On the Two-User SISO-Gaussian and MIMO-Fading MAC with Finite Input Alphabets

Constellation Constrained (CC) capacity regions of two-user SISO Gaussian Multiple Access Channels (GMAC) are computed in this paper for several Non-Orthogonal and Orthogonal Multiple Access schemes (abbreviated as NO-MA and O-MA schemes respectively). For NO-MA schemes, a metric is proposed to compute the angle(s) of rotation between the input alphabets such that the CC capacity regions are maximally enlarged. Further, code pairs based on Trellis Coded Modulation (TCM) are designed with (i) PSK alphabet pairs and (ii) PAM alphabet pairs such that any rate pair on the CC capacity region can be approached. Such a NO-MA scheme which employs capacity approaching trellis codes is referred to as Trellis Coded Multiple Access (TCMA). Then, CC capacity regions of O-MA schemes such as Frequency Division Multiple Access (FDMA) and Time Division Multiple access (TDMA) are also computed and it is shown that, unlike the Gaussian alphabets case, the CC capacity regions with FDMA and TDMA are strictly contained inside the CC capacity regions with TCMA. Hence, for finite alphabets, a NO-MA scheme such as TCMA is better than FDMA and TDMA which makes NO-MA schemes worth pursuing in practice for two-user GMAC. Subsequently, the idea of introducing rotations between the input alphabets is used to construct Space-Time Block Code (STBC) pairs for two-user Multiple-Input Single-Output (MISO) fading MAC. The proposed STBCs are shown to have reduced Maximum Likelihood (ML) decoding complexity and Information-loslessness property. Finally, STBC pairs are proposed for two-user Multiple-Input Multiple-Output (MIMO) fading MAC such that the sphere decoding complexity is reduced.