There is, I think, something ethereal about i —the square root of minus one. I remember first hearing about it at school. It seemed an odd beast at that time—an intruder hovering on the edge of reality.

Usually familiarity dulls this sense of the bizarre, but in the case of i it was the reverse: over the years the sense of its surreal nature intensified. It seemed that it was impossible to write mathematics that described the real world in …

I and i

Non-orthogonal multiple access (NOMA) is a strong candidate for next generation radio access networks due to its ability of serving multiple users using the same time and frequency resources. Therefore, researchers in academia and industry have been recently investigating the error performances and capacity of NOMA schemes. The main drawback of NOMA techniques is the interference among users due to the its non-orthogonal access nature, that is usually solved by interference cancellation techniques such as successive interference cancellation (SIC) at the receivers. On the other hand, the interference among users may not be completely eliminated in the SIC process due to the erroneous decisions in the receivers usually caused by channels. In this study, for the first time in the literature, the authors derive an exact closed-form bit error rate (BER) expressions under SIC error for downlink NOMA over Rayleigh fading channels. Besides, they derive one-degree integral form exact BER expressions and closed-form approximate expressions for uplink NOMA. Then, the derived expressions are validated by simulations. The numerical results are depicted to reveal the effects of error during SIC process on the performance for various cases such as power allocation for downlink and channel quality difference for uplink.

https://ietresearch.onlinelibrary.wiley.com/doi/epdf/10.1049/iet-com.2018.5278

BER performances of downlink and uplink NOMA in the presence of SIC errors over fading channels

We mathematically derive an upper bound of bit-error rate (BER) of uplink non-orthogonal multiple access (NOMA) systems with quadrature phase shift keying (QPSK) modulation in fading channels. In particular, we exploit the joint maximum-likelihood  (ML) detector at a base station (BS) with multiple antennas since it results in the optimal BER performance of a super-imposed QPSK modulated symbols from multiple users. In particular, we obtain a closed-form integral of Q-function with Erlang distributed random variable to derive the BER. We also obtain diversity order of the uplink NOMA systems. Through extensive computer simulations, we validate that our analytical results match well with the simulation results especially in high signal-to-noise ratio (SNR) regime.

BER Performance of Uplink NOMA With Joint Maximum-Likelihood Detector

In this paper, we investigate rate splitting (RS) for an uplink non-orthogonal multiple access (NOMA) system with a pair of near and far users adopting cyclic prefixed single carrier transmissions. Frequency-domain equalization is applied to assist successive interference cancellation at the base-station. Two kinds of RS schemes, namely, fixed RS (FRS) and cognitive RS (CRS) schemes, are proposed to realize RS for uplink NOMA with the aim of improving user fairness and outage performance in delay-limited transmissions. Corresponding to the split data streams, transmit power is allocated in either a fixed or cognitive manner for the FRS and CRS schemes, respectively. Based on achievable rate region analysis, the benefits of applying RS to uplink NOMA for enhancing the user fairness and outage performance are revealed. A modified Jain’s index is proposed to measure the user fairness for the considered delay-limited transmissions. Closed-form expressions are derived for the outage probabilities of the paired users, respectively, whereas the preferred system parameters are chosen based on asymptotic outage probability expressions. The enhanced user fairness and superior outage performance of the proposed RS schemes are corroborated by Monte Carlo simulation results.

Rate Splitting for Uplink NOMA With Enhanced Fairness and Outage Performance

This letter examines the bit error rate (BER) performance of downlink non-orthogonal multiple access networks for binary phase-shift keying modulation. Exact BER expression is derived for each user in closed-form under additive white Gaussian noise and Rayleigh fading channels in perfect and imperfect successive interference cancellation (SIC) cases. Next, in perfect SIC case, the asymptotic BER expression in a high signal-to-noise ratio (SNR) region is obtained to express the behavior of the network with diversity and array gains. On the other hand, in imperfect SIC case, the upper bound for BER is attained, and at high SNR values, the BER reveals an error floor, and hence a zero diversity gain is achieved. Then, a feasible range of power allocation coefficients is found such that a good BER performance can be provided for each user. Finally, through simulations and software-defined radio-based real-time tests, analytical results are validated.

