PLL performance of DS-CDMA systems in the presence of phase noise, multiuser interference, and additive Gaussian noise

The performance of decision-directed phase-locked loops (PLL) for use in direct-sequence code-division multiple-access (DS-CDMA) systems is investigated in the presence of phase noise, multiuser interference, and additive white Gaussian noise (AWGN). A unified and accurate analysis of the effect of these sources of noise on the PLL is carried out based on a nonlinear model (the Fokker-Planck method) since a linear analysis yields a large deviation between analytical results and actual performance at low signal-to-noise ratios (SNR). After describing the implementation of the PLL, the steady-state probability density function (PDF) of the phase estimator error in a first-order loop is derived. It is shown that a tradeoff exists between the effect due to the phase noise, the magnitude of the multiuser interference, and the AWGN as a function of loop bandwidth. The optimal loop bandwidth minimizing the impact of these sources of noise on the PLL and the requirements on the frequency uncertainty of the carrier source for a required accuracy of the phase estimator are detailed. Numerical results of the variance of the phase estimator error are discussed for Gold codes