Joint Design of Energy-Based Constellations for Noncoherent Massive SIMO Symmetric X-Channels

This paper proposes a joint finite-alphabet energy constellation design based on bit allocation for a noncoherent massive single-input multiple-output (SIMO) symmetric Xchannel (XC) with two transmitter-receiver pairs. We provide the feasibility region analysis concerning the transmission rates of the two-user symmetric XC under an average power constraint at each transmitter. Since the average error performance of the system is primarily determined by the smaller minimum Euclidean distance (MED) at the receiver side, we adopt the max-min criterion to balance the error performance of the two receivers. Specifically, we optimize the bit allocation between the two users by maximizing the minimum value of the MEDs of the two received constellations. The optimal energy constellation design is obtained through an efficient one-dimensional search. Finally, simulation results demonstrate that the proposed nonorthogonal multiple access (NOMA) designs can adapt to largescale channel variations and exhibit better average bit error rate (BER) performance compared to the traditional time division multiple access (TDMA) schemes.