Single Carrier Frequency Domain Equalization Systems Research Articles

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.

Joint Compensation of Transmitter and Receiver I/Q Imbalances for SC-FDE Systems

Due to the non-ideality of analog components, transmitters (TXs) and receivers (RXs) suffer from hardware impairments such as in-phase/quadrature (I/Q) imbalance, which manifests itself as the mismatches of amplitude, phase and frequency response between I/Q branches. Without compensation, I/Q imbalance can severely degrade the system performance. This paper addresses the joint compensation of TX and RX I/Q imbalances for single carrier frequency domain equalization (SC-FDE) systems. Specifically, we develop an expectation maximization (EM) based approach to separately estimate TX and RX I/Q imbalances, and the multipath channel. With the obtained estimates, we can readily fulfill the compensation of I/Q imbalances. Unlike previous methods, which only estimate the combined effect of I/Q imbalances and the multipath channel, we are able to obtain the separate estimates of the TX I/Q imbalance, the RX I/Q imbalance and the multipath channel. This will significantly alleviate the computation burden of the proposed compensation scheme in the long run. Simulation results show that the proposed scheme outperforms the counterparts, and can significantly mitigate the adverse effects of I/Q imbalances.

A Novel Signal Detection Scheme Based on Adaptive Ensemble Deep Learning Algorithm in SC-FDE Systems

Reliable signal detection plays an essential role in enhancing the quality of signal transmission in wireless communication systems. In this paper, we combine signal detection theory with a deep learning model and propose a novel signal detection scheme based on adaptive ensemble long short term memory (AE-LSTM) neural network to handle wireless single carrier frequency domain equalization (SC-FDE) systems in an end-to-end manner. The feature information used for offline training of the deep learning model is extracted from the received signal containing channel state information (CSI) after the multi-path channel and fast Fourier transform (FFT), and the labels are assigned according to the constellation map adopted at the transmitter. To improve the adaptability of the system, we utilize the received power under different delays as the adaptive factor to integrate the output of each sub-network. Then the original data generated by the channel model is recovered by using the trained model instead of channel estimation and frequency domain equalization. Comparative experiments on SC-FDE symbol detection demonstrate that the proposed scheme achieves better performance in terms of reliability than the traditional scheme and the similar deep learning scheme.

Online LSTM-Based Channel Estimation for HF MIMO SC-FDE System

The long distance high frequency (HF) communication suffers from time varying multipath fading. Multiple-Input Multiple-Output (MIMO) and Single-Carrier Frequency Domain Equalization (SC-FDE) have been introduced to HF communication system to combat fading. Because accurate channel estimation is essential for system operation, an architecture of signal flow chart has been designed for the HF MIMO SC-FDE system. In the architecture, an online Long Short-Term Memory (LSTM) estimator is proposed. Different from the channel responses time series created by the LSTM training and prediction loop, a corrected channel responses that are obtained through the received data symbols and the restored transmitting data symbols make up the channel responses time series. In order to evaluate the performance of channel estimators, a simulation system has been built. The uncorrelated and correlated channels are simulated referring to International Telecommunication Union (ITU)-R F.1487 standard and Kronecker model. The simulation results demonstrate that the online LSTM estimator outperforms Least Square (LS) and Recursive Least Square (RLS) estimators in terms of Bits Error Rate (BER) and Mean Square Error (MSE). The online LSTM estimator is capable of tracking the time varying HF MIMO channels. It has potentiality in actual long distance HF communication.

Compressive sensing-based channel estimation for SC-FDE system

The channel of wireless broadband communication system usually features time domain sparsity. The channel estimation of single carrier frequency domain equalization (SC-FDE) system was modeled as compressive sensing (CS)-based reconstruction of sparse signal. Matching pursuit algorithms based on greedy search were adopted to reconstruct channel information. Under the premise of reduced reference signal overhead, the system reliability can be effectively enhanced. This paper proposes a priori information aided scheme. By inserting the cyclic prefix of the first training sequence to a SC-FDE transmission frame, which is used as guard interval, the priori information including more accurate channel length and sparsity can be obtained with inter-block-interference (IBI)-free training sequence. The proposed scheme shows obvious superiority in slow fading channels. It effectively improves the reconstruction of probability, thereby improving the accuracy of channel estimation, meanwhile sacrificing less spectral efficiency.

