Optimal Rotation Angle For Finite Constellation Over Additive White Gaussian Noise Multiple Access Wiretap Channel

The achievable secrecy rate regions of various multi-user channels with Gaussian inputs are well-known in the literature. To gain more practical insights into the achievable rates, it is more useful to consider channels with inputs from finite constellations, such as M-ary quadrature amplitude modulation (M-QAM), M-ary phaseshift keying (MPSK), M-ary amplitude phase-shift keying (M-APSK) etc. The authors study the achievable secrecy rates with a constrained constellation input for a multiple access wiretap channel with an eavesdropper. They also show that if the constellation points are rotated relatively for the two users then the secrecy sum-rate can be improved. They perform Monte-Carlo simulations for computing these secrecy rates for classical modulation schemes including BPSK, quadrature phase-shift keying, M-QAM, M-PSK, M-PAM, and M-APSK. They also derived an approximate function, whose argument of supremum provides an approximately optimal rotation angle for obtaining a maximum secrecy sum-rate. they also show, via simulations, that rotation of constellation is helpful for some range of signal-to-noise ratio only, which is contrary to the results of multiple access channel without security constraint. Finally, they consider a more realistic scenario, where the channel from transmitters to receivers and eavesdroppers is time-varying. They consider the case of complex circularly symmetric Gaussian random channel gains and compute the optimal rotation angle, which will maximise the expected value of an upper bound of the secrecy sum-rate.