A Novel Power Allocation Scheme for Two-User GMAC with Finite Input Constellations

Harshan, J.; Rajan, B. Sundar

doi:10.1109/twc.2012.122212.120324

Cited by 22 publications

(29 citation statements)

References 28 publications

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“…The main principle 1 of these efforts is to ensure that the signal originated from each user can be uniquely decoded from the received sum-signal at the receiver side. By using mutual information as a performance measure, references [40], [41] considered the NOMA design in an ideal twouser Gaussian MAC with finite-input constellations under individual power constraint on each user. Specifically, NOMA was realized by strategically introducing certain constellation rotations (CR) to the adopted PSK signals in [40] or using proper power control in [41].…”

Section: A Related Workmentioning

confidence: 99%

“…By using mutual information as a performance measure, references [40], [41] considered the NOMA design in an ideal twouser Gaussian MAC with finite-input constellations under individual power constraint on each user. Specifically, NOMA was realized by strategically introducing certain constellation rotations (CR) to the adopted PSK signals in [40] or using proper power control in [41]. However, only numerical solutions to the optimal NOMA designs were provided in [40], [41].…”

Section: A Related Workmentioning

confidence: 99%

“…Inspired by the aforementioned work, in this paper we target a closed-form NOMA design for a classical two-user Gaussian MAC with finite-alphabet inputs and an optimal maximum likelihood (ML) detector at the receiver, where the two users are allowed to transmit simultaneously in the same frequency band. Finding the capacity bound of a Gaussian MAC with Gaussian inputs and adaptive power control has always been a classic problem, see e.g., [15]- [18], [22], [23], [29], [48]; the optimal power control scheme for the Gaussian MAC with finite-alphabet inputs, however, is still an open problem and only numerical solutions are available [38], [40], [41], [49]. 1 Note that the principle was originally proposed in the seminal work [45]- [47], wherein the finite-length codeword design problem in the binary domain were considered from an information-theoretical perspective.…”

Section: B Motivation and Contributionsmentioning

confidence: 99%

“…Although we use a complex baseband representation in (1), the modulated and demodulated signals are real since the oscillator at the transmitter can only generate real sinusoids rather than complex exponentials, and the channel then introduces amplitude and phase distortion to the transmitted signals [8]. As such, we follow [41] to decompose the considered complex Gaussian MAC given in (1) into two parallel real-scalar Gaussian MACs, which are called the in-phase and quadrature components, respectively [8]. This means that the original two-dimensional QAM constellation can be split into two one-dimensional PAM constellations to be transmitted via the in-phase and quadrature branches.…”

Section: Two-user Gaussian Multiple-access Channelmentioning

confidence: 99%

“…In other words, Problem 1 is a mixed continuous-discrete optimization problem and it is in general hard to solve. To the best of our knowledge, only numerical solutions to such kind of problems are available in the open literature [38], [40], [41], [49]. To optimally and systematically solve this problem, we now develop a design framework based on the Farey sequence [50], in which the entire feasible region of (w 1 ,w 2 ) is divided into a finite number of mutually exclusive sub-regions.…”

Section: A Problem Formulationmentioning

confidence: 99%

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Uplink Non-Orthogonal Multiple Access With Finite-Alphabet Inputs

Dong

Chen

Zhang

et al. 2018

IEEE Trans. Wireless Commun.

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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

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Section: A Related Workmentioning

confidence: 99%

Section: A Related Workmentioning

confidence: 99%

Section: B Motivation and Contributionsmentioning

confidence: 99%

Section: Two-user Gaussian Multiple-access Channelmentioning

confidence: 99%

Section: A Problem Formulationmentioning

confidence: 99%

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Uplink Non-Orthogonal Multiple Access With Finite-Alphabet Inputs

Dong

Chen

Zhang

et al. 2018

IEEE Trans. Wireless Commun.

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Optimal finite alphabet scheme for NOMA uplink channels

Zhen

Wong

et al. 2022

IET Communications

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The design of an optimal non-orthogonal multiple access (NOMA) transmission scheme with finite alphabet inputs for a typical two-user uplink wireless communication system is investigated in which each terminal is equipped with a single antenna. Each of the two users utilises a four quadrature amplitude modulation (4-QAM) constellation to transmit information data to a common base station, and the receiver employs a maximum likelihood (ML) detector to jointly estimate both transmitted signals. Assuming the availability of channel state information at both the transmitters and the receiver, it is aimed to design a pair of scalar beamformers for the two users such that the minimum Euclidean distance between elements of the received sum-constellation is maximised subject to the power constraints on the users. A thorough consideration of all the different conditions results in the derivation of a closed-form optimal beamformer design. As well, examination of the construction of sum-constellation resulted from the optimum design directly leads to the unique decoding of the original transmitted signal of each user. To facilitate practical implementation, a fast decoding procedure of the optimum NOMA scheme is further developed. The corresponding theoretic probability of ML detection error is also derived. The theoretical development of an optimum sum-constellation for the basic 2-user 4-QAM system provides a solid platform for the derivation of an optimum sum-constellation for a K -user and/or M -QAM system. Indeed, a simple development of the basic sumconstellation map facilitates such extensions. Numerical simulations not only demonstrate that the performance of the fast decoder agrees closely with the theoretical analysis, but also verify that it is superior in performance to other existing NOMA designs for the same system under high signal-to-noise ratio.

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Optimal Minimum Euclidean Distance-Based Precoder for NOMA With Finite-Alphabet Inputs

et al. 2019

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Non-orthogonal multiple access (NOMA) scheme with Gaussian input signals, which have no constellation constraint on the input alphabets, has been investigated intensively, whereas the research on finite input constellations is relatively few. This paper focuses on the power allocation in practical NOMA application with finite-alphabet inputs. We propose a practical power allocation scheme for downlink NOMA scenario based on the merit of maximizing the minimum Euclidean distance (MMED) by adopting the constellation-constrained (CC) capacity. Applying the nearest neighbor approximation and Jensen's inequality, we prove that optimal CC capacity can be achieved under the MMED criterion at high signal-to-noise ratio (SNR). Instead of updating power allocation coefficient instantaneously, a preset fixed power factor α MMED derived from the MMED criterion is preferred and thus reduces the complexity of overall system implementation. We take two cases into consideration, namely, Gaussian broadcast channel (GBC) and fading broadcast channel (FBC). We model close channel conditions, which are challenging for conventional NOMA as the GBC scenario, and model near-far effect as well Rayleigh fading as the FBC scenario. In these two cases, we show that the optimal performance can be guaranteed at high SNR without the knowledge of channel state information (CSI). We study the power coefficient pairs for the most commonly used Mary quadrature amplitude modulation (M-QAM) constellations based on the MMED criterion. We explore the relationship between the power allocation coefficients and the sizes of constellations. The numerical simulations on CC sum capacity and capacity regions are provided to validate our analysis.INDEX TERMS Constellation constrained capacity, finite-alphabet inputs, minimum Euclidean distance, non-orthogonal multiple access.

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A Novel Power Allocation Scheme for Two-User GMAC with Finite Input Constellations

Cited by 22 publications

References 28 publications

Uplink Non-Orthogonal Multiple Access With Finite-Alphabet Inputs

Uplink Non-Orthogonal Multiple Access With Finite-Alphabet Inputs

Optimal finite alphabet scheme for NOMA uplink channels

Optimal Minimum Euclidean Distance-Based Precoder for NOMA With Finite-Alphabet Inputs

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