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Symbol rate is one of the most important parameters in signal demodulation process. In real-time signal processing, traditional symbol rate estimation algorithms for the Multiple Phase Shift Keying (M-PSK) and the Multiple Quadrature Amplitude Modulation (M-QAM) are based on the Fourier transform of signal’s complex envelope. At the low signal-to-noise ratio (SNR), the accuracy of symbol rate estimation can be improved by increasing the number of symbols as much as possible. However, this improvement is infeasible in many applications such as the energy-limited Internet of Things devices and sporadic noncooperative transmissions. In this paper, we propose a data-driven bandpass filter (BPF) design scheme for accurate estimation of symbol rate under low SNR with only a small number of symbols available. The proposed scheme considerably improves the estimation performance by optimizing the BPF design using the equivalent dynamic linearization model with time-varying pseudo-partial derivatives. Specifically, the proposed scheme iteratively optimizes the upper and lower cut-off frequencies of the BPF based on the measured complex envelope spectrum until achieving the optimal BPF. Therefore, the peaks of the complex envelope spectrum are extracted as the estimate of the symbol rate by applying the optimal BPF. Experimental results indicate the promise of the proposed scheme as an efficient symbol rate estimator for sporadic signal at low SNR and with a small number of symbols.

In this paper, we propose a pre-coded multi-carrier M-ary chaotic vector cyclic shift keying (PC-MC-M-CVCSK) transceiver for reliable information transmissions. In this design, we exploit the principle of diagonalization to combat noises and interferences. At the PC-MC-M-CVCSK transmitter, we propose to precode the M-ary modulated symbols based on the discrete Fourier transform (DFT) and the reverse matrix of an eigenvalue matrix. Meanwhile, the chaotic generator outputs chaotic sequences, which are then cyclicly shifted and used to modulate precoded symbols. At the receiver, reverse operations are conducted to recover the data. Moreover, we prove that a circulant matrix can be constructed by selecting the cyclic shift length, while the DFT aided processing will diagonalize the circulant matrix. Thanks to the diagonalization design, the inner product of information-bearing chaotic vectors becomes zero, thus signals can be orthogonalized to suppress interferences. Furthermore, theoretical performances of the proposed transceiver, including the bit error rate (BER), the symbol rate, the energy efficiency and the spectrum efficiency, and the computational complexity are analyzed. Simulation results validate the exact analysis. Furthermore, the results demonstrate that the proposed PC-MC-M-CVCSK system outperforms the counterpart schemes, which can provide M-ary high symbol rate transmission services with enhanced reliability performances.

Aiming to shed light on the operation of fully-digital transmitters, we present the first symbol-rate baseband model that makes explicit the inter-symbol interference introduced by the RF pulse-width modulation (RF-PWM). The proposed model expresses the transmitter output as symbols plus interference, paving the way for the derivation of in-band performance metrics of the communication system. Then, we find an approximation for the error vector magnitude that allows us to evaluate the impact of the oversampling ratio, the statistics of the transmitted symbols and the shaping pulse in the transmitter performance. Another advantage of the model is that simulation times are much shorter since it does not require interpolation to appreciate the PWM distortion. To obtain the model, we first assume a generic expression of the continuous-time signal to be transmitted, in terms of the information symbols and the reconstruction filter. This allows us to express the nonlinear differential equation that models the intrinsic distortion also in terms of the sent symbols. Then, we elaborate on the formulation of the continuous-time RF-PWM distortion to procure an expression of the received signal sampled at symbol rate. The article concludes with a numerical validation of the model, and a simulation of the bit error rate of the system.

Frequency-domain equalization (FDE) is a computationally efficient method to recover underwater acoustic single-carrier transmissions in a multipath environment. The FDE receivers often operate in a block-by-block manner, assuming that the channel is time invariant during a block duration. This assumption implies that traditional block-based FDE receivers experience performance degradation in fast time-varying channel conditions, since the interfrequency interference (IFI) is often not considered. Here, we focus on the IFI cancelation (IFIC) in single-carrier transmissions. The IFI formulations are developed for a blockwise FDE receiver, where the time reversal (TR) processing is incorporated to alleviate the interblock interference. Based on the formulations, the IFI is estimated by the time-varying impulse responses, which are obtained from an adaptive basis expansion model. A soft two-step IFIC strategy is then employed to address the IFI. In the first step, the main IFI is removed by the time-varying TR processing and explicit IFI cancelation. The residual IFI is suppressed by the frequency-domain decision feedback equalization (FD-DFE) in the second step. To further enhance the communication performance, we develop a soft-symbol-based iterative receiver, referred to as IFIC-FD-DFE. The impulse responses, explicit IFI, and residual IFI are updated in an iterative fashion, based on the soft symbol estimates. The proposed receiver has been tested using the at-sea measurements collected at the Gulf of Mexico in August 2017. Communication packets at four ranges at the carrier frequency of 160 kHz with a symbol rate of 32 kHz have been decoded. The effectiveness of the IFIC-FD-DFE receiver has been demonstrated via comparisons with several FDE schemes in the current literature.

A cost-effective optical performance monitoring (OPM) scheme is proposed to realize modulation format identification (MFI), baud rate identification (BRI), chromatic dispersion identification (CDI), and optical signal-to-noise ratio (OSNR) estimation of optical signals simultaneously. This technique is based on multi-task learning (MTL) neural network model with adaptive asynchronous delay tap plot (AADTP) and asynchronous amplitude histogram (AAH) by direct detection in the intermediate nodes of optical networks. The generation of AADTP depends on the sampling rate but not the symbol rate, which makes the scheme transparent to the baud rate. The combined inputs of AADTP with AAH improve accuracies of the neural network, compared with a single input. This scheme is verified experimentally where signals with two formats, quadrature phase shift keying (QPSK) and 16 quadrature amplitude modulation (16QAM), two baud rates, 14 GBaud and 28 GBaud, and three CD situations, 0 ps/nm, 858.5 ps/nm, and 1507.9 ps/nm, are adopted. The best accuracies of MFI, BRI, CDI are 100%, 99.81%, and 99.83%, respectively. Meanwhile, the lowest average mean absolute error (MAE) of OSNR estimation is 0.2867 dB over the range of 10–24 dB (QPSK) and 15–29 dB (16QAM). It is cost-effective and practical for the proposed OPM technique to be applied in the intermediate nodes to construct smart optical networks since it uses only one photodetector assisted with an advanced deep learning algorithm.

