Chromatic dispersion mitigation using a SEFDM-based diversity technique for IM/DD long reach optical links.

In the spectral efficient frequency division multiplexing (SEFDM) system, in order to minimize mutual interference between subcarriers, a detector should be introduced at the receiver to handle the interference, but increases the complexity of system. In this paper, we propose a simplified precoding algorithm at transmitter instead of receiver, which can first implement higher 16QAM SEFDM transmission over standard single mode fiber (SSMF). The technique is based on interference information from non-orthogonality between subcarriers and uses nonlinear matrix operations to improve system performance with low complexity. The numerical results show that the precoding scheme achieves SSMF transmission of intensity modulation and direct detection (IM/DD) 16QAM SEFDM system under the premise of achieving higher spectral efficiency, and obtains good bit error rate performance.

Spectral efficient frequency division multiplexing (SEFDM) can improve the spectral efficiency for next-generation optical and wireless communications. In this work, we apply SEFDM in beyond 100-Gb/s optical intensity modulation and direct detection transmissions and propose a low-complexity logarithmic-maximum-a-posteriori (log-MAP) Viterbi decoding algorithm to achieve the maximum likelihood (ML) detection. We evaluate the likelihood of detections using a posteriori probability instead of Euclidean distance by taking both noise and inter-carrier interference into consideration. In order to balance the performance and complexity, we then employ Viterbi decoding principle to retain only certain paths with ML detections (a.k.a., the surviving paths) while discarding the others during the decoding procedure. Results show that the proposed log-MAP Viterbi decoding scheme achieves optimal performance due to the precise likelihood evaluation, which guarantees the retention of the global ML detection. By using the proposed decoding scheme, the data rate of SEFDM signals can reach 150-Gb/s in a 2-km standard single mode fiber transmission, using only 28-GHz bandwidth and 16-QAM modulation. Experimental results show that the 16-QAM modulated SEFDM signal with a bandwidth compression factor of 0.8 outperforms 32-QAM modulated OFDM, while both signals have the same bandwidth (28-GHz) and data rate (140-Gb/s), which demonstrate the superiority of SEFDM in optical short reach applications.

Spectrally Efficient Frequency Division Multiplexing (SEFDM) systems provide enhanced spectrum utilization compared with Orthogonal Frequency Division Multiplexing (OFDM) systems by relaxing the orthogonality condition among sub-carriers. However, in the SEFDM systems, the loss of orthogonality results in the inter-carrier-interference (ICI) thus reduces the transmission reliability. To alleviate the ICI and achieve better error performance, this paper proposes a novel SEFDM transmission scheme, called SEFDM with index modulation (SEFDM-IM). The index modulation, which was originally proposed for OFDM systems, performs an additional modulation besides conventional M-ary modulation by selecting the indices of the sub-carriers. Since a number of sub-carriers are switched off in index modulation, when the index modulation is applied in SEFDM systems, the ICI is reduced and better error performance can be obtained in comparison with the SEFDM systems using conventional Mary modulation. Simulation results confirm this conclusion that the joint applications of SEFDM and index modulation can effectively increase the transmission reliability.

In the spectrally efficient frequency division multiplexing (SEFDM) non-orthogonal multicarrier signal, higher spectral efficiency can be achieved at the expense of self-created inter carrier interference (ICI). The effective interference, which is contributed by all sub-carriers, has to be minimized and this results in a receiver of significant complexity. In order to mitigate the interference and simplify the receiver design, in this work, a precoding technique, based on eigenvalue decomposition of the sub-carrier correlation matrix, is utilised. Briefly, the technique is based on modifying the data sent on individual sub-carriers according to the signal quality of each, which is based on the sub-carrier to interference ratio (ScIR) of such sub-carrier as estimated from eigenvalue decomposition. A full system model is presented in this paper and simulations show that the precoding of SEFDM results in either better bit error rate (BER) performance compared to that of an orthogonal frequency division multiplexing (OFDM) system of the same spectral efficiency or in higher effective bit rate relative to an OFDM system with the same BER performance. Modelling is done in simple Gaussian noise channels and in a static frequency selective channel and for different modulation formats. Results show that for the same bandwidth a 128QAM precoded SEFDM system outperforms a 16QAM OFDM one by offering 75% bit rate increase. Furthermore, Turbo coding assisted BER performance comparisons are investigated in this work. Using 64QAM modulated symbols, the precoded SEFDM outperforms the typical OFDM by several dBs.

