Generalized Frequency Division Multiplexing Research Articles

An analysis of low complexity of 5G-MIMO communication system based CR using hybrid filter detection

The exponential growth in wireless communication has resulted in a high demand for novel wireless services within the frequency bands that can deal with the challenge pertaining to the current spectrum shortage. Thus, a 5G-MIMO based CR communication system has been developed to enhance the spectrum by employing a spectrum sensing (SS) algorithm. This recommended SS algorithm, based on the hybrid filter detection (HFD) method, employs the Cosine law for filtering the traffic signal, and then enables segmentation by applying the Welch algorithm. Then, the Hann algorithm is employed to window the traffic signal, and facilitates damping the MIMO impact for different waveforms. This also includes universal filtered multi-carrier (UFMC), filtered-orthogonal frequency division multiplexing (F-OFDM), filter bank multi-carrier (FBMC), non-orthogonal multiple access (NOMA), and Generalized Frequency Division Multiplexing (GFDM) waveforms. Also, evaluation of the operating parameters such as SNR, the antenna count, the signal span, and power as well as computational complexity was done. Based on the simulation results, a notable achievement was seen for the parameters that were below 0 dB of SNR, <0.09 % global system error probability, >96 % global detection probability, <0.06 % global false alarm probability, and possessing simple complexity. The recommended system’s parameters were assessed, which demonstrated its superiority versus other previously developed systems. This algorithm was found to identify all types of 5G signals and not just one type of 5G.

Review on Radio over Fiber Systems for Capacity Enhancement

Radio-over-fiber (RoF) system is one of the latest plans for future wideband wireless communication systems like mobile communications, suburban and residential areas. These are good nominees to build the backbone of the next generation of wireless networks. Besides, the fundamental requirement for next-generation radio optical fiber and mobile communication is the need for more capacity and speed which has a huge scope, that is further required for a better system to attain demands such as Fiber to The Home (FTTH) and 5G. The combination of RoF with spectrally-efficient modulation techniques can accomplish increasing demand for high data rates for mobile users. Currently, analog fronthaul is promoted as an energy-efficient and bandwidth solution that can reach the necessity of the 5G vision for high data rates, low latency, and energy efficiency. Mainly, this paper presents a review that focuses on various techniques which several approaches have been listed to perceive the large-capacity data transmission and describe them including Wavelength Division Multiplexing (WDM), Subcarrier Multiplexing (SCM), Mode Division Multiplexing (MDM), Polarization Division Multiplexing (PDM), Generalized Frequency Division Multiplexing (GFDM), Parallel&nbsp; Intensity Modulation (PIM)/Phase Modulation (PM) transmitter, and Millimeter-wave (Mm wave) generation techniques. Also, a comparison between them has been done

Pulse Based GFDM Modulation Technique for Future Generation Communication Systems

Future mobile communication systems are mainly focused on flexibility, reliability, scalability, spectral efficiency, and robustness. A higher data rate, increased capacity, higher mobility, lower latency, and improved quality are prime objectives that need to be improved in future communication systems. This paper investigates generalized frequency division multiplexing (GFDM), a suitable waveform candidate for future communication systems. It has low complexity compared to FBMC and is highly suitable for burst signal transmission. Due to the use of non-rectangular pulse shaping, out-of-band leakage is also less. This technique is more flexible in terms of frequency localization, scalability, and integration with MIMO. Its performance in terms of BER has been computed considering the number of subcarriers, number of sub-symbols, input power back-off, and roll-off factor as variable parameters. It has been observed that change in the BER is low when the number of sub-carriers is changed but is more for change in the number of sub-symbols. Its performance degrades when the number of subcarriers, the value of the roll-off factor, and the power back-off are increased. But BER performance improves with an increase in the number of sub-symbols.

