Non-orthogonal Frequency Division Multiplexing Research Articles

Adaptive multi-band modulation for robust and low-complexity faster-than-Nyquist non-orthogonal FDM IM-DD systems

Faster-than-Nyquist non-orthogonal frequency-division multiplexing (FTN-NOFDM) has been shown to have good robustness against the steep frequency roll-off in a bandwidth-limited optical communication system. Among various FTN-NOFDM techniques, the non-orthogonal matrix precoding (NOM-p) based FTN has relatively high compatibility, which can easily utilize the existing advanced digital signal processing (DSP) techniques in the conventional OFDM. In this work, we propose what we believe to be a novel FTN-NOFDM scheme with adaptive multi-band modulation. By dividing the single-band NOM-p into multiple-band NOM-p, the proposed scheme is able to assign different quadrature amplitude modulation (QAM) levels to different sub-bands, leading to better utilization of the low-pass-like channel as well as reduced computational complexity. The impacts of sub-band number and bandwidth compression factor on the bit-error-rate (BER) performance and complexity are experimentally analyzed in a 32.23-Gb/s and 20-km intensity modulation-direct detection (IM-DD) optical transmission system. Results show that the proposed scheme with a proper sub-band number can lower the BER and greatly reduce the complexity compared to the conventional single-band scheme.

Machine Learning-Based Non-Orthogonal Frequency Division Multiplexing for Data Overlay Transmission and Reception

Machine Learning-Based Non-Orthogonal Frequency Division Multiplexing for Data Overlay Transmission and Reception

Half-spectrum OFDM to quadruple the spectral efficiency of underwater wireless optical communication with digital power division multiplexing.

Improving the spectrum efficiency (SE) is an effective method to further enhance the data rate of bandwidth-limited underwater wireless optical communication (UWOC) systems. Non-orthogonal frequency-division multiplexing (NOFDM) with a compression factor of 0.5 can save half of the bandwidth without introducing any inter-carrier-interference (ICI) only if the total number of subcarriers is large enough, and we termed it as half-spectrum OFDM (HS-OFDM). To the best of our knowledge, this is the first reported work on a closed-form HS-OFDM signal in the discrete domain from the perspective of a correlation matrix. Due to the special mathematical property, no extra complex decoding algorithm is required at the HS-OFDM receiver, making it as simple as the conventional OFDM receiver. Compared with traditional OFDM, HS-OFDM can realize the same data rate, but with a larger signal-to-noise ratio (SNR) margin. To fully use the SNR resource of the communication system, we further propose a digital power division multiplexed HS-OFDM (DPDM-HS-OFDM) scheme to quadruple the SE of conventional OFDM for the bandwidth-starved UWOCs. The experimental results show that HS-OFDM can improve the receiver sensitivity by around 4dB as opposed to conventional 4QAM-OFDM with the same data rate and SE. With the help of the DPDM-HS-OFDM scheme, the data rate of multi-user UWOC can reach up to 4.5Gbps under the hard-decision forward error correction (HD-FEC) limit of a bit error rate (BER) of 3.8×10-3. Although there is some performance degradation in comparison with single-user HS-OFDM, the BER performance of multi-user DPDM-HS-OFDM is still superior to that of conventional single-user 4QAM-OFDM. Both single-user HS-OFDM and multi-user DPDM-HS-OFDM successfully achieve 2Gbps/75m data transmission, indicating that the DPDM-HS-OFDM scheme is of great importance in bandwidth-limited UWOC systems and has guiding significance to underwater wireless optical multiple access.

Dual-Mode Index Modulation for Non-Orthogonal Frequency Division Multiplexing

This paper presents dual-mode index modulation for spectral efficient frequency division multiplexing (SEFDM-DM). SEFDM is a non-orthogonal multicarrier technique created by compressing the subcarrier spacing of classical orthogonal frequency-division multiplexing (OFDM). SEFDM provides high spectrum efficiency (SE) at the expense of increased inter-carrier interference (ICI). SEFDM with index modulation (SEFDM-IM) has two information-bearing units, that is, a subcarrier activation pattern and modulated symbols, which reduce ICI at the expense of an SE deficit owing to inactive subcarriers. The proposed SEFDM-DM uses all available subcarriers while retaining the diversity gain of index modulation (IM). It enhances SE by transmitting distinct constellation modes through a subcarrier index selection mechanism. This study also presents SEFDM-DM with coordinate interleaving (SEFDM-CDM), which introduces space-time block codes with coordinate interleaving to enhance transmission diversity by sending real and imaginary parts of the constellation symbols over different subcarriers. Analytical and simulation results corroborate the benefits of the suggested work in terms of SE and bit error rate.

