Adaptive Bayesian equalizer with decision feedback

A Bayesian solution is derived for digital communication channel equalization with decision feedback. This is an extension of the maximum a posteriori probability symbol-decision equalizer to include decision feedback. A novel scheme utilizing decision feedback that not only improves equalization performance but also reduces computational complexity greatly is proposed. It is shown that the Bayesian equalizer has a structure equivalent to that of the radial basis function network, the latter being a one-hidden-layer artificial neural network widely used in pattern classification and many other areas of signal processing. Two adaptive approaches are developed to realize the Bayesian solution. The maximum-likelihood Viterbi algorithm and the conventional decision feedback equalizer are used as two benchmarks to asses the performance of the Bayesian decision feedback equalizer     

A DECISION FEEDBACK EQUALIZER FOR NON-LINEAR CHANNELS

A Simple and useful decision feedback equalizer used for non-linear channels with severe linear distortion and mild non-linear distortion is proposed. It is a combination of a nonlinear channel equalizer based on connectionist model and a common decision feedback equalizer for linear channels. For a typical non-linear channel model it is shown that the equalization performances of the proposed equalizer are improved significantly.     

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.     

Asymptotic Bayesian decision feedback equalizer using a set of hyperplanes

We present a signal space partitioning technique for realizing the optimal Bayesian decision feedback equalizer (DFE). It is known that when the signal-to-noise ratio (SNR) tends to infinity, the decision boundary of the Bayesian DFE is asymptotically piecewise linear and consists of several hyperplanes. The proposed technique determines these hyperplanes explicitly and uses them to partition the observation signal space. The resulting equalizer is made up of a set of parallel linear discriminant functions and a Boolean mapper. Unlike the existing signal space partitioning technique of Kim and Moon (1998), which involves complex combinatorial search and optimization in design, our design procedure is simple and straightforward, and guarantees to achieve the asymptotic Bayesian DFE.     

Dual decision feedback equalizer

The detector of Dahlman and Gudmundson (1988) ranks among the simplest known extensions of the decision feedback equalizer (DFE). The article develops a simplification of this detector, and evaluates its performance vis-a-vis other near maximum likelihood detectors. Comparable performances are observed at much lower complexity levels     

Adaptive MIMO decision feedback equalization for receivers with time-varying channels

In an attempt to reduce the computational complexity of vertical Bell Labs layered space time (V-BLAST) processing with time-varying channels, an efficient adaptive receiver is developed based on the generalized decision feedback equalizer (GDFE) architecture. The proposed receiver updates the filter weight vectors and detection order using a recursive least squares (RLS)-based time- and order-update algorithm. The convergence of the algorithm is examined by analysis and simulation, and it is shown that the proposed adaptive technique is considerably simpler to implement than a V-BLAST processor with channel tracking, yet the performances are almost comparable.     

The soft-feedback equalizer for turbo equalization of highly dispersive channels

The complexity of a turbo equalizer based on the Bahl-Cocke-Jelinek-Raviv (BCJR) algorithm is manageable only for mildly dispersive channels having a small amount of memory. To enable turbo equalization of highly dispersive channels, we propose the soft-feedback equalizer(SFE). The SFE combines linear equalization and soft intersymbol-interference cancellation. Its coefficients are chosen to minimize the mean-squared error(MSE) between the equalizer output and the transmitted sequence, under a Gaussian approximation to the a priori information and the SFE output. The resulting complexity grows only linearly with the number of coefficients, as opposed to the quadratic complexity of previously reported minimum-MSE structures. We will see that an SFE-based turbo equalizer consistently outperforms another structure of similar complexity, and can outperform a BCJR-based scheme when complexity is taken into account.     

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.     