MIMO spread spectrum GFDM communication systems with index modulation

SummaryIn the fourth‐generation communication system (4G), orthogonal frequency division multiplexing (OFDM) is widely used. However, due to the cyclic prefix (CP) being added, the low spectrum efficiency and high out‐of‐band radiation (OOB) cause OFDM not to be suitable for the beyond fifth‐generation (B5G) communication system. Therefore, to meet the rigorous demands in B5G for the Internet of Things (IoT) and massive machine‐type communications (MMTC), generalized frequency division multiplexing (GFDM) technology has received significant attention. On the other hand, index modulation (IM) can provide flexible settings of different parameters to achieve the ideal system goals. Therefore, this paper considers the combination of spread spectrum (SS) and IM under the framework of GFDM, called SS‐IM‐GFDM. In this scheme, the information bits are jointly conveyed by the indices of spreading codes and the conventional M‐ary modulated symbols, which increase the spectrum efficiency and improve the bit error rate performance. Furthermore, a low‐complexity maximum likelihood (ML) detector is proposed to recover the transmitted signal effectively at the receiver. Finally, the space‐time block code (STBC) is employed to construct the multi‐input multi‐output SS‐GFDM‐IM (MIMO SS‐GFDM‐IM) system to improve the system's reliability. The simulation results show that the proposed scheme is superior to the existing systems.

An efficient SLM technique based on chaotic biogeography-based optimization algorithm for PAPR reduction in GFDM waveform

ABSTRACT High data rates, extremely low power consumption, and minimal end-to-end latency are considered to be mandatory requirements for 5G wireless networks. Rapid improvements in design and performance of 5G physical layer waveforms have become necessary. The drawback of Orthogonal Frequency Division Multiplexing (OFDM) is high PAPR, that causes signal distortion, which reduces system efficiency. Generalized frequency division multiplexing (GFDM) is a promising non-orthogonal multicarrier transmission scheme, which has recently received a great deal of attention towards future fifth generation (5G) wireless networks. It overcomes the limitations of orthogonal frequency division multiplexing (OFDM), while preserving most of the advantages of it. Selective Level mapping (SLM) is one of the PAPR reduction techniques, that uses the phase shift technology. In this paper, SLM based on Chaotic Biogeography Based Optimization (CBBO) algorithm is proposed to offer an efficient solution to the problem of high PAPR, existing in the GFDM waveforms. Experimental results prove that, the proposed CBBO–SLM technique provides significant improvement in terms of PAPR reduction, as compared to the conventional SLM methods, such as conventional GFDM and OFDM-SLM. The proposed novel scheme is most suitable for QAM and QPSK applications, as it provides good PAPR reduction performance, at lower computational complexity.

Performance analysis of modulation techniques in 5G communication system

In the 5 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">th</sup> generation mobile communication (5G) system, better bitrate, better power consumption, and better Bit Error Rate are needed. To meet all these requirements in 5G, the waveform is important. Although the Orthogonal Frequency Division Multiplexing (OFDM) modulation scheme has been commonly used in 4G, it is difficult to meet the requirements of 5G. A lot of candidate waveforms are discussed in the 5G system included Filter Bank Multicarrier (FBMC), Universal Filtered Multicarrier (UFMC), Filtered OFDM (F-OFDM), and Generalized Frequency Division Multiplexing (GFDM), etc. However, since GFDM is no longer widely used, in this paper, FBMC, UFMC, and F-OFDM modulation schemes are discussed and compared with OFDM. Power Spectral Density (PSD), Bit Error Rate (BER), Transmitted Signal Power, Peak Average Power Ratio (PAPR) and Bit Rate parameters of the modulation schemes are studied and compared with OFDM. FBMC demonstrates to be the most promising modulation scheme for 5G systems.

QAM-DMT of Hybridly Integrated EAM-DFBLD Chip-on-Board With Adaptive Machine Learning Algorithm for 149.6-Gbit/s BtB and 138-Gbit/s 10-km-SMF Transmission

By using the generalized frequency division multiplexing (GFDM) and the machine learning algorithm for self-feedback amplitude/phase pre-distortion, the electro-absorption modulator integrated distributed-feedback semiconductor laser diode (EAM-DFBLD) is encoded with improved transmission quality and capacity. Both back-to-back (BtB) and 10-km single-mode fiber (SMF) transmissions are preliminarily demonstrated for inter-data-center applications. Optimizing the EAM-DFBLD transmitter at 1306.8 nm with a bias current of 100 mA and a bias voltage of −1.5 V can provide a 34.5-GHz bandwidth for 16-QAM discrete multitone (DMT) and GFDM formats. The parametric comparison reveals that the 16-QAM GFDM with <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">K</i> = 16 can improve its performance from BtB to 10-km SMF transmission with decoding BER slightly increasing from 1.44 × 10 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">−3</sup> to 2.82 × 10 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">−3</sup> . The EAM-DFBLD carried GFDM data also provides a better power penalty by -0.25 dB. This enables higher raw data rates of 149.6 Gbit/s under BtB case and 138 Gbit/s in 10-km SMF transmission link below the forward error correction (FEC) criterion. The GFDM format carried by the EAM-DFBLD transmitter thus becomes the more suitable candidate than the DMT to implement ultra-high-speed inter-data-center and data access link applications.