For high data rates satellite systems, where multiple carriers are frequency division multiplexed with a slight overlap, the overall spectral efficiency is limited. This work applies highly overlapped carriers for satellite broadcast and broadband scenarios to achieve higher spectral efficiency. Spectrally efficient frequency division multiplexing (SEFDM) compresses subcarrier spacing to increase the spectral efficiency at the expense of orthogonality violation. SEFDM systems performance degrades compared to orthogonal signals, unless efficient interference cancellation is used. Turbo equalisation with interference cancellation is implemented to improve receiver performance for variable coding, compression and modulation/constellation proposals that may be applied in satellite communications settings. Such parameters may be set to satisfy pre‐defined spectral efficiency values for a given quality index or associated application. Assuming low‐density parity check coded data, the work proposes two approaches to receiver design: a simple matched filter approach and an approach utilising an iterative interference cancellation structure specially designed for SEFDM. Mathematical models and simulations studies are presented indicating promising gains to be achieved for SEFDM transmission with advanced transceiver architectures at the cost of increased complexity at the receiver.

We comprehensively summarize experimental validations 1 of bandwidth compressed multicarrier waveforms for future 5th generation (5G) applications. The proposed waveforms are derived from an existing non-orthogonal multicarrier concept termed spectrally efficient frequency division multiplexing (SEFDM) where sub-carriers are non-orthogonally packed at frequencies below the symbol rate. This improves the spectral efficiency at the cost of self-created inter carrier interference (ICI). In this work, experiments are reported and testing is carried out in three scenarios including long term evolution (LTE)-like wireless link; millimeter wave radio-over-fiber (RoF) link and optical fiber link. In the first scenario, for a given 25 MHz bandwidth, the SEFDM testbed can provide 70 Mbit/s gross data rate while only 50 Mbit/s can be achieved for an OFDM system occupying the same bandwidth. For the millimeter wave experiment, occupying a 1.125 GHz bandwidth, the gross bit rate for OFDM is 2.25 Gbit/s and with 40% bandwidth compression, 3.75 Gbit/s can be achieved for SEFDM. Two experimental optical fiber links are described in this work; a 10 Gbit/s direct detection optical SEFDM system and a 24 Gbit/s coherent detection SEFDM system. The LTE-like signals and millimeter wave technologies are well suited to provide last mile communications to end users as both can support mobility in wireless environments. The lightwave signals delivered by optical fibers would offer higher data rates and support long-haul communications. The reported techniques, used individually or combined, would be of interest to future wireless system designers, where bandwidth saving is of importance, such as in 5G networks, aiming to provide high capacity and high mobility, simultaneously while saving spectrum.

In this paper, low-density parity-check (LDPC) codes are applied in spectrally efficient frequency-division multiplexing (SEFDM) with iterative decoder to eliminate the influence from inter-carrier interference (ICI). SEFDM has higher spectral efficiency than orthogonal frequency-division multiplexing (OFDM) by compressing the subcarrier spacing. This self-induced ICI is eliminated by LDPC codes and iterative decoder. The SEFDM scheme analyzed in this paper is not limited by subcarrier number and modulation order because the ICI cancellation scheme has relatively low computational complexity. With LDPC codes, the iterative-SEFDM scheme supports QPSK, 16QAM, 64QAM and 256QAM modulation formats. To the best of our knowledge, the SEFDM scheme with high-order 256QAM modulation is first demonstrated. With bandwidth compression and effective ICI cancellation, LDPC-coded iterative-SEFDM can achieve better bit error rate performance than its counterpart LDPC-coded OFDM at the same spectral efficiency.

