A Two-Dimensional Vectorized Secure Transmission Scheme for Wireless Communications

Wireless communication security can be enhanced by leveraging the characteristics of the physical (PHY) layer, where discriminatory scrambling can be employed at the symbol level to either improve the signal quality of the legitimate receiver or degrade that of the eavesdroppers. However, in the presence of multiple passive eavesdroppers with more antennas than the transmitter, the transmitted signals can still be reliably separated from random disturbances. To mitigate this challenge, we propose a two-dimensional vectorized secure transmission scheme. Unlike existing transmission schemes (where the same data symbol is sent over each antenna with a predesigned complex weight at a time), in the proposed scheme, a sequence of data symbols in a predefined order (named symbol vector) is first pre-superposed through pre-coding with a random complex matrix prior to been sent as a vector in parallel over each transmitting antenna at a time. As a result, physical randomness of the legitimate channel is introduced into the received signals at passive eavesdroppers in the pre-coding procedure. Moreover, to ensure that transmitted data symbols can be recovered in the right order, each symbol vector is sent repeatedly, according to the principle of maximum entropy. To ensure the intended receiver can recover the transmitted symbol vector, the random pre-coding matrices are selected such that a linear constraint imposed by the CSI of the legitimate channel is satisfied. In addition, an extended maximum likelihood (ML) detection method is developed for the desired receiver while the random pre-coding matrices are not required to be transmitted. We then analyze its security based on the signal detection theory to demonstrate that the intended receiver can recover the transmitted symbol vectors while the eavesdroppers are not capable of doing so. We also evaluate the performance of the proposed scheme to demonstrate its effectiveness.