An improved weather-forecast-based link-budget design technique for space-to-Earth links is described. The aim is the stochastic optimization of both transmission symbol rate and received signal-to-noise ratio. The proposed radiometeorological operations prediction (RadioMetOP) model takes into account the forecast uncertainty by a space–time ensemble method exploiting the temporal evolution of the predicted radiometeorological variables over the weather-forecast spatial grid. The unique possibility of testing and validating the RadioMetOP model is presented, thanks to the $Ka$ -band downlink measurements available from the support of the European Space Agency’s antenna tracking network to deep-space Hayabusa-2 (HB2) mission, operated by the Japan Aerospace Exploration Agency. First, the RadioMetOP model accuracy is tested by comparing the signal-to-noise ratio, measured during the transmission periods, with the simulated one, properly scaled to the symbol rate operated by HB2, finding correlation values of 0.9 that confirm the effectiveness of the proposed approach. Second, the $a$ posteriori analysis of the optimization process is accomplished, showing that depending on the considered criteria for the link-budget optimization, the use of the RadioMetOP model would have allowed a transmitted data volume more than doubled and an average signal-to-noise ratio gain between 2.1 and 3.8 dB.

In this paper, a novel joint symbol rate-modulation format identification (SR-MFI) and optical signal-to-noise ratio (OSNR) estimation scheme using the low-bandwidth coherent detecting and random forest (RF)-based ensemble learning is proposed for intermediate nodes in the flexible dense wavelength division multiplexing (F-DWDM) networks. By leveraging low-bandwidth coherent detecting with small bulk wavelength scanning, no chromatic dispersion compensation and low-complexity RF, the proposed scheme could serve as a reduced-complexity and cost-effective option to realize joint SR-MFI and OSNR estimation at intermediate nodes in F-DWDM networks. To verify the feasibility of the proposed scheme, the comprehensive simulations of 8/16 GBaud polarization division multiplexing (PDM)-4/16/32/64 quadrature amplitude modulation (QAM) systems are conducted. The simulation results show that the identification accuracy of SR-MFI reaches 100% and the mean absolute error of OSNR estimation is within 1 dB. Moreover, the proposed monitoring scheme is verified by 8/16 GBaud PDM-4/16/32QAM coherent transmission experiments.

Nyquist signals with low roll-off factors pose a challenge for non-data-aided blind symbol rate estimation problems in long-haul applications. We adopted the nonlinear least squares (NLS) approach to estimate the symbol rate of low roll-off factor signals. This method tolerates chromatic dispersion and additive Gaussian noise. In addition, this method can operate below two samples per symbol, thus enabling low-power-consumption receivers. Simulation and experimental results show that the mean squared error is below $10^{-4}$ with only 3000 samples needed for polarization-division-multiplexed (PDM) quadrature phase-shift keying (QPSK) or quadrature amplitude modulation (QAM) systems with a roll-off factor below 0.1 for an optical signal-to-noise ratio greater than 12 dB. Compared with the maximum likelihood estimation (MLE) method, our proposed method has a more robust performance under low roll-off factor signals and in low-sampling-rate scenarios. The mean squared error remains the same for a nominal symbol rate (i.e., the ratio of the symbol rate to the sampling rate, also widely known as oversampling rate) ranging from 0.1 to 0.9.

In video compression, throughputs of entropy encoders based on arithmetic coding are limited. This article presents the architecture of the entropy coder able to process in each clock cycle much more binary symbols than previous works. The architecture takes advantage of the multisymbol implementation of the binary arithmetic coder (BAC) developed earlier. To balance high throughputs of the BAC, fast implementations of binarization, context modeling, and probability model (PM) update are developed. The main improvement in the symbol rate stems from the decomposition of the processing path into many parallel ones. Critical paths associated with state transitions are shortened since each path updates the PM only for one context selected in each clock cycle. The negative impact on the symbol rate is compensated by the context-based symbol reordering. Although paths have variable bin/symbol rates, the applied buffering strategy improves the continuity of two data streams directed to the BAC, separately for context-coded and bypass-mode symbols. The entropy coder synthesized for the 90-nm TSMC technology consumes 273-k gates and operates at 570 MHz. It achieves the average symbol rate of 13.08 bins per clock cycle and the throughput of 7455 Mbins/s for high-quality H.265/HEVC compression.

We present an additive noise model for the signal-to-noise ratio prediction in optical systems employing low-resolution (4 bits and below) digital-to-analog and analog-to-digital converters. Firstly, the expected ASIC power consumption saving by employing low-resolution digital-to-analog and analog-to-digital converters rather than their high-resolution version (8 bits) is assessed and found to be up to 20% for a 4-bit physical resolution. Secondly, to assess the achievable data rate with low-resolution, we present a prediction model, which relies on two steps. First, the mean square error at the low-resolution quantizer output due to quantization and clipping is computed. Second, the mean square error is converted into a signal-to-noise ratio, carefully accounting for the operating parameters (sampling frequency, symbol rate, clipping factor). The domain of validity of this model is assessed for both quantization and clipping noises separately. The predictions are confronted with numerical simulations and a set of experiments in a back-to-back optical set-up. The results show that the signal-to-noise ratio can be predicted with an error of less than 0.5 dB within the domain of validity of the model. Finally, we use this model to establish the resolution requirements for the next generation of metropolitan optical systems (>400 Gbit/s) and compare them with most recent experiments using low-resolution digital-to-analog converters.