IM/DD (Intensity Modulation and Direct Detection) systems are widely used in short-haul optical transmission for its low complexity and low cost. IM/DD systems with PAM (Pulse Amplitude Modulation) can be applied to intra- and inter-DC (data center) which has an exponentially growing transmission rates demand. Meanwhile, PS (Probabilistic Shaping), as a channel coding method, can shape the probability of symbols in different amplitude in order to maximize the transmission rate to be close to the Shannon limit. Nonlinear compensation based on DSP (Digital Signal Processing) plays an important role in compensating the degradation of the channel. In this paper, a method which combines with PS and 2nd-order VNLE (Volterra Nonlinear Equalizer), is proposed to reduce signal degradation while VNLE is used for nonlinear compensation at the receiver. The compensation performances by (1) VNLE and FFE (Feedforward Equalizer) with PS, (2) VNLE with PS and without PS are compared in a DML (Directly Modulated Laser)-based IM/DD systems. PS is implemented with CCDM (Constant Composition Distribution Matching) which is used to shape the symbols. In a 10km PS based IM/DD systems, the SER (Symbol Error Rate) of the transmitted symbol obviously decreases compared to that without PS. The introduction of VNLE method gets a lower SER than that using FFE method. In summary, the proposed method is proved to have a better performance and is supposed to be implemented in the future IM/DD systems.

In visible light communications (VLCs) relying on intensity-modulation and direct detection (IM/DD), the conversion from electrical signals to optical signals and the limited dynamic range of the light-emitting diodes (LEDs) constitute the fundamental impediments in the way of high-integrity communications, especially when orthogonal frequency-division multiplexing (OFDM) is employed. In IM/DD VLCs, only real-valued positive signals are used for signal transmission. However, the Fourier transform of OFDM systems is operated in the complex domain. In order to meet the requirements of the IM/DD VLCs, the complex-to-real conversion is achieved at the cost of reducing the bandwidth efficiency. Moreover, OFDM signals experience a high peak-to-average power ratio; hence, typically clipping is used for confining the positive-valued signals within the LED’s dynamic range. However, hard clipping leads to the loss of orthogonality for optical OFDM (O-OFDM) signals, generating inter-carrier interference. As a result, the performance of the clipping-based O-OFDM systems may be severely degraded. In this paper, the concept of piecewise companding transform (CT) is introduced into the O-OFDM system advocated, forming the CTO-OFDM arrangement. We first investigate the general principles and design criteria of the piecewise CTO-OFDM. Based on our studies, three types of piecewise companders, namely, the constant probability sub-distribution function, linear PsDF (LPsDF), and the non-LPsDF-based CT, are designed. Furthermore, we investigate the nonlinear effect of hard clipping and of our CT on O-OFDM systems in the context of different scenarios by both analytical and simulation techniques. Our investigations show that the CTO-OFDM constitutes a promising signaling scheme conceived for VLCs, which exhibits a high bandwidth efficiency, high flexibility, high reliability, as well as a high data-rate, despite experiencing nonlinear distortions.

This work proposes and explores the use of probabilistic shaping for the non-orthogonal multicarrier spectrally efficient frequency division multiplexing (SEFDM) system. The system design considers the reverse concatenation architecture which cascades the constant composition distribution matching (CCDM) algorithm together with soft-decision forward error correction (SD-FEC)-LDPC code for the probabilistic shaping scheme. The non-orthogonal signalling is implemented by discrete Fourier transform (DFT)-based SEFDM modulation with matched filtering demodulation and advanced interference cancellation detection. The high achievable spectral efficiency, low computation complexity and reliability make SEFDM a good candidate for multicarrier signalling for beyond 5G communications. By adding extra shaping gain and flexibility of rate adaptation, the combination of two capacity-achieving techniques provides significant insight of further performance improvement. In this paper, we investigate the performance of the proposed probabilistically shaped-SEFDM (PS-SEFDM) system with regular QAM constellations. The presented results of the proposed system show less required power and bandwidth saving compared to OFDM when achieving the same error performance and same spectral efficiency.