F-OFDM in a novel form for analyzing 5G networks

The need for internet of things (IoT) and machine-to-machine communication (MTC) has been growing rapidly all across the world. To meet the client's needs, many literature reviews were undertaken in several countries. Orthogonal frequency division multiplexing (OFDM), Universal Filtered Multi-Carrier (UFMC), filter-bank multicarrier offset construction amplitude modulation (FBMC-OQAM), generalized frequency division multiplexing (GFDM), and others are candidates for LTE, LTE advance, and 5G, according to the majority of the researchers. However, because it is sensitive to propagation and noise, such as amplitude, with a huge dynamic range, it requires RF power amplifiers with a high peak to average power quantitative relationship; consequently, it is not recommended for LTE, LTE advance, or 5G. As a result, the same concerns were addressed by introducing innovative type filtered orthogonal frequency division multiplexing (F- OFDM), which was the subject of this study. In addition, F-OFDM mathematical models were constructed and simulated in the MATLAB software environment. To validate the proposed innovative F-OFDM, OFDM was compared. For innovative F-OFDM, the simulated result was 0.00083333 bit error rate (BER). Furthermore, the bit error rate (BER) of F-OFDM over OFDM was 89.4 percent, and the peak to average power ratio was 17 percent. The simulation results unmistakably show that the suggested innovative F-OFDM is the greatest fit for LTE, LTE advanced, and 5G contenders.

Hyperchaotic Modulo Operator Encryption Technique for Massive Multiple Input Multiple Output Generalized Frequency Division Multiplexing system

Hyperchaotic Modulo Operator Encryption Technique for Massive Multiple Input Multiple Output Generalized Frequency Division Multiplexing system

Analysis of GFDM in generalized [formula omitted] fading channel: A simple probability density function approach for beyond 5G wireless applications

Generalized frequency division multiplexing (GFDM) is a flexible radio waveform which offers high degree of freedom in varying the number of time slots, number of subcarriers, and pulse shaping filters. In addition to this, it also covers orthogonal frequency division multiplexing (OFDM) and single carrier frequency domain equalization (SC-FDE) as corner cases. A well-known fact is that the performance of a wireless communication system is predominately effected by the characteristics of the fading environment. In this paper, symbol error rate (SER) closed-form expression of GFDM system under the generalized η−μ fading channel is derived. The proposed derivation includes Rayleigh, Nakagami-m, and Nakagami-q fading channels as special cases. A Mote-Carlo simulation test-bed is carried out using MATLAB to compare with analytical results and to validate the derived expressions based on the probability density function (PDF) approach. Further, this paper investigates the performance of the GFDM system by varying various parameters such as fading values, pulse shaping filters, roll-off factor, and modulation order. The detailed analysis suggests that the probability of SER is highly dependent on the above parameters. The results obtained are more useful in evaluating the performance of GFDM based communication system in a generalized manner.

Physical Layer Performance Modeling of Modern Multicarrier Modulation Techniques

The fifth-generation (5G) and beyond standards are being challenged by the diverse requirements of modern use cases. Multicarrier modulation techniques are one of the key components of the physical layer (PHY) design, which has immense potential to improve efficiency and reliability. In current state-of-the-art wireless technologies (i.e., NR and IEEE 802.11ax) orthogonal frequency division multiplexing (OFDM) is used which has many disadvantages such as peak-to-average power ratio (PAPR), out-of-band emission (OOBE), and sensitivity to carrier frequency offset (CFO). To overcome these drawbacks several alternate multicarrier modulation techniques are being considered, such as discrete Fourier transform-spread-OFDM (DFT-s-OFDM), generalized frequency division multiplexing (GFDM), and orthogonal time-frequency space (OTFS). In this paper, we develop the physical layer abstraction (PLA) of these candidate multicarrier techniques to evaluate their performance under various use cases and scenarios. The PLA is a commonly used technique to avoid time-consuming PHY simulations in system-level simulators. To improve the accuracy of PLA in different fading conditions, we derive a fitting parameter as a function of the received signal-to-interference-plus-noise ratio (SINR) variance. The validation results show that performance can be accurately estimated through the proposed multicarrier PLA. Moreover, PLA techniques are at least thousands of times faster compared to PHY simulations.

