Frequency synchronization is essential to achieving the intended performance for single and multicarrier wireless systems. Blind techniques, which don't require prior channel knowledge or pilot symbols, are crucial for dynamic environments where self-adaptive synchronization is needed. A key objective of this paper is to provide the readers as well as the industry's professionals with a comprehensive understanding of the carrier frequency offset (CFO) problem in multicarrier communication systems like orthogonal frequency division multiplexing (OFDM), single carrier-frequency division multiple access (SC-FDMA), multiple input multiple output (MIMO)-OFDM, and MIMO-SC-FDMA. These waveforms are used in today's and future wireless communication systems such as wireless-fidelity (Wi-Fi), fifth-generation, and sixth-generation. Moreover, this paper also develops a taxonomy of the available solutions to address the CFO issue. We study blind techniques for CFO estimation presented in the recent literature and give potential future directions. We summarize various statistical methods and deep learning algorithms for CFO estimation and emphasize their advantages and limitations. We also incorporate the CFO impact on next-generation wireless systems such as orthogonal time frequency space and reconfigurable intelligent surface-assisted communication systems and provide a broader and deeper knowledge of the area. We provide simulation results of some existing estimators and their performance comparison in terms of mean square error for better understanding. Therefore, this paper is perfectly adapted to provide a comprehensive information source on blind CFO estimation techniques.

Lower-limb exoskeletons offer effective activeassist solutions for rehabilitating individuals with gait and mobility impairments. This study proposed a human-in-theloop control framework for a 3-DOF unilateral exoskeleton for the active assistance of a pediatric gait. The proposed HIL strategy incorporates the variable admittance control in the outer loop and non-singular terminal sliding mode (NSTSM) in the inner loop to enhance the trajectory tracking and offer safety and flexibility to the user. The variable admittance control modulates the admittance parameters of the exoskeleton using a simple adaptive law based on the human-exoskeleton interaction, while the NSTSM control provides a robust and accurate gait tracking at different walking speeds. Numerical simulations demonstrate that the HIL framework with variable admittance control effectively improves the safety and flexibility for pediatric users under human-exoskeleton interaction compared to the HIL framework with fixed admittance control. The fixed admittance parameters of stiffness ( 100 Nm/rad) and damping (2 Nms/rad) appear misestimated, as compliance modulation suggests varying parameters (65-95 Nm/rad and 1.8- 2.7 Nms/rad) for improved adaptability to interactions.

This letter presents a blind carrier frequency offset (CFO) estimator for multi-user multiple input multiple outputorthogonal frequency division multiple access (MIMO-OFDMA) uplink system by Capon method using covariance matrix decomposition in the presence of Rayleigh fading channel. In this method, a covariance matrix is derived from the received signal, followed by QR factorization of the covariance matrix to get the upper triangular matrix. Then, a cost function is formulated by calculating the inverse of the upper triangular matrix. The proposed estimator does not require channel state information or any pilot symbols, which makes the system spectrum efficient. The exact Cramer Rao lower bound is also derived, establishing a lower limit for the mean squared error of the proposed estimator. Simulation results indicate that our proposed method outperforms existing methods. The proposed method also provides a lower computational complexity.

Every communication system necessitates synchronization between the transceiver pair to ensure optimal performance at the receiver end. Reconfigurable intelligent surface (RIS)-assisted orthogonal frequency division multiplexing (OFDM) systems are also susceptible to the synchronization error, i.e., symbol timing offset (STO) and carrier frequency offset (CFO), Similar to conventional OFDM systems. Various techniques have been developed for estimating STO and CFO for OFDM systems. However, these existing methods do not specifically address the combined impact of STO and CFO in RIS-assisted OFDM systems. Motivated by this, we propose a joint STO and CFO estimator based on the zero correlation zone (ZCZ) sequence for RIS-assisted OFDM systems operating in a Rayleigh fading environment. The ZCZ sequences show ideal correlation properties in a zone. In terms of mean squared error (MSE), simulation results demonstrate that the proposed method outperforms other existing techniques. The bit error rate (BER) plot demonstrates that the proposed method is robust and effective against varying CFO and STO values after compensation.

