Capacity analysis for free space coherent optical MIMO transmission systems: with and without adaptive optics

This paper analyzes the capacity of the free space coherent optical MIMO transmission system. Two scenarios are considered (i.e., with and without the adaptive optics compensation). It is generally accepted that the adaptive optics compensation can significantly improve the system performance, which is rigorously true when the MIMO algorithm is not implemented. However, it might not be the case in the coherent MIMO systems. When the turbulence strength is weak or moderate, this work demonstrates that the phase-only wave-front corrector will increase the mean eigen value of the coherent system capacity matrix HHH and make the eigen value distribution more even, i.e. it will decrease the maximal eigen value while increasing the average eigen value. Hence, the capacity of the system with adaptive optics increases when the channel information is not available, because the sub-channels are placed with equal powers. When the channel information is perfectly available and the water filling algorithm is used to optimize the power allocation, the system with adaptive optics could have a deteriorated performance as the capacity is more related to the large eigen values especially in the low signal to noise ratio (SNR) regime. When the turbulence strength is strong, it is found that adaptive optics will decrease both the mean and maximal eigen values for the capacity matrix HHH, and therefore the system capacity degrades, whether the channel information is available or not.