Mismatched filtering of periodic quadriphase and 8-phase sequences

Quadriphase and 8-phase sequences with good autocorrelation properties are required in higher order digital modulation schemes, e.g., for channel estimation or synchronization. Since such sequences with perfect periodic autocorrelation function exist only for a few lengths, mismatched filtering is discussed. Mismatched filtering entirely suppresses all sidelobes of the correlation function at the expense of a slightly reduced signal-to-noise ratio (SNR). We present new construction methods for quadriphase and 8phase sequences which exist for many lengths and exhibit significantly lower SNR losses than any other known sequences.