For reentry communication, owing to the influence of the time-varying plasma sheath, the received IQ baseband signals are severely rotated on constellation. Researches have shown that the frequency of electron density varies from 20kHz to 100 kHz which is on the same order as the symbol rate of most TT&C communication systems and traditional estimation algorithms cannot track the variation of channel. In this letter, motivated by principal curve analysis, we propose a deep learning (DL) algorithm which is called symmetric manifold network (SMN) to extract the curves on the constellation and classify the signals based on the curves. The key advantage is that SMN can achieve joint optimization of demodulation and estimation. From our simulation results, the new algorithm significantly reduces the symbol error rate (SER) compared to existing algorithms and enables accurate estimation of fading with extremely high bandwidth utilization rate.

We propose in this letter the time-based receive transformation (TRT) to suppress the inter-block interference (IBI) in the single-input-single-output (SISO) system with faster-than-Nyquist (FTN) signaling under the multi-path channel. For the trailing-zeros based FTN signaling or the OFDM based FTN signaling, the achievable rate benefits from the increased symbol rate but is degraded by the increased number of symbols that multi-path inter-symbol interference (ISI) affects. We show that the TRT based FTN signaling can completely eliminate the effect of IBI so that its achievable rate benefits from both the increased symbol rate and the increased number of symbols that multi-path ISI affects. We also show that the achievable rate for the TRT based FTN signaling is larger than that for the trailing-zeros based FTN signaling and the OFDM based FTN signaling, and this advantage increases with the ratio of the symbol rate to the Nyquist rate.

Carrier frequency and symbol rate estimation are the main contents of parameter estimation, which is the basis of modulation recognition and further processing of signals especially in non-cooperative communication. With the development of wireless communication, the signal transmission environment has become increasingly bad, causing more difficulties in parameter estimation. It is well known that the signal cycle spectrum is robust to noises and signal parameters are closely related. In practice, it is impossible to calculate the cyclic spectrum of infinite length data signals. When using finite length data to obtain a cycle spectrum, the truncation noise is induced, resulting in interference. It is necessary to overcome the influence of noises in order to improve the detection ability of discrete spectral lines. An improved method of the discrete spectral line extraction algorithm is proposed by reflecting the amplitude advantage of discrete spectral lines through salient features of continuous noises in discrete spectral line neighborhood.

A lightweight two-stage convolutional (deep) neural network (CNN) based modulation format identification (MFI) scheme is proposed and demonstrated for the polarization domain multiplexing (PDM) fiber communication system with probabilistically shaped (PS) modulation formats. The scheme is tested on a PDM system at a symbol rate of 28 GBaud. Six probabilistically shaped (PS) modulation formats (of 3 bit/symbol PS-16QAM, PS-32QAM, and PS-64QAM, of 4 bit/symbol PS-32QAM and PS-64QAM, and of 5 bit/symbol PS-64QAM) along with six standard modulation formats (BPSK, QPSK, 8PSK and three uniformly shaped (US) QAM: US-16QAM, US-32QAM and US-64QAM) are identified by the trained CNN. By taking advantage of computer vision, the results show that the proposed scheme can provide very high accuracy and significantly improve the identification performance over the existing techniques. The influences of the learning rate of the CNN are also discussed.

A simple data-aided carrier synchronization scheme is proposed for variable modulation (VM) communication systems under the initial conditions of a low signal-to-noise ratio (SNR) and normalized carrier frequency offset (CFO) symbol rate of 20%. The proposed carrier synchronization scheme is simplified into two steps; a reconfigurable L&R (RLR) algorithm and pilot-aided (PA) phase linear interpolation algorithm is applied for carrier frequency recovery (CFR) and carrier phase recovery (CPR), respectively. Furthermore, the autocorrelation values of multi-pilot blocks are superimposed to improve the accuracy of the CFR algorithm, and the algorithm formulas are decomposed and modularized to simplify the implementation complexity of the RLR algorithm. Simulation results show that the RLR algorithm can track and lock the CFO up to a 33.2% symbol rate and reduce the CFO to 0.024%. The bit error rate (BER) performance of the carrier synchronization scheme almost coincides with the theoretical curve results. Comparison of hardware complexity shows that the multiplication resource consumption can be reduced by at least 72.47%.

As optical performance monitoring (OPM) requires accurate and robust solutions to tackle the increasing dynamic and complicated optical network architectures, we experimentally demonstrate an end-to-end optical signal-to-noise (OSNR) estimation method based on the convolutional neural network (CNN), named OptInception. The design principles of the proposed scheme are specified. The idea behind the combination of the Inception module and finite impulse response (FIR) filter is elaborated as well. We experimentally evaluate the mean absolute error (MAE) and root-mean-squared error (RMSE) of the OSNR monitored in PDM-QPSK and PDM-16QAM signals under various symbol rates. The results suggest that the MAE reaches as low as 0.125 dB and RMSE is 0.246 dB in general. OptInception is also proved to be insensitive to the symbol rate, modulation format, and chromatic dispersion. The investigation of kernels in CNN indicates that the proposed scheme helps convolutional layers learn much more than a lowpass filter or bandpass filter. Finally, a comparison in performance and complexity presents the advantages of OptInception.

A reception method is proposed to improve error rate performance of quadrature amplitude modulation (QAM) signals transmitted over fast fading channels. The method can be treated as a simplified version of generalized likelihood ratio test (GLRT). Instead of exhaustive search that is necessary in GLRT, the search in the proposed method is performed over possible values of only one QAM symbol located in the middle between two pilot symbols. This searched symbol is used as an additional pilot symbol to improve channel estimation quality in the case of fast fading. For other QAM symbols of the received block, hard decisions of the demodulator are used instead of complete search. In such a manner, all data symbols are involved in the process of channel state estimation. Simulation results showed that the proposed method can notably reduce error floor with error rate reduction factor from 3.5 to 8 for 16- and 64QAM at Doppler spread up to 0.01 of symbol rate.

