Nyquist Signaling Research Articles

Spectral Efficiency Maximization for Deliberate Clipping-Based Multicarrier Faster-Than-Nyquist Signaling

High peak-to-average power ratio (PAPR) is one of the common drawbacks of multicarrier signals at the transmitter. In this paper, we investigate the PAPR reduction of spectral efficient multicarrier faster-than-Nyquist (MFTN) signals, where the PAPR problem has still not been seriously considered yet in current literatures. Specifically, the low complexity deliberate clipping scheme is exploited in MFTN signaling system. In order to evaluate the practical system performance, we consider a memoryless high power amplifier PAPR-efficiency model, and the auxiliary channel model under low complexity symbol-by-symbol receiver is also derived. Moreover, the achievable spectral efficiency (ASE) which can be viewed as the low bound for any modulation and coding schemes is taken as a figure of merit throughout this paper. By jointly optimizing the time-frequency spacing and clipping ratio to maximization the ASE under the given shaping pulse and modulation format, we show that the ASE of clipping-based MFTN substantially outperforms conventional Nyquist signaling schemes.

Low Complexity Message Passing Receiver for Faster-Than-Nyquist Signaling in Nonlinear Channels

The modern and future communication systems demand higher data rate exceeds current capabilities. Faster-than-Nyquist (FTN) signaling is a promising technique for the reason it can improve the spectral efficiency. This paper deals with the receiver design for FTN signaling equalization in nonlinear channels. To handle the correlated noise samples induced by FTN signaling, we use the auto-regressive process to model the colored noise. Moreover, due to the nonlinearities, the complexity of receiver becomes prohibitively high. To reduce the complexity, we linearize the Volterra model and formulate the considered system as linear system. Then, based on the factor graph and message passing framework, the FTN symbols are detected with low complexity. Simulation results show that the proposed low complexity receiver can achieve similar performance of Nyquist signaling while increase 25% data rate.

All-optical demultiplexing of Nyquist OTDM signal using a biorthogonal Nyquist gate

We present an all-optical method for demultiplexing Nyquist optical time division multiplexed (OTDM) signals using a biorthogonal Nyquist gate, which is a Nyquist gate of reduced pulse width. The biorthogonality between the Nyquist symbol and Nyquist gate creates an intersymbol interference (ISI) free spectral region in the mixed product that theoretically allows for complete elimination of ISI in the demultiplexer. Furthermore, this format transparent all-optical method produces a Nyquist signal on the output suitable for further optical processing and multiplexing. We analyze the performance of this approach through simulation in the presence of nonidealities of imperfect pulse shape, timing jitter, and dispersion. Finally, we experimentally demonstrate the performance of this approach operating on an 80-GBd Nyquist OTDM signal.

A Novel IDFT/DFT Based Transceiver for Faster than Nyquist Signaling Optimization

Faster than Nyquist has gained a lot of interest lately since it can enhance OFDM spectral efficiency, which most of current telecommunication systems are based on. This makes it the optimum candidate technology to be deployed for the upcoming systems that are basically based on legacy OFDM systems such as 5G. Towards an era where all devices are predicted to be online, the ease of implementation has become a must as expensive and large chips will not suit wearable devices and micro-computers. In this paper, we offer a system that is not only beneficial for next generation of telecommunication systems, but also adaptive in sense of self-optimization and also in a way that it can be backward compatible with conventional OFDM systems.

Chirp Spread Spectrum Toward the Nyquist Signaling Rate—Orthogonality Condition and Applications

With the proliferation of Internet-of-Things (IoT), the chirp spread spectrum (CSS) technique is re-emerging for communications. Although CSS can offer high processing gain, its poor spectral efficiency and the lack of orthogonality among different chirps tend to limit its potential. In this paper, we derive the condition to orthogonally multiplex an arbitrary number of linear chirps. For the first time in the literature, we show that the maximum modulation rate of the linear continuous-time chirps satisfying the orthogonality condition can approach the Nyquist signaling rate, the same as single-carrier waveforms with Nyquist signaling or orthogonal frequency-division multiplexing signals. The performance of the proposed orthogonal CSS is analyzed in comparison to the emerging LoRa systems for IoT applications with power constraint, and its capability for high-speed communications is also demonstrated in the sense of Nyquist signaling.

