Frequency Domain Equalization Research Articles

A New Method to Enhance SC-FDMA Communication with Channel Estimation Errors

The single-carrier frequency division multiple access (SC-FDMA) system is a popular system in mobile communication because of its advantage of low peak-to-average-power-ratio (PAPR), and the use of frequency-domain equalizers to reduce inter-symbol interference (ISI) and inter-carrier interference (ICI). This paper presents a comprehensive study of the SC-FDMA system with PAPR reduction using clipping and filtering in the presence of channel estimation errors for two different versions of SC-FDMA adopting the FFT and the DCT. The effect of peak power reduction and the channel estimation error on the system bit error rate (BER) is investigated. Simulation results prove that the BER performance is not much affected by the PAPR reduction.

Equalization scheme of C-band PAM4 signal for optical amplified 50-Gb/s PON.

The bandwidth limit of devices and the chromatic dispersion (CD) of optical fiber severely distort the high-speed signal in a passive optical network (PON). In this paper, an efficient equalization scheme is proposed for optical amplified 50-Gb/s PAM4-PON with a 10G-class transmitter. The proposed equalization scheme is based on fast frequency domain equalization (FDE) with circular convolution, an optimized post-filter, and a low-complexity maximum likelihood sequence detector (MLSD), which requires only total 23 real-valued multiplications for each output symbol. Experimental results show that up to 33.2 dB power budget is successfully achieved over 20 km transmission without using any optical CD compensation module in the C-band. Moreover, there is only 0.5 dB penalty of receiver sensitivity compared to optical back to back (BTB) transmission. Therefore, the CD distortion has been nearly compensated for by the proposed equalization scheme. To the best of our knowledge, this is the best performance of an optical amplified 50-Gb/s PAM4-PON system in the C-band.

A Framework for Iterative Frequency Domain EP-Based Receiver Design

An original expectation propagation (EP) based message passing framework is introduced, wherein transmitted symbols are considered to belong to the multivariate white Gaussian distribution family. This approach allows deriving a novel class of single-tap frequency domain (FD) receivers with a quasi-linear computational complexity in block length, thanks to Fast-Fourier transform (FFT) based implementation. This framework is exposed in detail, through the design of a novel double-loop single-carrier frequency domain equalizer (SC-FDE), where self-iterations of the equalizer with the demapper, and turbo iterations with the decoder, provide numerous combinations for the performance and complexity trade-off. Furthermore, the flexibility of this framework is illustrated with the derivation of an overlap FDE, used for time-varying channel equalization, among others, and with the design of a FD multiple-input multiple-output (MIMO) detector, used for spatial multiplexing. Through these different receiver design problems, this framework is shown to improve the mitigation of inter-symbol, inter-block and multi-antenna interferences, compared to alternative single-tap FD structures of previous works. Thanks to finite-length and asymptotic analysis, supported by numerical results, the improvement brought by the proposed structures is assessed, and then completed by also accounting for computational costs.

Study on Frequency-domain Equalization Scheme for High-speed Digital Power Line Carrier Systems

Study on Frequency-domain Equalization Scheme for High-speed Digital Power Line Carrier Systems

A novel training sequence applied to DCS-based channel estimation

Studies have indicated that the distributed compressed sensing based (DCS-based) channel estimation can decrease the length of the reference signals effectively. In block transmission, a unique word (UW) can be used as a cyclic prefix and reference signal. However, the DCS-based channel estimation requires diversity sequences instead of UW. In this paper, we proposed a novel method that employs a training sequence (TS) whose duration time is slightly longer than the maximum delay spread time. Based on proposed TS, the DCS approach perform perfectly in multipath channel estimation. Meanwhile, a cyclic prefix construct could be formed, which reduces the complexity of the frequency domain equalization (FDE) directly. Simulation results demonstrate that, by using the method of simultaneous orthogonal matching pursuit (SOMP), the required channel overhead has been reduced thanks to the proposed TS.

A New Exact Low-Complexity MMSE Equalizer for Continuous Phase Modulation

This letter introduces a new low-complexity frequency-domain equalizer for continuous phase modulations (CPM). The derivation of a fractionally spaced representation for circular block-based CPM leads, without any approximation, to a simple yet efficient frequency-domain equalization. The proposed equalizer is compared to the state-of-the-art approaches. Simulation results show the equivalence in terms of performance with a lower or similar complexity.