Low-complexity MU-MIMO-GFDM joint receivers

ABSTRACT The Multiple-Input Multiple-Output (MIMO) scheme uses multiple antenna configurations to achieve high throughput data transmission in current communication systems. The new generation wireless communication system considers using generalised frequency division multiplexing (GFDM) due to its advantages such as lower out-of-band (OOB) emission and peak-to-average power ratio (PAPR), etc. However, inter-symbol interference (ISI) and inter-carrier interference (ICI) occur due to GFDM utilises the pulse shaping filter. This paper proposes a low-complexity joint minimum mean square error (MMSE) receiver to suppress ISI, ICI, and multi-user interference (MUI) for multi-user MIMO-GFDM (MU-MIMO-GFDM) system. The conventional approach is to design the equalisation and the GFDM demodulation separately. This paper jointly designs the equalisation and demodulation process that significantly reduces the complexity and enhances the error rate performance. This paper also analyzes the closed-form expression and two low-complexity methods for the proposed receiver. The simulations demonstrate the effectiveness of the proposed low-complexity multi-user MIMO-GFDM receivers.

Performance analysis of LDPC coded GFDM systems

This paper analyzes the error probability performance of low-density parity-check (LDPC) coded generalized frequency division multiplexing (GFDM) systems over Rayleigh fading and additive white Gaussian noise (AWGN) channels. The initial log-likelihood ratio (LLR) expressions used in the sum-product algorithm (SPA) decoder are first derived for the system model presented in this paper. Based on the decoding threshold of the system, the frame error rate (FER) in the low E b / N 0 $E_b/N_0$ region is estimated by modeling the channel variations using the observed bit error rate (BER). Then, a lower bound based on the absorbing sets is proposed for FER when quantized SPA decoders are used. For AWGN channels, the lower bound can act as an estimate of the FER in the error-floor region if the absorbing set is dominant and its multiplicity is known. For Rayleigh channels, the lower bound can still be used to estimate the FER performance of selected codes. The estimation approach for the FER in the low E b / N 0 $E_b/N_0$ region and the lower bound on the FER in the high E b / N 0 $E_b/N_0$ region can be used as practical tools for evaluating different designs of GFDM-based systems in terms of the error probability performance. The quantization scheme has an important impact on the FER and BER performances. Randomly constructed and array-based LDPC codes are used to obtain numerical results that show the system performance and the accuracy of the proposed FER estimations.

Design and performance evaluation of FBMC-based Orthogonal Time–Frequency Space (OTFS) system

The idea of an efficient multicarrier signaling technique is one of the critical challenges for beyond fifth-generation (B5G) of wireless communication networks. The B5G mobile networks require the multicarrier scheme featuring, immunity to multipath fading and inter-symbol interference (ISI), robustness against inter-carrier interference (ICI) and Doppler spread to outreach their purposes. Several Filter-based techniques such as Filter Bank Multicarrier (FBMC) and various Orthogonal Frequency Division Multiplexing (OFDM)-based techniques such as Universal Filtered Multicarrier (UFMC) and Generalized Frequency Division Multiplexing (GFDM) are proposed in recent studies. Besides, Orthogonal Time–Frequency Space (OTFS) technique is introduced newly as one of the potential waveform nominees for B5G which can outperform OFDM-based techniques in high mobility situations. One of the prominent benefits of the OTFS method is that it can be regarded as the pre- and post-processing steps for OFDM-based techniques. In this paper, we extended the FBMC scheme using the OTFS technique and propose a novel structure as FBMC-based OTFS technique which benefits from both strategies while reducing their deficiencies. Our concluded analyses and results can certificate our system superiority in error probability and time-spectral efficiency terms where the FBMC-based OTFS employing different types of filters are compared to the OFDM-based OTFS system.

