Frequency Domain Turbo Equalization Research Articles

Expectation-maximization vector approximate message passing-based frequency-domain turbo equalization for underwater acoustic communications.

Channel equalization plays a crucial role in single-carrier underwater acoustic (UWA) communications. Recently, a frequency-domain turbo equalization (FDTE) scheme enabled by the vector approximate message passing (VAMP) algorithm, was proposed, and it outperformed classic linear minimum mean square error FDTE at acceptable complexity cost. The operation of the VAMP-FDTE requires knowledge of noise power, which is predetermined before the equalization starts. In practice, however, it is difficult to obtain prior knowledge of noise power due to factors of unknown channel estimation errors and dynamic underwater environments. Motivated by this fact, we propose an enhanced VAMP-FDTE scheme, which learns the noise power knowledge during the equalization process via the expectation-maximization (EM) algorithm. The EM-based noise power estimation makes use of intermediate results of the VAMP-FDTE and, thus, only incurs a small extra computational overhead. The improved VAMP-FDTE, named EM-VAMP-FDTE, was tested by experimental data collected in shallow-sea horizontal UWA communication trials with MIMO configuration. It showed better performance than the existing VAMP-FDTE scheme, attributed to the online noise power learning.

Improved Frequency Domain Turbo Equalization with Expectation Propagation Interference Cancellation in Underwater Acoustic Communications.

This paper proposes an improved frequency domain turbo equalization (IFDTE) with iterative channel estimation and feedback to achieve both a good performance and low complexity in underwater acoustic communications (UWACs). A selective zero-attracting (SZA) improved proportionate normal least mean square (SZA-IPNLMS) algorithm is adopted by utilizing the sparsity of the UWAC channel to estimate it using a training sequence. Simultaneously, a set-membership (SM) SZA differential IPNLMS (SM SZA-DIPNLMS) with variable step size is adopted to estimate the channel status information (CSI) in the iterative channel estimation with soft feedback. In this way, the computational complexity for iterative channel estimation is reduced effectively with minimal performance loss. Different from traditional schemes in UWACs, an IFDTE with expectation propagation (EP) interference cancellation is adopted to estimate the a posteriori probability of transmitted symbols iteratively. A bidirectional IFDTE with the EP interference cancellation is proposed to further accelerate the convergence. THe simulation results show that the proposed channel estimation obtains 1.9 and 0.5 dB performance gains, when compared with those of the IPNLMS and the l0-IPNLMS at a bit error rate (BER) of 10-3. The proposed channel estimation also effectively reduces the unnecessary updating of the coefficients of the UWAC channel. Compared with traditional time-domain turbo equalization and FDTE in UWACs, the IFDTE obtains 0.5 and 1 dB gains in the environment of SPACE'08 and it obtains 0.5 and 0.4 dB gains in the environment of MACE'04 at a BER of 10-3. Therefore, the proposed scheme obtains a good BER performance and low complexity and it is suitable for efficient use in UWACs.

Probabilistic constellation shaping-aided underwater acoustic communication with vector approximate message passing iterative equalization.

A probabilistic constellation shaping (PCS)-aided single-carrier transceiver is proposed to improve spectral efficiency for underwater acoustic (UWA) communications. At the transmitter, the information bits are input into a distribution matcher followed by a systematic binary encoder, which yields a sequence of sign bits with a uniform distribution and a sequence of amplitude bits with a non-uniform distribution. Based on these two sequences, the PCS is then realized by mapping coded bits onto a quadrature amplitude modulation constellation. At the receiver, an improved frequency-domain turbo equalizer based on the vector approximate message passing (VAMP) is proposed for the PCS-UWA communication system to eliminate the multipath interference. It exploits the a priori symbol probability information benefiting from the PCS at the beginning of the turbo iteration and over the self-iteration of the VAMP soft equalizer, improving the symbol detection performance. Finally, the first experimental demonstration of a deep-sea PCS-UWA communication system and numerical simulation of shallower water are presented. The experimental results reveal the PCS-UWA communication system significantly outperforms traditional systems with no PCS. Also, the proposed receiver is superior to the classical adaptive turbo equalizer based on the improved proportionate normalized least mean square algorithm even with data reuse.