Channel equalisation and data detection for SEFDM over frequency selective fading channels

Spectrally efficient frequency division multiplexing (SEFDM) has been recognised as a promising multi-carrier technology since it can offer a higher spectral efficiency than orthogonal frequency division multiplexing (OFDM). In this study, the authors provide a framework for SEFDM transceiver design and investigate the techniques of channel equalisation and data detection of SEFDM over frequency selective fading scenarios. Specifically, they first demonstrate through mathematical analysis that SEFDM with the proposed frequency-domain equalisation scheme can benefit from the frequency diversity, and thus, performs more robust to the frequency selective fading environment than OFDM. To effectively mitigate inter-carrier interference raised by the non-orthogonality between sub-carriers of SEFDM, they then propose a low-computational data detection scheme based on the Viterbi principle and maximum a posteriori criterion. The proposed detector can provide an indistinguishable performance from the maximum likelihood detection using sphere decoding while entailing a much lower computation. Numerical results validate the superiority of SEFDM to OFDM over frequency selective fading channels.

Analysis of Single Carrier Frequency Domain Equalization Algorithm

This paper compare the different of single carrier frequency domain equalization (SCFDE) and orthogonal frequency division multiplexing (OFDM), list the disadvantage of the OFDM algorithm and the advantage of SC-FDE system and the frequency domain equalization algorithm. Perform the performance of SC-FDE under the different equalization algorithms is simulated, the comparison of two frequency equalization algorithm was emulate and there is a well method for the single carrier frequency domain equalization.

An Improved Iterative Frequency Domain Decision Feedback Equalization for STBC-SC-FDE

This article proposes an improved iterative frequency domain decision feedback equalization(IBDFE) for the unique word(UW) based system of space-time block coded-single carrier frequency domain equalization(STBC-SC-FDE). Compared with the conventional IBDFE, this algorithm uses minimum mean square error(MMSE) equalization and a noise prediction module based on UW instead of the feedback equalization part, while maintain the feedforward equalization. It is shown from the simulation results that the improved IBDFE can achieve satisfactory performance without iterations.

Low-Complexity Blind Selected Mapping Scheme for Peak-to-Average Power Ratio Reduction in Orthogonal Frequency-Division Multiplexing Systems

Orthogonal frequency-division multiplexing (OFDM) is an attractive multicarrier technique for the simplicity of equalization and high data throughput. However, the transmitted OFDM signal has a very high peak-to-average power ratio (PAPR), which severely degrades the performance of practical OFDM systems and reduces the efficiency of high-power amplifiers (HPA). The selected mapping (SLM) scheme is an effective PAPR reduction method of OFDM signals. However, this approach usually requires side information (SI) transmission, which increases the difficulty of the hardware implementation with high complexity and reduces the data transmission rate. In this paper, based on designing phase rotation vectors in the time domain, a novel blind SLM method with low complexity is proposed to reduce the PAPR of OFDM signals. At the transmitter, the proposed method properly designs the phase rotation vectors in the time domain, which can be considered as an equivalent wireless channel without SI transmission. At the receiver, the effect of phase rotation vectors can be removed by the conventional channel estimation method, and the data demodulation processing can be easily performed by the frequency domain equalization. Simulation results show that the proposed scheme can achieve low complexity in PAPR reduction and has great robustness in bit error rate (BER) performance compared to the other low-complexity SLM PAPR schemes.

Simplified approach for symbol error rate analysis of SC-FDMA scheme over Rayleigh fading channel

In this paper, we present a comprehensive analytical study of the symbol error rate (SER) of single-carrier frequency-division multiple access (SC-FDMA) with zero-forcing frequency domain equalization (ZF-FDE) over a Rayleigh fading channel. SC-FDMA is considered as a potential waveform candidate for fifth-generation (5G) radio access networks (RANs). First, the NC fold convolution of the noise distribution of an orthogonal frequency-division multiplexing (OFDM) system is computed for each value of the signal-to-noise ratio (SNR) in order to determine the noise distribution of the SC-FDMA system. NC is the number of subcarriers assigned to a user or the size of the discrete Fourier transform (DFT) precoding. Here, we present a simple alternative method of calculating the SER by simplifying the NC fold convolution using time and amplitude scaling properties. The effects of the NC fold convolution and SNR over the computation of the SER of the SC-FDMA system has been separated out. As a result, the proposed approach only requires the computation of the NC fold convolution once, and it is used for different values of SNR to calculate the SER of SC-FDMA systems.

