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The fourth Industrial Revolution is expected to lead to an era of technological innovation and digitization that would require connectivity by the users, anywhere and anytime. The fifth generation of wireless communication systems and the technologies therein are being explored to cater to high connectivity needs that encompass high data rates, very low latencies, energy-efficient systems, etc. A multiuser environment is anticipated that would require multiple access techniques, such as Nonorthogonal Multiple Access (NOMA). The user data in the power domain NOMA is superimposed, at the transmitter base station, which is in turn subjected to Successive Interference Cancellation at the user end. In the multiuser downlink, the desired user’s signal is subjected to imperfect SIC due to incomplete cancellation of the undesired user’s signal. Pulse-shaping of NOMA symbols using wavelet transform is proposed to mitigate the multiuser interference due to imperfect SIC. Closed-form symbol error rate (SER) expression is derived for the wavelet NOMA system for a three-user scenario. Analytical results show that wavelet transform pulse-shaped NOMA performs better compared to Fourier transform pulse-shaped NOMA symbols in mitigating SIC and thereby minimize the residual error due to imperfect SIC.

The number of wireless devices connected to the network is growing to billions, and the fifth-generation mobile communication networks (5G) is envisaged to cater to massive connectivity, high data rate with high reliability [

Although, mmWave frequencies are yet to be standardized, still 30 to 300 GHz spectrum could be the best option for 5G mobile networks [

In downlink NOMA, most of the researchers consider Fast Fourier transform-based Orthogonal Frequency Division Multiplexing (FFT-OFDM) as a pulse shaping technique [

To the best of our knowledge, none of the works in literature has evaluated wavelet NOMA performance for more than two users. Moreover, perfect SIC conditions are considered in the prior works for wavelet NOMA, which implies that undesired user’s signals are completely subtracted until the desired signal is recovered [

The rest of the paper is organized as follows: Section

The selection of a suitable pulse-shape plays an important role in the system’s complexity and other communication-related problems such as channel dispersion. Communication systems based on the OFDM technique possess many features, including receiver design with lower complexity, robustness to multipath delay spread, compatibility of MIMO systems, and simple equalizers.

In the cited literature, a typical NOMA system model comprises of two users in which User 1 is considered as the far user while the other is near to the base station (BS). In this research work, three user NOMA system model is considered that includes an intermediate user in addition to the far and the near user. By applying a superimposed algorithm, each user’s data is allocated with different power levels and converted into a single data stream, authorizing multiplexing of all the three users in a nonorthogonal way over the wireless communication channel as shown in Figure

System model for wavelet pulse-shaped NOMA.

The focus of this work is the influence of interference between User 2 and User 3 on their communication error rate. In the case of imperfect estimation of User 3 and User 1 channel, incomplete SIC at the receiver will result in a residual error. To mitigate this effect of incomplete SIC, wavelet filter banks are proposed in our system model. The three-user system model for both FFT-NOMA and W-NOMA is presented in this section. Figure

Transceiver design for wavelet pulse-shaped NOMA.

In this article, researchers have analysed the performance of the wavelet-based wireless communication system because it inherits some useful advantages compared to OFDM. Wavelet uses short waveforms to form an orthogonal base in comparison with OFDM applications that make it robust to suppress the ISI and ICI. Usually, wavelets are used for the multiresolution analysis of signals or images. Our focus is to reduce the power of interferences that have to be calculated according to the definition of ISI and ICI [

where,

and

These interferences occur because of imperfect SIC and CSI at the receiver side, and it can be reduced to the minimum as wavelets offer additional flexibility in signal reconstruction. The data

Magnitude response of FFT and wavelet filters.

In the literature [

here,

In the following discussion, assumptions of contribution are briefly explained to assess the SER performance of near, intermediate, and far users with perfect and imperfect CSI conditions in the downlink NOMA. Assuming QPSK modulation, power factors are allocated to each user based on the channel gains

Signal-space diagram for three users (QPSK).

