Soft Decision Feedback Research Articles

Successive Interference Cancellation Aided Bidirectional Soft Decision Feedback Equalization for OTFS Systems

Successive Interference Cancellation Aided Bidirectional Soft Decision Feedback Equalization for OTFS Systems

Multiple-Input-Multiple-Output Filtered Multitone Time Reversal Acoustic Communications Using Direct Adaptation-Based Turbo Equalization.

This paper proposes using direct adaptation (DA)-based turbo equalization in multiple-input-multiple-output (MIMO) filtered multitone (FMT) time reversal (TR) acoustic communications to jointly suppress noise, residual co-channel interference (CCI) and intersymbol interference (ISI) after the TR process. Soft information-based adaptive decision feedback equalization (ADFE) adjusted according to the recursive expected least squares (RELS) algorithm, including interference cancellation and decoding, is used to construct the DA-based turbo equalization. In the proposed method, soft information is exchanged between soft symbols with soft decisions of decoding iteratively, and interference suppression is proceeded successively and iteratively until the performance is stable. The principle of the proposed method is analyzed, and based on the acoustic channel responses measured in a real experiment, the performance is assessed in relation to that of anther two methods. Compared with the MIMO-FMT TR underwater acoustic communication using interference suppression without error control coding (ECC), the proposed method performs better, benefitting from the ECC included in turbo equalization. Additionally, compared with the MIMO-FMT TR underwater acoustic communication using interference suppression based on hard decision equalization and decoding, the proposed method exhibits superior performance by exploiting soft information.

A robust iterative receiver for single carrier underwater acoustic communications under impulsive noise

Achieving reliable underwater acoustic (UWA) communications is challenging due to the rapid changes of UWA channels and presence of impulsive noise. The soft decision feedback equalization (SDFE) has attracted much attention due to its capability of tackling the rapid changes of UWA channels. However, the existing SDFE exhibits error floor and even divergence due to the presence of severe impulsive noise. To overcome this problem, an improved SDFE (ISDFE) is proposed, which incorporates impulsive noise detection, clipping level estimation and damping to handle the impulsive noise. As the performance of the ISDFE also depends on the accuracy of channel estimation (CE), we propose a variable kernel width maximum complex correntropy criterion Kalman filter (VKW-MCCC-KF) algorithm to achieve robust and accurate CE under impulsive noise. With the proposed ISDFE and VKW-MCCC-KF, an iterative receiver for single carrier (SC) UWA mobile communication under impulsive noise is proposed, which incorporates the adaptive broadband Doppler compensation, VKW-MCCC-KF based CE and ISDFE, working in an iterative manner. Experimental results show that, compared with existing receivers, the proposed receiver achieves better performance and robustness to impulsive noise under fast changing UWA channels.

Improved Weighted Volterra DFE for C-Band 100-Gbit/s PAM-4 Transmission Over 60-km SSMF

To cope with the nonlinear distortions and the chromatic dispersion (CD) induced power fading in double-side band (DSB) intensity modulation and direct detection (IM/DD) transmission systems, high-performance Volterra decision-feedback equalizers (VDFEs) are widely applied. However, similar as linear DFE, the VDFEs suffer from error propagation in the case of wrong decisions. In this letter, to reduce the error propagation probability of VDFEs, we propose and experimentally demonstrate a diagonally-pruned improved weighted VDFE (DP-IWVDFE) in a C-band 4-level pulse amplitude modulation (PAM-4) transmission system. By replacing the hard-decision output by the soft-decision feedback symbol based on a compressed sigmoid nonlinear function in DP-IWVDFE, the error propagation probability can be significantly reduced, which lowers the bit error ratio (BER) by a factor of around two as compared to the DP-VDFE. Besides, 100-Gbit/s PAM-4 transmission over 60-km standard single-mode fiber (SSMF) using DP-IWVDFE is realized with the achieved BER below 3.8 <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\times 10^{-3}$ </tex-math></inline-formula> , achieving around 3.8-dB, 1.5-dB, and 1-dB improvements of the receiver sensitivity over the polynomial DFE (PDFE), improved weighted PDFE (IWPDFE), and DP-VDFE, respectively.