Capacity limit for faster-than-Nyquist non-orthogonal frequency-division multiplexing signaling

Faster-than-Nyquist (FTN) signal achieves higher spectral efficiency and capacity compared to Nyquist signal due to its smaller pulse interval or narrower subcarrier spacing. Shannon limit typically defines the upper-limit capacity of Nyquist signal. To the best of our knowledge, the mathematical expression for the capacity limit of FTN non-orthogonal frequency-division multiplexing (NOFDM) signal is first demonstrated in this paper. The mathematical expression shows that FTN NOFDM signal has the potential to achieve a higher capacity limit compared to Nyquist signal. In this paper, we demonstrate the principle of FTN NOFDM by taking fractional cosine transform-based NOFDM (FrCT-NOFDM) for instance. FrCT-NOFDM is first proposed and implemented by both simulation and experiment. When the bandwidth compression factor α is set to 0.8 in FrCT-NOFDM, the subcarrier spacing is equal to 40% of the symbol rate per subcarrier, thus the transmission rate is about 25% faster than Nyquist rate. FTN NOFDM with higher capacity would be promising in the future communication systems, especially in the bandwidth-limited applications.

1-Bit Quantization and Oversampling at the Receiver: Communication Over Bandlimited Channels With Noise

A bandlimited additive white Gaussian noise channel is considered where the output is 1-bit quantized and oversampled with respect to the Nyquist rate. We consider root raised cosine filters at the transmitter and receiver. In particular, we focus on a roll-off factor equal to 1 and 0. Because of the oversampling the channel has infinite memory. An auxiliary channel law is proposed which describes the resulting received sequences based on a truncated waveform. The random distortion due to the residual sidelobes can be considered as an additional noise term in the auxiliary channel law. The auxiliary channel law is utilized for computing a lower bound on the achievable rate and in a further step for optimizing a Markov source model. Different signaling schemes have been considered, such as BPSK and ASK. Moreover, Nyquist signaling and faster-than-Nyquist signaling are considered. The resulting achievable rates are superior as compared with results from the literature on bandlimited channels with noise, 1-bit quantization, and oversampling at the receiver.

All-optical Nyquist-OTDM to Nyquist-WDM conversion for high-granular flexible optical networks.

We have proposed and experimentally demonstrated all-optical multiplexing (MUX)-format conversion from Nyquist optical time division multiplex (OTDM) to Nyquist wavelength division multiplex (WDM). The system is simply configured with a straight-type phase modulator (PM) driven by a sinusoidal wave and an optical Nyquist filter. In the theoretical investigation, it is proved that the single Nyquist signal is completely converted to Nyquist WDM signal, which consists of two half-baud-rate signals with different carrier frequencies. The theoretical modulation voltage for the phase modulator is slightly lower than Vπ: 0.913 Vπ, and it is experimentally verified. In the experimental demonstrations, 50 Gbaud to 25 Gbaud x 2 and 25 Gbaud to 12.5 Gbaud x 2 conversions are successfully demonstrated with quite low optical signal-to-noise ratio (OSNR) penalties. In addition, cascaded MUX-format conversion is also demonstrated; 50 Gbaud Nyquist signal is converted to four channels of 12.5 Gbaud Nyquist signals.

10 Gbit/s mode-multiplexed QPSK transmission using MDM-to-MFDM based single coherent receiver for intra- and inter data center networking

Generalized few-mode-fiber (FMF) transmission uses N coherent receivers for mode detection, where N scales with the number of fiber modes. Multiple coherent receivers increase the cost of optical network units (ONUs) in access networks, specifically for intra- and inter data center applications. We have experimentally evaluated a cost effective low-complexity receiver architecture based on mode-division multiplexing (MDM) to mode frequency-division multiplexing (MFDM) conversion for data center connectivity. A single coherent receiver is used to efficiently detect 10Gbit/s QPSK Nyquist signals over 2.8km 4-LP mode graded index fiber reducing the ONUs complexity to N/4. All the transmitted modes are successfully detected below the forward-error-correction (FEC) limit, i.e. 1×10−3 BER.