On the Achievable Spectral Efficiency of Non-Orthogonal Frequency Division Multiplexing

On the Achievable Spectral Efficiency of Non-Orthogonal Frequency Division Multiplexing

Time-Reversal CNN-Based S-NOFDM Scheme for Underwater Acoustic Communication

Multicarrier modulation shows the advantages of improving bandwidth efficiency in underwater acoustic (UWA) communications, whereas the more spectrum-efficient nonorthogonal frequency division multiplexing (NOFDM) is seldom investigated in the underwater scenario. The main idea of the NOFDM is to use overlapped subcarriers for increasing spectral efficiency. However, the NOFDM suffers from severe distortions both in the time and frequency domains because of the UWA channel's multipath propagation and Doppler spread. Considering these problems, we propose a novel time-reversal convolutional neural network (TR-CNN) based sparse NOFDM (S-NOFDM) scheme for UWA communication. The S-NOFDM waveform is determined by solving the sparse representation of input symbols under a set of nonorthogonal subcarriers, which can allocate symbols sparser to subcarriers and reduce distortion caused by multipath propagation and Doppler spread. The proposed TR-CNN is constructed with a time-reversal (T-R) convolutional layer where the T-R process is used to deal with multipath propagation. After the received signal has passed through the T-R layer, the main path of the UWA channel strength is enhanced and the other paths are weakened. The TR-CNN is also used to learn the inherent information between S-NOFDM symbols, improving UWA channel adaptability. After the training, the proposed scheme can be applied in the real-time UWA communication implementation. The simulation and experimental results prove that the proposed scheme outperforms the traditional scheme in signal detection and recovery. It is also robust with general capabilities in various UWA channel environments.

Precoded Filterbank Multicarrier Index Modulation With Non-Orthogonal Subcarrier Spacing

In this paper, we propose a novel precoded non-orthogonal frequency division multiplexing (NOFDM) with subcarrier index modulation (SIM) to increase spectral efficiency for multicarrier systems. The proposed NOFDM-SIM scheme is constituted by a filterbank multicarrier system under reduced subcarrier spacing, where precoded index modulated symbols are mapped onto the subcarriers. The detrimental effects of inter-carrier interference (ICI) resulting from the non-orthogonality between subcarriers are efficiently mitigated with the aid of eigenvalue-decomposition-based precoding. Our simulation results demonstrate that the proposed precoded NOFDM-SIM system exhibits a similar peak-to-average power ratio to OFDM and OFDM-SIM counterparts while achieving the bit error rate limit of zero-ICI OFDM in a channel-uncoded setting. We analyze the power spectral density of the proposed scheme to demonstrate that the proposed scheme is strictly bandlimited, unlike its orthogonal counterpart. Furthermore, we present detailed investigations of the effects on ICI in the proposed scheme with and without precoding as well as power allocation. Finally, we introduce a three-stage iterative decoding architecture for our proposed scheme and show near-capacity error performance.

NOMA waveform technique using orthogonal supplementary signal for advanced 5G networks security

The rollout of the advanced communication network is going all around the world and the demands for wireless applications are increasing day by day. At the same time, the design of secured networks and efficient energy devices is considered a huge concern. In this work, we proposed an implementation of Non-Orthogonal Frequency Division Multiplexing (NOMA) for future networks in which supplementary signals are accurately implemented and spread over the peak of the subscriber signal. This method guarantees an ideal security against the external and internal intruders. In the second part of the work, we analyze and improve the battery performance of the user device by implementing a novel peak to average power ratio (PAPR) reduction algorithm. Other parameters such as Bit Error Rate (BER), PAPR are simulated using Matlab-2014. The outcomes of the work reveal that the proposed framework obtained a secured and less complicated network.

Optimal Resource Allocation for Multicarrier NOMA in Short Packet Communications

Wireless communication system needs a spectrum efficient, a power efficient and a cost efficient communication with high throughput to provide communication for ubiquities applications such as voice, data, picture, video, movies, multimedia services, Global Positional System (GPS), navigational system, telemedicine and other value added communication. Non-Orthogonal Frequency Division Multiplexing (NOMA) has become a popular technique for transmission of signals over wireless channels. In the first phase, MIMO system which uses NOMA is used. User signals are divided into parallel streams, using NOMA and are transmitted by the antenna array which propagates through the fading channel. signals are weighted using the Minimum Variance Distortionless Response (MVDR) where the weights are such that the output signal has minimum variance and the desired signal is not distorted. The parallel weighting scheme for interference cancellation leads to a faster, reliable and higher capacity system and results in parallel interference cancellation. Iterative process is also presented in this work, where the approximate weights are found out based on the minimum error value. Both the MVDR weighting and the approximate weighting are evaluated with the help of Bit Error Rate (BER) curves. The curves are plotted for both the Rayleigh and Rician channels. Various plots are obtained by varying the number of antennas in the array and also by varying the length of the user signal. All the BER curves achieved good results and from the analysis it is found that system performs better when Rayleigh channel was considered.