Improved soft-decision feedback turbo equalization algorithm with dual equalizers

In this paper, we propose a new soft-decision feedback equalization (SDFE) technique using dual equalizers (DE) over inter-symbol inference (ISI) channels. Unlike the most existing SDFE algorithms, the proposed DE-SDFE can efficiently suppress the residual interference from anti-causal symbols. In the proposed DE-SDFE, the scaled a posteriori information of the first equalizer is passed to the second one as the new a priori information. Furthermore, in order to handle the dependency within soft information, the scaling factor is theoretically derived. Simulation results reveal that the proposed DE-SDFE remarkably outperforms the state-of-the-art soft-decision turbo equalizers, with a complexity just twice that of the SDFE.

Delay-Doppler domain decision feedback turbo equalization for OTFS modulation

Emerging evidence indicates that orthogonal time–frequency space (OTFS) modulation is a potential candidate modulation scheme for high mobility wireless communications. However, OTFS may experience significant inter-symbol interference (ISI) and inter-Doppler interference (IDI) in the receiver. In this paper, we propose a soft decision feedback turbo equalization for OTFS transmission over delay-Doppler channels to jointly combat both interferences. A novel block decision feedback equalization (BDFE) algorithm is constructed using the band feature of the channels in the delay-Doppler domain. The feedforward and feedback filters are designed by the delay-time channels coefficients. According to the designed filter, an equivalent system model is employed to allow turbo equalization. The posterior probability is established using the soft prior information and feedback filter, and then fed back to the channel decoder as external information. Both theoretical analysis and simulation results demonstrate the effectiveness of the proposed scheme in improving the bit error rate (BER) performance and combat various interference. Numerical simulations are finally provided to justify the validity of the proposed scheme in improving the bit error rate (BER) performance and combating various interference.

Bayesian Iterative Channel Estimation and Turbo Equalization for Multiple-Input–Multiple-Output Underwater Acoustic Communications

This article investigates a robust receiver scheme for a single carrier, multiple-input-multiple-output (MIMO) underwater acoustic (UWA) communications, which uses the sparse Bayesian learning algorithm for iterative channel estimation embedded in Turbo equalization (TEQ). We derive a block-wise sparse Bayesian learning framework modeling the spatial correlation of the MIMO UWA channels, where a more robust expectation-maximization algorithm is proposed for updating the joint estimates of channel impulse response, residual noise, and channel covariance matrix. By exploiting the spatially correlated sparsity of MIMO UWA channels and the second-order a priori channel statistics from the training sequence, the proposed Bayesian channel estimator enjoys not only relatively low complexity but also more stable control of the hyperparameters that determine the channel sparsity and recovery accuracy. Moreover, this article proposes a low complexity space-time soft decision feedback equalizer (ST-SDFE) with successive soft interference cancellation. Evaluated by the undersea 2008 Surface Processes and Acoustic Communications Experiment, the improved sparse Bayesian learning channel estimation algorithm outperforms the conventional Bayesian algorithms in terms of the robustness and complexity, while enjoying better estimation accuracy than the orthogonal matching pursuit and the improved proportionate normalized least mean squares algorithms. We have also verified that the proposed ST-SDFE TEQ significantly outperforms the low-complexity minimum mean square error TEQ in terms of the bit error rate and error propagation.

Bidirectional Soft-Decision Feedback Equalization for OFDM Systems

A bidirectional soft-decision feedback equalizer (BiSDFE) for orthogonal frequency-division multiplexing (OFDM) systems over doubly selective channels is proposed. Soft, rather than hard, decision feedback equalizer (SDFE) is adopted to suppress intercarrier interference (ICI) and the band structure of the frequency-domain channel matrix is exploited to trade off between performance and computational complexity. By combining a conventional SDFE with a frequency-reversed SDFE, the proposed scheme can eliminate ICI induced by neighboring subcarriers of both sides, thereby obtaining frequency-reversal diversity and mitigating error propagation. Simulation results have demonstrated the advantage of this approach in bit error rate (BER), especially in the channels with large Doppler spreads.

