Since the invention of \turbo codes" by Berrou et al. in 1993, the \turbo principle" has been adapted to several communication problems such as \turbo equalization", \turbo trellis coded modulation", and iterative multi user detection. In this paper we study the \turbo equalization" approach, which can be applied to coded data transmission over channels with intersymbol interference (ISI). In the original system invented by Douillard et al., the data is protected by a convolutional code and a receiver consisting of two trellis-based detectors are used, one for the channel (the equalizer) and one for the code (the decoder). It has been shown that iterating equalization and decoding tasks can yield tremendous improvements in bit error rate (BER). We introduce new approaches to combining equalization based on linear ltering with the decoding. The result is a receiver that is capable of improving BER performance through iterations of equalization and decoding in a manner similar to turbo ...

Abstract—A number of important advances have been made in the area of joint equalization and decoding of data transmitted over intersymbol interference (ISI) channels. Turbo equalization is an iterative approach to this problem, in which a maximum a posteriori probability (MAP) equalizer and a MAP decoder exchange soft information in the form of prior probabilities over the transmitted symbols. A number of reduced-complexity methods for turbo equalization have recently been introduced in which MAP equalization is replaced with suboptimal, low-complexity approaches. In this paper, we explore a number of low-complexity soft-input/soft-output (SISO) equalization algorithms based on the minimum mean square error (MMSE) criterion. This includes the extension of existing approaches to general signal constellations and the derivation of a novel approach requiring less complexity than the MMSE-optimal solution. All approaches are qualitatively analyzed by observing the mean-square error averaged over a sequence of equalized data. We show that for the turbo equalization application, the MMSE-based SISO equalizers perform well compared with a MAP equalizer while providing a tremendous complexity reduction. Index Terms—Equalization, iterative decoding, low complexity, minimum mean square error. I.

Suppression of multiuser interference (MUI) and mitigation of multipath effects constitute major challenges in the design of third-generation wireless mobile systems. Most wide-band and multicarrier uplink code-division multiple-access (CDMA) schemes suppress MUI statistically in the presence of unknown multipath. For fading resistance, they all rely on transmit- or receive-diversity and multichannel equalization based on bandwidth-consuming training sequences or self-recovering techniques at the receiver end. Either way, they impose restrictive and difficult to check conditions on the finite-impulse response channel nulls. Relying on block-symbol spreading, we design a mutually-orthogonal usercode-receiver (AMOUR) system for quasi-synchronous blind CDMA that eliminates MUI deterministically and mitigates fading regardless of the unknown multipath and the adopted signal constellation. AMOUR converts a multiuser CDMA system into parallel single-user systems regardless of multipath and guarantees identifiability of users' symbols without restrictive conditions on channel nulls in both blind and nonblind setups. An alternative AMOUR design called Vandermonde--Lagrange AMOUR is derived to add flexibility in the code assignment procedure. Analytic evaluation and preliminary simulations reveal the generality, flexibility, and superior performance of AMOUR over competing alternatives. Index Terms---Blind equalization, multicarrier CDMA, multipath fading channels, multiple rates. I.

We study the convergence behavior of iterative decoding of a serially concatenated code. We rederive a existing analysis technique called EXIT chart [15] and show that for certain decoders the construction of an EXIT chart simplifies tremendously. The findings are extended such that simple irregular codes can be constructed, which can be used to improve the converence of the iterative decoding algorithm significantly. An efficient and optimal optimization algorithm is presented. Finally, some results on thresholds on the decoding convergence are outlined.

This paper proves large-system asymptotic normality of the output of a family of linear multiuser receivers that can be arbitrarily well approximated by polynomial receivers. This family of receivers encompasses the single-user matched filter, the decorrelator, the minimum mean square error (MMSE) receiver, the parallel interference cancelers, and many other linear receivers of interest. Both with and without the assumption of perfect power control, we show that the output decision statistic for each user converges to a Gaussian random variable in distribution as the number of users and the spreading factor both tend to infinity with their ratio fixed. Analysis reveals that the distribution conditioned on almost all spreading sequences converges to the same distribution, which is also the unconditional distribution. This normality principle allows the system performance, e.g., the multiuser efficiency, to be completely determined by the output signal-to-interference ratio (SIR) for large linear systems.

In this paper, the effect of spatial diversity on the throughput and reliability of wireless networks is examined. Spatial diversity is realized through multiple independently fading transmit/receive antenna paths in single-user communication and through independently fading links in multiuser communication. Adopting spatial diversity as a central theme, we start by studying its information-theoretic foundations, then we illustrate its benefits across the physical (signal transmission/coding and receiver signal processing) and networking (resource allocation, routing, and applications) layers. Throughout the paper, we discuss engineering intuition and tradeoffs, emphasizing the strong interactions between the various network functionalities.

Capitalizing on the tremendous performance gains of turbo codes and the turbo decoding algorithm, turbo equalization is an iterative equalization and decoding technique that can achieve equally impressive performance gains for communication systems that send digital data over channels that require equalization, i.e. those which suffer from intersymbol interference (ISI). In this paper, we discuss the turbo equalization approach to coded data transmission over ISI channels, with an emphasis on the basic ideas and some of the practical details. The original system introduced by Douillard, et al., can be viewed as an extension of the turbo decoding algorithm by considering the effect of the ISI channel as another form of error protection, i.e. as a rate-1 convolutional code.

We study the convergence behavior of turbo decoding, turbo equalization, and turbo bit-interleaved coded modulation in a unified framework, which is to regard all three principles as instances of iterative decoding of two serially concatenated codes. There is a collection of measures in the recent literature, which trace the convergence of iterative decoding algorithms based on a single parameter. This parameter is assumed to completely describe the behavior of the soft-in soft-out decoders being part of the iterative algorithm. The measures observe different parameters and were originally applied to different types of decoders. In this paper, we show how six of those measures are related to each other and we compare their convergence prediction capability for the decoding principles mentioned above. We observed that two measures predict the convergence very well for all regarded decoding principles and others suffer from systematic prediction errors independent of the decoding principle.

We consider a canonical model for coded CDMA with random spreading, where the receiver makes use of iterative Belief-Propagation (BP) joint decoding. We provide simple Density-Evolution analysis in the large-system limit (large number of users) of the performance of the exact BP decoder and of some suboptimal approximations based on Interference Cancellation (IC). Based on this analysis, we optimize the received user SNR distribution in order to maximize the system spectral efficiency for given user channel codes, channel load (users per chip) and target user bit-error rate. The optimization of the received SNR distribution is obtained by solving a simple linear program and can be easily incorporated into practical power control algorithms. Remarkably, under the optimized SNR assignment the suboptimal Minimum Mean-Square Error (MMSE) IC-based decoder performs almost as well as the more complex exact BP decoder. Moreover, for a large class of commonly used convolutional codes we observe that the optimized SNR distribution consists of a finite number of discrete SNR levels. Based on this observation, we provide a low-complexity approximation of the MMSE-IC decoder that suffers from very small performance degradation while attaining considerable savings in complexity. As

Abstract—We investigate turbo equalization, or iterative equalization and decoding, as a receiver technology for systems where data is protected by an error-correcting code, shuffled by an interleaver, and mapped onto a signal constellation for transmission over a frequency-selective channel with unknown time-varying channel impulse response. The focus is the concept of soft iterative channel estimation, which is to improve the channel estimate over the iterations by using soft information fed back from the decoder from the previous iteration to generate “extended training sequences ” between the actual transmitted training sequences. Index Terms—Channel estimation, high-frequency communications, iterative channel estimation, turbo equalization.