Parameter estimation algorithms for tropospheric compensation in uplink arrays

The concept of coherently combining X-band (7.2 GHz, nominally 4 cm wavelength) signals at a spacecraft from several 34 meter antennas, thus forming an Uplink Array that increases the signal power at the spacecraft or a radar target by a factor of N² (where N is the number of array elements), has been documented in previous publications. Although 4 cm wavelength X-band signals typically do not suffer significant losses from tropospheric delay fluctuations over the array, some degradation may occur due to fluctuating tropospheric delays when tracking with the array at low elevations, or under particularly unfavorable weather conditions such as rapidly moving thick clouds and rain. This degradation is exacerbated at higher carrier frequencies, such as Ka-band (32 GHz, nominal 1 cm wavelength) currently planned for future deep-space communications and radar applications, where a given differential delay generates four times greater phase fluctuations than at X-band. In this paper, optimum as well as suboptimum algorithms designed to estimate the relevant parameters for estimating tropospheric phase in real time are presented. For each parameter, the Cramer-Rao bound on estimator performance is derived, and compared with MATLAB simulations designed to test each algorithm´s performance.