Frequency Domain Equalization Research Articles

On the Performance of Partial LIS for 6G Systems

One of the key technologies of 6G communications relies on large intelligent surfaces (LIS), which can be viewed as a near-field beamformer that is supportive of extremely high symbol rates and enables a high level of interference avoidance. This article focuses on LIS systems, analysing the impact of the use of a whole LIS system or a subset of an antenna array. We analyse an LIS system associated with a single carrier with frequency domain equalization (SC-FDE), and with different receiver types of varying complexities. Because it is a function of the number of antennas, the computational complexity decreases when antenna elements that are closer to the user equipment are used instead of the whole LIS. Moreover, with a partial LIS, a reduction of energy consumption is achieved, and mitigation of the interference levels is obtained, allowing a performance very close to that obtained with the whole LIS system.

Secure image transmission through LTE wireless communications systems

Secure transmission of images over wireless communications systems can be done using RSA, the most known and efficient cryptographic algorithm, and OFDMA, the most preferred signal processing choice in wireless communications. This paper aims to investigate the performance of OFDMA system for wireless transmission of RSA-based encrypted images. In fact, the performance of OFDMA systems; based on different signal processing techniques, such as, discrete sine transforms (DST) and discrete cosine transforms (DCT), as well as the conventional discrete Fourier transforms (DFT) are tested for wireless transmission of gray-scale images with/without RSA encryption. The progress of transmitting the image is carried by firstly, encrypting the image with RSA algorithm. Then, the encrypted image is modulated with DFT-based, DCT-based, and DST-based OFDMA systems. After that, the modulated images are transmitted over a wireless multipath fading channel. The reverse operations will be carried at the receiver, in addition to the frequency domain equalization to overcome the channel effect. Exhaustive numbers of scenarios are performed for study and investigation of the performance of the different OFDMA systems in terms of PSNR and MSE, with different subcarriers mapping and modulation techniques, is done. Results indicate that the ability of different OFDMA systems for wireless secure transmission of images. However, the DCT-OFDMA system showed superiority over the DST-OFDMA and the conventional DFT-OFDMA systems.

Equalization methods for Filter Bank Multicarrier OQAM

Filter bank multi-carrier offset-quadrature amplitude modulation (FBMC OQAM) is a hot topic in 5G multi-carrier research. In order to achieve high data rates and reliable wireless communication, receiver channel equalization is required. This is because of the equalizer's excellent spectral efficiency, exceptionally low side-lobe leakage, zero periodic cyclic prefixes (CP), and multiphase filter design. However, a number of degradations, including fading, Doppler shifts, and intermittent symbol interference (ISI), are added to the transmitted data symbols as they traverse the wireless channel, reducing the network's overall quality. To mitigate the negative effects of channel defects, many channel equalization algorithms have been developed for use in modern telecommunications networks. Six different equalizer approaches have been implemented. Using the Pedestrian A and Vehicular B channel in our simulations, we examine how well they function. The system was simulated using MATLAB's Communications Toolbox (an M file). Bit-error-rate (BER) and signal-to-noise ratio (SNR) were used to evaluate the outcomes. The Bit error rate was calculated by checking for differences between the sent and received bit sequences. The best value of the bit error ratio using frequency domain equalization and the time domain equalization 5.4 and 4.7 , respectively.

An Improved Orthogonal Matching Pursuit Algorithm for CS-Based Channel Estimation

Wireless broadband transmission channels usually have time-domain-sparse properties, and the reconstruction of these channels using a greedy search-based orthogonal matching pursuit (OMP) algorithm can effectively improve channel estimation performance while decreasing the length of the reference signal. In this research, the improved OMP and SOMP algorithms for compressed-sensing (CS)-based channel estimation are proposed for single-carrier frequency domain equalization (SC-FDE) systems, which, in comparison with conventional algorithms, calculate the path gain after obtaining the path delay and updating the observation matrices. The reliability of the communication system is further enhanced because the channel path gain is calculated using longer observation vectors, which lowers the Cramér–Rao lower bound (CRLB) and results in better channel estimation performance. The developed method can also be applied to time-domain-synchronous OFDM (TDS-OFDM) systems, and it is applicable to the improvement of other matching pursuit algorithms.