Low-Complexity Detection of High-Order QAM Faster-Than-Nyquist Signaling

Faster-than-Nyquist (FTN) signaling is a promising non-orthogonal transmission technique to considerably improve the spectral efficiency. This paper presents the first attempt in the literature to estimate the transmit data symbols of any high-order quadrature amplitude modulation (QAM) FTN signaling in polynomial time complexity. In particular, we propose a generalized approach to model the finite alphabet of any high-orderQAMconstellation as a high degree polynomial constraint. Then, we formulate the high-order QAM FTN signaling sequence estimation problem as a non-convex optimization problem. As an example of a high-order QAM, we consider 16-QAM FTN signaling and then transform the high degree polynomial constraint, with the help of auxiliary variables, to multiple quadratic constraints. Such transformation allows us to propose a generalized approach semidefinite relaxation (SDR)-based sequence estimation (GASDRSE) technique to efficiently provide a sub-optimal solution to the NP-hard non-convex FTN detection problem, with polynomial time complexity. For the particular case of 16-QAM FTN signaling, we additionally propose a sequence estimation technique based on concepts from the set theory. We show that the set theory SDR-based sequence estimation (STSDRSE) technique is of lower complexity when compared with the proposed GASDRSE. Simulation results show the effectiveness of the proposed GASDRSE and STSDRSE techniques in increasing the data rate and spectral efficiency of 16-QAM FTN signaling, without increasing the bit-error-rate, the bandwidth, or the data symbols energy, when compared with the Nyquist signaling.

A Hybrid BP-EP-VMP Approach to Joint Channel Estimation and Decoding for FTN Signaling over Frequency Selective Fading Channels

This paper deals with low-complexity joint channel estimation and decoding for faster-than-Nyquist (FTN) signaling over frequency selective fading channels. The inter-symbol interference (ISI) imposed by FTN signaling and the frequency selective channel are intentionally separated to fully exploit the known structure of the FTN-induced ISI. Colored noise due to the faster sampling rate than that of the Nyquist signaling system is approximated by autoregressive process. A Forney style factor graph representation of the FTN system is developed and Gaussian message passing is performed on the graph. Expectation propagation (EP) is employed to approximate the message from channel decoder to Gaussian distribution. Since the inner product between FTN symbols and channel coefficients is infeasible by belief propagation (BP), we propose to perform variational message passing (VMP) on an equivalent soft node in factor graph to tackle this problem. Simulation results demonstrate that the proposed low-complexity hybrid BP-EP-VMP algorithm outperforms the existing methods in FTN system. Compared with the Nyquist counterpart, FTN signaling with the proposed algorithm is able to increase the transmission rate by over 40%, with only negligible BER performance loss.

FTN 기반 전송 시스템의 성능 평가 기준에 관한 연구

FTN(Faster-Than-Nyquist) 전송 방식은 송신 펄스를 중첩시켜 동일한 대역폭 내에서 나이퀴스트(Nyquist) 율보다 빠른 속도로 심볼을 전송하는 기법이다. FTN 전송 방식을 적용하면 동일한 시간 구간 동안 나이퀴스트 전송 방식보다 많은 수의 심볼이 존재하게 되므로, 심볼 당 에너지가 같을 때 신호의 송신 전력이 커진다. 따라서 FTN 기반 전송 시스템의 올바른 성능 평가를 위해서는 이 점에 유의하여 성능 평가 기준을 설정하여야 하며, 기존 나이퀴스트 기반 전송 시스템에서 활용되던 성능 평가 기준 간의 환산 공식 또한 주의하여 활용할 필요가 있다. 본 논문에서는 FTN 전송 방식이 적용된 시스템에서의 성능 평가 기준과 관계식에 대해 분석하고 타당한 성능 평가 기준을 제시한다. FTN(Faster-Than-Nyquist) signaling is a method of transmitting symbols at rates faster than the Nyquist rate in the same bandwidth by overlapping transmission pulses. The transmission power of the FTN signal is greater than that of the Nyquist signal, because the number of symbols in the FTN signal is larger than that in the Nyquist signal for the same time interval. Hence, to evaluate the performance of an FTN-based transmission system properly, the performance evaluation criterion should be carefully set, and conversion formulas among the criteria which are used in Nyquist-based system should also be applied attentively. In this paper, the performance evaluation criteria of the FTN-based transmission system is analyzed and a valid way to set the criteria is proposed.

