Sparse Non-Orthogonal Frequency Division Multiplexing for Secure Transmission Over Broadcast Channels

We propose a novel transmission scheme for the parallel Gaussian broadcast channel with confidential messages (BCCM). In this model, The source node wishes to transmit a confidential message to each user over
$N$
independent sub-channels, where each sub-channel is degraded for one user than others. Our objective is to design a secure transmission technique that maximizes the sum secrecy rate under an average power constraint. The most common technique to tackle this problem in practice is orthogonal frequency division multiplexing (OFDM). Nevertheless, the OFDM-based BCCM suffers from excessive bandwidth utilization due to the sub-carrier orthogonality requirement. We propose a sparse non-orthogonal frequency-division Multiplexing (SNOFDM) transmission scheme. In SNOFDM, sub-carriers are generated by first selecting a subset of orthogonal sub-channels to reduce spectral resources. Then, the selected sub-channels are multiplexed in time to generate non-orthogonal sub-carriers. This, in effect increases, the spectral efficiency compared to OFDM. To overcome the interference introduced due to the non-orthogonality of sub-carriers, the transmitter sends the sparsest representation of the transmitted codeword. Furthermore, we provide a sub-carrier selection and power control procedures to maximize the sum rate of SNOFDM according to CSI fed back from receivers to source node. Our numerical results show that SNOFDM offers better spectral efficiency and a higher secrecy rate compared to OFDM. We provide extensive simulation results to study the effects of transmission parameters of SNOFDM on the achievable secrecy rate.