Dynamic Secure Key Distribution Based on Dispersion Equalization and Cellular Automata for Optical Transmission

This paper proposes a dynamic secure key distribution scheme based on dispersion equalization and cellular automata (CAs). The scheme effectively eliminates the key inconsistency problem caused by imperfect channel reciprocity, and dynamic key sequences can be conveniently generated with large key space in long-haul optical transmission. In the process of communication, the legitimate parties obtain the secure core parameter from the frequency domain equalizer algorithm, and a final key sequence is generated through CA iterations on the basis of the core parameter. The randomness and reciprocity characteristics of the channel ensure the security and uniqueness of the core parameter and final key sequence. With 10G Baud 16 quadrature amplitude modulation over 400 km standard single-mode fiber transmission, the proposed scheme is verified with a free key error rate and an unlimited key generation rate. The security robustness of this scheme was theoretically analyzed and verified by sweeping the eavesdropper’s tapping position and improving CA operation processing. The proposed key distribution scheme is compatible with the existing transmission system for different signal modulation formats.

Robust equalization for single-carrier underwater acoustic communication in sparse impulsive interference environment

Impulse noise significantly distorts the background noise within communication systems, causing a notable departure from the Gaussian distribution. This distortion, in turn, exerts a detrimental influence on the performance of conventional single-carrier frequency domain equalization techniques. In this paper, we introduce a novel algorithm for joint channel, interference, and symbol estimation within single-carrier systems. This algorithm is grounded in the framework of variational Bayesian inference and possesses the unique capability of simultaneously accounting for the sparsity inherent in the channel and impulse interference. In the course of processing, it leverages multi-parameter probability distributions to effectively model the intricate posteriori probabilities associated with impulse interference vectors and channel vectors. This, in turn, facilitates the computation of maximum a posteriori estimates and subsequently enables the estimation and elimination of interference. We validate the efficacy of our proposed method through both numerical simulations and the processing of experimental data. Our results unequivocally demonstrate the robustness and manageable computational complexity of our approach within the context of impulse interference-prone environments.

Enhanced MIMO-DCT-OFDM system using cosine domain equaliser

ABSTRACT The Discrete Cosine Transform (DCT) can be used instead of the conventional Discrete Fourier Transform (DFT) for the Orthogonal Frequency Division Multiplexing (OFDM) construction, which offers many advantages. In this paper, the Multiple-Input-Multiple-Output (MIMO) DCT-OFDM is enhanced using a proposed Cosine Domain Equaliser (CDE) instead of a Frequency Domain Equaliser (FDE). The results are evaluated through the Rayleigh fading channel with Co-Carrier Frequency Offset (Co-CFO) of different MIMO configurations. The average bit error probability and the simulated time of the proposed scheme and the conventional one are compared, which indicates the importance of the proposed scheme. Also, a closed formula for the number of arithmetic operations of the proposed equaliser is developed. The proposed equaliser gives a simulation time reduction of about 81.21%, 83.74% compared to that of the conventional Linear Zero Forcing (LZF)-FDE and Linear Minimum Mean Square Error (LMMSE)-FDE, respectively, for the case of a 4 × 4 configuration.

An iterative subblock-based receiver for SC-FDE systems in time-varying underwater acoustic channels

Traditional single-carrier frequency domain equalization (SC-FDE) systems assume time-invariant channels that are difficult to realize in underwater acoustic (UWA) communication over block-based durations, leading to inter-frequency interference (IFI). Currently available approaches to resolving this issue involve shortening the block or inserting frequent training sequences at the cost of additional information from the channel and reduced spectral efficiency. This paper proposes an iterative subblock-based receiver algorithm that divides each time-varying block into multiple quasi-static subblocks. The designed receiver has a two-step structure consisting of block processing and cascaded subblock processing, where the former generates prior symbolic knowledge and the latter iteratively weakens IFI. We consider smoothly variant channels between adjacent subblocks and track them using a Kalman filter, leading to a more accurate estimation of the IFI and better equalization. The proposed algorithm was tested through simulations and experiments in Qiandao Lake and the Yellow Sea using blocks of different lengths and numbers of subblocks and elements in the array. The results provide a low bit error rate.

