Communications Ground Systems Section Noncausal smoothing fllters have signiflcant performance advantages over causal fllters for estimation of the phase of radio frequency signals. This article presents the optimum smoothing fllters for the cases where the spectral density of the carrier phase is of the form f ifi , where fi =3 is typical of oscillator noise and fi =8 = 3is typical of phase perturbations due to propagation through charged particles, such as solar wind. It is shown that the optimum smoothers perform approximately 5-dB better than causal fllters of optimum bandwidth, and that the performance of practical-to-implement smoothing fllters is within 0.03 to 0.24 dB of the optimum smoothers. Some important examples where smoothing can be used are in the Deep Space Network Galileo Telemetry System, where the data are recorded and processed in nonreal time; in the DSN Block V Receiver, which provides data bufiering of su‐cient size to enable near-real-time smoothing; and in processing recorded radio science data, where carrier amplitude and phase are the primary data.
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