Low complexity iterative frequency domain decision feedback equalization for faster-than-nyquist signaling

In broadband wireless communication systems, single-carrier transmission with frequency domain equalization (SC-FDE) is regarded as an alternative modulation technique to the orthogonal frequency division multiplexing (OFDM). Compared with OFDM systems, SC-FDE has similar implementation complexity and performance. However, SC-FDE with linear equalizer will suffer from serious performance deterioration under deep frequency selective fading channels. An effective method to solve this problem is to introduce non-linear decision feedback equalization (DFE) to SC-FDE. In this paper, a low complexity iterative decision feedback equalizer in the frequency domain for single- carrier systems is proposed. Based on the minimum mean square error (MMSE) criterion, a simplified parameter estimation method is introduced to calculate the coefficients of the feed-forward and feedback filters, which reduces the implementation complexity of the equalizer. Simulations show that the performance of the proposed algorithm is similar to the traditional iterative block DFE (IBDFE) under various multipath fading channels but with lower complexity.

Frequency-domain decision-feedback equalization (FD-DFE) for single carrier modulation avoids interblock interferences (IBIs) by using guard intervals located in between two data blocks. If the period of a guard interval is shorter than that of the channel impulse response, the IBIs cannot be removed by the FD-DFE, which significantly deteriorates its performance. To handle this IBI problem, this letter introduces the adaptive self-orthogonalizing per-tone FD-DFE without channel estimation, where time dispersiveness, one weakness of the per-tone equalization, is compensated by the self-orthogonalization coming from the lattice structure of the Levinson-Durbin algorithm, which dramatically reduces bit-error rates of the proposed FD-DFE, comparing with the existing FD-DFE.

This paper investigates the detection schemes for single-carrier underwater acoustic communications over the severe time-dispersive channels. A low-density parity-check (LDPC) code is employed for the improvement of the equalization performance. A detection scheme with Turbo conception is proposed which includes a LDPC decoder in the feedback loop of an iterative block decision feedback equalizer (IB-DFE), combining the iterative frequency domain equalization of IB-DFE with the iterative LDPC decoding. The external messages are fully exchanged between the IB-DFE and the decoder during the processing of the joint iterative equalization and decoding. The numerical results demonstrate that the decision signals with higher reliability from the LDPC decoder accelerate the convergence of the equalizer and enhance the detection performance, yielding up to 6 dB performance gains when compared with the scheme without LDPC code. Compared with the concatenated scheme in which the process of the iterative frequency domain equalization is serial concatenated with that of the iterative LDPC decoding, the combined scheme obtains about 2 dB performance gains.

This paper addresses the problem of low complexity iterative channel equalization in intersymbol interference channels using 8PSK modulation. In this paper, we apply a recently proposed low complexity iterative channel equalization technique, called the iterative decision feedback equalizer (IDFE) to a coded system using 8PSK modulation. In this system, the structure of the DFE has been modified to incorporate soft a priori information from previous iterations of the channel decoder in detection of the corrupted signal. As a result, in this algorithm complexity is only a linear function of channel memory length. Simulation results show that this technique, using a convolutional code with constraint length K=3 and interleaver size N=3000 over a known time invariant ISI channel achieves a remarkable gain of about 5 dB compared to the conventional DFE. Complexity evaluation also shows that the iterative DFE has advantages in terms of complexity compared to other types of turbo equalization techniques and is an appropriate candidate for EDGE (Enhanced Data rates for GSM Evolution) systems.

Data pages retrieved from a volume holographic storage channel (VHSC) suffer from inter-symbol interference (ISI) and noise. Assuming ISI does not change spatially (i.e., stationary), 2-D equalization/detection schemes has been previously developed for quadratic channels like VHSC. In practice, however, the point spread function of a VHSC changes spatially due to magnification and misalignment errors. In this paper, we develop a channel model for magnification error (ME) dominated VHSC and also evaluate the effect of ME on the equalization/detection performance. Results indicate that the recently introduced iterative magnitude-squared decision feedback equalization (IMSDFE) method is more robust to magnification error compared to linear minimum mean squared-error (LMMSE) equalization and adaptive threshold detection (ATD).

This paper proposes a frequency-domain iterative soft decision feedback equalization (SDFE) scheme for multiple-input---multiple-output orthogonal frequency division multiplexing communication systems in multi-path fading channels. Error propagation can seriously affect the performance of the adaptive decision feedback equalization. We propose an iterative SDFE to not only combat error propagation but also be suitable for multilevel modulation systems. Under a Gaussian approximation of the a priori information and the SDFE output, the output of an equivalent AWGN channel and expressions for the a posteriori log likelihood ratio (LLR) and the extrinsic LLR are derived for multilevel modulation. In addition, we also investigate the iterative receivers by employing irregular low-density parity check codes (LDPC) and turbo codes. The performance of the LDPC-coded iterative receiver is better than that of the turbo-coded iterative receiver. Some simulation examples are given to show the effectiveness and comparisons of the proposed receiver.