In this paper, a new blind adaptive equalization algorithm under noisy environment is proposed. We consider a practical case where the noise of each transmission channel is unknown. By oversampling the channel output at twice the symbol rate, a single-input double-output channel can be obtained. We apply the recursive-least-squares (RLS) to tackle the blind equalization problem. With the noise-induced bias, RLS algorithm is biased. In order to eliminate the bias, we present a bias-compensated RLS (BCRLS) algorithm that can estimate the unknown additive noise online and the noise-induced bias can be therefore removed. The unbiased estimate of the channel characteristics obtained can be used for channel equalization. Simulations results are presented to demonstrate the performance of the proposed algorithm.

In this paper, an algorithm is proposed to estimate the carrier frequency and symbol rate of binary phase shift keying modulation with Barker codes in a high noise environment. The proposed algorithm is based on cross-correlation functions between unknown and reference signals. This algorithm divides into two estimators. The first one is used to estimate the carrier frequency and second one is to estimate the symbol rate with different types of binary phase shift keying signals with Barker Codes (7, 11, and 13). The superiority of the proposed algorithm is demonstrated by the analysis and simulations. The simulation results show that the required value of signal-to-noise ratio is to obtain the perfect probability of correct estimations, where (P ce = 100%) is SNR ≥ -26 dB for all test BPSK signals. It was confirmed that the algorithm is suitable for detecting and estimating the carrier frequency and symbol rate of the binary phase shift keying signals in a low signal to noise ratio.

Efficient synchronization is of great importance for fiber optical coherent communication system. Here, we propose an accurate and low-complexity timing/frequency synchronization scheme based on sparse fast Fourier transform (S-FFT). The proposed scheme consists of coarse timing/frequency synchronization, fine timing synchronization, and fine frequency synchronization. Inspired by the idea of S-FFT, we take full advantages of the sparse nature of training symbols (TSs) and realize the synchronization in the frequency domain. The proposed scheme enables accurate timing synchronization at low signal-to-noise ratio (SNR) region. A complete frequency offset estimation (FOE) range of [−symbol rate/2, + symbol rate/2] can be realized with high resolution. Finally, the proposed scheme is experimentally verified through 10 Gbaud dual-polarization (DP) 16/32-quadrature amplitude modulation (QAM) transmission, without the BER performance penalty. In particular, the total computation complexity is reduced by nearly 200 times in comparison with that using conventional sliding window correlation scheme.

A novel method based on constellation structure is proposed to identify PSK and QAM modulation of different orders, in the slow and flat fading channel. The proposed method does not require training for threshold optimization and considers carrier frequency, symbol rate, and phase offset unknown. The symbol rate is estimated using the spectrum of the instantaneous phase of the complex baseband signal. Carrier frequency offset (CFO) is estimated and corrected from the downconverted signal and downsampled to the estimated symbol rate for extraction of constellation points. The phase offset is determined based on the symmetrical structure of constellation. The features extracted using k-medoids are used for classification of the final modulation scheme. Results show that the proposed algorithm outperforms some existing classifiers and offers lower computational complexity compared to algorithms based on subtractive clustering.

LoRa has established itself as one of the leading technologies within evolving low power wide area networks. In the patented LoRa modulation, a linearly increasing basis chirp signal spans the LoRa bandwidth. Cyclic shifts of this basis chirp signal create a multidimensional space for the orthogonal signaling of nonbinary LoRa symbols. The number of bits per LoRa symbol as well as the symbol rate depend on an applied spreading factor (SF) that could vary between 7 and 12. In this paper, interleaved chirp spreading LoRa (ICS-LoRa) is proposed as a physical layer-inspired approach to enhance data rates of the capacity-limited LoRa networks. In ICS-LoRa, interleaved versions of the nominal LoRa chirp signals constitute a new multidimensional space with the purpose of adding one extra bit within each transmitted ICS-LoRa symbol. The proposed interleaving pattern of ICS-LoRa maintains the same communication robustness of nominal LoRa. The ICS interleaving pattern is also designed to simplify implementation where both ICS-LoRa modulation and demodulation can share the same ICS-interleaver block. An accurate approximation for BER performance of the proposed ICS-LoRa is derived in order to evaluate the underlying reception sensitivities. It is shown that the 14% capacity gain of ICS-LoRa with an SF of 7 is associated with a sensitivity loss at the scale of only 0.8 dB. On the other hand, ICS-LoRa achieves more than 8% in capacity gain with virtually no impact on sensitivity performance when using an SF of 12 that governs the maximum coverage range.

In this work, we propose a closed-loop analog system to detect the source information of a binary data stream coded by a flexible finite automaton. We initially consider the dual sideband suppressed-carrier modulation of a base band binary amplitude waveform. The automaton introduces a symbol redundancy as phase contribution of the modulated signal by a simple mapping scheme. The proposed recovery system performs a coherent demodulation, presenting the base-band binary wave to a maximum likelihood hard detector, a simple analog trigger that estimates the source data within the symbol period. This wave is over-sampled, and the final decision comes by counting the positive samples and a majority vote. We prove our approach is valid answering the most important concerns: the stability of the closed loop, a first analytical expression of the error rate when a Markov birth process models the counting phase, and finally the role of this last loop to lower the bit error rate compared to a simple Costas loop. The analysis continues by solving the problem of carrier and symbol rate recovery and the impact of non-linearity and noise in the basic analog blocks. Behavioral simulations describe a competitive scenario in terms of error rate, comparing the proposed approach to the Costas Loop and the basic convolutional decoding strategies based on Viterbi algorithm both in the hard (Hamming metrics) and soft (Euclidean metrics) versions.

To further investigate the optical fast orthogonal frequency-division multiplexing (FOFDM) with sub-channel spacing equal to half of the symbol rate, an adaptive modulation scheme for FOFDM is proposed and experimentally demonstrated in low-cost short-reach intensity-modulated and direct-detection (IM/DD) systems using a directed modulated distributed feedback laser (DML). The experimental results and analyses indicate, it is feasible to transmit an adaptively modulated optical FOFDM signal over 20-km and 50-km standard single mode fibers (SSMFs). Compared with a single modulation format of 16-PAM, after 20-km SSMF transmission, the receiver sensitivity of the adaptive modulation scheme can be improved by about 2.3 dB at the bit error ratio (BER) of 2.4 × 10−2. Moreover, after 50-km SSMF transmission, the adaptive modulation scheme can still under 2.4 × 10−2 when received optical power (ROP) is larger than −1 dBm, while the 16-PAM modulation scheme cannot. In addition, an overlap frequency-domain equalization (OFDE) scheme is employed after sub-carrier de-multiplexing at the receiver to enable the effects of inter-symbol interference (ISI) to be effectively suppressed even though a cyclic prefix (CP) is not employed. Experimental results show that the FOFDM systems employing OFDE scheme have almost no performance degradation when compared to employing conventional FDE with an additional CP, but the spectral efficiency (SE) can be significantly improved by 12.37%.

