Linear Turbo Equalization Research Articles

Serially Connected Bidirectional Double EP-Based DFE for Turbo Equalization

In this letter, a new serially connected bidirectional double expectation propagation (EP)-based decision feedback equalizer (SBI-DEP-DFE) for turbo equalization over inter-symbol interference (ISI) channels is proposed. By cascading the normal and time-reversed DEP-DFEs without inner iterations, the bidirectional structure resembles inner iterations, and the SBI-DEP-DFE can emulate the EP behavior and harvest time-reverse diversity. Simulation results illustrate that the SBI-DEP-DFE achieves remarkably better performance than the state-of-the-art existing EP-based DFE, with a complexity just twice that of the minimum mean square error-based linear turbo equalizer. It also outperforms the EP-based linear receivers under certain conditions.

Performance Evaluation to Code-Aided Linear Iterative Equalizer Under a Fading Channel

A linear iterative turbo equalizer (LITE) with code aided scheme is presented to be employed in a fading channels. A method is proposed for exploiting transmittal diversity within a parallel independent fading channel together with an iterative equalizing receiver. The structure of the equalizer combines LITE, encoding, decoding interleaving, and de-interleaving schemes. The code-aided LITE employs encoding and interleaving at the transmitter and passes a priori information on the transmitted symbols between decode outputs at the receiver. The performance of a code-aided LITE is evaluated by means of computer simulation. It shows the proposed code-aided equalizer functions benefits a better system performance in the fading channel.

Research on the Iterative Stopping Criterion Based on Linear Turbo Equalization

Although turbo equalization has superior performance, the data processing delay produced by large iterations has become its major drawback for real-time situations. Based on the MMSE criterion, the normal-probability-plot (NPP) of linear equalizer’s extrinsic information is studied in this paper, with the conclusion of the extrinsic information’s approximate Gaussian distribution obtained. In various conditions, the iterative number can be controlled dynamically based on the extrinsic information statistics. The simulation results approves that the technique is able to make delay dwindle largely with small performance degradation.

Low Complexity Turbo-Equalization: A Clustering Approach

We introduce a low complexity approach to iterative equalization and decoding, or “turbo equalization”, which uses clustered models to better match the nonlinear relationship that exists between likelihood information from a channel decoder and the symbol estimates that arise in soft-input channel equalization. The introduced clustered turbo equalizer uses piecewise linear models to capture the nonlinear dependency of the linear minimum mean square error (MMSE) symbol estimate on the symbol likelihoods produced by the channel decoder and maintains a computational complexity that is only linear in the channel memory. By partitioning the space of likelihood information from the decoder based on either hard or soft clustering and using locally-linear adaptive equalizers within each clustered region, the performance gap between the linear MMSE turbo equalizers and low-complexity least mean square (LMS)-based linear turbo equalizers can be narrowed.

Adaptive Linear Turbo Equalization Over Doubly Selective Channels

Over the last decade, tremendous gains, leading to near-capacity achieving performance, have been shown for a variety of communication systems through the application of the turbo principle, i.e., the exchange of extrinsic information between constituent algorithms for tasks such as channel decoding, equalization, and multiple-input–multiple-output (MIMO) detection. In this paper, we study the practical application of such an iterative detection and decoding (IDD) framework to underwater acoustic communications. We explore complexity and performance tradeoffs of a variety of turbo equalization (TEQ)-based receiver architectures. First, we elaborate on two popular but suboptimal turbo equalization techniques: a channel-estimate-based minimum mean-square error TEQ (CE-based MMSE-TEQ) and a direct-adaptive TEQ (DA-TEQ). We study the behavior of both TEQ approaches in the presence of channel estimation errors and adaptive filter adjustment errors. We confirm that after a sufficient number of iterations, the performance gap between these two TEQ algorithms becomes small. Next, we demonstrate that an underwater receiver architecture built upon the least mean squares (LMS) DA-TEQ technique can leverage and dramatically improve the performance of the conventional implementation based on the decision-feedback equalizer at a feasible complexity. To maintain performance gains over time-varying channels, the slow convergence speed of the LMS algorithm has been improved via two methods: 1) repeating the weight update for the same set of data with decreasing step size and 2) reducing the dimensionality of the equalizer by capturing sparse channel structure. This receiver architecture was used to process collected data from the SPACE 08 experiment (Martha's Vineyard, MA). Receiver performance for different modulation orders, channel codes, and hydrophone configurations is examined at a variety of distance, up to 1 km from the transmitters. Experimental results show great promise for this approach, as data rates in excess of 15 kb/s could readily be achieved without error.

Low-Complexity Soft-Decision Feedback Turbo Equalization for MIMO Systems With Multilevel Modulations

Many communication systems today encounter the problem of data transmission over a channel with intersymbol interference (ISI). The purpose of this paper is to develop a low-complexity iterative soft-decision feedback equalization (SDFE) receiver for severe frequency-selective ISI channels in multiple-input-multiple-output (MIMO) communication systems. The proposed SDFE algorithm offers a novel approach to combat error propagation. In addition, its computational complexity only linearly grows with the number of equalizer coefficients, compared with the quadratic complexity of minimum mean square error (MMSE)-based linear turbo equalizer with time-varying coefficients. The performance of the proposed detection scheme is verified through simulations using different signal constellations. In addition, convergence properties of the proposed SDFE algorithm are also analyzed using an extrinsic information transfer (EXIT) chart and verified by simulations in a severe ISI channel. Simulation results show that our proposed algorithm has significant improvement over the Approximate MMSE linear turbo equalizer proposed by Tüchler et al. Moreover, we show that the performance of the proposed equalization scheme significantly improves when higher order constellations are used for digital modulation.