Recently [16], we have proposed using faster than Nyquist (FTN) signaling to achieve transmission over continuous-time broadcast channels and shown that it can achieve the capacity region of the two-user Gaussian broadcast channel. Benefits of FTN broadcasting include separate encoding and explicit transmission of all users' data, i.e., unlike the previously proposed broadcast coding schemes, no joint encoding is needed. This paper presents a design of a Turbo-coded broadcast transmitter based on the FTN signaling. The proposed receiver architecture has a low implementation complexity and is based on Turbo decoding and successive cancellation of FTN-induced intersymbol interference. The presented simulation results indicate that the designed FTN broadcast architecture can be superior to the time-sharing broadcasting used in practice, and shows the potential to perform close to the capacity boundaries of the Gaussian broadcast channel.

The achievement of the boundary values of spectral efficiency is associated with the development of methods for generating and receiving signals with a compact spectrum. The reason is a constant increase in the capacity of existing communication channels caused by an increase in the volume of transmitted information. Moreover, the allocated frequency bandwidths have natural limitations, and they are almost all reached. The effective way to approach the boundary values of spectral efficiency is the application of spectrally efficient signals, such as FTN (Faster-Than-Nyquist) signals. This article proposes to synthesize optimal FTN signals that are more compact in the spectrum than RRC (root raised cosine) pulses-based signals. The criterion of maximum energy concentration in the occupied frequency bandwidth and the constraint on the cross-correlation coefficient are used to solve the optimization problem. The contribution of this work is the optimization of FTN signal shape. The obtained optimal FTN signals provide a 24% increase in spectral efficiency compared to the RRC pulses-based signals. At the same time, the energy loss stays almost unchanged. To the best of authors’ knowledge, this is the first case when the frequency bandwidth reduction is achieved at practically no energy loss. The simulation modeling in channels with additive white Gaussian noise and fading channels is done with regard to the FTN-SC-FDE (Faster-Than-Nyquist - Single Carrier system with Frequency Domain Equalization) structure. The optimal FTN signals presented in this work can be used to increase the spectral efficiency of satellite broadcasting systems, such as DVB-S2/S2X.

Faster-Than-Nyquist (FTN) Signaling is a non-orthogonal transmission scheme which violates the Nyquist zero-ISI criterion providing higher throughput and better spectral efficiency than a Nyquist transmission scheme. This comes with a cost of higher transceiver complexity. In this paper, we focus on understanding pulse shapes and their inter-symbol-interference (ISI) and show that, under certain conditions on pulse shapes and τ (time acceleration factor), the ISI can be avoided completely with the help of precoding. This leads to a symbol-by-symbol detection. Further, we extend this idea to Orthogonal Frequency Division Multiplexing (OFDM) FTN systems and show that, under certain conditions, the average performance of OFDM system reaches that of a Nyquist system. Finally, simulation results of the performance of precoded and non-precoded single carrier and OFDM FTN systems are compared to a Nyquist system.

Faster-than-Nyquist (FTN) signaling is deemed a promising candidate for enabling high spectral efficiency in next-generation optical data center interconnects (DCIs). Trellis-based sequence detectors, such as maximum likelihood sequence estimation (MLSE) and maximum a posteriori (MAP) sequence estimation, operating with long memory lengths, are by far the most commonly adopted strategy for deciphering the original symbol from severe inter-symbol interference (ISI). Nevertheless, the inherent high complexity of this approach poses significant challenges to its practical implementation. In this paper, a partial-response decision feedback equalizer (PR-DFE) is proposed to realize ultra-low complexity and high-performance FTN signaling. The fundamental principle of the proposed scheme involves combining the transmitter-side precoding and receiver-side partial response equalization criteria, which significantly reduces the occurrence of the error propagation issue of the typical DFE in the FTN system. The effectiveness of the proposed scheme is experimentally verified in a 56Gbaud FTN 4-ary pulse amplitude modulation (PAM4) system with a compression factor of 0.8. According to the experimental results, PR-DFE achieves 2.4 dB and 1.5 dB receiver sensitivity improvement compared to the typical DFE and PR-FFE at a bit-error-rate (BER) of 4.5 × 10-3 (BER threshold of 6.7% overhead staircase hard-decision forward error correction code). Moreover, the implementation of the PR-DFE has successfully reduced the probability of two consecutive symbol errors from 4.83 × 10-3 to 0 compared to the typical DFE. According to experimental results, the proposed PR-DFE FTN signaling scheme is a promising candidate for ultra-low complexity and high spectral efficiency intra-datacenter interconnect (intra-DCI) applications.