Cyclostationary analysis has several applications in communications, e.g., spectral sensing, signal parameter estimation, and modulation classification. Most of them consider the additive white Gaussian noise (AWGN) channel model, although wireless communication systems may also be subject to non-Gaussian interference and impulsive noise. In this context, the communication channel can be better modeled by heavy-tailed distributions, such as the non-Gaussian alpha-stable one. Some applications of the cyclostationary approach based on the spatial sign cyclic correlation function (SSCCF), fractional lower-order cyclic autocorrelation function (FLOCAF), and cyclic correntropy function (CCF) demonstrate that these are promising solutions for the analysis of signals in the presence of impulsive non-Gaussian noise. However, the investigation of functions above applied to digital modulation recognition in impulsive environments, and the comparison among them are topics that did not adequately explore yet. This work demonstrates that SSCCF is a particular case of the FLOCAF. Besides, a detailed analysis of the use of the FLOCAF and CCF is presented to obtain cyclostationary descriptors for the recognition of digital modulations BPSK, QPSK, 8-QAM, 16-QAM, and 32-QAM. Automatic modulation classification (AMC) architectures, based on the functions mentioned above, are also proposed. Besides, another contribution showed is that both the FLOCAF and CCF allow the symbol rate parameter estimation. The performances of AMC architectures were evaluated in the scenario with modulated signals contaminated with additive non-Gaussian alpha-stable noise. The results demonstrate that both architectures can classify signals in different contamination scenarios. However, the architecture based on the CCF is more efficient than the FLOCAF-based one.

We present a novel method to estimate chromatic dispersion with ultra-low sampling rate based on training sequence. The under-sampling can be equivalent to over-sampling by splicing points with periodic sequence. The functional relationship between equivalent over-sampling rate and symbol rate, actual sampling rate and sequence period is deduced. To demonstrate the feasibility of the method, the simulation of a 28 GBaud QPSK optical fiber communication system is carried, in which 76 MSa/s sampling rate is equivalent to 66.5 GSa/s sampling rate. The results show that maximum estimation error is less than 160 ps/nm after 100 km to 2300 km SSMF transmission. We also demonstrate the robustness of the proposed method to amplified spontaneous emission and nonlinear noise in a three-channel optical fiber communication system. Moreover, the proposed method has been experimentally verified with a 20.5 GBaud QPSK system, 1.25 GSa/s sampling rate is equivalent to 51.25 GSa/s sampling rate, and estimation error is less than 100 ps/nm and 150 ps/nm after 100 km and 200 km SSMF transmission, respectively. The proposed method eliminates the requirement of high speed ADC and is cost effective, which can be used for optical performance monitoring.

The article is devoted to studying the features of the application of the frequency synchronization algorithms in the second generation satellite broadcasting standard DVB-S2X for LEO satellites. In the course of the work, we calculated the Doppler shift values for a low-orbit satellite in the Ka-band, estimated minimum symbol rate, showed that the conventional set of algorithms could work with small changes, simulated frequency synchronization, and found the optimal parameters of the algorithms for normal and VLSNR frames.

The adaptive communication system is going to play a major role for fifth-generation (5G) and beyond wireless communication where the physical layer signal parameters need to be changed at the transmitters as per system requirement and the receiver needs to estimate them to recover the signal. In this paper, we have proposed an efficient and robust automated symbol rate estimation model for single carrier system over frequency-selective fading environment by using deep neural network (DNN) approach. The proposed scheme estimates symbol rate without having any prior knowledge of the signal bandwidth which was the main assumption for existing statistical methods. In the proposed scheme, no additional knowledge such as channel state information (CSI) and synchronization parameters are required to estimate the symbol rate. The proposed model outperforms the existing statistical models in terms of the performance. The performance of the symbol rate estimator is depicted by the normalized mean square error (NMSE).

Many blind detection algorithms for paired carrier multiple access (PCMA) signals in satellite communications require information about the signal and channel parameters. A blind receiver needs to obtain knowledge of at least some of these prior to the symbol detection process. In this paper, schemes for the blind estimation of the symbol rates and carrier frequencies of the two overlapping co-channel signals in PCMA are proposed. The methods exploit the cyclic statistics of the PCMA signal for the estimation of the desired parameters. Effects of the mutual interference of the carriers in the estimation process are analyzed and the performance of the proposed methods is evaluated via numerical simulations.

In this paper, we propose a novel receiver structure for single-carrier transmission with frequency domain equalization (FDE) that is exposed to power amplifier (PA) nonlinearities. A two-stage approach is adopted, in which linear communication channel is equalized at the first stage, and it is followed by a post-distortion where nonlinear distortion is reduced. In literature, nonlinear processing techniques are proposed, which performs memoryless compensation of nonlinear distortion together with FDE. However, in this study, we show that even if a memoryless nonlinearity exists, the received signal is impaired by nonlinear inter-symbol-interference. Therefore, we propose a class of symbol rate post-distortion techniques, which use neighboring received symbols to suppress the nonlinear interference. Two different post-distortion techniques, Gaussian process regression (GPR) and neural network (NN) based post-distorters, are considered. Also, a decision metric, combining outputs of fractional delayed bank of FDE's after post-distortion, is proposed to overcome performance degradation of FDE for frequency selective channels under nonlinear distortion. Performances of the proposed techniques are compared with that of the state-of-the-art techniques in terms of bit error rate and achievable information rate metrics via simulations. Simulation results demonstrate that GPR and NN based post-distortion methods together with bank of FDE outperform state-of-the-art techniques., Submitted to IEEE Transactions on Communication