An Efficient Turbo Decoding and Frequency Domain Turbo Equalization for LTE Based Narrowband Internet of Things (NB-IoT) Systems.

This paper addresses the main crucial aspects of physical (PHY) layer channel coding in uplink NB-IoT systems. In uplink NB-IoT systems, various channel coding algorithms are deployed due to the nature of the adopted Long-Term Evolution (LTE) channel coding which presents a great challenge at the expense of high decoding complexity, power consumption, error floor phenomena, while experiencing performance degradation for short block lengths. For this reason, such a design considerably increases the overall system complexity, which is difficult to implement. Therefore, the existing LTE turbo codes are not recommended in NB-IoT systems and, hence, new channel coding algorithms need to be employed for LPWA specifications. First, LTE-based turbo decoding and frequency-domain turbo equalization algorithms are proposed, modifying the simplified maximum a posteriori probability (MAP) decoder and minimum mean square error (MMSE) Turbo equalization algorithms were appended to different Narrowband Physical Uplink Shared Channel (NPUSCH) subcarriers for interference cancellation. These proposed methods aim to minimize the complexity of realizing the traditional MAP turbo decoder and MMSE estimators in the newly NB-IoT PHY layer features. We compare the system performance in terms of block error rate (BLER) and computational complexity.

Single-carrier with index modulation for underwater acoustic communications

Index modulation (IM) has emerged as a promising technology for future wireless communications due to its potential to enhance both spectral efficiency and energy efficiency of wireless communication systems in recent years. In this paper, we propose a single-carrier with index modulation (SC-IM) for underwater acoustic communications. Besides, to combat the severe channel effects, we present frequency-domain turbo equalization (FDTE) with sparse channel estimation for the SC-IM system. The proposed iterative receiver outperforms the conventional frequency domain equalization. The simulation and lake experiment results verify the proposed SC-IM method and demonstrate its efficiency.

Expectation Propagation Aided Frequency Domain Turbo Equalizer for Single-Carrier Spatial Modulation Systems

An efficient frequency-domain equalizer is developed for single-carrier (SC) aided spatial modulation (SM) systems over frequency-selective fading channels, by employing the idea of expectation propagation (EP) algorithms. Specifically, we design an EP-aided frequency domain turbo equalizer (EP-FDTE) for iterative information exchange between the equalizer and the soft decoder, leading to more reliable a posterior probability (APP) estimation for signal detection. Our simulation results demonstrate that the proposed equalizer outperforms conventional frequency-domain turbo equalizer (FDTE) and generalized approximate message passing (GAMP)-aided turbo equalizer for SC-SM transmission.

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.

Time-Frequency Domain Turbo Equalization for Single-Carrier Underwater Acoustic Communications

Single-carrier frequency-domain equalization (SC-FDE) is a promising technique for coherent high-rate underwater acoustic (UWA) communications. In this paper, a time-frequency domain turbo equalization (TFD-TE) scheme is proposed for single-carrier modulation. The TFD-TE scheme is to couple a multi-channel frequency domain equalizer with phase rotation compensation and a low-order single-channel time-domain turbo equalizer. To mitigate the error propagation and further enhance receiver performance, a bidirectional equalizer that combined the soft outputs of a conventional equalizer and a backward equalizer is introduced into the proposed TFD-TE scheme (Bi-TFD-TF). The sparse channel is estimated by the improved proportionate normalized least mean squares (IPNLMS) algorithm block by block. Both the simulated and experimental results show the proposed TFD-TE can effectively improve system performance with acceptable complexity. The proposed TFD-TE scheme is evaluated using communication data collected from the DJK15 lake experiment. For the $1\times 4$ single-input multiple-output (SIMO) communication system using quadrature phase shift keying (QPSK) and 8-phase shift keying (8PSK) modulations, the proposed scheme achieves error-free transmission after a few iterations. Our receiver achieves a maximum raw data rate of 12 kbit/s and a reliable net data rate of 4 kbit/s within 4-kHz bandwidth at a range of 10.8 km. Compared with conventional frequency domain turbo equalization (FD-TE), the proposed TFD-TE scheme can enhance 0.8–1.3 dB in terms of output signal-to-noise ratio (OSNR). The related bi-TFD-TE provides an additional 0.8–1.7-dB OSNR improvements.