Designing an intelligent or adaptive transceiver system is becoming a promising technology for upcoming generations of wireless communication systems due to its adaptivity, spectrum efficiency, and low-latency characteristics. However, there is no work available until now that characterizes and demonstrates complete adaptation in the physical layer for orthogonal frequency-division multiplexing (OFDM) systems. In this article, we propose and implement sequential blind parameter estimation methods for OFDM signals using radio frequency (RF) testbed setup in a realistic scenario. The estimations include the number of subcarriers, symbol duration, cyclic prefix, oversampling factor, symbol timing offset (STO), and carrier frequency offset (CFO). The proposed algorithms also include blind modulation classification for linearly modulated signals over a frequency-selective fading channel. The parameter estimation has been carried out through a cyclic cumulant process. The modulation formats are classified by using normalized fourth-order cumulant in the frequency domain. The STO and CFO are estimated by a proposed modified maximum likelihood algorithm. The performances of parameter estimations, modulation classification, and synchronization are measured through analytical, simulation, and measurement studies. The overall performance of the OFDM system is provided in terms of the received constellation diagram and bit error rate (BER) over an indoor propagation environment.

In this article, we design and implement a tree-based blind modulation classification algorithm for asynchronous multiple-input–multiple-output and orthogonal frequency-division multiplexing (MIMO-OFDM) systems. It can classify many of the linearly modulated signals, such as binary phase shift keying (BPSK), quadrature phase shift keying (QPSK), offset QPSK, minimum shift keying, and 16-quadrature amplitude modulation. The proposed classifier works in the presence of unknown frequency, timing, and phase offsets and with no prior knowledge of channel state information. Classification is performed in three steps. In the first step, preprocessing is done on the received signal to nullify the effect of timing offset. In the second step, key features are extracted by calculating higher order cumulants of the frequency-domain signal. In the third step, thresholds are determined by using the likelihood ratio test. A closed-form theoretical derivation for the probability of correct classification is obtained. The Monte Carlo simulations are conducted to compare the performance of the proposed algorithm with the existing algorithms. Finally, the proposed algorithm is validated through radio frequency testbed measurements over an indoor propagation environment.

Single carrier frequency division multiple access (SC-FDMA), a modified form of orthogonal frequency division multiple access (OFDMA), is a promising technique for high data rate and low peak-to-average power ratio for uplink communications in cellular networks. However, similar to OFDMA, SC-FDMA also suffers from carrier frequency offset (CFO). Particularly, in the presence of multiple users, the uplink SC-FDMA introduces multiple CFOs. The CFOs must be estimated and compensated before demodulating the signal to minimize the inter-carrier interference (ICI) and ensure the efficiency of the SC-FDMA uplink system. In this paper, we propose a method for multi-user CFOs estimation that exploits the property of minimum variance of signal amplitudes at the receiver across different subcarriers. It utilizes the mean and variance of the output magnitude based on its probability density function. The variance approaches minimum value when CFO is fully compensated. The CFO estimation performance is evaluated on the basis of simulation and comparison with other methods over frequency selective fading channel environments.

Blind modulation classification (MC) is an integral part of designing an adaptive or intelligent transceiver for future wireless communications. However, till date, only a few works have been reported in the literature for blind MC of orthogonal frequency division multiplexing (OFDM) system over frequency-selective fading environment. In this paper, a blind MC algorithm has been proposed and implemented over National Instruments (NI) testbed setup for linearly modulated signals of OFDM system by using discrete Fourier transform (DFT) and normalized fourth-order cumulant. The proposed MC algorithm works in the presence of synchronization errors, i.e., frequency, timing, and phase offsets and without the prior information about the signal parameters and channel statistics. To nullify the effect of timing offset in the feature extraction process, a statistical average has been taken over OFDM symbols after introducing uniformly distributed random timing offsets in each of the OFDM symbols. In this work, we have classified a more extensive pool of modulation formats for OFDM signal, i.e., binary phase-shift keying (BPSK), quadrature PSK (QPSK), offset QPSK(OQPSK), minimum shift keying (MSK), and 16 quadrature amplitude modulation (16-QAM). Classification is performed in two stages. At the first stage, a normalized fourth-order cumulant is used on the DFT of the received OFDM signal to classify OQPSK, MSK, and 16-QAM modulation formats. At the second stage, first we compute the DFT of the square of the received OFDM signal and then a normalized fourth-order cumulant is used to classify BPSK and QPSK modulation formats. The success rate of the proposed MC algorithm is evaluated through analytical and Monte Carlo simulations and compared with existing methods. Finally, the work is validated by providing an experimental setup on NI hardware over an indoor propagation environment.