Soft-Decision Feedback Turbo Equalization for Multilevel Modulations

Error propagation phenomena is the major drawback for existing hard-decision feedback turbo equalizers. In this paper, we propose a new soft-decision feedback equalizer (SDFE) suitable for multilevel modulation systems employing turbo equalization. The proposed SDFE offers a low computational complexity growing only linearly with the number of equalizer coefficients, as opposed to the quadratic complexity of MMSE-based linear turbo equalizer with time-varying coefficients (Exact-MMSE-LE). The performance and convergence property of the proposed SDFE are analyzed using extrinsic information transfer (EXIT) chart and verified by simulations in a severe intersymbol interference channel set by Proakis. Results show that our approach performs close to Exact-MMSE-LE for BPSK/QPSK modulation. And for 8PSK/16QAM modulations, the proposed SDFE performs much better. It exhibits lower SNR threshold (SNR required for “waterfall” BER) and much faster convergence than Exact-MMSE-LE.

Multi‐group linear turbo equalization with intercell interference cancellation for MC‐CDMA cellular systems

AbstractIn this paper, we investigate multi‐group linear turbo equalization using single antenna interference cancellation (SAIC) techniques to mitigate the intercell interference for multi‐carrier code division multiple access (MC‐CDMA) cellular systems. It is important for the mobile station to mitigate the intercell interference as the performance of the users close to cell edge is mainly degraded by the intercell interference. The complexity of the proposed iterative detector and receiver is low as the one‐tap minimum mean square error (MMSE) equalizer is employed for mitigating the intracell interference, while a simple group interference canceller is used for suppressing the intercell interference. Simulation results show that the proposed iterative detector and receiver can mitigate the intercell interference effectively through iterations for both uncoded and coded signals. Copyright © 2009 John Wiley & Sons, Ltd.

Factor-Graph Algorithms for Equalization

In this paper, we use the factor-graph framework to describe the statistical relationships that arise in the equalization of data transmitted over an intersymbol interference channel, and use it to develop several new algorithms for linear and decision feedback approaches. Specifically, we examine both unconstrained and constrained linear equalization and decision feedback equalization of a sequence of nonidentically distributed symbols that are transmitted over a linear, possibly time-varying, finite-length channel and then corrupted by additive white noise. Factor graphs are used to derive algorithms for each of these equalization tasks, including fast implementations. One important application of these algorithms is linear turbo equalization, which requires a linear equalizer that can process observations of nonidentically distributed transmitted symbols. We show how the output of these factor-graph-based algorithms can be used in an efficient implementation of a linear turbo equalizer

Linear turbo equalization analysis via BER transfer and EXIT charts

In this paper, two analytical methods are presented to investigate the soft information evolution characteristics of a soft-input soft-output (SISO) linear equalizer and its application to the design of turbo equalization systems without the reliance on extensive simulation. Given the channel and a SISO equalization algorithm, one method explored is to analytically compute the bit-error rate (BER) of the SISO equalizer in two extreme cases (no and perfect a priori information) from which a BER transfer characteristic is estimated. The second approach is to compute the mutual information [a key parameter of the extrinsic information transfer (EXIT) chart] at the two end points of the EXIT function. Then, by modeling the SISO equalizer BER transfer and EXIT functions as linear, some of the behavior of linear turbo equalization, such as how the BER performance can be improved as iterations proceed, can be predicted. Further, soft information evolution characteristics of different linear SISO equalizers can be compared and the usefulness of iterative methods such as linear turbo equalization for a given channel can be determined. Compared with existing methods for generating EXIT functions, these predictive methods provide insight into the iterative behavior of linear turbo equalizers with substantial reduction in numerical complexity.

Energy Efficient VLSI Architecture for Linear Turbo Equalizer

In this paper, energy efficient VLSI architectures for linear turbo equalization are studied. Linear turbo equalizers exhibit dramatic bit error rate (BER) improvement over conventional equalizers by enabling a form of joint equalization and decoding in which soft information is iteratively exchanged between the equalizer and decoder. However, turbo equalizers can be computationally complex and hence require significant power consumption. In this paper, we present an energy-efficient VLSI architecture for such linear turbo equalizers. Key architectural techniques include elimination of redundant operations and early termination. Early termination enables powering down parts of the soft-input soft-output (SISO) equalizer and decoder thereby saving power. Simulation results show that energy savings in the range 30---60% and 10---60% are achieved in equalization and decoding, respectively. Furthermore, we present finite precision requirements of the linear turbo equalizer and an efficient rescaling method to prevent overflow.

Linear turbo equalization for parallel isi channels

We propose a method for exploiting transmit diversity using parallel independent intersymbol interference channels together with an iterative equalizing receiver. Linear iterative turbo equalization (LITE) employs an interleaver in the transmitter and passes a priori information on the transmitted symbols between multiple soft-input/soft-output minimum mean-square error linear equalizers in the receiver. We describe the LITE algorithm, present simulations for both stationary and fading channels, and develop a framework for analyzing the evolution of the a priori information as the algorithm iterates.