Non-Orthogonal Discrete Multi-Tone: Toward Higher Spectral Efficiency for Optical Networks

Achieving higher spectral efficiency is an efficient approach to address the bandwidth crisis of optical networks, but it faces significant technical challenges. High-spectral-efficiency non-orthogonal frequency-division multiplexing (NOFDM) has been proposed for meeting the requirement of optical networks' capacity upgrade. Compared to orthogonal frequency-division multiplexing, NOFDM can achieve higher spectral efficiency by compressing the subcarrier spacing narrower than the Nyquist orthogonal spacing, but this inevitably induces inter-carrier interference (ICI). ICI cancellation algorithms are crucial in NOFDM for correctly recovering the transmitted signal at the expense of extra processing power. Nowadays, processing power is no longer the obstacle to eliminate ICI due to the rapid development of application-specific integrated circuits for efficient implementation of digital signal processing. In this article, fast multiplexing and demultiplexing for NOFDM are implemented based on inverse fast Fourier transform and fast Fourier transform, respectively. Meanwhile, three representative ICI cancellation algorithms are discussed, and one of them is experimentally implemented. Furthermore, we propose non-orthogonal discrete multitone (NODMT) by integrating the advantages of NOFDM and DMT, which has the potential to achieve improved spectral efficiency for future optical networks.

Series Editorial: Optical Communications and Networks

In 2021, as optical technologies continue to demonstrate their advantages in telecom and data-center networks, we are also witnessing the attractive and promising progress on free-space optical communications and new technologies for fiber optic communications. Therefore, in this last issue of the Optical Communications and Networks Series in 2021, we have selected three contributions that address the (i) intelligent reflecting surface-assisted free-space optical communications, (ii) routing techniques for elastic optical networks with space division multiplexing, and (iii) non-orthogonal frequency-division multiplexing in optical networks.

Impact of Inter-Frame Interference on Eigendecomposition-Precoded Non-Orthogonal Frequency-Division Multiplexing

This letter first investigates the effects of inter-frame interference (IFI) on the recent eigendecomposition-precoded (EVD) non-orthogonal frequency-division multiplexing (NOFDM) transmission scheme, where subcarrier spacing is set smaller than that of orthogonal frequency-division multiplexing (OFDM). More specifically, the system model of EVD-NOFDM is generalized to support multi-frame transmission, and we propose an optimal power allocation for the multi-frame EVD-NOFDM architecture. The NOFDM scheme's information rate bound is derived and evaluated by our theoretical analysis by assuming the presence of IFI, whereas most previous NOFDM studies ignored IFI effects. Our performance results demonstrate that the proposed multi-frame NOFDM scheme eliminates the detrimental IFI effects while attaining its specific benefits of bandwidth efficiency.

Sparse Non-Orthogonal Frequency Division Multiplexing for Secure Transmission Over Broadcast Channels

We propose a novel transmission scheme for the parallel Gaussian broadcast channel with confidential messages (BCCM). In this model, The source node wishes to transmit a confidential message to each user over N independent sub-channels, where each sub-channel is degraded for one user than others. Our objective is to design a secure transmission technique that maximizes the sum secrecy rate under an average power constraint. The most common technique to tackle this problem in practice is orthogonal frequency division multiplexing (OFDM). Nevertheless, the OFDM-based BCCM suffers from excessive bandwidth utilization due to the sub-carrier orthogonality requirement. We propose a sparse non-orthogonal frequency-division Multiplexing (SNOFDM) transmission scheme. In SNOFDM, sub-carriers are generated by first selecting a subset of orthogonal sub-channels to reduce spectral resources. Then, the selected sub-channels are multiplexed in time to generate non-orthogonal sub-carriers. This, in effect increases, the spectral efficiency compared to OFDM. To overcome the interference introduced due to the non-orthogonality of sub-carriers, the transmitter sends the sparsest representation of the transmitted codeword. Furthermore, we provide a sub-carrier selection and power control procedures to maximize the sum rate of SNOFDM according to CSI fed back from receivers to source node. Our numerical results show that SNOFDM offers better spectral efficiency and a higher secrecy rate compared to OFDM. We provide extensive simulation results to study the effects of transmission parameters of SNOFDM on the achievable secrecy rate.

