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.

在本文中，我们研究如何构建用作物理层安全中数据包检测的导频信号所需的序列。我们的构建从频域开始，其中一组正交频率覆盖整个给定带宽。该构造是 Milewski 构造的广义构造，其中它采用给定频域序列的离散傅里叶逆变换。在本文中，我们将频域中具有等距离、非零频率响应的长度为\(\ell q\)的q序列集合称为频率距离序列集合( FDSS ) 以及从该集合交织的序列称为FDSS交错序列。通过应用频域和时域关系，我们表明这样的集合是相互正交的，并且当且仅当种子序列是完美的（即在所有异相偏移处零自相关）时，它才是互补序列集。当且仅当种子序列是完美的时，FDSS 交织序列才是完美的。我们将所提出的序列应用于现实世界的实验，作为粗同步的导频序列。在我们的实验中，我们在构建中选择了 Frank-Zadoff-Chu 序列和 Golay 对序列，与 Analog Devices 的 ADALM-Pluto SDR 一起使用并进行仿真，并且我们展示了与替代方案相比，在不同噪声信道条件下的导频检测率飞行员选择。当 SNR 为 20 dB 时，我们的导频的误报检测率降至零。相比之下，一般的OFDM QPSK导频在相同SNR下的漏检率接近70%。 一般来说，我们的导频序列始终比 OFDM QPSK 导频具有较低的误报率，而 OFDM QPSK 导频未能检测到 ADALM-Pluto SDR 环境中的大多数数据包。