Numerical and analytical approaches to dynamic beam waist optimization for LEO-to-GEO laser communication

Abstract

We study a dynamic scheme for optimizing the beam waist in low earth orbit-to-geostationary orbit (LEO-to-GEO) laser communication for small satellites under the influence of the pointing error on the transmitting side. Using the Marcum Q-function, we express the channel gain of the link in a closed form. Based on this expression, we obtain an accurate approximation of the optimal value of the laser beam waist via both numerical and analytical approaches to achieve the minimal average bit error probability (ABEP) of the LEO-to-GEO communication. The analytical approximation has a simple form and can be straightforwardly calculated and employed in practice. We numerically compute the ABEP with our analytical solution and the sub-optimal solution proposed in the literature. The results show a strong agreement between our solution and previous work.

Dynamic Adaptive Beam Control System Using Variable Focus Lenses for Laser Inter-Satellite Link

“…The optimum divergence increases linearly with the pointing error. This agrees well with the previously reported results in [16].…”

“…2(b) also shows that when the AoA is larger than 100 rad, the optimum beam radius can be approximated to be linearly proportional to AoA, which is depicted by the dashed line in the figure. This agrees very well with the result reported in [16].…”

“…This is because mechanical vibrations could be faster than the feedback correction and the angular resolution of the PAT system might not be fine enough to achieve accurate alignment. The adaptive beam control (ABC) technique has been recently proposed and demonstrated to mitigate the adverse effect of optical beam misalignment [8]- [16]. In this technique, the beam divergence angle at the transmitter and (focused) beam radius at the detector, respectively, are adjusted adaptively to the channel conditions including the transmission distance and the amount of vibrations.…”

“…Another reason for slow control is that the static technique requires the handshake between the transmitter and receiver to exchange the statistical information. On the other hand, the dynamic ABC technique compensates for pointing errors and AoA fluctuations induced by mechanical vibrations instantaneously [15], [16]. In the transmitter-side dynamic ABC technique, for example, the beam divergence angle is adjusted adaptively to 2 > REPLACE THIS LINE WITH YOUR MANUSCRIPT ID NUMBER (DOUBLE-CLICK HERE TO EDIT) < the instantaneous amount of transmitter vibration, whose information is provided by the rate sensors equipped in the satellite [15].…”

“…It is worth noting that there are a couple of previous works on the performance improvement and evaluation of laser ISL using the dynamic ABC technique [15], [16]. However, they employed only the transmitter-side ABC to mitigate the adverse effect of pointing error.…”