Non-relatively measurable spread-sequences for secure transmission of direct-sequence spread-spectrum signals

In this paper, a new technique to design signals for secure transmissions is proposed. The proposed technique does not allow to an unauthorized third party to discover the modulation format and, hence, to demodulate the signal. The proposed signal-design technique consists in adopting a non relatively measurable sequence as spreading sequence for a direct-sequence spread-spectrum signal. Non relatively measurable sequences are such that the appropriate time averages do not converge as the data-record length approaches infinite. Thus, none of their statistical functions defined in terms of infinite-time averages is convergent. Therefore, also the modulated continuous-time signal exhibits non convergent statistical functions. Consequently, all modulation classification methods based on measurements of statistical functions such as the autocorrelation function, moments, and cumulants fail to identify the characteristics of the modulation format. Simulation results are provided to show the lack of convergence, as the data record is increased, of the estimators of the second-order cyclic statistics of the designed signal.