Compensation of Chromatic Dispersion and Nonlinear Phase Noise Using Iterative Soft Decision Feedback Equalizer for Coherent Optical FBMC/OQAM Systems

In this article, we propose an iterative soft decision feedback (ISDF) equalizer to compensate for the chromatic dispersion and nonlinear phase noise effects in 30-Gbaud coherent optical filter bank multicarrier with off-set quadrature amplitude modulation (FBMC/OQAM) system. Conventional optical FBMC/OQAM system usually uses a 1-tap zero-forcing equalizer per subcarrier to combat the inter-symbol interference (ISI) caused by the chromatic dispersion (CD) in optical fiber. However, residual ISI and inter-carrier interference (ICI) still remain in the system and have significant impact on the system performance. To overcome this problem, a new ISDF N-tap frequency sampling (FS) equalizer is proposed to jointly mitigate the residual ISI and ICI which permits a better trade-off between performance and complexity. Simulation results show that, the proposed technique is capable of suppressing the interference more effectively than using only 1-tap equalizer. The feedback branch of the proposed ISDF equalizer can be exploited further to compensate for the nonlinear effect of the optical fiber. With compensation of linear and nonlinear impairments the proposed technique acts as a backpropagation method for optical FBMC/OQAM system.

Joint Iterative Channel Estimation and Frequency-Domain Turbo Equalization for Single-Carrier Spatial Modulation

Single-carrier frequency-domain turbo equalization (SC-FDTE) has gained widespread adoption in the emerging broadband spatial modulation (SM) systems operating in frequency-selective channels, where the channel model considered is a quasi-static Rayleigh fading channel. In this paper, a new class of robust FDTE designs based on the minimum mean-square error (MMSE) criterion is conceived for broadband single-carrier SM (SC-SM) systems relying on realistic imperfect channel knowledge. First, a robust time-domain soft-decision feedback (TDSDF)-aided FDTE is proposed to cope with channel estimation errors at the receiver. Furthermore, its robust frequency-domain soft-decision feedback (FDSDF)-aided counterpart is derived to offer a low-complexity approximate solution. Finally, by exploiting the carefully selected reliable soft-decision output of the channel decoder as pilots, we refine the resultant decision-directed channel estimation. As a benefit, the performance of the two robust FDTEs can be further improved. Both our simulation results and our extrinsic information transfer (EXIT) chart analysis demonstrate that the proposed robust FDTEs achieve significant performance improvements over the conventional FDTEs.

Low-Complexity Progressive MIMO-OFDM Receiver for Underwater Acoustic Communication

Multiple Input Multiple Output Orthogonal Frequency Division Multiplexing (MIMO-OFDM) proves to be a better choice for high speed underwater acoustic (UWA) communication as it increases the data rate and solves the bandwidth limitation issue; however, at the same time, it increases the design challenges and complexity of the receivers. Inter-Symbol Interference (ISI) and Inter-Carrier Interference (ICI) are introduced in the received signal by the extended multipath and Doppler shifts along with different types of noises due to the noisy acoustic channel. Here we propose two iterative receivers: one is ICI unaware iterative MIMO-OFDM receiver, which uses a novel cost function threshold based soft information decision feedback method. The second one is ICI aware progressive iterative MIMO-OFDM receiver, which adapts and increases the progressions according to the level of ICI present in the received signal, while fully utilizing the soft information from the previous iterations, therefore reducing the complexity. Orthogonal Matching pursuit (OMP) channel estimation, low density parity check (LDPC) decoding and minimum mean square error (MMSE) equalization schemes are exploited by both the receivers. The proposed receivers are analyzed and compared with the standard Alamouti MIMO receiver as a reference and also compared with the non-iterative, basic turbo iterative and non-progressive iterative MIMO receivers. Simulations and experimental results prove the efficiency and effectiveness of the proposed receivers.

Cost Function based Soft Feedback Iterative Channel Estimation in OFDM Underwater Acoustic Communication

Underwater Acoustic (UWA) communication is mainly characterized by bandwidth limited complex UWA channels. Orthogonal Frequency Division Multiplexing (OFDM) solves the bandwidth problem and an efficient channel estimation scheme estimates the channel parameters. Iterative channel estimation refines the channel estimation by reducing the number of pilots and coupling the channel estimator with channel decoder. This paper proposes an iterative receiver for OFDM UWA communication, based on a novel cost function threshold driven soft decision feedback iterative channel technique. The receiver exploits orthogonal matching pursuit (OMP) channel estimation and low density parity check (LDPC) coding techniques after comparing different channel estimation and coding schemes. The performance of the proposed receiver is verified by simulations as well as sea experiments. Furthermore, the proposed iterative receiver is compared with other non-iterative and soft decision feedback iterative receivers.