Nonlinearity-Based Ranging Technique in SC-FDE Communication System With Oversampled Signals

Ground-based positioning systems are necessary as the conventional satellite-based systems suffer from weak received signals. In this paper, we proposed a precise ranging method in single-carrier frequency domain equalization (SC-FDE) system using the amplitude nonlinearity of oversampled signals. A new pattern of the preamble and the unique word was designed for SC-FDE system, where the preamble can be exploited in correlation-based timing algorithm to obtain impulse-like timing metric. Combining with the coarse timing procedure, we proposed a fine ranging method relying on the oversampled signals in SC-FDE receiver employing Qth-power nonlinearity, and then analyzed its estimation mean and variance. The extensive simulations were conducted to validate the proposed method with distinct modulation schemes, rolling-off factors, block lengths, and nonlinearity factors. The results show that the proposed ranging method can achieve unbiased estimate and its root mean square errors will reach the order of centimeter at medium-to-high signal-to-noise ratio region in flat-fading channels, whereas the observed performance degradation in frequency selective channel can be mitigated by using equalized oversampled signals.

Iterative IQ Imbalance Compensation Receiver for Single Carrier Transmission

It is well known that low-cost RF front-end implementation such as direct conversion transmitter suffers from serious in-phase/quadrature phase (IQ) imbalance. Most existing works in single carrier transmission employ linear compensation methods, such as Least Square and minimum mean square error, to combat the interference caused by IQ imbalance. Actually, for single carrier transmission, it is possible for the receivers to adopt advanced nonlinear compensation methods to improve the system performance under IQ imbalance. In this paper, we design a new iterative decision feedback receiver to compensate the IQ imbalance caused by unideal radio front end for single carrier frequency domain equalization (SC-FDE). Numerical results shows that, compared with the conventional linear method, our proposed iterative IQ imbalance compensation can significantly improve the performance of SC-FDE system under IQ imbalance.

Iterative Decision Feedback Equalization for SC-FDE Systems Without Fine Timing Synchronization

This letter deals with frequency domain equalization (FDE) in the presence of residual timing offsets. A novel iterative decision feedback equalizer for single-carrier FDE systems is proposed. Different from conventional schemes based on explicit point time-delay estimates, the proposed scheme operates directly on the oversampled matched filter output. For each iteration, FDE is performed first, and based on which, joint posterior distribution of the channel and timing parameters is obtained. A set of weights obtained from the corresponding posterior distribution, rather than explicit point time-delay estimate, are utilized for the time-delay compensation, eliminating the need of fine timing synchronization. Simulation results show that the proposed scheme enables evident performance improvement in terms of symbol error rate compared with conventional schemes under relative low sampling rate.

Performance Enhancement of Faster-Than-Nyquist Signaling Based Single-Carrier Frequency-Domain Equalization Systems

This paper provides a method that appends and removes efficiently the cyclic prefix and the cyclic suffix by means of an inter-block interference elimination for a frequency domain equalization (FDE) in faster-than-Nyquist (FTN) signaling schemes. Furthermore, we propose various transmission schemes to integrate such an FTN signaling in the single-carrier FDE system. We propose FTN transmission schemes combined with various FDE techniques such as a post-equalization, a pre-equalization, and a balanced equalization in the FTN-SC-FDE system. We prove that the proposed transmission schemes yield improved performances by deriving the instantaneous bit error rate and error probability. Finally, we evaluate the analytical results and the simulation results of the performance of various FTN-SC-FDE schemes. Our proposed schemes can be applied to enhance the spectral efficiency of the satellite broadcasting systems like DVB-S2/S2X as well as the return channels of interactive broadcasting systems.

A Simple Sparse Channel Estimation Method for Single-Carrier Frequency Domain Equalization Based on Noise Space

It is widely accepted that SC-FDE (Single-Carrier Frequency Domain Equalization) is an excellent candidate for broadband wireless systems. Channel estimation is one of the key challenges in SC-FDE, since accurate channel estimation can significantly improve the equalization at the receiver and consequently enhance the communication performances. In this paper, we proposed a simple sparse channel estimation method for SC-FDE system based on noise space, through sorting the results of the Least-squares (LS) channel estimation, channel tap locations and value are evaluated. The proposed system can realize channel estimation at a very low complexity, and simulation result shows that it can achieve significantly improved performance in frequency selective fading sparse channel.

Joint Estimation for I/Q Imbalance and Multipath Channel in Millimeter-Wave SC-FDE Systems

A single-carrier frequency-domain equalization (SC-FDE) system operating at 60-GHz millimeter-wave band suffers from in-phase (I) and quadrature (Q) imbalance, which refers to the mismatch between the I and Q branches in analog front-end processing. The I/Q imbalance incurs unwanted image interference on top of the desired signal and can severely degrade system performance if left uncompensated. In this paper, a training-based approach is proposed to estimate and compensate for the I/Q imbalance in the SC-FDE system. First, we derive the likelihood function capturing the I/Q imbalance and multipath channel. By iteratively maximizing the likelihood function, we can simultaneously and separately estimate the I/Q imbalance and the multipath channel. Then, with the estimate of the I/Q imbalance, the corresponding image interference is removed by simple substitution. Finally, we use the channel estimate to conduct equalization in the frequency domain, as is done in the conventional SC-FDE without the I/Q imbalance. It is shown through simulations compliant with the IEEE 802.11ad Standard that the proposed approach can effectively mitigate the adverse effect of I/Q imbalance and, consequently, can achieve the performance very close to the ideal case without I/Q imbalance.

