Optimal Trade-off Between Transmission Rate and Secrecy Rate in Gaussian MISO Wiretap Channels

The future wireless networks require both high data transmission rates and secure communications. However, there exists a trade-off between secure and non-secure rates since only a fraction of the maximal achievable reliable rate in a wiretap channel can be considered as secure. This paper studies the optimal transmit strategies that achieve the optimal trade-off between the communication rate and secrecy rate for the MISO wiretap channels with different power constraint settings including sum power constraint only, per-antenna power constraints only, and joint sum and per-antenna power constraints. First, a necessary and sufficient condition to ensure a positive secrecy capacity is shown. After that, closed-form solutions to find an optimal transmit strategy of related problems are derived. This provides a parametrization of the boundary of the maximal achievable rate and secrecy rate without additional time-sharing. The optimal trade-off is characterized by the convex hull of the region. Lastly, the results are illustrated by numerical examples.