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

TL;DR

This paper demonstrates that for a two-user Gaussian multiple access channel with finite input alphabets, non-orthogonal multiple access (NO-MA) schemes like TCMA outperform traditional orthogonal schemes such as FDMA and TDMA in terms of capacity regions.

Contribution

The paper shows that, unlike the Gaussian alphabet case, NO-MA schemes like TCMA achieve larger capacity regions than O-MA schemes for finite alphabets, especially as bandwidth increases.

Findings

CC capacity region with FDMA is strictly contained inside TCMA.

Gap between TCMA and FDMA increases with power constraint.

Gap decreases with increasing bandwidth.

Abstract

For a two-user Gaussian multiple access channel (GMAC), frequency division multiple access (FDMA), a well known orthogonal-multiple-access (O-MA) scheme has been preferred to non-orthogonal-multiple-access (NO-MA) schemes since FDMA can achieve the sum-capacity of the channel with only single-user decoding complexity [\emph{Chapter 14, Elements of Information Theory by Cover and Thomas}]. However, with finite alphabets, in this paper, we show that NO-MA is better 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 multiple access (TDMA) and compare them with the CC capacity regions with trellis coded multiple access (TCMA), a recently introduced NO-MA scheme. Unlike the Gaussian alphabets case, it is shown that the CC capacity region with FDMA is strictly contained inside the CC capacity region with TCMA. In particular, for a given bandwidth, the gap between the CC capacity regions with TCMA and FDMA is shown to increase with the increase in the average power constraint. Also, for a given power constraint, the gap between the CC capacity regions with TCMA and FDMA is shown to decrease with the increase in the bandwidth. Hence, for finite alphabets, a NO-MA scheme such as TCMA is better than the well known O-MAC schemes, FDMA and TDMA which makes NO-MA schemes worth pursuing in practice for a two-user GMAC.