Coded-GFDM for Reliable Communication in Underwater Acoustic Channels.

The performance of the coded generalized frequency division multiplexing (GFDM) transceiver has been evaluated in a shallow underwater acoustic channel (UAC). Acoustic transmission is the scheme of choice for communication in UAC since radio waves suffer from absorption and light waves scatter. Although orthogonal frequency division multiplexing (OFDM) has found its ground for multicarrier acoustic underwater communication, it suffers from high peak to average power ratio (PAPR) and out of band (OOB) emissions. We propose a coded-GFDM based multicarrier system since GFDM has a higher spectral efficiency compared to a traditional OFDM system. In doing so, we assess two block codes, namely Bose, Chaudari, and Hocquenghem (BCH) codes, Reed-Solomon (RS) codes, and several convolutional codes. We present the error performances of these codes when used with GFDM. Furthermore, we evaluate the performance of the proposed system using two equalizers: Matched Filter (MF) and Zero-Forcing (ZF). Simulation results show that among the various block coding schemes that we tested, BCH (31,6) and RS (15,3) give the best error performance. Among the convolutional codes that we tested, rate 1/4 convolutional codes give the best performance. However, the performance of BCH and RS codes is much better than the convolutional codes. Moreover, the performance of the ZF equalizer is marginally better than the MF equalizer. In conclusion, using the channel coding schemes with GFDM improves error performance manifolds thereby increasing the reliability of the GFDM system despite slightly higher complexity.

A Novel Selective Mapping Method based on Cumulative Symbol Optimization for PAPR Minimization in Low Complexity GFDM Transmitter

In this paper, the problem of high peak-to-average power ratio (PAPR) in the low complex version of the generalized frequency division multiplexing (LC-GFDM) is handled by developing a novel PAPR reduction method called cumulative symbol optimization-selective mapping (CSO-SLM). With this new method, the disadvantage caused by the symbol addition process that greatly reduces the SLM performance in the LC-GFDM transmitter was eliminated thanks to the combination of SLM technique with the cumulative symbol optimization procedure. In order to demonstrate the benefit of integrating the CSO procedure into the SLM scheme, our proposed CSO-SLM strategy was compared to the conventional SLM technique with regard to both PAPR reduction and power spectral density (PSD) performance in the simulations. Moreover, the CSO-partial transmit sequence (CSO-PTS) technique, which was specially developed for the LC-GFDM system as the CSO-SLM strategy, and a robust PAPR reduction method named GreenOFDM were also used for comparison. According to the simulation results, the proposed CSO-SLM technique clearly outperforms each of the benchmark strategies considered in this paper by leaving them behind with regard to the amounts of PAPR and PSD improvements achieved in the LC-GFDM transmission signal.

Evaluation of cooperative spectrum sensing with filtered bank multi carrier utilized for detecting in cognitive radio network

AbstractCognitive radio (CR) is defined as a procedure that uses the range with and without impedance. Elements of psychological radio systems incorporate spectrum sensing, spectrum sharing, spectrum mobility and spectrum decision. This manuscript proposes cooperative spectrum sensing (CSS) with filtered bank multi carrier (FBMC) in cognitive radio network (CRN) for mitigating the interference with proficient bandwidth utilization. Here, five primary users (PU) and one secondary user (SU) are considered. The secondary user occupies the slot only in the absence of primary user. During cooperative spectrum sensing with FBMC evaluation, it produces problem in hidden terminal, false alert and auxiliary client identification with effective radio spectrum sharing for the secondary users, which automatically reduces the channel capacity, energy efficiency, and channel interference. To overcome the issues, optimal red deer algorithm (ORDA) is used in FBMC Weight parameters. The proposed method is executed in MATLAB platform. The simulation outcomes demonstrate that the performance of the proposed CSS‐FBMC‐ORDA has high efficiency with less error rate. The proposed CSS‐FBMC‐ORDA attains higher efficiency of 3.99%, 8.90%, and 4.09%, higher reliability of 5.66%, 9.44%, and 2.43%, lower bit error rate (BER) of 4.756%, 4.86%, and 8.97% when compared with the existing methods, such as spectrum resource optimization for non‐orthogonal multiple access (NOMA) based cognitive radio at 5G communications joint optimization algorithm (JOA) (CSS‐CRN‐NOMA‐JOA), maximizing the total throughput for generalized frequency division multiplexing (GFDM) system using hybrid particle swarm optimization (PSO)‐pattern search (PSO‐PS) approach (CSS‐CRN‐GFDM‐Hyb PSO‐PS), energy efficiency for various spectrum sensing scenarios using a novel hybridization of particle swarm optimization (PSO) with gravitational search algorithm (GSA) (CSS‐CRN‐OFDM‐Hybrid PSO‐GSA) respectively.

