Improving frequency estimation performance for burst transmissions by optimising reference symbol distribution

The theoretical lower bound on data-aided (DA) frequency estimation error for bursts transmissions containing reference symbols is known to decrease if the reference symbols are distributed throughout the burst. In practice, DA frequency estimators exhibit threshold behaviour where the performance rapidly degrades if the signal-to-noise ratio (SNR) is lower than a certain threshold value. Lowering the SNR threshold is often an important goal in the design of both estimators and signal formats.This article examines DA frequency estimation for burst transmissions, specifically analysing the threshold behaviour for both regular and irregular reference symbol distributions. We demonstrate through analysis and simulation results that threshold behaviour can be determined from the frequency estimation likelihood function, particularly the magnitude and location of secondary likelihood peaks. We also demonstrate, for a specific test case, that significant improvements in threshold performance can be gained with irregular distribution of reference symbols, with little degradation in the frequency estimation error.The methods described in this paper allow the signal designer to select a reference symbol distribution to optimise and trade-off estimation performance parameters such as estimation error, acquisition range, outlier probability and threshold behaviour.