Secrecy rates of finite-input intersymbol interference channels

Due to the broadcast nature of the communication medium, security is a critical problem in wireless networks. Securing the transmission at the physical layer is a promising alternative or complement to the conventional higher level techniques such as encryption. During the past decade, various studies have been carried out which investigate such possibilities in providing secrecy for different scenarios. On the other hand, secrecy over intersymbol interference (ISI) channels has not received significant attention, and much work remains to be done. With this motivation, we focus on secrecy rates of finite-input ISI channels for both fixed and fading channel coefficients. We argue that the secrecy rates of ISI channels can be computed by the forward recursion of the BCJR algorithm. Moreover, by utilizing Markov input distributions for transmission over the ISI channels, achievable secrecy rates can be increased. However, the existing iterative method in the literature to obtain the optimal Markov input distribution is computationally complex as many BCJR recursions are needed. Thus, we propose an alternative solution by introducing a codebook based approach. Particularly, among the existing Markov input distributions in the codebook, we propose to select the one which spectrally matches the main channel. Our numerical results reveal that the proposed low complexity approach undergoes a minimal loss with respect to the existing iterative algorithm while offering a considerably reduced complexity. We also propose injection of artificial noise (AN) to increase the secrecy rates, and show that this is especially useful for moderate and high signal to noise ratio (SNR) values where the use of Markov input distributions is not beneficial. We inject AN to frequencies where the eavesdropper's channel is better than the main channel. We show that this approach significantly increases the secrecy rates compared to the existing methods. Furthermore, we consider the effect of channel state information (CSI) on the secrecy rates, and demonstrate that availability of eavesdropper's CSI at the transmitter is highly beneficial in terms of the achievable secrecy rates.