DFT-Precoded MIMO OFDM Underwater Acoustic Communications

The discrete Fourier transform (DFT) precoded orthogonal frequency-division multiplexing (OFDM) has been adopted as the uplink transmission technique in the long-term evolution terrestrial communication standard, for its lower peak-to-average power ratio (PAPR) and similar receiver complexity, compared with the standard OFDM. However, its application in the underwater acoustic (UWA) communications remains doubtful, mainly for the lack of systematic studies as well as sufficient experimental verifications. This paper provides a comprehensive investigation on the DFT-precoded OFDM UWA communication with a multiple-input–multiple-output (MIMO) configuration, and corroborates its superiority for implementing a practical UWA communication modem. The DFT precoding is applied on the data symbols to achieve a lower PAPR than that of the standard OFDM, and it is optional for the pilot symbols. The frequency-domain turbo equalization (FDTE) technique, especially suitable for interference-intensive scenarios, is employed on the receiver side to combat the intersymbol interference (ISI) and the multiplexing interference. Experimental results are provided to demonstrate the performance of the proposed transceiver scheme. It is shown reliable communication is achieved for the two-transducer transmission with a QPSK modulation and the one-transducer transmission with a 16QAM modulation, even without running any iteration for the FDTE. With the help of turbo iterations, a two-transducer transmission with a 16QAM modulation also achieves a satisfactory performance.

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.

Frequency-Domain Turbo Equalization With Iterative Channel Estimation for MIMO Underwater Acoustic Communications

This paper proposes a new iterative receiver for single-carrier multiple-input–multiple-output (SC-MIMO) underwater acoustic (UWA) communications, which utilizes frequency-domain turbo equalization (FDTE) and iterative channel estimation. Soft-decision symbols are not only fed back to the equalizer to cancel the intersymbol interference (ISI) and cochannel interference (CCI), but also used as training signals in the channel estimator to update the estimated channel state information (CSI) after each turbo iteration. This iterative channel estimation scheme helps to combat the problem commonly suffered by block-processing receivers in fast time-varying channels. Compared with time-domain turbo equalization, FDTE achieves comparable performance with significantly reduced computational complexity. Using soft-decision symbols to reestimate the time-varying channels, iterative channel estimation further improves the accuracy of the estimated CSI. The proposed iterative receiver has been verified through undersea experimental data collected in the Surface Processes and Acoustic Communications Experiment 2008 (SPACE08).

Iterative nonlinear detection for SFBC SC–FDMA uplink MIMO transmission systems

SummarySingle‐carrier frequency division multiple access (SC‐FDMA) systems with space frequency block coding (SFBC) transmissions achieve both spatial and frequency diversity gains in wireless communications. However, SFBC SC‐FDMA schemes using linear detectors suffer from severe performance deterioration because of noise enhancement propagation and additive noise presence in the detected output. Both issues are similar to inter‐symbol‐interference (ISI). Traditionally, SC‐FDMA system decision feedback equalizer (DFE) is often used to eliminate ISI caused by multipath propagation. This article proposes frequency domain turbo equalization based on nonlinear multiuser detection for uplink SFBC SC‐FDMA transmission systems. The presented iterative receiver performs equalization with soft decisions feedback for ISI mitigation. Its coefficients are derived using minimum mean squared error criteria. The receiver configuration study is Alamouti's SFBC with two transmit and two receive antennas. New receiver approach is compared with the recently proposed suboptimal linear detector for SFBC SC‐FDMA systems. Simulation results confirm that the performance of the proposed iterative detection outperforms conventional detection techniques. After a few iterations, bit‐error‐rate performance of the proposed receiver design is closely to the matched filter bound. Copyright © 2016 John Wiley & Sons, Ltd.