Orthogonal Frequency Division Multiplexing (OFDM) is one of the upcoming techniques for achieving large data rates in 4G/5G wireless communication. In OFDM system, the data are transmitted over sizable subcarriers and modulated with low symbol rate. High-peak-to-average-power ratio (PAPR) is the major disadvantage in OFDM systems that results in out of band energy distortion, intermodulation among the subcarriers, and saturation in power amplifiers. This paper deals with the analyzing the PAPR reduction in OFDM systems using digital communication codes. Adaptive Huffman codes (AHC) is selected and applied in OFDM transmitter section for reducing the high peak signals. The encoding part selected in AHC is Vitter’s algorithm. QAM16 and PSK mapping schemes are used for modulating the data. Simulation is carried out for the proposed work using MATLAB software, and PAPR results are showed in Complementary Cumulative Distribution Function (CCDF) plot. Further, the PAPR results are compared with Huffman coding and using no codes. Simulation results show that for all subcarriers, the PAPR reduction of adaptive Huffman codes dominates the Huffman codes and using no codes.

Under the assumption that data and carrier phase are known to the receiver unit, the modified Cramer-Rao lower bound (CRLB) for symbol rate estimation has been developed by the authors in a previous contribution, whereas the current paper concentrates on a carrier-blind and non-data-aided (NDA) scenario. Because a closed-form solution of the true CRLB is not available and numerical methods turned out to be too complex from the computational point of view, a theoretical limit of the jitter variance for carrier-blind NDA algorithms is derived, which is in particular helpful at lower values of the signal-to-noise ratio.

Carrier and symbol synchronization are the key prerequisite for the accurate reception of the Quadrature Phase Shift Keying (QPSK) signal. The traditional synchronization methods have some intrinsic problems, such as slow speed, difficult to design the coefficients for the loop filter. In this paper, an adaptive carrier and symbol joint synchronization method is proposed, which applies the idea of segmented synchronization. The proposed approach divides the synchronization process into two stages: coarse stage and fine stage. In the coarse stage, loop filters with large bandwidth are used to fast capture the range of the carrier frequency offset (CFO) and symbol timing offset (STO). While, in the fine stage, filters with small bandwidth are adopted to accurately calculate and track the offsets. In addition, the proposed method can track the variation of the offsets dynamically, thus, it can adaptively identify the synchronization status and select the suitable structure and coefficients for different synchronization stages. Simulation results show that, compared with the traditional joint method, our proposed method can take into account the synchronization speed and stability simultaneously, and the speed and stability can be increased by 1.2 times and 21.77%, respectively, when the CFO is 1.5% of the symbol rate and STO is 0.5% of the symbol rate. Our proposed method can be used to solve the synchronization problem for the harsh environment, especially for the field of satellite communications, which has extremely large frequency and timing offsets.

In this paper, we consider the application of neural network for equalization of Faster-than-Nyquist (FTN) Signaling. First, we formulate the detection problem as a supervised regression task in machine learning framework. Then a recurrent neural network (RNN) called Bi-directional long short-term memory (Bi-LSTM) is proposed to characterize the feature of inter-symbol interference (ISI) introduced in FTN Signaling. Moreover, we describe a “mismatch SNR” strategy for building the training Dataset that can effectively help to prevent overfitting. Numerical results prove that the BER performance of the proposed neural network based detector is close to the theoretical optimal maximum likelihood sequence estimation (MLSE) when symbol rate within the Mazo Limit, and Bi-LSTM could be a more realistic scheme compare with MLSE when symbol rate exceeds the Mazo Limit.

In radio communications, using wavelet signal analysis to recover the symbol rate timing clock of orthogonal frequency-division multiplexing (OFDM) is a new approach that can tolerate signal distortion from intersymbol interference (ISI) and intercarrier interference of encoding digital data on multiple carrier frequencies. Typically, the reception synchronization with wavelet signal analysis in OFDM can improve the performance over the fourier transform-based OFDM. However, a synchronization procedure that is stable against distortion and noise is essential to diminish the symbol synchronization establishment and operation sampling period. In this paper, we propose an OFDM synchronization system and analyze the impact of the wavelet denoise procedure on the OFDM system, which extracts the symbol rate of the OFDM frame. The evaluation results show that the proposed system can optimize the frequency window size to enable an efficient timing and frequency offset estimation with high and stable performance in terms of bit error rate (BER) and Frame Error Rate (FER) especially when the value of EbN0 (a normalized signal-to-noise ratio SNR measure) is greater than 8 dB, thanks to the wavelet transform.

A novel compressing transform (CT) function based cyclic autocorrelation (CTCA) under the cyclostationary framework is presented, which is intended for the symbol rate estimation of phase-shift keying (PSK) signals in the presence of alpha-stable noise. The domain of the CT function built in this paper can be divided into the approximate linear zone (ALZ) and the suppression zone (SZ). The ALZ helps the proposed CT function keep the useful information of signals-of-interest unchanged and because of the SZ, the CT function can mitigate effectively the large amplitudes of the impulsive noise. Subsequently, motivated by the excellent parameter estimation performance of the cyclic autocorrelation and based on the constructed CT function, the CTCA is proposed for symbol rate estimation in alpha-stable noise. Afterwards, the estimation accuracy of the proposed CTCA is measured by the normalized root mean square error in Monte Carlo simulations. According to the simulation results, the proposed method is feasible for PSK symbol rate estimation, and it distinctively outperforms the equivalent cyclic autocorrelation based counterparts especially in a strong impulsive noise environment.

