Blind Equalization for Single Carrier Frequency Domain Equalization with Low Complexity

Recent research has shown that single carrier frequency domain equalization (SC-FDE) is an attractive technology for broadband wireless communications for its advantages such as lower peak-to-average power ratio and reduced sensitivity to carrier frequency offset, when compared to orthogonal frequency-division multiplexing (OFDM) systems. In this paper, we propose a novel structure, FDE-NP, which consists of a linear frequency domain equalizer (FDE) and a time domain noise predictor (NP). It is shown that the proposed scheme has lower complexity and achieves better performance and complexity trade-off than the conventional FDE designs. In particular, by using a simple block interleaver/deinterleaver pair to rearrange the order of the received signals prior to decoding, delayed reliable decisions can be fed back to predict and cancel their post-cursor inter-symbol interference (ISI) effects to the following signals. Simulation results show that the proposed FDE-NP scheme achieves 1.5-2 dB performance improvement over the conventional FD-LE and FD-DFE schemes. Furthermore, we extend the design of unbiased and biased time domain equalizers (TDEs) into the frequency domain and propose the unbiased FDE. It is shown that although the unbiased FDE has a larger MSE than the biased one, it reduces the required SNR by about 0.3 dB in some cases

Recent research has shown that single carrier frequency domain equalization (SC-FDE) is an attractive technology for broadband wireless communications because it does not have the problems of OFDM systems such as large peak-to-average ratio and the sensitivity to carrier frequency offsets. The FD-DFE structure, which combines a frequency domain feedforward equalizer and a time domain feedback filter, has been proposed to bring better performance than the linear ME scheme for severely distorted channels. However, this structure cannot be applied directly to coded systems because of the decision delays associated with these systems. In this paper, we propose a novel structure, which consists of a linear frequency domain equalizer and a time domain noise predictor. By using a simple block interleaver/deinterleaver pair to rearrange the order of the received signals prior to decoding, delayed reliable decisions can be used for feedback. By doing so, significant performance improvement over the conventional FD-LE and the FD-DFE schemes can be achieved in the proposed FDE-NP scheme. It is also demonstrated that the performance complexity tradeoff of the proposed scheme can be obtained by only changing the order of the noise predictor. This is in contrast to the conventional FD-DFE scheme where both the ME and the time domain feedback filter must be modified simultaneously.

This letter addresses the application of Linear Dispersion Codes (LDC) in space and frequency domains in Single Carrier-Frequency Domain Equalization (SCFDE) systems. Space-frequency (SF)-LDCs are more suitable than space-time (ST) LDC in high mobility environments. However, the application of LDCs in space and frequency domains in SCFDE systems is not straightforward as in orthogonal frequency division multiplexing (OFDM) systems because in this case there is no direct access to subcarriers at the transmitter. This letter shows that it is possible to induce a target SF symbol dispersion in SCFDE by using a simple linear pre-coder and a conventional LDC that spreads the symbols in time and space domains according to specific ST dispersion matrices. The letter shows how to derive the ST dispersion matrices to be used at the transmitter as a function of the dispersion matrices describing the target SF dispersion. The presented procedure can be applied to both pure transmit diversity and pure multiplexing schemes, which are special cases of LDCs. Therefore, the proposed scheme provides a low complexity implementation of any dispersion in space and frequency over SCFDE systems, which alternatively would require the use of FFT/IFFT also at the transmitter side. The letter also shows a performance comparison of SF-LDCs and ST-LDCs in a typical propagation environment for future radio systems. The comparison confirms the suitability of using the dispersion in frequency rather than time for a wide range of coherence bandwidths.

In a freedom Visible Light Communication (VLC) system based on circularly polarized light for transmission and polarization diversity for reception, a novel Windowed Single Carrier Frequency Domain Equalization (WSCFDE) preequalization method based on SCFDE and Digital Zobel network (DZN) pre-equalization has been proved. Compared with DZN pre-equalization, this new method has improved the Q factor by 1.42 dB and increased the transmission rate by 0.61 Gb/s, and achieved a transmission rate of 14 Gbps.