Simplified block adaptive diversity equalizer for cellular mobileradio

We propose a reduced complexity antenna diversity combiner-equalizer receiver structure to combat multipath fading in cellular mobile radio (CMR) communications. The technique utilizes block adaptation based on interpolated channel estimates and linear or decision feedback equalization. The receiver offers complexity reduction relative to previously proposed block adaptation methods without sacrificing performance     

A decision feedback equalizer with time-reversal structure

This work describes the use of a receiver with a time-reversal structure for low-complexity decision feedback equalization of slowly fading dispersive indoor radio channels. Time-reversal is done by storing each block of received signal samples in a buffer and reversing the sequential order of the signal samples in time prior to equalization. As a result, the equivalent channel impulse response as seen by the equalizer is a time-reverse of the actual channel impulse response. Selective time-reversal operation, therefore, allows a decision feedback equalizer (DFE) with a small number of forward filter taps to perform equally well for both minimum-phase and maximum-phase channel characteristics. The author evaluates the theoretical performance bounds for such a receiver and quantifies the possible performance improvement for discrete multipath channels with Rayleigh fading statistics. Two extreme cases of DFE examples are considered: an infinite-length DFE; and a DFE with a single forward filter tap. Optimum burst and symbol timing recovery is addressed and several practical schemes are suggested. Simulation results are presented. The combined use of equalization and diversity reception is considered     

A fast computation algorithm for the decision feedback equalizer

A novel fast algorithm for computing the minimum MSE decision feedback equalizer settings is proposed. The equalizer filters are computed indirectly, first by estimating the channel, and then by computing the coefficients in the frequency domain with the discrete Fourier transform (DFT). Approximating the correlation matrices by circulant matrices facilitates the whole computation with very small performance loss. The fractionally spaced equalizer settings are derived. The performance of the fast algorithm is evaluated through simulation. The effects of the channel estimation error and finite precision arithmetic are briefly analyzed. Results of simulation show the superiority of the proposed scheme     

An LMS-based decision feedback equalizer for IS-136 receivers

In digital mobile communication systems, intersymbol interference is one of the main causes of degrading system performance. Decision feedback equalization (DFE) is the commonly used remedy for this problem. Since the channel is fast-varying, an adaptive algorithm possessing a fast convergence property is then required. The least mean square (LMS) algorithm is well known for its simplicity and robustness; however, its convergence is slow. As a consequence, the LMS algorithm is rarely considered in this application. In this paper, we consider an LMS-based DFE for the North American IS-136 system. We propose an extended multiple-training LMS algorithm accelerating the convergence process. The convergence properties of the multiple-training LMS algorithm are also analyzed. We prove that the multiple-training LMS algorithm can converge regardless of its initial value and derive closed-form expressions for the weight error vector power. We further take advantage of the IS-136 downlink slot format and divide a slot into two subslots. Bidirectional processing is then applied to each individual subslot. The proposed LMS-based DFE has a low computational complexity and is suitable for real-world implementation. Simulations with a 900-MHz carrier show that our algorithm can meet the 3% bit error rate requirement for mobile speeds up to 100 km/hr     

CCK demodulation via symbol decision feedback equalizer

A symbol decision feedback equalization (DFE) technique is developed for demodulating complementary code keying (CCK) signals. The efficacy of the proposed receiver is demonstrated on the physical layer (PHY) specified in the IEEE 802.11b wireless local area network (WLAN) standard. Packet error rate (PER) performance is compared with that of the conventional RAKE receiver. The proposed receiver structure and its low complexity variations demonstrate significant performance advantages over the RAKE receiver, especially in severe multipath channels. While a large delay spread can limit the performance of two low-complexity variations discussed here, performance of the optimal symbol DFE receiver is not limited by delay spread as long as the channel signal-to-noise ratio (SNR) is sufficiently high.     

Bayesian decision feedback techniques for deconvolution

There has been great interest in reduced complexity suboptimal MAP symbol-by-symbol estimation for digital communications. We propose a new suboptimal estimator suitable for both known and unknown channels. In the known channel case, the MAP estimator is simplified using a form of conditional decision feedback, resulting in a family of Bayesian conditional decision feedback estimators (BCDFEs); in the unknown channel case, recursive channel estimation is combined with the BCDFE. The BCDFEs are indexed by two parameters: a “chip” length and an estimation lag. These algorithms can be used with estimation lags greater than the equivalent channel length and have a complexity exponential in the chip length but only linear in the estimation lags. The BCDFEs are derived from simple assumptions in a model-based setting that takes into account discrete signalling and channel noise. Extensive simulations characterize the performance of the BCDFE and BCDPE for uncoded linear modulations over both known and unknown (nonminimum phase) channels with severe ISI. The results clearly demonstrate the significant advantages of the proposed BCDFE over the BCDFE in achieving a desirable performance/complexity tradeoff. Also, a simple adaptive complexity reduction scheme can be combined with the BCDFE resulting in further substantial reductions in complexity, especially for large constellations. Using this scheme, we demonstrate the feasibility of blind 16QAM demodulation with 10^-4 bit error probability at E _b/N₀≈ 18.5 dB on a channel with a deep spectral null     

