Merit factor of Chu and Frank sequences

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Abstract
The merit factor of optimally decimated and shifted Chu and Frank sequences was determined. These are perfect sequences, i.e. the out-of-phase values of their periodic auto-correlation functions (PACF) vanish. However, this property does not correspond to a large merit factor, which is defined as the ratio of the squared energy of the sequence to the sum of the squared sidelobes in their aperiodic autocorrelation function (ACF). Therefore, we apply two invariance operations to the sequences, which do not change the PACF sequences, but may improve the merit factor.These sequences find applications in radar and synchronisation systems.

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