We propose and experimentally demonstrate a novel integrated passive optical network (PON) and indoor visible light communication (VLC) system based on Nyquist single carrier frequency domain equalization (N-SC-FDE) modulation with direct detection. In this system, a directly modulated laser and a commercially available red light emitting diode are served as the transmitters of the PON and VLC, respectively. To enable high spectral efficiency, high-speed transmission, and flexible multiple access with simplified optical network unit-side digital signal processing, multilevel, multiband quadrature amplitude modulations 128/64/16 are implemented here. VLC N-SC-FDE signals are successfully delivered a further 30 cm indoor distance after transmitting over a span of 40 km single mode fiber (SMF) together with 3 sub-band PON signals. As a proof of concept, a 10 Gb/s PON and 500 Mb/s VLC integrated system for three wired users and one wireless user is successfully achieved, which shows the promising potential and feasibility of this proposal to extend multiple services from metropolitan to suburban areas.

In this paper, we propose a new space-frequency adaptive equalization (SFAE) method for single carrier frequency domain equalization (SC-FDE) systems that can deal with multipath interference from the highly delay-dispersive channel as well as the multiuser interference. Based on the minimum mean square error (MMSE) criterion, we derive the adaptive weights by combining the received multi-antenna signals in the frequency domain. The main computation burdens of the proposed SFAE and the conventional space-time adaptive equalization (STAE) lie in the calculation of the autocorrelation matrix R and its inversion. The autocorrelation matrix in the SFAE is exactly a block Toeplitz matrix whose calculation can be efficiently implemented by the fast Fourier transformation (FFT) and its inversion also has fast algorithms. Compared with the conventional STAE method, the proposed SFAE method has comparable interference suppression performance, but with a lower order computational complexity. Hence, the proposed SFAE should be more attractive from a practical point of view. The numerical results are provided to corroborate the proposed studies.

In this work we propose two hybrid time-and frequency-domain microwave imagingschemes aimed to improve time-to-solution of quantitative time-domain imaging algorithms and image resolution of quantitative frequency-domain imaging algorithms. The proposed hybrid methods combine discontinuous Galerkin method (DGM) implementations of the time-domain (TD) forward-backward time-stepping (FBTS) algorithm and the frequency-domain (FD) contrast source inversion (CSI) or Gauss Newton Inversion (GNI). Simply put, an initial inversion in one domain (time or frequency) is used as prior information for the other. These schemes, referred to as FD-TD when FD prior is used in a TD algorithm, and TD-FD when TD prior is used in a FD algorithm, are applied to experimental and synthetic data. The results of the hybrid imaging approaches manifest an appreciable improvement relative to the stand-alone of FD and TD algorithms. Specifically, this study demonstrates that low-resolution frequency-domain prior information improves TD convergence. Additionally, we show that early-iteration time-domain solutions improves FD algorithm performance. We hope that these hybridization techniques pave the way for future investigations of optimal strategies for combining TD and FD schemes.

SummaryIn this paper, the channel estimation and signal‐to‐noise ratio (SNR) estimation technique of single‐carrier frequency domain equalization (SC‐FDE) system under low SNR in aeronautical multipath channel are studied, a SNR estimation algorithm which is easy to implement in engineering and an improved LS channel estimation algorithm based on Kalman filter using minimum error entropy (MEE‐KF) are proposed. This paper first introduces the SC‐FDE system and introduces the principle of MEE‐KF, and then, the channel estimation flow based on MEE‐KF is obtained by combining it with the traditional LS channel estimation algorithm, which makes the estimation results perform better. Simulation results show that after getting more accurate noise variance, the channel estimation results can better follow the changes of the channel after MEE‐KF processing, so as to resist the doppler frequency offset effect and make the channel estimation results more accurate, that is the channel response results of the data part can be closer to the real situation, so that the communication performance of SC‐FDE system has also been greatly improved.

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.

