LAUSR

This paper proposes a practical synchronization waveform that is resilient to frequency error for machine-type communications with applications in massive Internet of Things (IoT). Mathematical properties of the waveform are derived, which are keys to addressing the practical issues. In particular, it is shown that this type of waveform is asymptotically optimal in the presence of a frequency error, in the sense that its asymptotic performance is the same as the optimal matched-filter detector that is free of frequency error. This asymptotic property enables optimization of the waveform under the constraints imposed by an application. It is also shown that such optimized waveform comes in pairs, which facilitates the formation of a new waveform capable of frequency error estimation and timing refinement at the receiver. Detailed comparisons with the LTE narrowband IoT primary synchronization signal are provided.