User 1 and User 2 constellations are grouped, shown by the elliptical circles in Figure

The closed-form SER for traditional NOMA is a function of symbol energy to noise ratio. To evaluate the exact form of SER, it is essential to find the value of noise, i.e., channel noise and multiuser interference that affects the demodulation process. Consider a three-user case, where users are equally spaced, and the channel gain of three users are in the order that User 1 is with the worst channel condition, and User 2 interfere with User 1 and User 3 both. The channel conditions are expressed as

Most of the literature work assumes a perfect SIC scenario, which is one of the key aspects in realizing the performance gain of NOMA technology [

where

where

since User 1 is the far user and can decode its data by treating User 2 and User 3 signal as noise. The desired signal is expressed as,

While for the SIC performing users, due to imperfect channel conditions, the SIC leads to the residual error, affecting the SER of the intended user. Thus, User 2 will perform SIC to decode User 1 data from the composite signal, and there will remain some residual data of User 1 which can be expressed as,

After performing SIC, the signal at User 2 can be expressed as,

So, if we consider the three users’ case, then the signal after SIC at the User 3 will be given as,

From (

The output of the DWT filter bank is given as,

On similar lines, SER expressions are derived for

In this article, the authors presented the work including mathematical analysis of three users for NOMA system under imperfect SIC constraint and thus preference is given to the numerical results. Specifications for the system of a three user NOMA are described in Table

Parameters for the simulation of wavelet-OFDM and FFT-based NOMA.

Parameters | Value | Parameters | Value |
---|---|---|---|

Wavelet levels | 4 | Number of subchannels | 512 |

Wavelet family | Daubechies | Cyclic prefix | 25% |

Available BW (wavelet) | 100% | Available BW (FFT) | 75% |

Modulation scheme | QPSK | SIC | Imperfect |

Number of users | 3 | Near user channel gain | 0, -5 dB |

Intermediate user channel gain | -5, -10 dB | Far user channel gain | -10, -15 dB |

Residual error at the intermediate and near user using FFT-NOMA.

SNR in dB | -10 | -5 | 0 | 5 | 10 |
---|---|---|---|---|---|

Residual error (intermediate user) | 0.2023 | 0.1504 | 0.0781 | 0.0058 | |

Residual error (near user) | 0.1452 | 0.1106 | 0.0565 | 0.0024 |

Residual error at the intermediate and the near user using wavelet NOMA.

SNR in dB | -10 | -5 | 0 | 5 | 10 |
---|---|---|---|---|---|

Residual error (intermediate user) | 0.1736 | 0.1195 | 0.0625 | 0.0055 | |

Residual error (near user) | 0.0814 | 0.0511 | 0.0255 |

Comparing Tables

Furthermore, for relatively poor channel conditions where channel gains at 10 dB with FFT-noise, the absolute value of the residual error for User 3 is

Moreover, Figure

SER comparison of three users without FFT or wavelet filters.

SER comparison of three users with imperfect SIC for wavelet NOMA and FFT-NOMA.

For future wireless communication networks, wavelet is gaining popularity in communication system design [

For the next-generation (5G/B5G) wireless communication technology, NOMA is presented in the literature as a promising multiple access scheme. In 5G, limited bandwidth can be efficiently used by implementing NOMA utilizing the user’s channel conditions and QoS requisites, while for channel impairments and imperfect SIC, current research has already proved the ability of wavelet NOMA to increase system throughput and efficiency. Closed-form SER expressions for three users, that are equally spaced with each other, are already shown. Numeric results show that wavelet filter banks help to detect and demodulate the signal better than the FFT-based NOMA system for imperfect CSI conditions. Further studies can be carried out to validate the mathematical model of the assumption to compare the analytical and theoretical findings using a cooperative relay sharing network. MIMO NOMA and FD-NOMA can be studied for the most suitable wavelet filter banks to improve 5G system performance.

The data that support the findings of this study are available from the corresponding author upon reasonable request.

The authors declare that they have no conflicts of interest.

The authors would like to acknowledge the Energy Research Center, COMSATS University Islamabad, Lahore Campus, and SQU for their support and encouragement throughout. The research reported in this publication was partly funded by the Natural Sciences and Engineering Research Council of Canada (NSERC) of Canada and the in-kind support of the University of Waterloo, Ontario, Canada.