Loss of Lock Induced by Doppler or Code Rate Mismatch in Code Tracking Loops

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Abstract
The relative motion of the transmitter and receiver or a clock rate mismatch lead to the introduction of a Doppler (or offset) term in a first order non-coherent code tracking loop equation (in DS-SPSP systems). The combined effect of both noise (jamming) and the Doppler shift on the mean time to loss of lock is analyzed for two types of loops, the delay locked loop (DLL) and taudither loop (TDL). The effect of an AGC circuit in front of the DLL is also discussed. We derive an explicit expression for the mean time to loss of lock (MTLL) which includes dependence on the Doppler shift. We present, among others, a graph of the MTLL vs. timing error variance for different values of the Dopler shift and a graph of the SNR vs. Doppler shift at constant MTLL. The effect of the Doppler shift is shown to be important and should not be ignored for high processing gain systems. It is shown that a TDL is more sensitive to the Doppler shift than a DLL. It is also found that an AGC circuit can amplify the Doppler term and cause loss of lock at higher SNR. The calculations are based on a singular perturbation method and can be readily extended to higher order loops.

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