In [J26], a new technique to design signals for secure transmissions is proposed, which provides data securing at the physical layer in non-cooperative environments. Specifically, the proposed technique does not allow to an unauthorized third party to discover the modulation format and, hence, to demodulate the signal. The technique consists in generating signals whose time-averaged statistical functions such as autocorrelation, moments, and cumulants, do not converge as the data-record length approaches infinity. Therefore, all modulation classification methods based on estimates of these functions, as well as their spectral counterparts, fail to identify the characteristics of the modulation format. The proposed technique is based on the concept of non relatively measurable functions and sequences [J24]. Non relatively measurable functions are such that the empirical distribution function does not converge as the data-record length approaches infinity. Thus, none of their statistical functions defined in terms of infinite-time averages is convergent. Sufficient conditions to get non relatively measurable functions are given. Moreover, examples to build such signals are provided and the receiver performance for the authorized party is analyzed. Simulation experiments on the estimation of second-order cyclic statistical functions are performed to show the lack of convergence of the cyclic estimators as the data record is increased.