Frequency Domain Equalization and Post Distortion for LED Communications With Orthogonal Polynomial Based Joint LED Nonlinearity and Channel Estimation

The light-emitting diode (LED) is the major source of nonlinearity in LED communications, and the nonlinearity needs to be effectively modeled and mitigated to avoid the degradation of communication performance. In indoor LED communications, multipath dispersion can lead to inter-symbol interference (ISI) at high data rates. In this paper, we jointly estimate the LED nonlinearity and ISI channel based on an orthogonal polynomial based technique. Then, frequency domain equalization and post-distortion are adopted to mitigate the ISI and nonlinearity. Simulation results are provided to demonstrate the effectiveness of the proposed technique.

Experimental demonstration of adaptive VFF-RLS-FDE for long-distance mode-division multiplexed transmission.

We experimentally demonstrate adaptive variable-forgetting-factor (VFF) recursive-least-square frequency-domain equalization (RLS-FDE) for mode-division multiplexing. The VFF-RLS-FDE algorithm improves convergence speed as transmission distance increases. For MDM transmission over a 1,000-km few-mode fiber, the convergence speed was increased by 18.7 times in comparison with LMS-FDE. In the meantime, the convergence error performance of VFF-RLS is also much superior to LMS while fixed-forgetting-factor RLS has a 0.2 dB penalty compared with LMS. The proposed VFF-RLS algorithm achieves better performances than conventional RLS in terms of convergence speed and convergence error.

Robust Single-Carrier Frequency-Domain Equalization for Broadband MIMO Systems With Imperfect Channel Estimation

Single-carrier frequency-domain equalization (SC-FDE) with multi-input multi-output (MIMO) has been recognized as an alternative technology to orthogonal frequency-division multiplexing with MIMO for broadband wireless communication systems because of its single carrier transmission advantages. Conventional SC-FDE MIMO schemes are designed under the assumption of perfect channel estimation. In this paper, we investigate the robust SC-FDE MIMO design for systems with imperfect channel estimation. Based on a statistical model for channel estimation, the optimal equalization coefficients for the robust SC-FDE MIMO schemes with both parallel interference cancellation and successive interference cancellation (SIC) are derived with the objective of minimizing the sum of the multiple data streams’ mean square errors (sum-MSE). We propose an optimal ordering algorithm in the sense of minimum sum-MSE for the SC-FDE MIMO scheme with SIC, and further propose a low complexity sub-optimal ordering algorithm. The bit-error-rate (BER) performance in the uncoded case is analyzed and a tight BER approximation is derived. Numerical results show that the proposed robust SC-FDE MIMO schemes achieve 1.5dB~4dB gains in $ E_{b}/N_{0}$ over the conventional non-robust schemes.

Coded color shift keying with frequency domain equalization for low complexity energy efficient indoor visible light communications

The adaptive tri-chromatic color shift keying (CSK) modulation standardized in IEEE 802.15.7 and the advanced quad-chromatic CSK are unable to utilize their entire spectral efficiency range over dispersive indoor VLC channels and incur large power penalties without the use of channel equalization and forward error correction. This degrades the energy efficiency and limits the throughput capability of CSK schemes to approximately half of the data-rates specified in the IEEE standard for multimedia services in wireless personal area networks. To comply with the desire for low latency and minimal implementation complexity in the CSK standardization framework, we consider an industry standard binary convolutional code and frequency domain equalization (FDE) which provide one-shot data packet processing. Our results show that when operating over hybrid indoor visible light communication (VLC) links, the FDE based rate-adaptive coded modulation CSK scheme achieves a significant 11 dB SNR gain over an uncoded, unequalized system.

Analysis of the Impact of the Receiver I/Q Imbalance on the Achievable Rate of SC-FDE Systems

This paper analyzes the achievable rate of the single-carrier system with a frequency-domain equalizer (SC-FDE) under the receiver in-phase/quadrature phase (I/Q) imbalance in the radio frequency front-end. We consider linear schemes based on the minimum mean square error (MMSE), zero-forcing equalization, and a matched filter. We derive the achievable rate of the SC-FDE system hit by the I/Q imbalance for the mentioned scenarios. We show that depending on the value of I/Q imbalance parameters, the achievable rate of the system approaches a saturation level. To examine the validity of our analysis, we compare it with the simulation results and exhibit their consistency. We also consider nonlinear schemes such as an iterative block decision feedback equalizer (IB-DFE), which is an iterative scheme. We obtain the mutual information achieved by the IB-DFE in the high-signal-to-noise-ratio regime and after enough number of iterations.