Novel Pilot Position Detection for SC-FDE Systems With Frequency Domain Pilot Multiplexing Technique

Frequency domain pilot multiplexing technique (FDPMT) has recently emerged as an appealing technique for channel estimation in single-carrier frequency domain equalization systems as it achieves high spectral efficiency at the expense of tiny signal distortion. In FDPMT, pilot positions are dynamically selected to achieve a relatively low level of signal distortion, rendering pilot position detection (PPD) indispensable at the receiver. In this letter, by exploiting both the prior known pilots and the statistical information of the data tones, we propose a novel PPD scheme based on the maximum-likelihood criterion. Simulation results show that our proposed PPD scheme significantly improves the PPD accuracy and outperforms the existing counterparts in terms of bit error rate.

Iterative Decision-Aided Compensation of Phase Noise in Millimeter-Wave SC-FDE Systems

In this letter, we propose a novel decision-aided phase noise (PHN) compensation scheme for 60 GHz millimeter-wave single-carrier frequency-domain equalization (SC-FDE) systems. The proposed scheme works in an iterative manner. During each iteration, we first chop each received data block into several equi-length sub-blocks, and use the data decision obtained from the previous iteration to estimate the PHN in each sub-block. Then we use the PHN estimate newly obtained to compensate for the PHN effect. Last, we conduct FDE and data decision for each received data block. With increasing iterations, the length of sub-blocks is gradually decreased, which leads to increasingly accurate PHN estimation and data decision. It is shown through simulations compliant with the IEEE 802.11ad standard that the proposed scheme outperforms the counterpart of similar complexity and can effectively alleviate the adverse effect of PHN.

Novel Pilot Design and Signal Detection for SC-FDE Systems With Frequency-Domain Pilot Multiplexing Technique

The performance of single-carrier frequency-domain equalization systems with the frequency-domain pilot multiplexing technique is affected by the level of signal distortion, which highly depends on the pilot position selection (PPS) scheme at the transmitter and the signal detection (SD) scheme at the receiver. In this letter, by exploring the relationship between distorted symbols and decision boundaries, we propose a novel PPS scheme to confine the distorted symbols within their designated decision regions, which dispenses with a priori knowledge of the channel. Based on the maximum-likelihood criterion, we also propose a novel SD scheme to avoid error propagation, which operates on a symbol-by-symbol basis. Simulation results on bit error rate show that our proposed PPS scheme achieves almost the same performance as the optimal one and our proposed SD scheme outperforms the existing one in additive white Gaussian noise channels; in addition, both proposed schemes outperform their existing counterparts in frequency-selective Rayleigh fading channels.

Polar-Based OFDM and SC-FDE Links Toward Energy-Efficient Gbps Transmission Under IM-DD Optical System Constraints [Invited

Recent studies have investigated the use of orthogonal frequency division multiplexing (OFDM) and single carrier frequency-domain equalization (SC-FDE) for gigabyte per second (Gpbs) short-range optical wired and wireless access networks based on direct intensitymodulation with direct detection (IM-DD). OFDM systems have an inherent high peak-to-average power ratio (PAPR). SC-FDE systems have lower PAPR and thus outperform comparable OFDM systems in terms of bit-error performance under various practical considerations, mainly the limited dynamic range of operation at the transmitter. In RF-based OFDM and SC-FDE systems, the output signal is bipolar, complex, and cannot be transmitted in IM-DD systems. Therefore, several power efficient schemes, however spectrally inefficient, have been proposed to make positive OFDM and SC-FDE signals, e.g., asymmetrically clipped optical OFDM (ACO-OFDM) and repetition and clipping optical SCFDE (RCO-SCFDE). To increase the data rate, novel OFDM and SC-FDE signal formats, called polar OFDM (P-OFDM) and polar SC-FDE (P-SC-FDE), based on a polar representation of complex symbols, are proposed. The proposed format offers twice as much spectral efficiency as state-of-the art unipolar OFDM and SC-FDE formats. Moreover, using a power allocation approach on the time-domain positive samples, the PAPR is further reduced, and the numerical evaluation of the bit-error performance under optical source power and dynamic range constraints demonstrates superior results toward Gpbs transmission.

