Achieving Secure Transmission with Equivalent Multiplicative Noise in MISO Wiretap Channels

In this letter, we verify that equivalent multiplicative noise, which is generally introduced by random beamforming security scheme, can also guarantee available secrecy rate in MISO wiretap channels. The multiplicative noise is transformed into additive one via a logarithmic operation which is further demonstrated to be information preserving. Then the achievable secrecy rate is quantitatively characterized when the amplitude and phase of the multiplicative noise are independently generated and follow lognormal and uniform distributions, respectively. Finally, power allocation between the multiplicative noise and the desired signal is optimized and discussed by numerical simulation when the eavesdropping channel is known.