MIMO Free-Space Optical Communications Using Photon-Counting Receivers Under Weak Links

Spatial diversity techniques are usually used to mitigate the influence of turbulence in the free-space optical communication (FSOC) with photon-counting receivers, especially when the communication links are weak. A maximum likelihood (ML) detection can be directly applied to the outputs of photon-counting receivers. However, it is challenging to obtain an analytical error probability for the ML detection. In this letter, we derive the analytical error probability of the ML detection under both turbulent and non-turbulent cases by equivalently considering
$L$
detected photons; and the approximating error is in the order of magnitude
$O\left({\frac {\lambda _{b}^{L}}{L!}}\right)$
, where
$\lambda _{b}$
is the background noise. Besides, we prove that the ML detection equals a threshold detection following an equal-gain combining when the signal strengths are close to each other in non-turbulent cases. Numerical results show that
$L\leq 10$
is sufficient for typical scenarios with small background noises
$\lambda _{b} \leq 1$
. Besides, we demonstrate that the derived analytical error probability can achieve a higher precision and computational efficiency compared with Monte-Carlo methods.