Uplink Non-Orthogonal Multiple Access With Finite-Alphabet Inputs

Abstract

This paper focuses on the non-orthogonal multiple access (NOMA) design for a classical two-user multiple access channel (MAC) with finite-alphabet inputs. In contrast to most of existing NOMA designs using continuous Gaussian input distributions, we consider practical quadrature amplitude modulation (QAM) constellations at both transmitters, the sizes of which are assumed to be not necessarily identical.We propose to maximize the minimum Euclidean distance of the received sum-constellation with a maximum likelihood (ML) detector by adjusting the scaling factors (i.e., instantaneous transmitted powers and phases) of both users. The formulated problem is a mixed continuous-discrete optimization problem, which is nontrivial to resolve in general. By carefully observing the structure of the objective function, we discover that Farey sequence can be applied to tackle the formulated problem. However, the existing Farey sequence is not applicable when the constellation sizes of the two users are not the same.Motivated by this, we define a new type of Farey sequence, termed punched Farey sequence. Based on this, we manage to achieve a closed-form optimal solution to the original problem by first dividing the entire feasible region into a finite number of Farey intervals and then taking the maximum over all the possible intervals. The resulting sum-constellation is proved to be a regular QAM constellation of a larger size, and hence a simple quantization receiver can be implemented as the ML detector for the demodulation. Moreover, the superiority of NOMA over time-division multiple access (TDMA) in terms of minimum Euclidean distance is rigorously proved. Furthermore, the optimal rate allocation among the two users is obtained in closed-form to further maximize the obtained minimum Euclidean distance of the received signal subject to a total rate constraint. An asymptotic solution is also derived to reveal more insights on how to allocate the rate to each user. Finally, simulation results are provided to verify our theoretical analysis and demonstrate the merits of the proposed NOMA over existing orthogonal and non-orthogonal designs.Z. Dong is with Shenzhen University, China and he is also with McMaster

Signal Design for AF Relay Systems Using Superposition Coding and Finite-Alphabet Inputs

“…In this section, we aim to solve Problem 2 to find the differential pairs (m, n) having the minimum Euclidean distance. For this purpose, we first introduce the definition of the punched Farey sequence developed in [9].…”

“…The formulated problem is a mixed continuousdiscrete problem that is in general non-trivial to resolve. To tackle it, we resort to the punched Farey sequence framework developed in [9] to strategically segment the entire feasible region of the formulated optimization problem into a finite number of sub-intervals and obtain the closed-form optimal solution of the formulated problem in each sub-interval. We then acquire the optimal solution to the formulated problem by comparing the solutions on each sub-interval.…”

Time-Collaborative Constellation Design With Finite-Alphabet Inputs for Two-User Multi-Access Visible Light Communications

“…This system model can be seen as the equivalent model of many common scenarios, such as the one-cell system with two users [22] or two-cell system with the user located in the two cells' overlapping area [23]. We consider that the transmitted signals are drawn from unipolar pulse amplitude modulation constellations, motivated by the fact that 1) the transmitted signals in realistic communication systems are drawn from finite-alphabet constellations [19], [24], [25] 2) the transmitted signals in VLC systems must be nonnegative and real-valued. We assume that the i -th (i = 1, 2) user transmits K i bit data to the PD receiver over L successive channels.…”

Optimal rotation angle for finite constellation over additive white Gaussian noise multiple access wiretap channel

“…It is shown that the relative rotation of the constellation on one user enhances the achievable rate region. This result has been extended to several other channel models including multiple‐input multiple‐output (MIMO) channel, non‐orthogonal multiple access (NOMA) [4], and NOMA with a rotation of constellation [5]. A finite constellation over a fast fading wiretap channel is studied in [6] and further finite constellations over an AWGN wiretap channel is also reported in [7].…”