Transmitter beamforming and artificial noise with delayed feedback: Secrecy rate and power allocation


Utilizing artificial noise (AN) could be a smart means to guarantee security against eavesdropping in a very multi-input multi-output system, where the AN is meant to lie within the null space of the legitimate receiver's channel direction info (CDI). But, imperfect CDI will cause noise leakage at the legitimate receiver and cause vital loss within the achievable secrecy rate. In this paper, we contemplate a delayed feedback system, and investigate the impact of delayed CDI on security by using a transmit beamforming and AN scheme. By exploiting the Gauss-Markov fading spectrum to model the feedback delay, we derive a closed-type expression of the upper certain on the secrecy rate loss, where Nt = 2. For a moderate range of antennas where Nt > a pair of, 2 special cases, primarily based on the primary-order statistics of the noise leakage and massive number theory, are explored to approximate the respective upper bounds. In addition, to keep up a continuing signal-to-interference-and-noise ratio degradation, we analyze the corresponding delay constraint. Furthermore, primarily based on the obtained closed-kind expression of the lower bound on the achievable secrecy rate, we tend to investigate an optimal power allocation strategy between the knowledge signal and the AN. The analytical and numerical results obtained primarily based on initial-order statistics will be thought to be a sensible approximation of the capacity that can be achieved at the legitimate receiver with a sure range of antennas, Nt. As well, for a given delay, we tend to show that optimal power allocation is not sensitive to the number of antennas in an exceedingly high signal-to-noise ratio regime. The simulation results any indicate that the achievable secrecy rate with optimal power allocation will be improved considerably as compared to that with fastened power allocation. Further, as the delay increases, the ratio of power allotted to the AN should be decreased to scale back the secrecy rate degradation.

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