Blind decision feedback equalization of time-varying channels withDPSK inputs

This paper presents a new method to the blind equalization of a class of linear time-varying mobile channels for differentially encoded channel input signals. Through reparameterization, the equivalent discrete system can be modeled as a single-input multiple-output system. Unlike some existing methods, this new algorithm does not require prior knowledge on the cyclic frequency of the channel response. The algorithm is simple and relies only on a decision feedback structure and the differential encoding nature of the channel input signals. The convergence analysis of the decision feedback system is presented along with simulation examples     

Adaptive multichannel decision feedback equalization for volterra type nonlinear communication channels

A model-based approach for the decision feedback equalization of Volterra type nonlinear communication channels is proposed such that the linear model-based decision feedback equalization can be considered as a special case of the proposed approach. In designing the decision feedback equalizer, the nonlinear decision feedback equalization problem is visualized as a linear, multichannel equalization problem. A complete modified Gram–Schmidt orthogonalization of the input vector is achieved by using modified sequential processing multichannel lattice stages. The elements of the multichannel desired signal vector are then estimated from the new orthogonal set by using only scalar operations. The probability of error performance of the proposed equalizer is improved by the estimation of the elements of the desired signal vector through a sigmoid activation function so that a polynomial perceptron equalizer is realized. The comparative computational complexity calculations and performance results of the proposed decision feedback equalizer are also provided.     

Adaptive turbo reduced-rank equalization for MIMO channels

An adaptive iterative (turbo) decision-feedback equalizer (DFE) for channels with intersymbol interference (ISI) is presented. The filters are computed directly from the soft decisions and received data to minimize a least-squares (LS) cost function. Numerical results show that this method gives a substantial improvement in performance relative to a turbo DFE computed from an exact channel estimate, assuming perfect feedback. Adaptive reduced-rank estimation methods are also presented, based on the multistage Wiener filter (MSWF). The adaptive reduced-rank turbo DFE for single-input/single-output channels is extended to multiple-input/multiple-output (MIMO) channels with ISI and multiple receive antennas. Numerical results show that for MIMO channels with limited training, the reduced-rank turbo DFE can perform significantly better than the full-rank turbo DFE.     

Adaptive MBER decision feedback multiuser receivers in frequency selective fading channels

In this letter we investigate adaptive minimum bit error rate (BER) decision feedback multiuser receivers for DS-CDMA systems in fast frequency selective Rayleigh fading channels. We examine stochastic gradient adaptive algorithms and introduce fast algorithms for minimizing the BER cost function from training data.     

Efficient decision feedback equalization for sparse wireless channels

A new efficient decision feedback equalizer (DFE) appropriate for channels with long and sparse impulse response (IR) is proposed. Such channels are encountered in many high-speed wireless communications applications. It is shown that, in cases of sparse channels, the feedforward and feedback (FB) filters of the DFE have a particular structure, which can be exploited to derive efficient implementations of the DFE, provided that the time delays of the channel IR multipath components are known. This latter task is accomplished by a novel technique, which estimates the time delays based on the form of the channel input-output cross-correlation sequence in the frequency domain. A distinct feature of the resulting DFE is that the involved FB filter consists of a reduced number of active taps. As a result, it exhibits considerable computational savings, faster convergence, and improved tracking capabilities as compared with the conventional DFE. Note that faster convergence implies that a shorter training sequence is required. Moreover, the new algorithm has a simple form and its steady-state performance is almost identical to that of the conventional DFE.     

