On the Secrecy Sum-Rate of Uplink Multiuser Networks with Potential Eavesdroppers

In this paper, we investigate achievable secrecy sumrate in uplink multiuser networks where some base stations are compromised to operate as potential eavesdroppers. Due to the difficulty of analyzing the exact secrecy capacity region in multiuser networks, we focus on analyzing the secrecy sumrate scaling in terms of the number of transmitters based on multiuser diversity (MUD). We propose an opportunistic user scheduling scheme able to achieve optimal MUD gain in uplink multiuser networks where $N$ transmitters (users), a single desired receiver (i.e., base station), and $K$ potential eavesdroppers (i.e., compromised base stations) are assumed. The proposed scheme enables multiuser transmissions in one scheduling time slot by employing orthogonal random beamforming at the receiver. In addition, the proposed scheme can fully exploit the degrees-of-freedom (DoF) gain when each transmitter is equipped with a single antenna, and base station and potential eavesdroppers are equipped with $M$ antennas. The main results show that the proposed scheduling scheme achieves the optimal secrecy sum-rate scaling indicating that the achievable secrecy sum-rate scales as $M$ log (SNR log N) in a high signal-to-noise ratio (SNR) regime when a certain user scaling condition.