Soft-Feedback Time-Domain Turbo Equalization for Single-Carrier Generalized Spatial Modulation

In this paper, a new class of soft-decision feedback aided time-domain turbo equalizer (TDTE) based on the minimum mean-square error criterion is proposed for broadband single-carrier (SC) generalized spatial modulation (GSM) systems. First, a time-domain soft-decision feedback (TDSDF) aided TDTE is proposed, which operates on a vector-by-vector basis. In order to provide a flexible tradeoff between complexity and performance, time-invariant filter coefficients are derived to provide a low-complexity approximate solution to the proposed TDSDF-TDTE. Furthermore, a soft-feedback interference cancelation (SFIC) aided TDTE is proposed for SC-GSM systems with a lower complexity, where the computation of the second-order moment of matrices is completely avoided. Finally, bi-directional soft-decision feedback aided TDTEs are proposed by using a time-reversed TDSDF-TDTE/SFIC-TDTE in conjunction with a ordinary TDSDF-TDTE/SFIC-TDTE so as to harvest time-reverse diversity and to mitigate the error propagation. An extrinsic information transfer chart based analysis and bit error rate simulation results are presented to demonstrate the superior performance of the proposed soft-decision feedback aided TDTEs as opposed to the original TDTEs, while achieving a lower complexity.

An Ordered Successive Interference Cancellation Detector With Soft Detection Feedback in IDMA Transmission

In this paper, an ordered successive interference cancellation algorithm is proposed to realize efficient multi-user detection in interleave-division multiple access. In the proposed algorithm, the multi-user detection is implemented in the frequency domain and the bit detection results are obtained by de-spreading the chip detection results. Afterwards, the bit detection results are spread and interleaved to obtain regeneration soft chip results. The regeneration soft chip results are combined with the priori information provided by the channel decoder to obtain soft decision feedback symbols. In the proposed algorithm, the soft decision feedback symbols of detected users are exploited to cancel their interference to the subsequent un-detected users. In addition, the user detection order is optimized according to the signal-to-interference-plus-noise-ratio. The simulation results show that the proposed algorithm can achieve better performance in both single-input-single-output and multiple-input-multiple-output scenario.

An Improved Frequency Domain Turbo Equalizer for Single-Carrier Spatial Modulation Systems

In this paper, a new time-domain soft-decision feedback (TDSDF) aided frequency domain turbo equalizer (FDTE) is proposed for broadband single-carrier (SC) spatial modulation (SM) systems. Specifically, the proposed equalizer operates on a frame-by-frame basis and is designed based on the minimum block-averaged mean-square error (MBMSE) criterion. To tackle the error propagation problem, a metric in consideration of the reliability of the feedback information is considered. The optimal coefficients of the forward and feedback filters involved in the TDSDF-FDTE design are derived analytically. Simulation results show that the proposed nonlinear TDSDF-FDTE detector is capable of offering a better tradeoff between the bit-error-rate (BER) performance and the imposed computational complexity than the conventional linear frequency domain turbo demapper (FDTD) conceived for SC-SM systems. Furthermore, a 4 dB improvement is observed for the unbalanced channel.

Performance of Iterative Soft Decision Feedback Equalizers for Single-Carrier Transmission

In this paper, we consider iterative soft-decision feedback equalizers (sDFE), a.k.a. turbo equalizers for single-carrier transmission. Turbo equalizer takes log-likelihood ratio (LLR) feedback from channel decoder and convert the LLR into symbol estimates and variances to be used for the LLR update at the sDFE. Specifically, we consider both time domain and frequency-domain sDFE and compare their performances. The results shows that frequency-domain sDFE performs better than time-domain one and also that considerable gain can be obtained especially when the channel has deep nulls.