Investigation on Nyquist pulse generation by optical frequency comb

Compared with OFDM, Nyquist signal transmission has several unique advantages, such as lower receiver complexity, lower receiver bandwidths, and lower peak-to-average power ratios, which give better performances under fiber nonlinear impairments. Since the sinc-shaped waveforms in the time domain correspond to a rectangular spectrum in the frequency domain, the Nyquist pulses can also be obtained directly from the generation of a flat frequency comb with electro-optic modulators. In this paper, a complete theoretical analysis of Nyquist pulse generation with 3 comb lines generated with a single intensity modulator is developed. It is proved that both the amplitude and phase of the sidebands in the optical frequency comb are important for generation of Nyquist pulses. Theoretically, it is found that it is impossible to generate Nyquist pulses with more than 3 comb lines using a single intensity modulator even if 5 flat comb lines are realized. A Nyquist pulse can be generated with 9 comb lines by two cascaded intensity modulators, but the sum of the phase shift caused by the two DC voltages of the intensity modulators must be π.

An Efficient Turbo Equalization for Faster than Nyquist Signal

An Efficient Turbo Equalization for Faster than Nyquist Signal

75GBAUD NYQUIST QPSK signal transmission with orbital angular momentum multiplexing

ABSTRACTIn this article, for the first time the generation, multiplexing, and detection of 75GBaud Nyquist QPSK signal transmission over two orthogonal Laguerre–Gaussian modes carrying orbital angular momentum (OAM) were experimentally demonstrated. To further increase spectrum efficiency, Nyquist signal was generated by all‐optical method to produce sinc‐shaped Nyquist pulses and received by full‐band signal coherent detection with digital signal processing. Two OAM modes with same absolute value of charge but opposite sign were generated, multiplexed, and demultiplexed. The bit error ratio performance of the received signal was under forward error correction threshold with optical signal‐to‐noise ratio of 20 and 22 dB for +8 mode and −8 mode, respectively. To our best knowledge, this is the highest baud rate ever achieved in OAM based wireless optical transmission systems, which clearly validate the feasibility and benefit of Nyquist signal transmission with OAM mode multiplexing to increase the spectrum efficiency and system capacity. © 2016 Wiley Periodicals, Inc. Microwave Opt Technol Lett 58:1866–1869, 2016

Searching for Binary and Nonbinary Block and Convolutional LDPC Codes

A unified approach to search for and optimize codes determined by their sparse parity-check matrices is presented. Replacing the nonzero elements of a binary parity-check matrix (the base or parent matrix) either by circulants or by companion matrices of elements from a finite field GF $(2^{m})$ , we obtain quasi-cyclic low-density parity-check (LDPC) block codes and binary images of nonbinary LDPC block codes, respectively. By substituting monomials of a formal variable $D$ , we obtain the polynomial description of an LDPC convolutional code. A set of performance measures applicable to different classes of LDPC codes is considered, and a greedy algorithm for code performance optimization is presented. The heart of the new optimization algorithm is a fast procedure for searching for LDPC codes with large girth of their Tanner graphs. For a few classes of LDPC codes, examples of codes combining good error-correcting performance with compact representation are obtained. In particular, we present optimized convolutional LDPC codes and conclude that the LDPC block codes are still superior to their convolutional counterparts if both decoding complexity and coding delay are considered. Moreover, a specific channel model can easily be embedded into the optimization loop. Thereby, the code can be optimized for a specific channel. The efficiency of such an optimization is demonstrated via an example of faster than Nyquist (FTN) signaling using LDPC codes. The FTN strategy combined with a rate $R=1/2$ LDPC code of length 64 800 optimized for effective data rate $R=3/4$ gains more than 0.5 dB compared with the standard LDPC codes of the same rate and length. The obtained gain corresponds to transmission at the capacity of the binary input additive white Gaussian noise channel. In most numerical examples, we consider codes with bidiagonal structure of the parity-check matrix. This restriction preserves low encoding complexity and allows fair comparison with codes selected for communication standards.