Bit Error Rate for NOMA Network

Non-orthogonal multiple access (NOMA) is an attractive multiple access technique to achieve the optimal system capacity region. A great deal of recent attention has been devoted to the study of the NOMA system capacity performance. However, the exact bit error rate (BER) expressions of NOMA systems have not been derived yet. We provide the exact closed-form BER expressions of the QPSK constellation for an uplink NOMA system over an additive white Gaussian noise channel. Finally, the validity of our derived BER expressions is verified through simulations.

/pdf/closed-form-ber-expressions-of-qpsk-constellation-for-uplink-51vq4bjmuz.pdf

Closed-Form BER Expressions of QPSK Constellation for Uplink Non-Orthogonal Multiple Access

We propose a new variant of a block transmission based on 4-Weighted Fractional Fourier Transform (4-WFRFT), which contains a compatible process of single-carrier (SC) and multi-carrier (MC) modulation. The 4-WFRFT system has an even and symmetrical bit energy distribution on the timefrequency plane that it could achieve a better performance than or equal to those of SC and MC systems in selective fading channels. The approach of 4-WFRFT may facilitate unification of the two competitive carrier schemes, and improve the distortion resistance capability of communication system.

The approach to carrier scheme convergence based on 4-weighted fractional fourier transform

In this letter, we present a new approach to narrowband interference (NBI) suppression utilizing the weighted-type fractional Fourier transform (WFRFT) as a precoding scheme in the DFT-based communications systems. The proposed scheme can degenerate into a single carrier (SC) or a multi-carrier (MC) frequency division multiple access block transmission system by means of WFRFT parameter selection, which also leads to a variation of residual energy distribution of NBI following a frequency domain avoidance strategy. By virtue of parameter optimization of the WFRFT, the proposed system can outperform both SC and MC systems with regards to NBI suppression.

WFRFT Precoding for Narrowband Interference Suppression in DFT-Based Block Transmission Systems

The paper reveals the relationship between the weighting coefficients and weighted functions via the research of coefficients matrix and based on the original definition of 4-weighted fractional Fourier transform (4-WFRFT). The multi-parameters expression of weighting coefficients are given. Moreover, the 4-WFRFT of discrete sequences is defined by introducing DFT into it, which makes it suitable for digital communication systems. After analyzing the properties of WFRFT, a typical scheme for modulation/demodulation is proposed, which could make the statistics properties of the real and image part on both of the time and frequency domain and the phase properties have a significant variation. Such a variation could be controlled by the adjustment of transform parameters. If the WFRFT of multi-parameters is implemented, it will be more difficult to intercept and capture the modulated signals than normal.

Research on the application of 4-weighted fractional Fourier transform in communication system

A hybrid carrier (HC) system employing a frequency domain linear equalization based on minimum mean square error (MMSE) criterion is analyzed in this letter. The analytical studies prove that HC modulation scheme achieves a trade-off between circularly prefixed orthogonal frequency division multiplexing (OFDM) and single-carrier (SC) systems in terms of resisting doubly-selective fading. By dispersing the aggregated residual interference effectively, the HC system with particular modulation orders outperform OFDM and SC systems within a specific signal noise ratio (SNR) interval. Both analysis and simulation results over a typical double selective fading channel verify the superiority of HC modulation in suppressing residual interferences.

Lin Mei

Papers

Closed-Form BER Expressions of QPSK Constellation for Uplink Non-Orthogonal Multiple Access

The approach to carrier scheme convergence based on 4-weighted fractional fourier transform

WFRFT Precoding for Narrowband Interference Suppression in DFT-Based Block Transmission Systems

Research on the application of 4-weighted fractional Fourier transform in communication system

Performance Analysis of Hybrid Carrier System with MMSE Equalization over Doubly-Dispersive Channels