Improved carrier tracking for low-threshold telemetry using a smoother

This work establishes the threshold performance of noncausal smoothing filters used for tracking residual carrier signals when performance is limited by both phase process noise and additive receiver noise. Previous work based entirely on linear theory predicts significant improvements in phase estimation by using smoothing filters as compared with using causal phase-locked loops (PLLs). For phase process noise having a 1/f³ spectral density, which is typical of many oscillators, linear theory predicts a reduction in phase estimation error of 5 dB for the same phase-noise and receiver-noise magnitudes. Alternatively, linear theory predicts the ability of a smoother to track a 7.5-dB weaker signal with the same mean-square phase error, under the same conditions of phase process noise. Simulations show that the smoothers achieve an effective loop signal-to-noise ratio (SNR) within 0.5 dB of linear theory when the linear theory predicts an effective loop SNR as low as 11.4 dB. Under the same conditions, an optimum PLL would have a linear-model effective loop SNR of only 6.4 dB and would perform more than 1-dB worse than this, with many cycle slips