An efficient decision feedback equalizer for the ATSC DTV receiver

In this paper an efficient decision feedback equalizer is presented for the equalization of the received signal in the eight level vestigial sideband, Advanced Television Systems Committee, digital television system, adopting a novel detection rule for symbol detection at the output of the equalizer. The conventional hard limiter is replaced by an efficient symbol detection algorithm, based on the underlying trellis coded modulated coding of the transmitted symbols. The proposed decision device has a marginal computational cost and it can be implemented using simple combinatorial and sequential logic circuitry. When the equalizer operates in the decision directed mode, the normalized least mean squared algorithm is utilized for the adaptation of the equalizer coefficients, in a “stop-and-go” like mode, triggered by a reliability signal associated to the detected symbols. The performance of the proposed method is illustrated by typical computer simulation.     

Frequency domain decision feedback equalizer for time-reversal space-time block coding

In this paper,a frequency domain decision feedback equalizer is proposed for single carrier transmission with time-reversal space-time block coding (TR-STBC).It is shown that the diagonal decision feed...     

Fuzzy stochastic gradient decision feedback equalizer for VSBterrestrial HDTV broadcasting

We present a fuzzy stochastic gradient (FSG) decision feedback equalizer (DFE) for VSB terrestrial HDTV broadcasting. This equalizer employs a well-designed fuzzy Takagi-Sugeno (1985) model to automatically regulate the step size of the descent gradient vector, combining a fast convergence rate and a low excess mean square error (MSE). The only penalty paid is a slight increase in the computational complexity compared with the LMS algorithm. Simulation results show that this equalizer provides 3.5 dB signal-to-noise ratio (SNR) improvement at a BER of 3.0×10^-6 with respect to the conventional LMS DFE recommended by the Grand Alliance     

A blind decision feedback equalizer incorporating fixed lagsmoothing

A new type of blind decision feedback equalizer (DFE) incorporating fixed lag smoothing is developed in this paper. The structure is motivated by the fact that if we make full use of the dependence of the observed data on a given transmitted symbol, delayed decisions may produce better estimates of that symbol. To this end, we use a hidden Markov model (HMM) suboptimal formulation that offers a good tradeoff between computational complexity and bit error rate (BER) performance. The proposed equalizer also provides estimates of the channel coefficients and operates adaptively (so that it can adapt to a fading channel for instance) by means of an online version of the expectation-maximization (EM) algorithm. The resulting equalizer structure takes the form of a linear feedback system including a quantizer, and hence, it is easily implemented. In fact, because of its feedback structure, the proposed equalizer shows some similarities with the well-known DFE. A full theoretical analysis of the initial version of the algorithm is not available, but a characterization of a simplified version is provided. We demonstrate that compared to the zero-forcing DFE (ZF-DFE), the algorithm yields many improvements. A large range of simulations on finite impulse response (FIR) channels and on typical fading GSM channel models illustrate the potential of the proposed equalizer     

Adaptive modulation and decision feedback equalization for frequency‐selective MIMO channels

In this paper, an adaptive modulation scheme for the multiple‐input multiple‐output (MIMO) frequency‐selective channels is investigated. We consider a scenario with precoded block‐based transceivers over spatially correlated Rayleigh multipath MIMO channels. To eliminate the inter‐block interference, the zero‐padding is used. The receiver is equipped with a MIMO minimum‐mean‐squared‐error decision feedback equalizer. The precoder aims to force each subchannel to have an identical signal‐to‐interference‐plus‐noise ratio (SINR). To adjust the constellation size, the unbiased mean square error at the equalizer output is sent back to the transmitter. To simplify our analysis, the feedback channel is considered as instantaneous and error free. We first derive the probability density function of the overall SINR for flat fading and frequency‐selective channels. On the basis of the probability density function of the upper bound of the SINR, we evaluate the system performance. We present accurate closed‐form expressions of the average spectral efficiency, the average bit error rate and the outage probability. The derived expressions are compared with Monte Carlo simulation results. Furthermore, we analyze the effect of the channel spatial correlation. Copyright © 2013 John Wiley & Sons, Ltd.     

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.