Cramer Rao-Lower Bound and Parameter Estimation for Multibeam Satellite Links

Data throughput and availability of multibeam satellite links are limited by interference problems, in particular when the design is determined by an aggressive reuse of frequency bands. Usually, this is mitigated by appropriately selected techniques like precoding or multi-user detection. Before such methods are applicable, however, the most important transmission parameters have to be recovered successfully even under very challenging conditions caused by (full) frequency reuse. The detailed analysis of the log-likelihood function characterizing the multibeam scenario shows that a beamwise decoupling of the estimation task is possible, if the following three conditions are met: (i) alignment of all frequency offsets; (ii) symbol synchronicity; (iii) orthogonal synchronization sequences. Based on these assumptions, it turns out that the modified Cramer-Rao lower bound (MCRLB) for carrier frequency and phase, symbol timing and signal amplitude is the same, no matter whether we are dealing with a single or a multiple beam situation. Furthermore, because a maximum likelihood framework for parameter estimation is not available in closed form, we introduce a sub-optimal concept of low-complex algorithms. Finally, it is verified by simulation results that the jitter variance of each recovery scheme is close to the related MCRLB, when the decoupling conditions are satisfied.