Multiple carrier frequency offsets (CFOs) estimation in high speed single carrier frequency division multiple access (SC-FDMA) uplink system is a challenging issue. Most of the existing blind CFO estimation methods work for a certain type of carrier mapping scheme (CMS) or address a single CFO estimation by utilizing long data over frequency selective fading channel. These estimation methods become irrelevant at high speed and multi-user scenarios where CFO changes with symbols and users. In this paper, we propose a blind multiple CFOs estimation method for all CMS of SC-FDMA and implement over testbed. The proposed method requires only one SC-FDMA symbol to attain reliable estimation even in a high mobility environment, i.e., in a doubly selective channel. It exploits the phase difference present between even and odd samples of the received oversampled signal to estimate CFOs. Subsequently, an iterative joint CFO estimation and compensation (IJCEC) method is introduced to remove residual interference and increase CFOs estimation accuracy. Cramer-Rao lower bound is derived to characterize the CFO estimation accuracy of the proposed method. The work is compared with the conventional methods such as MUSIC, ESPRIT, CAZAC, and some existing methods and validated through Monte Carlo simulations. Finally, we authenticate the proposed IJCEC method by performing implementation and measurement on National Instrument testbed setup in an indoor propagation environment.

In this paper, a blind symbol timing offset (STO) estimation method is proposed for offset quadrature phase‐shift keying (OQPSK) modulated signals, which also works for other linearly modulated signals (LMS) such as binary‐PSK, QPSK, π/4‐QPSK, and minimum‐shift keying. There are various methods available for blind STO estimation of LMS; however, none work in the case of OQPSK modulated signals. The popular cyclic correlation method fails to estimate STO for OQPSK signals, as the offset present between the in‐phase (I) and quadrature (Q) components causes the cyclic peak to disappear at the symbol rate frequency. In the proposed method, a set of close and approximate offsets is used to compensate the offset between the I and Q components of the received OQPSK signal. The STO in the time domain is represented as a phase in the cyclic frequency domain. The STO is therefore calculated by obtaining the phase of the cyclic peak at the symbol rate frequency. The method is validated through extensive theoretical study, simulation, and testbed implementation. The proposed estimation method exhibits robust performance in the presence of unknown carrier phase offset and frequency offset.

This paper proposes a blind modulation classification (MC) algorithm for linearly modulated signals of orthogonal frequency division multiplexing (OFDM) system. The proposed MC algorithm works with unknown frequency, timing, and phase offsets and without the prior requirement of channel statistics. In this research, a larger pool of modulation formats, i.e., binary phase-shift keying (BPSK), quadrature PSK (QPSK), offset QPSK (OQPSK), minimum shift keying (MSK), and 16-quadrature amplitude modulation (16-QAM) for OFDM signal has been classified. Classification takes place in two stages. First, we compute the discrete Fourier transform (DFT) of the received OFDM signal and then a normalized fourth-order cumulant is used in frequency domain to classify OQPSK, MSK, and 16-QAM modulation formats. At the second stage, the normalized fourth-order cumulant is used on the DFT of the square of the received OFDM signal to classify BPSK and QPSK modulation formats. The success rate and computation of the proposed MC algorithm are evaluated and compared with the previous methods.

Frequency synchronization in single-carrier frequency division multiple access (SC-FDMA) uplink system is a challenging task due to the presence of different carrier frequency offsets (CFOs) for different users. In this paper, we propose a blind CFOs estimation algorithm for SC-FDMA uplink system by oversampling method in the presence of frequency selective fading channel. A cost function is derived which minimizes the power of the off-diagonal elements of a signal covariance matrix while estimating the correct CFOs. The off-diagonal elements are nothing but inter-carrier interference and multiple-access interference introduced in the presence of multiple CFOs. A complete mathematical model has been presented for multiple CFOs estimation under multiple access scenarios. The proposed CFOs estimation method does not require channel-state information which results in lower computational complexity. The higher iteration complexity of grid search algorithm has been further reduced by a deterministic approach. We also derive the Cramer-Rao bound for CFO estimation. The simulation results show that the proposed CFOs estimation method outperforms the existing subspace theory-based methods, specifically in the low signal-to-noise ratio region.

In multi-standard wireless communication receivers, automatic modulation classification is critical to blindly demodulate received signal. In this paper, a new method for automatic modulation classification of any received signal has been proposed. The proposed method exploits cyclostationary features of received signal in wavelet domain. Received signal is sampled at estimated symbol rate followed by quantization operation. Next, modulation type is identified from the histogram plot of the features of the received signal. Simulation results in AWGN channel shows the superiority of the proposed approach over existing approaches.

In multi-standard wireless communication receivers, an estimation of the symbol rate is critical to blindly demodulate received signal. Symbol rate estimation at high signal-to-noise (SNR) ratio has been studied extensively in the literature and many computationally efficient methods have been proposed. However, symbol rate estimation at low SNR environment is still a challenging task. In this paper, a new method for accurately estimating the symbol rate of any received signal has been proposed. To the best of our knowledge, proposed method is the first which exploits cyclostationary features of received signal in wavelet domain. Simulation results validate the superiority of the proposed method over others especially at low SNR values. At the end, detailed complexity analysis based on total number of gate counts is presented.