In this paper, single carrier frequency domain equalization with space time transmit diversity was implemented and evaluated in real-time using a DSP-based wireless MIMO test-bed. A new pilot structure for joint carrier frequency offset (CFO) and channel estimation is proposed and evaluated, to address the adverse inter-symbol interference and the severe CFO due to hardware impairments. The channel estimation method is done in the frequency domain using a non-parametric interpolation method. The new pilot scheme results in significant reduction of the required overhead signalling compared to previous schemes.

Among the useful blind equalization algorithms, there are stochastic-gradient iterative equalization algorithms. Because these algorithms basically use a linear FIR filter except to adopt a memoryless nonlinear function of the equalizer output to generate the desired response, only linear channel distortion can be corrected well. To overcome nonlinear channel distortion two new blind equalization schemes using the structure of the complex multi-layer perceptron that can deal with signals of any constellation size are proposed. One is a modification of the constant modulus algorithm (CMA), the most widely used blind algorithm. The other is a modification of the radius-directed equalization (RDE) algorithm with multiple constant modulus that is more suitable for the node activation function having a multi-saturated output region. The experimental results show that the proposed schemes have very low MSE in the steady state and at the same time can recover the arbitrary phase rotation due to the channel when the major channel distortion is both linear and nonlinear.

The CMA (Constant Modulus Algorithm) was developed for the adaptive receiving systems to capture the desired signal having the constant modulus property such as FM, PSK and FSK signals. The CMA is an algorithm suitable for mobile communications because it has the great advantage of not requiring a reference signal as the LMS aluorithm does.

Underwater acoustic channel is a time varying, strong multipath, serious Doppler frequency shift, and high noise interference channel. Aiming at the requirements of strong stability and high reliability to support reliable transmission over long distance, a direct sequence spread spectrum based on single carrier underwater acoustic communication system using dual spread spectrum code (SC-CDMA/DSSC) is proposed in this paper. And a data frame structure based on training sequence is given out according to this system. With the good correlation characteristics of the Gold sequence, it is used as spread code. The long spread code is used as the training sequence for data frame detection and synchronization, Doppler estimation and compensation, channel estimation and equalization. And the short spread code is used to spread effective data. For Doppler estimation and compensation, a delayed cross-correlation method is used to estimate the Doppler factor and then compensate the Doppler frequency shift by resampling. For channel estimation and equalization, firstly, we estimate the time-domain channel impulse response (CIR) using the training sequence, and use the single carrier frequency domain equalization (SC-FDE) algorithm for channel equalization. Simulation results show that the BER can be as low as 0 when the SNR>-9 in an environment with multipath and Doppler, the communication rate can achieve 387bps, which demonstrated that the proposed system has strong ability of anti-multipath and anti-interference.

We propose a channel estimation and adaptive transmission algorithm for single carrier frequency domain equalization (SC-FDE) systems with variable symbol rate. In this algorithm, signal-to-interference-plus-noise ratio (SINR) after equalization is estimated and adaptive transmission strategy is designed. A step rate adjusting method is proposed to satisfy the bandwidth variance due to the variable symbol rate. Simulation results show that this algorithm can increase the channel capacity in multipath channel.

In block-mode transmission, single carrier frequency domain equalisation-based ultra-wide-band technique is a promising physical-layer candidate scheme. Here, the authors address the noise variance estimation problem for signal-to-noise ratio estimation in such systems. Our investigations focus on the estimation schemes both robust to the pilot sequence and the channel type. First, the authors, respectively, define the correlated noise samples and the uncorrelated ones, where the difference signals or the sum signals of two adjacent received pilot signals are included. Then, with the help of the Cramer–Rao lower bound (CRLB) theorem, the authors either use the correlated or the uncorrelated samples to estimate the noise variance based on the difference signals and the sum signals, respectively, regardless of the pilot sequences. The corresponding CRLBs are also given and analysed. Finally, under either the correlated or the uncorrelated noise samples, the authors propose to linearly combine the estimator of the difference signals with that of the sum signals where the weight coefficients are optimised. Since the proposed two combined estimators are not only robust to the pilot sequence but also automatically adapt the weights to the channel condition, they can significantly outperform the existing estimators.