Near-optimum soft decision equalization for frequency selective MIMO channels

In this paper, we develop soft decision equalization (SDE) techniques for frequency selective multiple-input multiple-output (MIMO) channels in the quest for low-complexity equalizers with error performance competitive to that of maximum likelihood (ML) sequence detection. We demonstrate that decision feedback equalization (DFE) based on soft-decisions, expressed via the posterior probabilities associated with feedback symbols, is able to outperform hard-decision DFE, with a low computational cost that is polynomial in the number of symbols to be recovered and linear in the signal constellation size. Building on the probabilistic data association (PDA) multiuser detector, we present two new MIMO equalization solutions to handle the distinctive channel memory. The first SDE algorithm adopts a zero-padded transmission structure to convert the challenging sequence detection problem into a block-by-block least-square formulation. It introduces key enhancement to the original PDA to enable applications in rank-deficient channels and for higher level modulations. The second SDE algorithm takes advantage of the Toeplitz channel matrix structure embodied in an equalization problem. It processes the data samples through a series of overlapping sliding windows to reduce complexity and, at the same time, performs implicit noise tracking to maintain near-optimum performance. With their low complexity, simple implementations, and impressive near-optimum performance offered by iterative soft-decision processing, the proposed SDE methods are attractive candidates to deliver efficient reception solutions to practical high-capacity MIMO systems. Simulation comparisons of our SDE methods with minimum-mean-square error (MMSE)-based MIMO DFE and sphere decoded quasi-ML detection are presented.     

Robust OFDM receivers for dispersive time-varying channels: equalization and channel acquisition

In orthogonal frequency-division multiplexing, time variations of a multipath channel lead to a loss of orthogonality between the subcarriers, and thereby limit the achievable throughput. This paper proposes a general framework for a controlled removal of intercarrier interference (ICI) and channel acquisition. The core idea behind our method is to use a finite power series expansion for the time-varying frequency response, along with the known statistical properties of mobile radio channels. Channel acquisition and ICI removal are accomplished in the frequency domain and allow for any desired tradeoff between the residual ICI level, the required training for channel acquisition, and processing complexity. The proposed approach enables a high spectral efficiency (64-quadrature amplitude modulation mode) of digital video broadcasting-terrestrial in highly mobile environments.     

Blind adaptive decision feedback CDMA receivers for dispersive channels

Blind adaptive decision feedback (DF) receivers for direct sequence code division multiple access (DS-CDMA) systems in dispersive channels are proposed. Blind adaptive stochastic gradient algorithms are developed for use with the constrained minimum variance and constrained constant modulus receivers along with successive and parallel DF structure.     

Joint coding and decision feedback equalization for broadbandwireless channels

This paper introduces a new approach for joint convolutional coding and decision feedback equalization (DPE). To minimize error propagation, the DFE uses a combination of soft decisions and delayed tentative decisions to cancel intersymbol interference (ISI). Soft decisions are obtained by passing the DFE output through a (soft) nonlinear device. This simple method is shown to perform almost as well as an optimum soft feedback approach on wireless channels with diversity. Tentative decisions from the Viterbi decoder are used to cancel ISI due to multipath with large delays, thus remedying the increasing effect of error propagation in channels with large delay spreads. We consider the use of this soft/delayed feedback DFE (S/D-DFE) technique in broadband wireless channels (with delay spreads up to several tens of the symbol period) typical in high-bitrate mobile data applications. Simulation results indicate that the proposed joint coding and S/D-DFE technique performs to within 1-2 dB [in required signal-to-noise ratio (SNR)] of an ideal coded DFE without error propagation. When combined with antenna diversity and a reduced-complexity DFE concept with adaptive feedforward tap assignment, it provides high packet throughput against Rayleigh fading, severe delay spreads, and high Doppler rates     

A new framework for soft decision equalization in frequency selective MIMO channels

We introduce a novel framework for soft-input, soft-output (SISO) equalization in frequency selective multipleinput multiple-output (MIMO) channels based on the well-known belief propagation (BP) algorithm. As in the BP equalizer, we model the multipath channels using factor graphs (FGs) where the transmitted and received signals are represented by the function and variable nodes respectively. The edges connecting the function and variable nodes illustrate the dependencies of the multipath channel and soft decisions are developed by exchanging information on these edges iteratively. We incorporate powerful techniques such as groupwise iterative multiuser detection (IMUD), probabilistic data association (PDA) and sphere decoding (SD) in order to reduce the computational complexity of BP equalizer with relatively small degradation in performance. The computational complexity of this new reduced-complexity BP (RCBP) equalizer grows linearly with block size and memory length of the channel. The proposed framework has a flexible structure that allows for parallel as well as serial detection. We will illustrate through simulations that the RCBP equalizer can even handle overloaded scenarios where the channel matrix is rank deficient, and it can achieve excellent performance by applying iterative equalization using the low-density parity check codes (LDPC).     