Energy-Efficient Resource Allocation for Simultaneous Wireless Information and Power Transfer in GFDM Cooperative Communications

Simultaneous wireless information and power transfer (SWIPT) for generalized frequency division multiplexing (GFDM) cooperative communications is proposed to save consumed energy of relay and destination. GFDM subsymbols are allocated for information decoding (ID) and energy harvesting (EH), respectively. Energy efficiency of SWIPT based GFDM system is maximized by jointly optimizing subsymbol and power allocations for ID and EH. A joint optimization algorithm is proposed to obtain the optimal solution to the energy-efficiency optimization problem. Simulation results show that energy efficiency of this scheme is 5bps/J/Hz higher than that of power-splitting SWIPT at total transmit power of 5mW.

Novel Successive Interference Cancellation (SIC) With Low-Complexity for GFDM Systems

Generalized frequency-division multiplexing (GFDM) is one of the promising multi-carrier modulation schemes suitable for next-generation wireless communication systems. The main characteristic of GFDM is the flexible time-frequency structure of data blocks. However, this degree of freedom is obtained at the cost of loss of sub-carrier orthogonality, which leads to self-interference. In this paper, we propose a new model that classifies the GFDM self-interferences into two independent categories as inband and adjacent sub-carriers interferences and show their corresponding mathematical formulations. Building on this model, we propose a successive interference cancellation (SIC) technique with low complexity to eliminate these self-interference effectively. The main distinct feature of our proposed technique is its low computational complexity compared to similar interference cancellation techniques. Our analytical findings and numerical experiments indicate that the proposed model and SIC technique considerably improve the system performance in terms of bit error rate (BER) and signal to interference ratio (SIR). We also show that the results of our analytical findings are in good agreement with those of computer simulations.

Low-Complexity Detection Algorithms Applied to FTN-GFDM Systems

New applications for mobile networks are pushing the data rates to higher numbers, requiring new solutions to support the demand for throughput. In urban and dense areas, the use of massive multiple-input multiple-output, high bands in millimeter waves, and ultra-dense networks based on small cells are being used to provide high data rates. However, these solutions are not applicable to the enhanced remote areas communications scenario, where large cells must be deployed using vacant VHF or UHF bands using an opportunistic spectrum allocation approach. In this case, one reasonable solution to increase the overall system data rate is to enhance the waveform spectrum efficiency. This paper proposes a scheme to improve the generalized frequency division multiplexing spectral efficiency by exploiting the faster-than-Nyquist principles in the time and frequency domains without introducing any penalties in terms of bit error rate. This achievement is obtained by under-sampling the time-frequency grid, which results in transmitting more data symbols per waveform sample, while introducing a controlled amount of interference in the transmitted waveform. On the receiver side, low complexity detectors, such as sphere decoder, successive symbol-by-symbol sequence estimation, successive symbol-by-symbol with go-back K sequence estimator, and frequency-domain equalization, can be used to reconstruct the transmitted data. This paper presents the details for adapting the mentioned detectors for the proposed waveform and it also analyzes their performance in terms of bit error rate under different channel models and implementation complexity. From all the detectors considered in this paper, the sphere decoder stands out because it presents an interesting tradeoff between complexity and bit error rate, even in high interference scenarios. Other detection schemes initially proposed for multiple-input multiple-output systems can be adapted to deal with the interference introduced by the faster-than-Nyquist generalized frequency division multiplexing with affordable complexity and acceptable bit error rate performance. Hence, one may conclude that the faster-than-Nyquist generalized frequency division multiplexing is a feasible candidate waveform for the enhanced remote areas communications scenario when high spectrum efficiency is necessary.