Transmission and full-band coherent detection of polarization-multiplexed all-optical Nyquist signals generated by Sinc-shaped Nyquist pulses

All optical method is considered as a promising technique for high symbol rate Nyquist signal generation, which has attracted a lot of research interests for high spectral-efficiency and high-capacity optical communication system. In this paper, we extend our previous work and report the fully experimental demonstration of polarization-division multiplexed (PDM) all-optical Nyquist signal generation based on Sinc-shaped Nyquist pulse with advanced modulation formats, fiber-transmission and single-receiver full-band coherent detection. Using this scheme, we have successfully demonstrated the generation, fiber transmission and single-receiver full-band coherent detection of all-optical Nyquist PDM-QPSK and PDM-16QAM signals up to 125-GBaud. 1-Tb/s single-carrier PDM-16QAM signal generation and full-band coherent detection is realized, which shows the advantage and feasibility of the single-carrier all-optical Nyquist signals.

Nyquist 4-ary pulse amplitude modulation scheme based on electrical Nyquist pulse shaping and fiber Bragg grating filter

Intensity modulation and direct detection signal are sensitive to power fading and nonlinear intersymbol interference (ISI) induced by modulator chirp, fiber dispersion, and square-law photo-detection. We propose and experimentally demonstrate a Nyquist 4-ary pulse amplitude modulation and direct detection scheme relying on pulse-shaping with an electrical filter and optical equalization with a vestigial-sideband (VSB) filter in the transmitter. The power fading could be eliminated by using the VSB filter. Compared with conventional 4-ary pulse amplitude modulation, the Nyquist signal has a stronger resistance to nonlinear ISI.

Spectrally Efficient Enhanced-Performance Bidirectional Coherent PON With Laserless 10 Gb/s ONU [Invited

We present and experimentally characterize a spectrally efficient, bidirectional, ultradense wavelength-division multiplexing passive optical network (PON) (2 × 120 Gb/s at 50 GHz) over 30 km standard single-mode fiber. This is achieved using a 4 GHz grid with partial spectrum overlapping, Nyquist-shaped 16-ary quadrature amplitude modulation, and digital frequency shifting. This scheme is based on a laserless, self-homodyne PON with centralized wavelength control. We achieve reduced impact of the Rayleigh back-scattering effect due to Nyquist-pulse shaping and frequency upshifting. Self-homodyne detection relaxes the laser linewidth requirement and digital signal processing complexity at the optical network unit. To demonstrate the extra benefit of the proposed PON system, we also experimentally and theoretically evaluate the impact of nonlinear Raman crosstalk in video overlay. Compared to a baseband Nyquist signal and baud rate non-return-to-zero equivalent, the proposed system improves the carrier-to-Raman crosstalk ratio of video overlay by 4 and 6 dB, respectively.

Optical Nyquist channel generation using a comb-based tunable optical tapped-delay-line.

We demonstrate optical Nyquist channel generation based on a comb-based optical tapped-delay-line. The frequency lines of an optical frequency comb are used as the taps of the optical tapped-delay-line to perform a finite-impulse response (FIR) filter function. A single optical nonlinear element is utilized to multiplex the taps and form the Nyquist signal. The tunablity of the approach over the baud rate and modulation format is shown. Optical signal-to-noise ratio penalty of 2.8 dB is measured for the 11-tap Nyquist filtering of 32-Gbaud QPSK signal.