Multistage soft decision equalization technique for MIMO systems in frequency selective channels

This article proposes a multistage soft decision equalization （SDE） technique for block transmission over frequency selective multi-input multi-output （MIMO） channels. Using the Toeplitz structure, the general signal model can be converted into a series of small-sized sub-signal models. For each sub-signal model, soft interference cancellation （SIC） is used firstly to remove partial effects of interfering symbols, then max-log-map sphere decoder is performed to get the desired a posteriori information. Simulation shows that with lower complexity the proposed method outperforms the probability data association SDE and the Schnorr-Euchner sphere decoder.     

Adaptive decision feedback equalization for digital satellitechannels using multilayer neural networks

This paper introduces an adaptive derision feedback equalization using the multilayer perceptron structure of an M-ary PSK signal through a TDMA satellite radio channel. The transmission is disturbed not only by intersymbol interference (ISI) and additive white Gaussian noise, but also by the nonlinearity of transmitter amplifiers. The conventional decision feedback equalizer (DFE) is not well-suited to detect the transmitted sequence, whereas the neural-based DFE is able to take into account the nonlinearities and therefore to detect the signal much better. Nevertheless, the applications of the traditional multilayer neural networks have been limited to real-valued signals. To overcome this difficulty, a neural-based DFE is proposed to deal with the complex PSK signal over the complex-valued nonlinear MPSK satellite channel without performing time-consuming complex-valued back-propagation training algorithms, while maintaining almost the same computational complexity as the original real-valued training algorithm. Moreover, a modified back-propagation algorithm with better convergence properties is derived on the basis of delta-bar-delta rule. Simulation results for the equalization of QPSK satellite channels show that the neural-based DFE provides a superior bit error rate performance relative to the conventional mean square DFE, especially in poor signal-to-noise ratio conditions     

Adaptive Bayesian decision feedback equalizer for dispersive mobileradio channels

The paper investigates adaptive equalization of time-dispersive mobile radio fading channels and develops a robust high performance Bayesian decision feedback equalizer (DFE). The characteristics and implementation aspects of this Bayesian DFE are analyzed, and its performance is compared with those of the conventional symbol or fractional spaced DFE and the maximum likelihood sequence estimator (MLSE). In terms of computational complexity, the adaptive Bayesian DFE is slightly more complex than the conventional DFE but is much simpler than the adaptive MLSE. In terms of error rate in symbol detection, the adaptive Bayesian DFE outperforms the conventional DFE dramatically. Moreover, for severely fading multipath channels, the adaptive MLSE exhibits significant degradation from the theoretical optimal performance and becomes inferior to the adaptive Bayesian DFE     

Transmit antenna selection for decision feedback detection in MIMO fading channels

In this paper, we investigate a transmit antenna selection (TAS) approach for the decision-feedback detector (DFD) over Rayleigh fading channels. In particular, for a multipleinput multiple-output (MIMO) channel with M transmit and N (N ⩾ M) receive antennas, we derive a lower bound on the outage probability for the TAS approach. The selected transmit antennas are those that maximize the post-processing signalto- noise ratio (SNR) at the receiver end. It is shown that the proposed TAS approach achieves a performance close to optimal selection based on exhaustive search, introduced in the literature, but at a lower complexity. Simulation results are presented to validate and demonstrate the performance gain of the proposed TAS approach.     

Simple equalization of time-varying channels for OFDM

We present a block minimum mean-squared error (MMSE) equalizer for orthogonal frequency-division multiplexing (OFDM) systems over time-varying multipath channels. The equalization algorithm exploits the band structure of the frequency-domain channel matrix by means of a band LDL/sup H/ factorization. The complexity of the proposed algorithm is linear in the number of subcarriers and turns out to be smaller with respect to a serial MMSE equalizer characterized by a similar performance.     