SVD-Based Design for Non-Orthogonal Frequency Division Multiplexing

Conventional non-orthogonal frequency division multiplexing (NFDM) suffers from inter-channel interference (ICI) due to the loss of orthogonality among subcarriers. The ICI significantly degrades system performance and complicates the design of the receiver. In this letter we propose a novel NFDM design based on singular-value decomposition of the modified Fourier matrix, which is able to completely eliminate ICI over an AWGN channel, while enjoying a simple transceiver structure. We also introduce a novel cyclic prefix extension scheme for the proposed NFDM design which is shown to reduce out-of-band emissions as compared to the traditional method of NFDM cyclic prefix extension. The spectral efficiency of our proposed technique is investigated and carefully compared to that of OFDM. The results show that the proposed scheme achieves up to 23% higher bandwidth efficiency than OFDM while meeting the same target bit error rate performance.

Sphere decoder with box optimisation for faster‐than‐Nyquist non‐orthogonal frequency division multiplexing

In 1975, the pioneering work of J. E. Mazo showed the potential faster-than-Nyquist (FTN) gain of single-carrier binary signal. If the inter-symbol interference is eliminated by an optimal detector, the FTN single-carrier binary signal can transmit 24.7% more bits than the Nyquist signal without any loss of bit error rate performance, which is known as the Mazo limit. In this paper, we apply sphere decoder (SD) with box optimization (BO) to reduce inter-carrier interference (ICI) in FTN non-orthogonal frequency division multiplexing (FTN-NOFDM) system. Compared with the conventional SD, SD with BO can achieve the same performance to reduce ICI, but its average number of expanded nodes in search process is significantly decreased especially for high-order modulation format, which can reduce the complexity of the receiver. When the bandwidth compression factor $\alpha$ is set to 0.802, the transmission rate of QPSK-modulated FTN-NOFDM is 24.7% faster than the Nyquist rate, and it has almost the same performance as orthogonal frequency division multiplexing (OFDM), which agrees well with the Mazo limit. The QPSK-modulated FTN-NOFDM with $\alpha$ equal to 0.5 (the spectral efficiency is 4 bit/s/Hz) outperforms 16QAM-modulated OFDM by about 1.5 dB. The 16QAM-modulated FTN-NOFDM with $\alpha$ equal to 0.67 and 0.5 (the spectral efficiency is 6 bit/s/Hz and 8 bit/s/Hz, respectively) outperforms 64QAM-modulated and 256QAM-modulated OFDM by about 1.5 dB and 2 dB, respectively. Therefore, FTN-NOFDM will be a promising modulation scheme for the future bandwidth-limited wireless communications.

Eigenvalue-Decomposition-Precoded Ultra-Dense Non-Orthogonal Frequency-Division Multiplexing

This paper proposes a novel ultra-dense non-orthogonal frequency-division multiplexing (NOFDM) transmission, where subcarrier spacing is set significantly lower than that of orthogonal frequency-division multiplexing (OFDM). In order to eliminate the detrimental effects of NOFDM-specific inter-carrier interference and correlated additive noises, eigenvalue-decomposition-aided precoding is conceived. The classical capacity formula is extended to one supporting our precoded NOFDM scheme. Optimal power allocation (PA) is developed in order to maximize the derived capacity of the proposed scheme. Furthermore, truncated PA is developed to combat the limitations due to significantly low eigenvalues, which are specifically imposed by the proposed ultra-dense NOFDM. Through analytical and numerical results, we demonstrate that the proposed NOFDM schemes with optimal and truncated PA outperform the conventional NOFDM and the classical OFDM schemes.

A Novel Baseband Faster-Than-Nyquist Non-Orthogonal FDM IM/DD System With Block Segmented Soft-Decision Decoder

