not larger than 2 cm. In Fig.(3c) we can see the link margin in terms of the T_x transmit power in Watt again for three different mispointing angles θ_mp. For no misalignment we can have a trustful link for transmit power of less than 1 mW, while for an angle of 64 urad the transmit power must be larger than 90 mW.

Likewise, in Fig.(3d) we show the relation between the link margin with respect to the detector’s sensitivity in dBm, again for three different mispointing angles θ_mp. For up to θ_mp = 10 μrad the detector’s sensitivity could be up to −23 dBm, while for θ_mp = 64 μrad could be maximum around −40 dBm.

In Fig.(3e) we show the effect of the link distance to the link margin, considering the case of a LEO satellite (i.e. 402 – 1609 km). As we expect, for no misalignment, i.e. θ_mp = 0, we can have a reliable link between the LEO satellite and the OGS in the whole range of the Leo Earth Orbit. What is noticeable is that as the misalignment angle gets larger the link distance where we can have a reliable optical link gets smaller. More specifically, for θ_mp = 64 urad we cannot have a reliable link for a distance greater than 577 km.

3.3

Effect of the turbulent atmosphere

In order to simulate the propagation of the T_x beam through a turbulent atmosphere we preformed 2 + 1D numerical simulations using a slit step technique involving the propagation of the angular spectrum.¹⁴ The effect of atmospheric turbulence was approximated by a sequence equally spaced of thin random phase screens placed along the propagation^{4, 15} using the modified von-Karman power spectral density of the refractive index fluctuations Φ_n(κ) described by the equation:^{4, 16, 17}

where κ_l = 0.33/l₀, , , is the refractive index structure constant indicating the strength of turbulence, and l₀, L₀ refer to the inner and outer scale of the turbulence respectively. Likewise, the function f_n is defined as:

In our simulations the values of the refractive index structure constant , as well as, the values of the inner and outer scales (l₀, L₀) were a function of the altitude.⁵ Assuming that turbulence is important bellow an altitude of 3 km and using typical reference values for the inner and outer scales⁵ we have simulated turbulence effect on the R_x receiver.

In Fig.(4) we depict typical results of the effect of turbulence both on the plane of the R_x telescope primary mirror and on the R_x receiver (focal plane of the telescope) for moderate turbulence. In our simulations, the values of the refractive index structure constant depend on altitude⁵ and vary between 4·10⁻¹⁵ at R_x altitude and 2·10⁻¹⁷ at 3 km.

Figure 4:

Numerical simulation results on the effect of atmospheric turbulence on R_x signal detection. Columns indicate different time instances. The two first rows indicate the phase Φ and intensity I in the input plane of the R_x telescope mirror (obscurations from secondary mirror and it’s mounting are not taken into account). Lower row: Intensity distribution on the R_x telescope focal plane. (The R_x detector is denoted by a dotted red circle).

Likewise, in order to simulate the effect of temporal variations we have repeated the simulations, using different phase screens in every iteration. As we can observe in the lower row of Fig.(4) this moderate turbulence has an observable effect to the R_x telescope focus. The focal spot is blurred and turbulence results to beam wonder, equivalent to a 4.7 urad misalignment, a value very close to the measured median seeing ∼ 3.4 urad of the Skinakas Observatory. This temporal variation of the signal intensity and phase as collected by the R_x telescope results in scintillation (i.e. temporal signal variation) of the R_x detector signal. The scintillation is measured by means of the scintillation index σ_I defined as:

In our study, in order to simulate the effect of temporal variation, we have repeated the simulations using every time a new set of random screens. By repeating the process for a large number of iterations we were able to numerical estimate the expected value of the scintillation index σ_I ∼ 0.16 for a 200 um detector in the focal plane. We have to note here that for a more complete analysis of the scintillation effect, the temporal spectrum of the R_x signal intensity variations should be taken into account.