Equivalence of Frequency Domain Turbo Equalization Schemes for Single Carrier Multiple-Input Multiple-Output Systems

This paper investigates two typical frequency-domain turbo equalization (FDTE) schemes, i.e., frequency-domain equalization (FDE) with parallel interference cancelation (FDE-PIC) and FDE with frequency-domain decision feedback (FDE-FDDF) in single-carrier (SC) multiple-input–multiple-output (MIMO) systems. These two FDTE schemes are proven to be equivalent under the condition that we derived. We discover that the covariance matrix of the low-complexity FDE-PIC scheme and the correlation matrix of the FDE-FDDF scheme satisfy a unique relationship for constant-modulus modulations, and the original FDE-FDDF scheme suffers numerical instability for non-constant-modulus modulations because the estimation of the correlation matrices leads to the inversion of ill-conditioned matrices. By proposing a new estimation method of the correlation matrices, we guarantee that the non-constant-modulus FDE-FDDF scheme is numerically stable and that the relationship between these two FDTE schemes holds for both constant-modulus and non-constant-modulus modulations. Furthermore, we prove that the FDE-PIC and FDE-FDDF schemes are equivalent under this relationship. The equivalence of these two FDTE schemes is also verified through numerical simulations in terms of bit error rate (BER) at each turbo iteration and the estimation of the correlation matrices.

DSP based real-time single carrier underwater acoustic communications using frequency domain turbo equalization

In this paper, a DSP based real-time single carrier underwater acoustic communication system is developed. The designed receiver system operates in frequency domain for low complexity equalization. The turbo principle is incorporated into channel equalization and channel estimation processes to improve the system reliability. The channel is treated as stable within each small block and iteratively estimated based on LMS method and soft information provided by channel decoder. The soft LMS channel estimation is able to achieve better performance than conventional phase compensation scheme in single carrier frequency domain system. The receiver system is implemented on a floating point DSP running at 350 MHZ. Through careful optimization, the real-time processing is achieved with sufficient margin for both single-hydrophone receiver and multi-hydrophone systems. The designed system has been tested by both tank experiment and sea trials and achieves satisfied performance.

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.

Single-RF Spatial Modulation Requires Single-Carrier Transmission: Frequency-Domain Turbo Equalization for Dispersive Channels

In this paper, we propose a broadband single-carrier (SC) spatial modulation (SM)-based multiple-input–multiple-output (MIMO) architecture relying on a soft decision (SoD) frequency-domain equalization (FDE) receiver. We demonstrate that conventional orthogonal-frequency-division-multiplexing (OFDM)-based broadband transmissions are not readily suitable for the single-radio-frequency-assisted SM-MIMO schemes since this scheme exhibits no substantial performance advantage over single-antenna transmissions. To circumvent this limitation, a low-complexity SoD FDE algorithm based on the minimum mean square error (MMSE) criterion is invoked for our broadband SC-based SM-MIMO scheme, which is capable of operating in a strongly dispersive channel having a long channel impulse response at moderate decoding complexity. Furthermore, our SoD FDE attains a near-capacity performance with the aid of a three-stage concatenated SC-based SM architecture.

Single-Carrier Frequency-Domain Turbo Equalization With Various Soft Interference Cancellation Schemes for MIMO Systems

Single-carrier frequency-domain turbo equalization (SC-FDTE) is investigated, with the focus on the design of soft-decision frequency-domain equalizer (SD-FDE) under minimum mean square error (MMSE) criteria. Existing SD-FDEs perform equalization on each frequency bin individually, which however only achieves suboptimal performance, and with the availability of the a priori input, block-wise operation is required to achieve optimal performance. In this paper, optimal MMSE SD-FDE designs with three soft interference cancellation (SIC) schemes are introduced. The first SIC scheme, SIC-I, utilizes the a priori knowledge from the channel decoder, the second SIC scheme, SIC-II, relies on the decoder a priori knowledge as well as the symbol-wise a posteriori soft-decision feedback of the SD-FDE itself, and the third SIC scheme, SIC-III, is comparable to the SIC-II while with a block-wise soft-decision feedback. The optimal SD-FDEs incur high computation complexity due to block-wise processing, then a suboptimal bin-wise SD-FDE with SIC-III is proposed to achieve complexity-performance tradeoff. It is shown that the suboptimal SD-FDE with SIC-III considerably outperforms existing suboptimal SD-FDE with SIC-I, while at a similar magnitude of complexity. It also achieves better performance than the optimal SD-FDE with either SIC-I or SIC-II. Compared to the optimal SD-FDE with SIC-III, the performance loss is marginal.

