Under-sampling spectrum-sparse signals based on active aliasing for low probability detection

Because of the broadcast nature of the wireless communication medium, their security issues are receiving extensive concern. In this paper, we propose a spectrum-sparse signal based on multi-carrier modulation for secure wireless communication. The proposed signal is a summation of multiple sub-band signals over several equally spaced carriers. The power spectrum density of the proposed signal can be reduced to a level even lower than the background noise, provided the number of sub-bands is sufficiently large. Thus, the proposed signal possesses a favorable low probability detection property similar to that of spread spectrum signals. At the intended receiver, an under-sampling method based on active aliasing is proposed. In this way, the intended receiver can coherently collect the transmitted signal power over all sub-bands and extract the information reliably. We also derive a closed-form expression for bit error rate performance of the proposed scheme in additive white Gaussian channel with binary phase shift keying modulation. Finally, numerical and simulation results to testify the effectiveness of the proposed scheme are generated for both binary phase shift keying and eight-phase shift keying modulations in additive white Gaussian channel.