This paper presents the design and the experimental demonstration of transmission of spectrally efficient frequency division multiplexing (SEFDM) signals, using a single 5-GHz channel, from 81 to 86 GHz in the E-band frequency allocation. A purpose-built E-band SEFDM experimental demonstrator, consisting of transmitter and receiver GaAs microwave integrated circuits, along with a complete chain of digital signal processing is explained. Solutions are proposed to solve the channel and phase offset estimation and equalization issues, which arise from the well-known intercarrier interference between the SEFDM signal subcarriers. This paper shows the highest transmission rate of 12 Gb/s over a bandwidth varying between 2.67 to 4 GHz depending on the compression level of the SEFDM signals, which results in a spectral efficiency improvement by up to 50%, compared to the conventional orthogonal frequency division multiplexing modulation format.

Spectrally efficient frequency division multiplexing (SEFDM) improves spectral efficiency relative to the well known orthogonal frequency division multiplexing (OFDM). Optimal detection of SEFDM, to recover signals corrupted by inter carrier interference (ICI), has major drawbacks in the exponentia

This paper explores new multicarrier signals and systems for 5G; spectrally efficient frequency division multiplexing (SEFDM), in which higher spectral efficiency (SE) compared to conventional orthogonal frequency division multiplexing (OFDM) is achieved by violating the orthogonality of its subcarriers. This work proposes new system and receiver models and then investigates the employment of various forward error correction (FEC) techniques, as well as a new interference cancellation receiver architecture to improve the overall system performance by ameliorating the effects of inter-carrier interference (ICI). Results show that the use of coded SEFDM system can drastically increase the SE by up to 67% relative to OFDM, at the expense of a power penalty below 3dB.

Visible light communication (VLC) is a technology that is currently being employed to achieve high data rates. Orthogonal frequency division multiplexing (OFDM) is a powerful scheme for intensity modulation and direct detection (IM-DD) that is becoming increasingly important. OFDM systems based on VLC are accomplished through the implementation of IM-DD constraints, including direct current biased optical OFDM (DCO-OFDM), asymmetrically clipped optical OFDM (ACO-OFDM), and asymmetrically clipped DC-biased (ADO-OFDM), among others. The OFDM technique based on VLC is inefficient in terms of spectral efficiency and has a high peak to average power ratio (PAPR). In this article, the symbol time compression-image adjust (STC-IMADJS) technique will be proposed for throughput maximization and PAPR reduction in the DCO-OFDM, ACO-OFDM, and ADO-OFDM systems. Furthermore, the STC technique enables the simultaneous transmission of two sub-carriers through Walsh spreading codes without inference between them. As a result, the OFDM symbol has been reduced by 50%. The IMADJS strategy reduces the high PAPR of transmitted signals by compressing large signals and expanding small signals, as long as the average power level remains constant after compression. Therefore, the proposed STC-IMADJS technique doubles the throughput as well as significantly reduces the PAPR for OFDM systems based on VLC. The simulation results are performed using Matlab-2021a for 1024 sub-carriers. As a result, the simulation results show that the proposed technique reduces the PAPR by 3.7 dB (86%), 8.16 dB (93%), and 1.81 dB (20%) for DCO-OFDM, ACO-OFDM, and ADO-OFDM systems respectively. Furthermore, the technique has a significantly lower computational complexity than conventional OFDM systems based on VLC. Finally, the measures of performance through this article are bit error rate and complementary cumulative distribution function.

Laser phase noise conversion to intensity noise due to fiber chromatic dispersion is analyzed by deriving the noise power spectral density. Theory predicts that the phase-modulation-amplitude-modulation conversion noise is a principal limiting factor of the gigabit-per-second nonregenerative transmission using an external modulator when the linewidth of the laser transmitter is above several tens of megahertz and the total chromatic dispersion of fibers exceeds several thousand picoseconds per nanometer. This fact is confirmed by the 2.4-Gb/s transmission experiments using multiple inline Er-doped fiber amplifiers. The system penalty due to this noise in the intensity modulation and direct detection (IM-DD) optical transmission using an external modulator is evaluated.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>