TURBO EQUALIZATION WITH JOINTLY GAUSSIAN EQUALIZER

A Jointly Gaussian (JG) equalizer is derived for turbo equalization based on an augmented real matrix representation of channel model and a Gaussian approximation of the received symbol sequence. Using matrix inversion lemma and Cholesky decomposition, a lowcomplexity implementation of JG equalizer is also presented. The simulation results and complexity comparison confirm that turbo equalization with JG equalizer has a better performance and a lower complexity than the existing turbo equalization with linear minimum mean squared error equalizer.

Soft Direct-Adaptation Based Bidirectional Turbo Equalization for MIMO Underwater Acoustic Communications

This paper proposes a soft direct-adaptation based bidirectional turbo equalizer for multiple-input multiple-output underwater acoustic communication systems. Soft, rather than hard, direct-adaptation based equalizer combined with the fast self-optimized least mean square algorithm is employed to achieve a faster convergence rate, and the second-order phase-locked loop is embedded into the equalizer to track the time-varying channel. Meanwhile, by utilizing a weighted linear combining scheme, the conventional soft direct-adaptation based equalizer is combined with the time-reversed soft direct-adaptation based equalizer to exploit bidirectional diversity and mitigate error propagation. Both the simulation and experimental results demonstrate that the soft direct-adaptation based bidirectional turbo equalizer outperforms the single-direction soft direct-adaptation based turbo equalizer, and achieves a faster convergence rate than the hard direct-adaptation based bidirectional turbo equalizer.

A Reduced Search Soft-Output Detection Algorithm and Its Application to Turbo-Equalization

To decrease the complexity of MAP algorithm, reduced state or reduced search techniques can be applied. In this paper we propose a reduced search soft output detection algorithm fully based on the principle of M algorithm for turbo equalization, which is a suboptimum version of the Lee algorithm. This algorithm is called soft output M algorithm (denoted as SO M algorithm), which applies the M strategy to both the forward recursion and the extended forward recursion of the Lee algorithm. Computer simulation results show that, by properly selecting and adjusting the breadth parameter and depth parameter during the iteration of turbo equalization, this algorithm can obtain good performance and complexity trade off.

INTERFERENCE SUPPRESSING FOR CELLULAR MIMO SYSTEM BASED ON TURBO RECEIVER

Space-Time Coding （STC）, which combines channel coding, modulation, and multiple transmit antennas, is a powerful scheme to achieve higher data rates and combat fading in wireless systems, in this paper, we propose a soil/cancellation turbo equalization scheme to suppress Co-Channel Interference （CCI） in STC systems. The simulation results show that the proposed method significantly improves the system＇s ability of interference suppression, while preserving the space-time structure.

JOINT MF COMBINING AND TURBO EQUALIZATION FOR WIRELESS COMMUNICATIONS OVER ISI CHANNELS WITH DIVERSITY RECEPTION

A new method called joint Matched Filter (MF) combining and turbo equalization is proposed for wireless communications over Inter-Symbol Interference (ISI) channels with diversity reception. This method takes diversity combining and equalization as integrity and need just one turbo equalizer for all diversity branches. Computer simulations prove that our method can take advantage of turbo equalization and diversity reception to combat fading of wireless channels.

TURBO AIDED CYCLIC PREFIX RECONSTRUCTION FOR CODED SINGLE-CARRIER SYSTEMS WITH FREQUENCY-DOMAIN EQUALIZATION (SC-FDE)

In this paper, a Turbo aided Cyclic Prefix (CP) reconstruction scheme, termed Turbo- CPR, is proposed for Single-Carrier systems with Frequency-Domain Equalization (SC-FDE) that employ insufficient CP in the transmitter. In Turbo-CPR, the decoder output is incorporated in the process of equalization, i.e. Turbo equalizer is employed. It is shown in the simulation results that Turbo-CPR not only recovers the performance loss due to insufficiency of CP, but also provides extra gains over the lower bound of performance for conventional CP reconstruction schemes.

Adaptive Turbo Equalization for Probabilistic Constellation Shaped Underwater Acoustic Communications

To increase the spectral efficiency of the underwater acoustic(UWA)communication system,the high order quadrature amplitude modulations(QAM)are deployed.Recently,the prob-abilistic constellation shaping(PCS)has been a novel technology to improve the spectral efficiency.The PCS with high-order QAM is introduced into the UWA communication system.A turbo equal-ization scheme with PCS was proposed to cancel the severe inter-symbol interference(ISI).The non-zero a priori information is available for the equalizer and decoder before turbo iteration.A pri-ori hard decision approach is proposed to improve the detection performance and the equalizer con-vergence speed.At the initial turbo iteration,the relation between the a priori information and the probability of the amplitude of 16QAM symbols in one dimension is given.The simulation results verified the efficiency of the proposed method,and compared to the uniform distribution(UD),the PCS-16QAM had a significant improvement of the bit error rate(BER)performance with PCS-ad-aptive turbo equalization(PCS-ATEQ).The UWA communication experiments further verified the performance superiority of the proposed method.