Neural-Network-Based Equalization and Detection for Underwater Acoustic Orthogonal Frequency Division Multiplexing Communications: A Low-Complexity Approach

The performance of the underwater acoustic (UWA) orthogonal frequency division multiplexing (OFDM) system is often restrained by time-varying channels with large delays. The existing frequency domain equalizers do not work well because of the high complexity and difficulty of finding the real-time signal-to-noise ratio. To solve these problems, we propose a low-complexity neural network (NN)-based scheme for joint equalization and detection. A simple NN structure is built to yield the detected symbols with the joint input of the segmented channel response and received symbol. The coherence bandwidth is investigated to find the optimal hyperparameters. By being completely trained offline with real channels, the proposed detector is applied independently in both simulations and sea trials. The results show that the proposed detector outperforms the ZF and MMSE equalizers and extreme learning machine (ELM)-based detectors in both the strongly reflected channels of the pool and time-variant channels of the shallow sea. The complexity of the proposed network is lower than the MMSE and ELM-based receiver.

Swarm Intelligence Based MMSE Frequency Domain Equalization for MIMO Systems

The automatic upgradation of equalizer weights in channel equalization demands a low-complexity, highly accurate estimation of recovery at the minimum possible time. The low-complexity frequency domain equalization improves the minimum mean square error (MMSE) of the equalization process. Adding the superiority of particle swarm optimization (PSO) to the equalizer coefficient selection process enhances the MMSE. This work proposes frequency-domain channel equalization along with a modified PSO (MPSO) as an adaptive algorithm for equalizer weight selection in MIMO systems. The simulation results validate the performance with the time domain linear and decision feedback equalizer structures for BPSK and QAM systems. The parameters are carefully selected by analyzing MMSE thoroughly under timevarying channel conditions.

Traveling-Wave Mach-Zehnder Modulator Integrated With Electro-Optic Frequency-Domain Equalizer for Broadband Modulation

Broadband modulator is a key component of future high-capacity and high-baud-rate optical fiber communication. An electro-optic (EO) frequency-domain equalizer is proposed and investigated to increase the 3-dB bandwidth of optical modulators. The equalizer can be integrated with conventional traveling-wave modulators using a crossing waveguide, U-turn waveguide, or ferroelectric-domain-inversion. The 3-dB bandwidth of the modulator can be doubled by integrating the equalizer. As a theoretical consideration, we modeled several types of EO equalizers and investigated the function and parameter dependency of the equalizers in detail. For the experimental demonstration, a titanium-diffused lithium niobate optical waveguide modulator integrated with the EO equalizer was fabricated. The optical loss including fiber-coupling was as low as 5.4 dB, and the half-wave voltage was 3.7 V. The measured electro-optic response at 110 GHz is –0.4 dB, and that of the 3-dB bandwidth is larger than 110 GHz, which is the upper frequency limit of our measurement equipment. The 3-dB bandwidth of the modulator estimated using the fitting curve obtained from the measured electrical propagation loss of the modulator electrode was approximately 200 GHz.

Fractionally spaced frequency domain equalization system based on FQPSK modulation

Severe multi-path effects in the process of high-speed data transmission cause inter-symbol interference (ISI). The single carrier frequency domain equalization (SC-FDE) method combining the benefits of Feher-patented quadrature phase shift keying (FQPSK) modulation is raised to solve this problem, including the constant envelope, high spectrum efficiency, and insensitivity to nonlinear distortion. Furthermore, a fractionally spaced frequency domain equalization (FS-FDE) system based on FQPSK modulation is modeled based on the proposed algorithm. Simulation results confirm the superior performance of the proposed model on erasing ISI, comparing to the symbol-spaced FDE (SS-FDE) system based on FQPSK modulation and the FS-FDE system based on QPSK modulation.