Sampling-based soft equalization for frequency-selective MIMO channels

We consider the problem of channel equalization in broadband wireless multiple-input multiple-output (MIMO) systems over frequency-selective fading channels, based on the sequential Monte Carlo (SMC) sampling techniques for Bayesian inference. Built on the technique of importance sampling, the stochastic sampler generates weighted random MIMO symbol samples and uses resampling to rejuvenate the sample streams; whereas the deterministic sampler, a heuristic modification of the stochastic counterpart, recursively performs exploration and selection steps in a greedy manner in both space and time domains. Such a space-time sampling scheme is very effective in combating both intersymbol interference and cochannel interference caused by frequency-selective channel and multiple transmit and receiver antennas. The proposed sampling-based MIMO equalizers significantly outperform the decision-feedback MIMO equalizers with comparable computational complexity. More importantly, being soft-input soft-output in nature, these sampling-based MIMO equalizers can be employed as the first-stage soft demodulator in a turbo receiver for coded broadband MIMO systems. Such a turbo receiver successively improves the receiver performance through iterative equalization, channel re-estimation, and channel decoding. Finally, computer simulation results are provided to demonstrate the performance of the proposed sampling-based soft MIMO equalizers in both uncoded and turbo coded systems.     

Adaptive decision feedback equalization: can you skip the trainingperiod?

This paper presents a novel unsupervised (blind) adaptive decision feedback equalizer (DFE). It can be thought of as the cascade of four devices, whose main components are a purely recursive filter (ℛ) and a transversal filter (𝒯). Its major feature is the ability to deal with severe quickly time-varying channels, unlike the conventional adaptive DFE. This result is obtained by allowing the new equalizer to modify, in a reversible way, both its structure and its adaptation according to some measure of performance such as the mean-square error (MSE). In the starting mode, ℛ comes first and whitens its own output by means of a prediction principle, while 𝒯 removes the remaining intersymbol interference (ISI) thanks to the Godard (1980) (or Shalvi-Weinstein (1990)) algorithm. In the tracking mode the equalizer becomes the classical DFE controlled by the decision-directed (DD) least-mean-square (LMS) algorithm. With the same computational complexity, the new unsupervised equalizer exhibits the same convergence speed, steady-state MSE, and bit-error rate (BER) as the trained conventional DFE, but it requires no training. It has been implemented on a digital signal processor (DSP) and tested on underwater communications signals-its performances are really convincing     

基于PR—QMF理论的判决反馈均衡器

根据完全重构正交镜像滤波器（PR-QMF）的理论,我们构造了一类正交变换并且用于交换域判决反馈均衡器（OFE）的设计。在此基础上我们进一步讨论了该类DFE的优化设计。通过与卡胡南一洛也夫变换（KLT）和离散余弦变换（DCT）比较得出这样的结论：经过最优化设计,本文提出的算法具有更快的收敛速度,同时,它还具有复杂程度低和设计灵活的优点。     

Blind decision feedback equalization for terrestrial televisionreceivers

In December 1996 the Federal Communications Commission (FCC) adopted the Grand Alliance (GA) system as the digital television broadcasting standard for the United States ending a seven-year-long search for a fully digital television standard. MPEG-2 was chosen as the video compression standard, and trellis-coded 8-vestigial sideband (VSB) with a training sequence was chosen as the transmission standard. The laboratory tests that were performed on the final two competing systems, 8-VSB with training sequence and 32-quadrature amplitude modulation (QAM) with blind equalization, showed a need for blind equalization in dynamic channels that could not be adequately handled by an equalizer training on the training sequence alone. Hence, the final GA system recommended the use of blind equalization in the receiver. In this paper, we describe the U.S. digital television transmission standard as it pertains to the equalization problem, typical transmission channel characteristics and the need for blind equalization in terrestrial television receivers     

MIMO decision feedback equalization from an H/sup /spl infin// perspective

We approach the multiple input multiple output (MIMO) decision feedback equalization (DFE) problem in digital communications from an H/sup /spl infin// estimation point of view. Using the standard (and simplifying) assumption that all previous decisions are correct, we obtain an explicit parameterization of all H/sup /spl infin// optimal DFEs. In particular, we show that, under the above assumption, minimum mean square error (MMSE) DFEs are H/sup /spl infin// optimal. The H/sup /spl infin// approach also suggests a method for dealing with errors in previous decisions.