Design of low update rate phase locked loops with application to carrier tracking in OFDM systems

In this paper, we develop design procedures for carrier tracking loop for orthogonal frequency division multiplexing (OFDM) systems or other systems of blocked data. In such communication systems, phase error measurements are made infrequent enough to invalidate the traditional loop design methodology which is based on analog loop design. We analyze the degradation in the OFDM schemes caused by the tracking loop and show how the performance is dependent on the rms phase error, where we distinguished between the effect of the variance in the average phase over the symbol and the effect of the phase change over the symbol. We derive the optimal tracking loop including optional delay in the loop caused by processing time. Our solution is general and includes arbitrary phase noise and additive noise spectrums. In order to guarantee a well behaved solution, we have to check the design against margin constraints subject to uncertainties. In case the optimal loop does not meet the required margin constraints subjected to uncertainties, it is shown how to apply a method taken from control theory to find a controller. Alternatively, if we restrict the solution to first or second order loops, we give a simple loop design procedure which may be sufficient in many cases. Extensions of the method are shown for using both pilot symbols and data symbols in the OFDM receiver for phase tracking. We compare our results to other methods commonly used in OFDM receivers and we show that a large improvement can be gained.