On Low-Complexity Soft-Input Soft-Output Decision-Feedback Equalizers

Compared with the soft-input, soft-output linear equalizer, the soft-input, soft-output decision-feedback equalizer (Soft-DFE) is much less investigated. This letter aims to provide a better understanding of the Soft-DFE, achieved via two comparisons: first, the two categories of designs classified by the way of treating the soft input and the soft-decision feedback (SDF), random or deterministic, are compared; second, the two different assumptions on the SDF, perfect or imperfect, are compared. The first comparison reveals the condition under which the two categories of designs are equivalent, and it is further shown that the equivalence always holds for constant-modulus modulations. The second comparison indicates that the perfect SDF assumption only incurs slight performance degradation.

Bidirectional Soft-Decision Feedback Turbo Equalization for MIMO Systems

This paper proposes a bidirectional soft-decision feedback turbo equalizer for severe triply selective fading channels. The proposed bidirectional soft-decision feedback equalizer (Bi-SDFE) uses a time reversed SDFE in conjunction with a normal SDFE to harvest time-reverse diversity and mitigate error propagation. A simple and effective linear combining scheme is derived for combining the extrinsic information on the two SDFEs for multiple-input–multiple-output (MIMO) systems with multilevel modulation. The bit-error-rate (BER) simulation results show that the proposed Bi-SDFE exhibits a lower signal-to-noise-ratio (SNR) threshold than the original SDFE and outperforms the well-known exact turbo minimum mean square error (MMSE) linear equalizers (LEs) at medium-to-high SNRs. Moreover, both extrinsic information transfer (EXIT) chart analysis and BER simulation results show that the Bi-SDFE achieves better performance than the original SDFE, whereas the Bi-SDFE uses only half the number of iterations of the SDFE. Therefore, the total computational complexity of the Bi-SDFE is similar to that of the original SDFE, which is a linear function of the channel length, MIMO size, and modulation constellation size. The performance gain of the proposed Bi-SDFE is also verified through an underwater acoustic (UWA) communication experiment with tough channel conditions.

Iterative Channel Estimation and Turbo Equalization for Multiple-Input Multiple-Output Underwater Acoustic Communications

This article investigates a robust receiver scheme for a single carrier, multiple-input–multiple-output (MIMO) underwater acoustic (UWA) communications, which uses the sparse Bayesian learning algorithm for iterative channel estimation embedded in Turbo equalization (TEQ). We derive a block-wise sparse Bayesian learning framework modeling the spatial correlation of the MIMO UWA channels, where a more robust expectation–maximization algorithm is proposed for updating the joint estimates of channel impulse response, residual noise, and channel covariance matrix. By exploiting the spatially correlated sparsity of MIMO UWA channels and the second-order a priori channel statistics from the training sequence, the proposed Bayesian channel estimator enjoys not only relatively low complexity but also more stable control of the hyperparameters that determine the channel sparsity and recovery accuracy. Moreover, this article proposes a low complexity space-time soft decision feedback equalizer (ST-SDFE) with successive soft interference cancellation. Evaluated by the undersea 2008 Surface Processes and Acoustic Communications Experiment, the improved sparse Bayesian learning channel estimation algorithm outperforms the conventional Bayesian algorithms in terms of the robustness and complexity, while enjoying better estimation accuracy than the orthogonal matching pursuit and the improved proportionate normalized least mean squares algorithms. We have also verified that the proposed ST-SDFE TEQ significantly outperforms the low-complexity minimum mean square error TEQ in terms of the bit error rate and error propagation.

Turbo equalization for single-carrier underwater acoustic communications

Recent research in underwater acoustic communications has taken advantage of MIMO technologies to achieve reliable communication with 10–100 times increase of data rate in comparison to traditional systems. The powerful turbo equalization and FEC coding techniques enable both single-carrier modulation and OFDM systems to combat triply selective UWA channels. This article reviews the time-domain and frequency-domain turbo equalizer schemes for MIMO SCM systems. Low-complexity techniques are presented with both turbo linear equalizers and turbo soft decision feedback equalizers in both the time and frequency domains. Although results are shown specifically for UWA channels, these turbo equalizer techniques are also suitable for terrestrial RF communication systems.