A Virtual Pilot-Assisted Channel Estimation Algorithm for MIMO-SCFDE Systems Over Fast Time-Varying Multipath Channels

This paper considers a novel virtual pilot-assisted channel estimation algorithm for multiple input multiple output single carrier frequency domain equalization (MIMO-SCFDE) systems over fast time-varying multipath channels. Given that the fast time-varying channels can no longer support the assumption that the channel frequency-domain response remains invariant for the duration of one SC-FDE symbol, most of the channel estimation methods cannot be directly applied to MIMO-SCFDE systems. We put forward an iterative interfrequency interference cancellation method for the time-varying multipath channels over one SC-FDE symbol. The proposed method utilizes the virtual pilot-assisted channel estimation and partial minimum-mean-square-error equalization to improve the accuracy of the estimation. Simulation results validate the improved performance of the proposed method for MIMO-SCFDE systems over fast time-varying multipath channels.

BER analysis of STBC hybrid carrier system based on WFRFT with frequency domain equalization

The inherent characteristic of hybrid carrier (HC) scheme based on the weighted-type fractional Fourier transform (WFRFT) is revealed.The proposed linear combination of single carrier (SC) and multi-carriers (MC) characteristics is helpful to balance the conflicting requirements and achieve the comparative analysis of SC/MC.As an example, analytical SER/BER expressions of HC system with zero forcing (ZF) and minimum mean square error (MMSE) equalization are derived.In addition, the derived BER expressions are extended to multi-input systems.A unified framework of space time block code (STBC) HC scheme is proposed with two WFRFT modules at the transmitter or receiver,where STBC-SC and STBC-MC systems are the special cases of the novel structure.

Joint Channel-Estimation and Equalization of Single-Carrier Systems via Bilinear AMP

We propose a novel soft-input soft-output equalizer for single-carrier transmissions over unknown frequency-selective block-fading channels. Our equalizer leverages the recently proposed parametric bilinear generalized approximate message passing algorithm for joint channel-estimation and symbol-detection, and exploits fast Fourier transform (FFT)-processing to achieve a per-symbol complexity that grows only logarithmically in the channel delay-spread. Furthermore, it supports the use of Gaussian mixture models to support the approximately sparse nature of wideband wireless channel responses. Numerical experiments, conducted using physically motivated Saleh–Valenzuela channel models, show that the proposed approach achieves channel normalized mean square error and bit error rate that are significant improved over existing turbo frequency-domain equalization approaches for unknown channels. Additional experiments show that the proposed scheme facilitates much higher spectral efficiencies than sparse deconvolution methods based on convex relaxation.

Uplink Spectral Efficiency Analysis and Optimization for Massive SC-SM MIMO With Frequency Domain Detection

Recently the combination of massive multiple-input multiple-output (MIMO) and spatial modulation (SM), has been considered as a promising concept for uplink transmission, in which each user equipment (UE) uses SM for uplink transmission and base station (BS) is equipped with massive antennas. In this paper, we evaluate a massive single-carrier (SC) SM-MIMO system with frequency domain equalization, where SC transmission is combined with SM (SC-SM) to combat the negative impact of broadband frequency-selective fading, and frequency domain equalization is utilized to mitigate the intersymbol-interference with a low complexity. With frequency domain processing, a framework is proposed to analyze the achievable uplink spectral efficiency (SE) of single-cell massive SC-SM MIMO systems. Based on this framework, the closed-form SE lower bound of frequency domain maximum ratio combining is derived, and both the derivation of framework and SE lower bound are much more complicated than those of systems with time domain combining. Monte Carlo simulations verify the tightness of proposed SE lower bound, and show that massive SC-SM MIMO systems can outperform the SE of conventional single transmit antenna (TA) massive MIMO systems. The systems can even have a better SE performance than massive MIMO systems with spatial multiplexing UEs in a low signal-to-noise ratio. Finally, the SE gain is found to be mainly dependent on the specific number of UE's TAs, which facilitates an SE maximization via optimizing the number of TAs.