In this paper, a joint application of simplified Tomlinson-Harashima precoding (THP) and <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">M</i> -log-maximum a posteriori probability ( <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">M</i> -log-MAP) decoder at transceivers is proposed for low complexity faster than Nyquist (FTN) 4-ary pulse amplitude modulation (PAM4) signaling. A THP with only two taps is applied at the transmitter for FTN-induced inter-symbol interference elimination and equalization-induced noise amplification issue mitigation, which effectively relieves the burden of the receiver. At the receiver, a low complexity M-log-MAP decoder is equipped for residual impairments cancellation, thus a feedback channel is not required to accurately obtain the channel state information for the transmitter. Taking advantage of this collaborative approach, the proposed scheme performs much better than applying the two schemes separately. We experimentally demonstrate the proposed scheme in 70, 75, and 80GBaud PAM4 systems with a 32-GHz brick-wall filter, corresponding to 0.914, 0.853, and 0.8 FTN compression factor, respectively. The results show that the 80GBaud PAM4 signal is successfully transmitted over 2-km single mode fiber with the bit-error-rate (BER) under the 7% hard-decision forward error correction (HD-FEC) threshold of 3.8×10 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">−3</sup> . It is also observed that the proposed scheme shows about 0.7dB receiver sensitivity improvement compared to the error propagation-free decision feedback equalizer, namely the performance upper bound of the THP, at BER of 7% HD-FEC threshold in a 75GBaud FTN PAM4 system. According to the experimental results, the proposed scheme is a promising solution for bandwidth-starved low-cost intra-datacenter interconnect.

CDMA and MIMO-CDMA systems using RAKE receivers are heavily limited by self- and multiple-access-interference. Linear equalization is a means to remove this interference; however, it is often not practical due to the enormous complexity, especially in the MIMO case. The paper presents an approach to reduce greatly the complexity of linear MIMO equalizers. It discusses the complexity reduction of the equalizer itself and describes a suboptimal low-complexity method to compute its coefficients. The application of frequency domain equalization, using the overlap/add FFT method, to MIMO systems is suggested. The coefficients of the joint equalizer/MIMO detector are also derived in the frequency domain, based on an approximation of an MMSE criterion. Performance results in terms of BER are quantified through simulations of a MIMO-extended UMTS-FDD downlink.

Single carrier (SC) modulations employing frequency domain equalization (FDE) have been shown to be appropriate for severe time-dispersive channels, having similar or better performances than OFDM modulations, while offering the same complexity and lower peak-to-average power ratio. In this paper we introduce a class of low complexity linear frequency domain precoders (multiple-beamformers) for spatially correlated frequency selective multiple-input-multiple-output MIMO systems employing SC modulations. The specific designs targets minimization of a lower bound on the mean-square-error (MSE) under the assumption that only second order statistics of channel (covariance matrix of channel and noise) is available at the transmitter. These precoders are designed for different wideband receivers such as BLAST, MIMO-DFE, linear FDE. The proposed designs are assessed and compared for relatively large correlations and severely frequency selective channels.

In this manuscript, we consider the uplink of a single carrier frequency division multiple access (SC-FDMA) based system, where a set of small-cells coexist with a macro-cell using the same spectrum. To deal with both the inter-carrier interference (ICI) and inter-system interference we combine interference alignment (IA) precoding at the small-cell transmitters with iterative decision feedback equalization at the macroreceiver. The transmitter and receiver design is performed jointly, by considering both full-coordination and limited inter-system information exchange between macro and small-cells. At the small cells side, we assume that the access points are connected through a limited capacity backhaul network to a central unit, where the separation of a quantized version of the small-cell signals is performed. For this case the iterative feedback equalizer is designed by explicitly taking into account the impact of signal quantization. Moreover, a semi-analytical approach for the performance of the proposed schemes is provided. The results show that the proposed schemes are robust to both inter-system and inter-carrier interferences and thus are able to efficiently separate the macro and small cells spatial streams under limited information exchange.

In this paper, we design a practical time-reversal quasi-orthogonal space-time block code (TR-QO-STBC) system for broadband multi-input multi-output (MIMO) communications. We first modify the TR-QO-STBC encoding structure so that the interference between the transmitted blocks can be completely removed by linear processing. Two low complex decision-feedback equalization (DFE) schemes are then proposed. One is built from the frequency-domain decision-feedback equalization (FD-DFE). The derived bi-directive FD-DFE (BiD-FD-DFE) cancels the interference among the successive symbols along the time axis. The other one is the enhanced V-BLAST, which cancels the interference between the real and imaginary parts of the spectral components. They have distinct performance characteristics due to the different interference-cancellation strategies. The underlying orthogonal and symmetric characters of TR-QO-STBC are exploited to reduce the computational complexity. Computer simulations confirm that the proposed equalizers can achieve better performance than the existing schemes.