Phase-Domain Injected Training for Channel Estimation in Constant Envelope OFDM

Constant envelope orthogonal frequency division multiplexing (CE-OFDM) is a multi-carrier waveform with 0 dB peak-to-average power ratio (PAPR). This property enables the exploitation of multi-carrier waveforms with non-linear power amplifiers, avoiding the undesirable clipping effects. However, the existing channel estimation techniques designed for OFDM cannot be reused, since the use of a phase modulator makes CE-OFDM a non-linear waveform. Previous works assumed that the channel estimation process relies on the transmission of preambles, and the data symbols are equalized using a frequency domain equalizer (FDE). To avoid the overhead induced by preambles, a phase-domain injected training (PIT) is proposed, where the pilot sequence is embedded in the phase dimension of the data symbols. This novel approach does not waste time and/or frequency resources as in preamble-based schemes. Moreover, it does not require additional power for the training. The received symbols are averaged with a dual procedure, and owing to the particular structure of CE-OFDM, the channel estimates are recovered. Also, the analytical expression of the channel estimation mean squared error (MSE) is derived. Finally, several numerical results illustrate the performance of the proposal, showing that the MSE, bit error rate (BER) and achievable rate are improved, as compared to the existing works.

A Long-Distance Underwater Wireless Optical Link Enabled by a Solar Array With a Baseline Compensator

In this paper, a self-designed solar cell-based optical detector is proposed and demonstrated in a long-distance underwater wireless optical communication (UWOC) link. Benefitting from a large detection area, the detector could successfully capture optical signals with a received power density of 5.62 μW/cm <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> . To resist the baseline drift caused by the low-frequency cut-off of the system, an envelope detector-based baseline compensator is proposed. Comparing with digital solutions, the proposed compensator could be established in analog domain with common electronic components. With the compensator, a frequency domain equalizer (FDE) and a maximum ratio combing (MRC) algorithm, an 18 Mbps non-return-to-zero (NRZ) on-off keying (OOK) modulated link over an 80 m underwater channel is finally achieved. The proposed baseline compensator could compensate the low-frequency components effectively with low cost. Moreover, under a strong ambient light of approximately 1200 lux, the performance of the link shows little degradation. Our work shows a potential solution of long-distance UWOC system with ambient light tolerance, which is compatible with practical environment.

Long-Wave Infrared Discrete Multitone Free-Space Transmission Using a 9.15-μm Quantum Cascade Laser

A free-space optical (FSO) transmission system is experimentally demonstrated in the long-wave infrared (LWIR, 9.15 μm) using a directly modulated quantum cascade laser (DM-QCL) and a commercial mercury-cadmium-telluride infrared photovoltaic detector. At room temperature, the DM-QCL is current-modulated by discrete multitone signals pre-processed with bit-/power-loading. Up to 5.1 Gbit/s data rate is achieved with bit error rate performance below the 6.25% overhead hard-decision forward error correction limit of 4.5 × 10 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">-3</sup> , enabled by a frequency domain equalizer. The stability study of the FSO system is also performed at multiple temperature values. This study can provide a valuable reference for future terrestrial and space communications.

Performance Analysis of Orthogonal Multiplexing Techniques for PLC Systems with Low Cyclic Prefix Length and Symbol Timing Offset.

This paper investigates the degradation caused by interference resulting from cyclic prefix violation and symbol timing offset in narrowband power line communication systems. In this sense, it presents a unified formulation from which Hermitian symmetric orthogonal frequency division multiplexing (HS-OFDM), orthogonal chirp division multiplexing (OCDM), single-carrier cyclic prefix (SCCP), and orthogonal time-frequency division multiplexing (OTFDM) can be easily derived. The paper then provides closed-form expressions for quantifying the aforementioned interference in the presence of a frequency domain equalizer. The numerical analyses exhibit the performances of these schemes under various data communication conditions, such as the availability of channel state information, the presence or absence of interference, modeling of additive noise as a white or colored Gaussian random process, frequency domain equalizer type, and the use of bit and power allocation techniques. The closed-form expressions and performance analyses regarding achievable data rate and bit error probability provide guidance for dealing with distinct constraints in narrowband power line communication (PLC) systems using the HS-OFDM, OCDM, SCCP, or OTFDM scheme. Lastly, the unified formulation and results obtained motivate the design of multi-scheme transceivers.