In this paper, we systematically investigate our recently proposed faster-than-Nyquist non-orthogonal frequency-division multiplexing (FTN-NOFDM) generation technique for intensity modulation/direct detection (IM/DD) optical systems. The proposed scheme is based on modified fractional discrete Fourier transform (mFrDFT), and presents several advantages compared to other existing generation methods. Due to the exemption of guard bands, the proposed scheme achieves higher tolerance to narrow-bandwidth filtering. Besides, without the constraints on compression factor and modulation formats, the proposed system gives better signal flexibility and compatibility to various advanced signal processing techniques. To meet the demand on a large number of FTN-NOFDM subcarriers and high-order modulation formats, we further propose an efficient block segmented soft-decision decoder (BSSDD), which does not need to adjust the signal architecture or sacrifice the spectral efficiency. A 22.24-Gb/s 4-QAM FTN-NOFDM signal with up to 25% bandwidth saving has been successfully implemented over 20-km standard single mode fiber (SSMF) in an IM/DD optical communication system while keeping the bit error ratio (BER) below the hard-decision forward error correction (HD-FEC) limit. For both 4-QAM and 16-QAM FTN-NOFDM systems, the proposed BSSDD achieves better performance than the conventional decoder. All the results indicate that the proposed FTN-NOFDM technique has great potential to be used in high-speed IM/DD optical systems.

Radius-aided QRM-MLD for faster-than-Nyquist non-orthogonal FDM systems

In this paper, a radius-aided maximum likelihood detection with QR decomposition and M-algorithm (QRM-MLD) is proposed for inter-carrier interference (ICI) cancellation in a faster-than-Nyquist non-orthogonal frequency-division multiplexing (FTN-NOFDM) system. With almost the same ICI cancellation performance, the radius-aided QRM-MLD has lower computational complexity than the conventional QRM-MLD by predicting the search radius with the radius-predicted symbol. There is not any redundancy induced by radius-predicted symbol because the transmitted data also can be obtained from it. In order to validate the proposed algorithm in the experiment, the 28-Gb/s FTN-NOFDM signal was transmitted through a bandwidth-limited experimental system, and the radius-aided QRM-MLD is applied for ICI cancellation. In this bandwidth-limited system, the 3-dB equivalent bandwidth is only approximately 5.5 GHz. The experimental results reveal that the bandwidth-compressed FTN-NOFDM with radius-aided QRM-MLD has better bit error rate performance than orthogonal frequency-division multiplexing, which shows the superiority of the proposed scheme in bandwidth-limited systems.

A Novel Receiver Design of Nonorthogonal FDM Systems in Underwater Acoustics Communication

While orthogonal frequency-division multiplexing (OFDM) has been studied for a decade, the study of nonorthogonal frequency-division multiplexing (NOFDM) in the underwater acoustics (UWA) communication has never been reported, to the best of our knowledge. Therefore, we investigate the NOFDM technique for the UWA communication considering the doubly dispersive channel. The main feature of the NOFDM is that it involves more closely packed subcarriers compared to the OFDM, which results in higher spectral efficiency. However, this transmission suffers from severe intercarrier interference. Since, we are considering the doubly dispersive channel, intersymbol interference is also encountered due to the multipath propagation. Therefore, the traditional receiver of the NOFDM system in the UWA channel tends to have high computational complexity. Considering this problem, we design a receiver for the NOFDM system, where the basis expansion model is used along with the compressed sensing channel estimation technique, i.e., orthogonal matching pursuit (OMP), which can effectively reduce the computational complexity. However, while implementing this technique in the real sea environment, the problem of long delay/Doppler spread is encountered due to guard intervals. Therefore, we propose the use of a time-domain equalizer to mitigate the effect of long delay/Doppler spread. Simulation and experimental results based on the bit error rate demonstrate the performance degradation due to severe interference in our proposed receiver. On the contrary, the mean-square-error performance shows that our proposed receiver with the OMP channel estimation outperforms the OFDM receiver. Similarly, higher spectral efficiency gain is attained due to the closely packed subcarriers.

Efficiency Analysis of Time Synchronization and PAPR Reduction of N-OFDM Modem

Non-Orthogonal Frequency Division Multiplexing (N-OFDM) remains to be a promising digital modulation technique for high-data-rate wireless transmission. This research is focused on the efficiency analysis of a technique for data frames time synchronization in a white noise communication channel and on an optimal demodulation in the N-OFDM system. N-OFDM signals are generated using the Hartley transform and the Cauchy method is applied for the evaluation signal amplitude the demodulation procedure. The peak-to-average power ratio (PAPR) for different frequency spacing between N-OFDM subcarriers is analyzed. As a result, the mathematical expression for the subcarrier initial phase over subcarrier frequency is derived that allows calculating initial phase with the minimum of PAPR. The paper contains experimental results confirming the operability of the proposed time synchronization scheme. In the experiment, bit error rate estimation was performed for various spacing frequencies and signal-to-noise ratio in the range from 0 to 25 dB. The experimental results have shown the opportunity of PAPR reduction through the calculation of reasonable initial phase for each subcarrier. The experiment was based on simulation in MATLAB with the use of a sound card of a personal computer.