Comparative Study of Open-Loop Transmit Diversity Schemes with Four Antennas in DFT-Precoded OFDMA Using Turbo FDE and Iterative Channel Estimation

This paper compares the block error rate (BLER) performance of open-loop (OL) transmit diversity schemes with four antennas in the uplink for discrete Fourier transform (DFT)-precoded orthogonal frequency division multiple access (OFDMA). One candidate is a quasi-orthogonal (QO) - space-time block code (STBC) in which four-branch minimum mean-square error combining (MMSEC) is achieved at the cost of residual inter-code interference (ICI). Another candidate is a combination of STBC and selection diversity called time switched transmit diversity (TSTD) or frequency switched transmit diversity (FSTD). We assume a turbo frequency domain equalizer (FDE) associated with iterative decision-feedback channel estimation (DFCE) at a receiver to reduce the influences of the residual ICI and channel estimation (CE) error. From the extensive link-level simulation results, we show that a combination of STBC and TSTD (FSTD) is suitable as four-antenna OL transmit diversity scheme for DFT-precoded OFDMA using turbo FDE and iterative DFCE.

Spectrally Efficient Frame-Format-Aided Turbo Equalization With Channel Estimation

Chained turbo equalization (CHATUE) has been recently recognized as a low-complexity frequency-domain turbo equalization technique that eliminates the necessity of transmitting the cyclic prefix (CP), and hence allows for spectrally efficient signaling in wireless communications. However, two issues arise from the original version of CHATUE (referred to as CHATUE1) as a consequence of eliminating the CP, which are the noise enhancement and the latency due to the time-concatenated structure. This paper proposes a new version of CHATUE (referred to as CHATUE2) to solve the noise enhancement problem. CHATUE2 retrieves the circulant structure of the channel matrix, originally inherent within the CP transmission, by utilizing composite replica signals that combine the received signals and the soft reference signals replicated from the log-likelihood ratio (LLR) fed back from the decoder. For this purpose, this paper determines the optimal combining ratio based on the minimum-mean-square-error (MMSE) criterion. CHATUE2 is hence able to achieve an improvement in bit-error-rate (BER) performance over CHATUE1. In addition, this paper provides a solution to solving the latency problem by making a practical assumption on the training sequence (TR) transmission, which is required to perform channel estimation generally, in practical systems. Furthermore, this paper proposes a new channel estimation technique, i.e., chained turbo estimation (CHATES), which improves the spectrum efficiency and asymptotically achieves the Cramer–Rao bound (CRB). CHATES assumes that the TR length is exactly equal to the channel impulse response (CIR) length, although the conventional technique requires twice as long or even longer TR lengths. Numerical results show that CHATUE2 with CHATES achieves a gain of 1 dB over conventional turbo equalization with a CP at a BER of $\hbox{10}^{-5}$ in realistic propagation scenarios represented by channel sounding measurement data and in model-based frequency-selective fading channels.

Single-carrier frequency-domain turbo equalization without cyclic prefix or zero padding for underwater acoustic communications

A frequency-domain turbo equalization (FDTE) scheme without cyclic prefix (CP) or zero padding is proposed for single-carrier, multiple-input-multiple-output underwater acoustic communication. In the first iteration of the FDTE, the received continuous data stream is divided into consecutive blocks and a combined inter-block-interference (IBI) cancellation and overlapped windowing scheme is used to diagonalize each data block for low-complexity detection in the frequency domain. Since the second iteration, IBI cancellation and CP reconstruction are applied on each block to enable effective symbol detection. This work extends the authors' previous work on frequency-domain hard-decision equalization to soft-decision turbo equalization so that it not only retains high data transmission efficiency, but also improves the bit error rate performance with slightly increased complexity due to multiple iterations. Its feasibility and effectiveness have been tested by field trial data from the ACOMM09 underwater communication experiment.