Spatial Beam Tracking for Hermite-Gaussian-Based Free-Space Optical Communications
The problem of spatial tracking for Hermite-Gaussian free-space optical (HG-FSO) links is addressed. Since HG waveforms allow for the simultaneous presence of orthogonal spatial channels, FSO-HG has the potential of offering a considerable increase in system capacity as compared with the standard FSO systems. To harness this capacity gain, the problem of spatial tracking becomes of paramount importance as the presence of spatial error significantly impacts the orthogonality of the HG waveforms. We, then, consider spatial tracking using a standard quad-detector arrangement and assume that the background noise and/or receiver thermal noise are large enough to warrant a Gaussian detection statistics. The performance is assessed in terms of the probability density function of the spatial tracking error for HG order of up to 3. In assessing performance, it is assumed that the impact of the cross-talk among the spatial modes is negligible under the steady-state condition. Numerical results are presented to assess the viability of the tracking loop. Numerical results show that among the HG waveforms with orders ranging from 1 to 3, the second-order HG waveform offers the best tracking performance and, hence, must be selected for the purpose of tracking in HG-FSO systems.