LOW COMPLEXITY LMMSE TURBO EQUALIZATION FOR COMBINED ERROR CONTROL CODED AND LINEARLY PRECODED OFDM

The turbo equalization approach is studied for Orthogonal Frequency Division Multiplexing （OFDM） system with combined error control coding and linear precoding. While previous literatures employed linear precodcr of small size for complexity reasons, this paper proposes to use a linear precoder of size larger than or equal to the maximum length of the equivalent discrete-time channel in order to achieve full frequency diversity and reduce complexities of the error control coder/decoder. Also a low complexity Linear Minimum Mean Square Error （LMMSE） turbo equalizer is derived for the receiver. Through simulation and performance analysis, it is shown that the performance of the proposed scheme over frequency selective fading channel reaches the matched filter bound; compared with the same coded OFDM without linear precoding, the proposed scheme shows an Signal-to-Noise Ratio （SNR） improvement of at least 6dB at a bit error rate of 10 6 over a multipath channel with exponential power delay profile. Convergence behavior of the proposed scheme with turbo equalization using various type of linear precoder/transformer, various interleaver size and error control coder of various constraint length is also investigated.

CRC-AIDED TURBO EQUALIZATION FOR MIMO FREQUENCY SELECTIVE FADING CHANNELS

This paper presents a CRC (Cyclic Redundancy Check)-aided turbo equalization approach to reduce the computational complexity. In this approach,CRC code bits are padded to the end of each transmit block,and a cyclic redundancy check is performed after decoding each block at the receiver end. If the check sum is zero,which means the receive block is correct,the corresponding LLRs (Log Likelihood Ratios) of this block are set high reliable values,and all the computations corresponding to this block can be cancelled for the subsequent outer iterations. With a lower computational complexity the proposed approach can achieve the same as or even better performance than the conventional non-CRC method.

Shipborne Underwater Acoustic Communication System and Sea Trials with Submersible Shenhai Yongshi

The Shipborne acoustic communication system of the submersible Shenhai Yongshi works in vertical, horizontal and slant channels according to the relative positions. For ease of use, an array combined by a vertical-cone directional transducer and a horizontal-toroid one is installed on the mothership. Improved techniques are proposed to combat adverse channel conditions, such as frequency selectivity, non-stationary ship noise, and Doppler effects of the platform’s nonlinear movement. For coherent modulation, a turbo-coded single-carrier scheme is used. In the receiver, the sparse decision-directed Normalized Least-Mean-Square soft equalizer automatically adjusts the tap pattern and weights according to the multipath structure, the two receivers’ asymmetry, the signal’s frequency selectivity and the noise’s spectrum fluctuation. The use of turbo code in turbo equalization significantly suppresses the error floor and decreases the equalizer’s iteration times, which is verified by both the extrinsic information transfer charts and bit-error-rate performance. For noncoherent modulation, a concatenated error correction scheme of nonbinary convolutional code and Hadamard code is adopted to utilize full frequency diversity. Robust and lowcomplexity synchronization techniques in the time and Doppler domains are proposed. Sea trials with the submersible to a maximum depth of over 4500 m show that the shipborne communication system performs robustly during the adverse conditions. From the ten-thousand communication records in the 28 dives in 2017, the failure rate of the coherent frames and that of the noncoherent packets are both below 10%, where both synchronization errors and decoding errors are taken into account.

M-BCJR Algorithm with Channel Shortening Based on Ungerboeck Observation Model for Faster-than-Nyquist Signaling

The M-BCJR algorithm based on the Ungerboeck observation model is a recent study to reduce the computational complexity for faster-than-Nyquist(FTN)signaling[1].In this paper,we propose a method that can further reduce the complexity with the approximately same or better bit error rate(BER)performance compared to[1].The information rate(IR)loss for the proposed method is less than 1%compared to the true achievable IR(AIR).The proposed improvement is mainly by introducing channel shortening(CS)before the M-BCJR equalizer.In our proposal,the Ungerboeck M-BCJR algorithm and CS can work together to defeat severe inter-symbol interference(ISI)introduced by FTN signaling.The ISI length for the M-BCJR algorithm with CS is optimized based on the criterion of the IR maximization.For the two cases=0.5 and=0.35,compared to Ungerboeck M-BCJR without CS benchmark[1],the computational complexities of Ungerboeck M-BCJR with CS are reduced by 75%.Moreover,for the case=0.35,the BER performance of Ungerboeck M-BCJR with CS outperforms that of the conventional M-BCJR in[1]at the low signal to noise ratio region.