Digital Signal Processing for Training-Aided Coherent Optical Single-Carrier Frequency-Domain Equalization Systems

In this paper, we present the design of digital signal processing (DSP) algorithms for training-aided coherent optical single-carrier frequency-domain equalization (SC-FDE) systems. Based on two training-aided channel estimation (TA-CE) schemes, the requirements for training sequence to achieve the minimum mean square error performance of channel estimation (CE) are outlined. Moreover, the practical implementation issues of constant-amplitude zero-autocorrelation sequence and Golay sequences are discussed. We propose to perform time-domain windowing to the CE taps for further noise suppression to improve the CE and achieve large overhead saving with the optimized CE. Furthermore, frame timing synchronization and frequency offset compensation algorithms based on Golay sequences are developed, which provide bandwidth-efficient solution with robust performance for long-haul transmission. Finally, a low-complexity fractionally spaced frequency-domain equalizer is reported to effectively reduce the computational complexity of the whole system. A total of 28-Gbaud coherent polarization division multiplexing (PDM) system simulations and 10-Gbaud coherent PDM system experiments are conducted to verify that the proposed DSP solutions provide robust performance and are suitable for implementation in high-speed long-haul digital coherent receivers.

Single-carrier fractional Fourier domain equalization system with zero padding for fast time-varying channels

Single-carrier frequency domain equalization (SC-FDE) has been shown to be an attractive transmission scheme for broadband wireless channels. However, its performance would degrade a lot if the channel is fast time-varying. In this paper, we analyzed the single-carrier fractional Fourier domain equalization (SC-FrFDE) system and applied it to the fast time-varying channel. It can solve the time-varying problem by selecting the optimal fractional Fourier transform order. To this SC-FrFDE system, its transmitter uses chirp-periodic circular prefix to eliminate ISI and this has an evident disadvantage that the receiver need to feedback the optimal fractional Fourier transform order to the transmitter through a feedback channel. To simplify the system, we propose to use zero padding (ZP) at the transmitter. There is already the overlap-add method as ZP in SC-FDE system. But the overlap-add method cannot be used in fast time-varying channels. Thus, we propose a new method as ZP. Simulation results show that our proposed method can significantly improve the system performance.

Three-Stage Treatment of TX/RX IQ Imbalance and Channel with CFO for SC-FDE Systems

Direct-conversion transceiver obtains increasing attentions due to its low power consumption, but it confronts with serious IQ imbalance. In this paper, a three-stage treatment of transmitter/receiver (TX/RX) IQ imbalance and channel, in the presence of carrier frequency offset (CFO), is proposed for single-carrier-frequency-domain-equalization (SC-FDE) systems. First, RX IQ imbalance and CFO are handled with a repetitive preamble. Second, joint responses of TX IQ imbalance and channel are estimated by designing another preamble via complementary Golay codes. Third, joint compensation of TX IQ imbalance and time-varying channel is conducted using the minimal-mean-square-error criterion. Simulations are presented to verify the proposed method, in terms of normalized mean square error for the estimation and bit error rate for the overall system.

A Blind Fine Synchronization Scheme for SC-FDE Systems

This work presents a blind fine synchronization scheme, which estimates and compensates residual carrier-frequency offset (RCFO) and symbol timing offset (STO) , for single-carrier frequency-domain equalization (SC-FDE) systems. Existing fine synchronization schemes for SC-FDE systems rely on time-domain unique words (UW) sequences as reference signals to assure the estimation accuracy, at the cost of decreased system throughput. The proposed technique, named simplified weighted least-square method for single-carrier systems (SWLS-SC), combines the decision feedback structure and SWLS estimator for OFDM systems. Together with specifically derived weighting factors, it has much better estimation accuracy than the well-known linear least-square (LLS) method for SC-FDE systems, and its BER performance can approach that of the ideal synchronization condition. The proposed technique is more effective than existing techniques, in terms of both performance and throughput. Theoretical estimation bounds are also derived to verify the effectiveness of the proposed method.

Frequency domain response estimation of underwater acoustic channel and noise estimation for single-carrier frequency domain equalization

Single-carrier frequency domain equalization (SC-FDE) has drawn increasing researches because of its lower computational complexity and better performance of mitigating intersymbol interference (ISI) as compared with the time domain equalization. The practical SC-FDE systems, however, require the knowledge of the channel frequency domain response and the noise power to calculate filter coefficients of the frequency domain equalizer. Improper channel and noise estimations have been shown to result in error floor at high signal-to-noise ratio (SNR), which may impede the utilization of SC-FDE in the high-rate underwater acoustic (UWA) communications. In this paper, we discuss the possible influence of inaccurate noise estimation on the error floor at high SNR, and propose a joint estimation scheme for the channel time domain and frequency domain responses and also the noise power based on Chu sequence. The channel energy concentration region is determined by the threshold and the sparse channel impulse response (CIR) of UWA channels, used in denoising process of the CIR and the noise power computation. The bite error ratio performance of the SC-FDE variation versus the threshold is simulated via the UWA models, and accurate noise power estimation is shown to be desirable to improve the SC-FDE performance. Numerical examples also indicate that our joint estimation scheme can eliminate the error floor and improve the performance of SC-FDE at high SNR.