This paper proposes a new technique to increase the symbol rate in Quadrature Amplitude Modulation (QAM) using a new set of orthonormal functions. The proposed technique increases the rate of QAM symbols without increasing the bandwidth of the modulated signal or increasing the modulation order of the QAM symbol. The set of orthonormal functions consists of four shaped-sinusoidal functions. The shaping functions are Hilbert-Transform pair. The proposed QAM modulator modulates two independent complex symbols in the same time. Each modulated symbol uses two different functions from the proposed set. The paper shows the structure of the modulator and demodulator of the proposed system. The paper presents different shaping pulses, which can be used with the proposed system. Keywords: Quadrature amplitude modulation, Orthogonal shaping shapes, Hilbert transform, Complex exponential carriers, Inter-symbol interference

Traditional serial demodulator cannot meet the requirement of data rates up to Multi-Gigabits due to the constraints of digital chips. Compared with time domain parallel demodulator, frequency domain parallel demodulator has the lowest complexity. The paper presents an improved full frequency domain parallel matched filter and symbol synchronization algorithm on the basis of Lin's algorithm. Here, we adopt Barton's algorithm to estimate timing error instead of O&M algorithm. On one hand, we can estimate timing error in frequency domain directly with Barton's algorithm. On the other hand, the oversample rate for Barton's algorithm is a half of O&M algorithm when the symbol rate is the same. Also, we propose frequency aliasing to decrease the points of IFFT to a half of FFT. Final, the MATLAB floating simulation results shows that the performance our proposed improved algorithm is close to the theoretical curve with the employment of two samples per symbol and the performance loss is less than 0.2dB compared with Lin's algorithm with the employment of four samples per symbol.

In this paper, we introduce the time-space MIMO system (where the signals received at different time instants and spatial spots are jointly processed) and propose the interference-unaware time-space receive transformation (IUTSRT), which can integrate the time diversity with the spatial diversity for the time-space MIMO system under cochannel interferences (CCI) and intersymbol interference (ISI). We show that IUTSRT can completely eliminate the effect of CCI and the inter-frame ISI (between different data frames) so that the time diversity provided by the intra-frame ISI (within the same data frame) can maximize the achievable rate. We also show that the achievable rate of the time-space MIMO system with IUTSRT can be larger than the CCI-free and ISI-free MIMO channel capacity and this advantage increases with the symbol rate and/or the number of symbols per frame.

In this paper, we propose the interference-unaware time-based receive transformation (IUTRT), which can employ the time diversity provided by cochannel interferences (CCI) and intersymbol interference (ISI) in the single-input-single-output (SISO) system. We show that IUTRT can completely eliminate the effect of CCI and the inter-frame ISI (between different data frames) so that the time diversity provided by the intra-frame ISI (within the same data frame) can maximize the achievable rate. We also show that the achievable rate of the SISO system with IUTRT can be larger than the CCI-free and ISI-free SISO channel capacity and this advantage increases with the symbol rate and/or the number of symbols per frame.

Conventional modulation formats for single carrier transmission do not provide the flexibility to gradually scale the data rate and spectral efficiency. By using multidimensional pulse-amplitude modulation, fractional numbers of bits per symbol can be achieved, which extends the flexibility and reach of intensity modulation and direct detection systems but keeps the signal processing simple. By using pseudo-Gray coding, we are able to achieve optimum mappings for various non-integer bits-to-symbol assignments. We show a transmission experiment with data rates ranging from 56 to 168 Gb/s in fine granularity over different link lengths at a symbol rate of 56 GBd.

An efficient procedure is presented for evaluating the performance of multidimensional modulation formats in terms of the achievable information rate (AIR). It allows the explicit properties of signal constellations to be captured and is applicable to fully loaded dense wavelength-division multiplexed transmission systems. The efficiency of the procedure facilitates formulating multidimensional quadrature amplitude modulation (QAM) constellation subset selection as a combinatorial optimization problem. The attained solutions for the quadrature phase shift keying (QPSK) 8D constellation subset selection suggest that a known 8D power and polarization balanced constellation (PPB constellation, 4 bits/8D symbol) and its different variations are the closest 8D QPSK subsets to the Shannon limit at 4 bits/8D symbol. 8D constellation subset selection of a QPSK constellation at 6 bits/8D symbol allows obtaining an 8D polarization balanced version of polarization-switched QPSK (PB-PS-QPSK). Using the proposed procedure, the performance of these constellations and their nonpolarization balanced counter parts, i.e., dual polarization binary phase shift keying (DP-BPSK) and PS-QPSK, is assessed in terms of the estimated AIR. The results exhibit good agreement with those of full system simulations for a single channel and five channels. Moreover, the impact of QAM constellation subset selection on the system performance is evaluated by comparing the reduction in information rate for a symbol rate of 35 Gbaud as a function of the number of channels. For 41 channels, the PPB constellation outperforms DP-BPSK by 2 Gb/s in information rate for a 12,000 km dispersion-managed (DM) link due to the improved linear and nonlinear constellation properties. Finally, PB-PS-QPSK enables an increase of 1.5 Gb/s in information rate compared to PS-QPSK for a 10,000 km DM link.

Cyclic frequency detection of cyclostationary signals and its application in modulation parameters estimation is the aim of this paper. A simple frequency shifted (FRESH) model is structured. The normalized least mean square (NLMS) algorithm is engaged to estimate the unknown weights of the considered model. The norm of the parameter estimate is related to the model accuracy. A high (low) value indicates that the FRESH structure is based on an accurate (inaccurate) cyclic frequency and the weight estimate of the NLMS algorithm converges to a nonzero (zero) vector. Accordingly for two given values which only one of them is the true cyclic frequency of the received signal, two FRESH structures are considered and simultaneously two NLMS algorithms are executed. If the norm of the weight estimate of the first algorithm exceeds the resulted norm of the second one, according to the proposed method, the first given value is the true cyclic frequency and vice versa. The method is used to estimate the modulation parameters of three different problems: chip rate estimation of a spread spectrum signal, carrier frequency and bit rate estimation of BPSK and QPSK signals, and symbol rate estimation of OFDM signals.