On the Performance of LDPC-Coded Large Intelligent Antenna System

This article studies Large Intelligent Systems (LIS) along with Single Carrier with Frequency Domain Equalization (SC-FDE), utilizing Low-Density Parity-Check (LDPC). Four different receivers are studied in the scenarios described above, namely Equal Gain Combining (EGC), Maximum Ratio Combining (MRC), Zero Forcing (ZF), and Minimum Mean Squared Error (MMSE). The results of this article show that the use of LDPC codes leads to an improvement of performance by about 2 dB for a 4X25 LIS system and by 3 dB for a 4X225 LIS system, as compared to similar systems without LDPC codes. Moreover, for all simulations, the MMSE receiver achieves the best overall performance, while EGC performs the worst.

VAMP-Based Iterative Equalization for Index-Modulated Multicarrier FTN Signaling

The spectrally efficient multicarrier faster-than-Nyquist (MFTN) signaling provides an efficient and robust solution for enhancing transmission rate and resisting channel impairments. In this paper, an evolutionary non-orthogonal physical waveform is proposed for simultaneously achieving high spectral and energy efficiency via combining MFTN signaling with index modulation (IM). Exploiting the implicit transmission of IM, the inactivated subcarriers alleviate the inherent two-dimensional interferences imposed by time-frequency packing in MFTN. Then, we develop a pair of iterative equalization algorithms based on vector approximate message passing (VAMP). For the first time-domain equalization (TDE), an extended constellation set is constructed for uniformly characterizing the activated and inactivated subcarriers. To further reducing the computational complexity, we establish a subcarrier-based segment-wise frequency-domain received signal model and accordingly develop low-complexity VAMP-based frequency-domain equalization (FDE) combined with interference elimination. Corroborated by simulations, the novel MFTN-IM waveform achieves superior bit error rate (BER) performance over benchmark waveforms in the high signal noise ratio (SNR) regions. Interestingly, while the proposed VAMP-TDE outperforms the proposed VAMP-FDE in BER performance, the latter is more competitive in balancing demodulation performance and computational complexity.

Beyond 300-Gbps/λ photonics-aided THz-over-fiber transmission employing MIMO single-carrier frequency-domain equalizer.

We experimentally realized a 320-GHz 320-Gbps/λ terahertz (THz) radio-over-fiber (RoF) system based on a photonics-aided scheme with the help of polarization-division multiplexing (PDM) technology and multiple-input, multiple-output (MIMO) transmission. In this system, the low-complexity MIMO single-carrier frequency-domain equalizer (SCFDE) is implemented to compensate for the polarization-related impairments of the PDM signal, and the demultiplexing performances between SCFDE and the commonly used constant modulus algorithm (CMA) are also compared in this proposed system. After 20-km standard single-mode fiber (SSMF) and 3-m 2 × 2 MIMO wireless link transmission, the bit error rate (BER) of the received 46-GBaud PDM 16-ary quadrature amplitude modulation (16QAM) signal satisfies the soft-decision forward error correction (SD-FEC) threshold with 15% overhead, which corresponds to a record-breaking net bit rate of 320 Gbit/s.

Comparing the Performance of OFDM and OCDM-based Visible Light Communications: Numerical and Experimental Analysis

Numerical and experimental analysis of visible light communication (VLC) systems based on orthogonal chirp division multiplexing (OCDM) and orthogonal frequency division multiplexing (OFDM) are presented in this paper. Unlike most of the related publications, in this work we numerically compared OCDM and OFDM based VLC systems with the same equalization process, i.e., employing an one tap equalizer (OTE) in both systems. Simulation results in line-of-sight VLC channels show that both systems have the same performance when baseband multicarrier signals are used. The impact of the optical modulation index and the bias current of a previously characterized light-emitting diode were also evaluated. Nevertheless, the experimental demonstrations, in which bandpass signals were used due to the bandpass characteristic of the exploited setup, show that OFDM-based system outperforms the VLC links with OCDM signals, when the OTE equalizer is used in both systems. The performance of the OCDM-based system was improved by using a zero forcing frequency domain equalizer.