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For a two-user Gaussian multiple access channel (GMAC), frequency divisionmultiple access (FDMA), a well known orthogonal-multiple-access (O-MA) schemehas been preferred to non-orthogonal-multiple-access (NO-MA) schemes since FDMAcan achieve the sum-capacity of the channel with only single-user decodingcomplexity [\emph{Chapter 14, Elements of Information Theory by Cover andThomas}]. However, with finite alphabets, in this paper, we show that NO-MA isbetter than O-MA for a two-user GMAC. We plot the constellation constrained(CC) capacity regions of a two-user GMAC with FDMA and time division multipleaccess (TDMA) and compare them with the CC capacity regions with trellis codedmultiple access (TCMA), a recently introduced NO-MA scheme. Unlike the Gaussianalphabets case, it is shown that the CC capacity region with FDMA is strictlycontained inside the CC capacity region with TCMA. In particular, for a givenbandwidth, the gap between the CC capacity regions with TCMA and FDMA is shownto increase with the increase in the average power constraint. Also, for agiven power constraint, the gap between the CC capacity regions with TCMA andFDMA is shown to decrease with the increase in the bandwidth. Hence, for finitealphabets, a NO-MA scheme such as TCMA is better than the well known O-MACschemes, FDMA and TDMA which makes NO-MA schemes worth pursuing in practice fora two-user GMAC.

Orthogonal vs Non-Orthogonal Multiple Access with Finite Input Alphabet and Finite Bandwidth