Random modulation-based realization of optical channel measurement sample de-correlation analysis

  Objective   Based on channel-based key extraction technology, the reciprocal random channel is treated as a public random source from which shared keys are generated. During the optical channel transmission, the received optical signals may exhibit correlation due to unstable factors such as atmospheric turbulence, indicating a degree of correlation between adjacent signal samples. In order to extract highly random key sources from the optical channel, it is necessary to reduce the measurement rate of the channel state based on the correlation time of the channel, ensuring the lack of correlation between consecutive channel measurements. To some extent, the correlation time of optical fluctuations caused by turbulence limits the number of uncorrelated optical channel measurement samples that can be obtained per second. Therefore, it is necessary to perform decorrelation on the continuous observed optical channel measurement samples obtained by the legitimate party at a sampling interval shorter than the correlation time of optical fluctuations caused by turbulence. In this paper, a simulation experiment based on random modulation is constructed to achieve decorrelation of measurement samples, and the impact of random modulation on the autocorrelation of measurement samples is analyzed.

  Methods   Based on existing relevant theories, an experimental system for measuring sample decorrelation based on random modulation has been designed. The schematic diagram of the transmitting and receiving terminal principles based on random modulation is shown (Fig.1), and theoretical analysis has been conducted (Fig.2). Through analysis, the impact of the normalized variance of the modulation signal source on the correlation coefficient of consecutive measurements is explained. Utilizing OptiSystem software, a simulation experiment of the sample measurement system based on random modulation in optical channels was constructed (Fig.3).

  Results and Discussions  The power samples of received signals over time were analyzed under three conditions of no modulation, single modulation, and double modulation (Fig.4). Moreover, the autocorrelation of measurement samples as a function of lag time was examined under different modulation conditions (Fig.5). In the absence of random modulation, it was observed that the autocorrelation after a lag of 100 samples is 0.676. Contrarily, under single modulation and double modulation conditions, the autocorrelation after a lag of 100 samples is 0.083 and 0.035, respectively. The utilization of random modulation effectively decreased the autocorrelation of optical channel measurement samples. Additionally, concerning the single modulation case, a separate analysis was conducted to assess the impact of varying the coherence time of the atmospheric optical channel transmission coefficient (Fig.6) and the effect of different pseudo-random code generation rates on the autocorrelation of optical channel measurement samples (Fig.7). When the sampling rate is 6.4 × 10⁶ Hz, and the generation rate is 6 × 10⁶ bit/s, the autocorrelation of adjacent measurement samples is 0.112. This indicates that the use of random modulation enables obtaining nearly uncorrelated consecutive observations of optical channel measurement samples at a smaller sampling interval than the correlated time caused by turbulence-induced optical fluctuations. Finally, the impact of transmission distance (Fig.8) and signal-to-noise ratio (Fig.9) on the autocorrelation of measurement samples was analyzed.

  Conclusions  The impact of three scenarios, namely no modulation, single modulation, and dual modulation, on the autocorrelation of the observed optical channel measurement samples was studied. The research results show that compared to the case without modulation, the number of measurement data variations in the observed optical channel measurement samples increases within the same time interval. Moreover, applying random amplitude modulation to the transmitted optical signal reduces the autocorrelation of the observed optical channel measurement samples at a sampling interval shorter than the correlation time of optical fluctuations caused by turbulence. When other parameters remain unchanged, as the coherence time of the atmospheric optical channel transmission coefficients decreases and the delay time increases, the autocorrelation of the measurement samples decays faster and the variation becomes more pronounced. Similarly, when other parameters remain unchanged, as the generation rate of pseudo-random codes increases and the delay time increases, the autocorrelation of the measurement samples decays faster. Additionally, the impact of increasing generation rate of pseudo-random codes on the autocorrelation of adjacent optical channel measurement samples was analyzed.