In view of the issue that the single-signal symbol rate estimation methods are unsuitable for time–frequency overlapped signals in underlay cognitive radio network (CRN), a novel symbol rate estimation method for time–frequency overlapped multiple phase shift keying (MPSK) signals in underlay CRN is proposed under low signal-to-noise ratio (SNR) conditions. In this method, the magnitude spectrum of teager energy operator (TEO) for the time–frequency overlapped MPSK signals is estimated first, and then, the nonlinear filter is employed to improve the spectral resolution of the TEO magnitude spectrum. Finally, the symbol rates of component MPSK signals are estimated by extracting the position information of the spectrum line, respectively. The modified Cramer-Rao bound of symbol rate estimation for the time–frequency overlapped MPSK signals is also derived in this paper. Simulation results are provided to confirm that the proposed method could estimate the symbol rate of the time–frequency overlapped MPSK signals effectively in low SNR regions.

Prefixes, in forms of cyclic-prefixes or zero-padding, have often been viewed as indispensable in underwater acoustic single-carrier transmissions to avoid inter-block interference (IBI) and to formulate circular convolution. However, the prefix introduces overhead and reduces spectral efficiency. This is especially true in fast time-varying channel conditions. Here, we propose a prefix-free scheme to facilitate frequency-domain equalization (FDE) in an underwater acoustic communication system, based on the time-reversal processing. In the proposed scheme, three main procedures, block partitioning, IBI cancellation, and prefix reconstruction, precede the FDE operation. The block partitioning at the receiver provides flexibility to support channel equalization in different channel fluctuation rates. The utilized prefix reconstruction scheme requires a strong first arrival to minimize the noise enhancement. Our solution is to use the time-reversal processing, because the resultant equivalent impulse response, also known as the $q$ -function, has a stable and compact peak. To further enhance receiver performance, we incorporate two strategies. One is overlapping partitioning. The other is iterative prefix reconstruction. The proposed schemes have been tested using the field measurements obtained from the Gulf of Mexico in August 2016. Communications over four ranges at the carrier frequency of 85 kHz with a symbol rate of 17 kHz have been demonstrated. The overlapping partitioning and iterative prefix reconstruction strategies have been shown to generate improvements in the receiver performance.

This Letter proposes a blind symbol packing ratio estimation for faster-than-Nyquist (FTN) signalling based on state-of-the-art deep learning technology. The symbol packing ratio (also named speeding parameter, time packing parameter etc.) is a vital parameter to obtain the real symbol rate and recover the origin symbols from the received symbols by calculating the intersymbol interference. To the best of the authors' knowledge, this is the first effective estimation approach for symbol packing ratio in FTN signalling and has shown its fast convergence and robustness to signal-to-noise ratio by numerical simulations. Benefiting from the proposed blind estimation, the packing-ratio-based adaptive FTN transmission without dedicate channel or control frame becomes available. Also, the secure FTN communications based on the secret symbol packing ratio can be easily cracked.

The degrees of freedom (DoF) gain due to excess bandwidth is lost in case of Symbol Rate (SR) sampling where Faster than Symbol Rate (FTSR) sampling emerges as a promising approach to exploit this gain. In this direction, FTSR sampling is studied to increase the total number of users in a network for a given fixed bandwidth. The rank analysis indicates that FTSR sampling brings rank advantage proportional to the excess bandwidth for unequally spaced channel taps. With the help of an iterative FTSR sampled MMSE multiuser receiver, this rank advantage can be employed in the separation of two users’ signals from each other that transmit simultaneously on the same frequency band.

A novel modulation format recognition (MFR) scheme based on multiple Stokes sectional planes images by generative adversarial network (GAN) is proposed and demonstrated to adapt to next-generation elastic optical network (EON). The application of the encoder, along with the suitable loss function, is able to achieve better performance with regards to MFR of GAN. Experimental verifications were performed for the polarization division multiplexing (PDM)-EON system at a symbol rate of 12.5GBaud. Five modulation formats, including PDM-BPSK, PDM-QPSK, PDM-8PSK, PDM-8QAM, PDM-16QAM, were recognized by our scheme under the condition of practical optical signal-to-noise ratio (OSNR) over both back-to-back transmission and 25km standard signal-mode fiber (SSMF). Specifically, the minimum required OSNR of PDM-16QAM signal to achieve 100% MFR success rate is 18 dB, which is lower than its corresponding 7% forward error correction (FEC) threshold. Results show that, compared with three other machine learning algorithms, the proposed scheme obtains the higher recognition accuracy in the case of the same OSNR. Moreover, the training data required by the proposed scheme is less than the traditional convolutional neural network (CNN) in MFR task, which means the training cost of the neural network is greatly reduced by using GAN.

We propose a full real-time clock recovery algorithm based on the Gardner algorithm with extended first-in-first-out (FIFO), data buffer, and add/delete state machine parts. The proposed algorithm has long-term stable bit error rate (BER) performance as well as tolerates a maximum clock frequency offset up to 330 ppm when we conducted a real-time experiment with high clock frequency errors on the Altera Stratix-V 5SGXMA7K2F40C3 FPGA platform with a symbol rate of 2.5 GBaud.

This paper investigates an iterative receiver for time-domain oversampled orthogonal frequency division multiplexing (OFDM) over time-varying underwater acoustic channels for both single-input, single-output (SISO), single-input, multiple-output (SIMO) and multiple-input, multiple-output (MIMO) scenarios. We extend two widely used parametric models for time-varying channels: (i) Doppler rate model (DRM) and (ii) basis expansion model (BEM) to work with oversampled OFDM systems. To exploit the inherent sparsity of underwater acoustic channel, iterative orthogonal matching pursuit (OMP) algorithm is adopted for channel estimation. To further reduce computational complexity, fast Fourier transform (FFT) based low-complexity implementations for iterative OMP algorithm are proposed for both BEM and DRM. The proposed receiver is evaluated by sea trial conducted in the Trondheim Fjord, Norway. Both 8-phase shift keying modulation scheme and 16-quadrature modulation (16-QAM) scheme are carried out during the sea trial. The experimental results show that the proposed iterative time-domain oversampled OFDM receiver achieves lower bit error rates (BERs) than conventional iterative symbol rate sampled OFDM receiver.