Factor-graph-based iterative channel estimation and signal detection algorithm over time-varying frequency-selective fading channels

The problem of soft-input so,output （ SISO ） detection for time-varying frequency-selec- tive fading channels is considered. Based on a suitably-designed factor graph and the sum-product al- gorithm, a low-complexity iterative message passing scheme is proposed for joint channel estima- tion, equalization and decoding. Two kinds of schedules （parallel and serial） are adopted in message updates to produce two algorithms with different latency. The computational complexity per iteration of the proposed algorithms grows only linearly with the channel length, which is a significantly de- crease compared to the optimal maximum a posteriori （MAP） detection with the exponential com- plexity. Computer simulations demonstrate the effectiveness of the proposed schemes in terms of bit error rate performance.

A NOVEL ITERATIVE SCHEME FOR PARALLEL INTER-SYMBOL INTERFERENCE CHANNELS

In this paper,we propose a novel iterative scheme for exploiting transmit diversity using parallel independent Inter-Symbol Interference (ISI) channels. In this adaptive iterative scheme,we use EXtrinsic Information Transfer (EXIT) chart tool to choose appropriate iterative method from Itera-tive Combining (IC),used as parallel concatenation turbo-like scheme,and Turbo Equalization (TE),used as serial concatenation turbo-like scheme. It is show that the proposed iterative scheme provides excellent performance both analytically and through simulations without any compute complexity increase comparable to IC.

Switching Equalization Algorithm Based on a New SNR Estimation Method

It is well-known that turbo equalization with the max-log-map （MLM） rather than the log-map （LM） algorithm is insensitive to signal to noise ratio （SNR） mismatch. As our first contribution, an improved MLM algorithm called scaled max-log-map （SMLM） algorithm is presented. Simulation results show that the SMLM scheme can dramatically outperform the MLM without sacrificing the robustness against SNR mismatch. Unfortunately, its performance is still inferior to that of the LM algorithm with exact SNR knowledge over the class of high-loss channels. As our second contribution, a switching turbo equalization scheme, which switches between the SMLM and LM schemes, is proposed to practically close the performance gap. It is based on a novel way to estimate the SNR from the reliability values of the extrinsic information of the SMLM algorithm.

Reduced-Complexity Turbo Equalization for Turbo Coded MIMO/OFDM Systems

This paper derives a low-complexity turbo equalization algorithm for turbo coded multiple input multiple output/ orthogonal frequency division multiplexing systems. This algorithm consists of soft-output decision-feedback equalization with a probabilistic data association algorithm and a soft-input soft-output turbo channel decoder using iterative operations. In each iteration, extrinsic information extracted from the probabilistic data association algorithm detector and from the channel decoder is used as the prior information for the next iteration to realize iterative channel equalization and channel decoding, Our simulation results show that the algorithm improves the signal noise ratio around 1 dB with bit error rate reaching 10 -6 when the Eb/ N0 - 4 dB compared to minimum mean square error and match filter, and can greatly reduce the intersymbol interference at a low overall complexity of O（ N^3） after 2 iterations.

Bidirectional turbo equalization for underwater acoustic communications

A direct-adaptation based bidirectional turbo equalizer for underwater acoustic communications is proposed.Abandoning the channel estimation process,the direct-adaptation based turbo equalizer embedded with digital phase-locked loop is adopted to track time-varying channel.The fast self-optimized algorithm is used to adjust the step size,thus a good tradeoff between the convergence speed and performance has been made.Furthermore,by minimizing the mean squared error,an optimal weighting factor is derived to exploit bidirectional diversity gain.The forward turbo equalizer is combined with the backward turbo equalizer to eliminate error propagation effect.Simulated and experimental results demonstrate that the bidirectional turbo equalizer outperforms the single directional one.It can be seen from the experimental results that,compared with the channel estimation based algorithm,the direct-adaptation based algorithm is less sensitive to the time-varying channel and has a lower bit error rate.

Performance Analysis of Hard Iterative Channel Estimation in Turbo Equalization

Reasonable bit error rate performance requires perfect channel state information （CSI） in traditional turbo equalization （TE）, which is hard to obtain in practice. Soft and hard iterative algorithms have been developed to address the channel estimation problem with the performance of the soft iteratwe channel estimate based on the recursive least square algorithm. This paper presents an analysis of the performance of hard iterative channel estimation （HICE） based on the least mean square algorithm. The analysis uses a cost function with the hard decision on the TE output. An iterative channel correction （ICC） algorithm based on the gradient descent algorithm is used to iteratively minimize the cost function. The simulation results agree with the theoretical lower bound for the mean square error （MSE） of the estimated channels. Simulations show that, given an imperfect CSI with an MSE below the upper bound, the linear minimum mean squared error TE （LMMSE-TE） using the ICC has only small performance degradation compared to that with a perfect CSI, while the traditional LMMSE-TE suffers from severe error floor effect even with more iterations.