Asymptotic analysis of large MIMO wire-tap channel via replica method

Security has been one of the most significant problems surrounding wireless communications, in large part due to the openness of wireless medium where eavesdropping can be easily accomplished. In this work, the prior results on secrecy capacity is extended to the Gaussian MIMO wire-tap channel, where the transmitter, the receiver and illegal wire-tapper all employ multiple antenna technique. A reasonable security criterion is firstly defined for the MIMO wire-tap channel in this paper. Next the secrecy capacity and the achievable rate-equivocation (R, d) region in this multiple antenna scenario are derived. Finally, the analyzed results are validated by the numerical simulations.