Frequency distance sequences for packet detection in physical-layer security

In this paper, we investigate how to construct the required sequences to be used as pilot signals for packet detection in physical-layer security. Our construction starts from the frequency domain, where a set of orthogonal frequencies cover an entire given bandwidth. The construction is a generalized construction from Milewski’s construction, where it takes the inverse discrete Fourier transform of the given frequency domain sequences. In this paper, we call a set of the q sequences of length \(\ell q\) with an equal distanced, nonzero frequency response in the frequency domain a frequency distance sequence set (FDSS) and a sequence interleaved from this set an FDSS interleaved sequence. By applying frequency and time domain relations, we show that such a set is mutually orthogonal, and is a complementary sequence set if and only if the seed sequence is perfect (i.e., zero autocorrelation at all out-of-phase shift). The FDSS interleaved sequence is perfect if and only if the seed sequence is perfect. We apply the proposed sequences to real world experiments as pilot sequences for coarse synchronization. In our experiments, we selected Frank–Zadoff–Chu sequences and Golay pair sequences in our construction for use with an ADALM-Pluto SDR from Analog Devices and simulations, and we show the pilot detection rate under different noisy channel conditions, when compared to alternative pilot selections. The false negative detection rate of our pilot decreases to zero when the SNR is 20 dB. In contrast, a general OFDM QPSK pilot has a false-negative detection rate near 70% at the same SNR. In general, our pilot sequence consistently has a lower false-negative rate to the OFDM QPSK pilot, which failed to detect most packets in the ADALM-Pluto SDR environment.