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.     

Space-time turbo equalization in frequency-selective MIMO channels

A computationally efficient space-time turbo equalization algorithm is derived for frequency-selective multiple-input-multiple-output (MIMO) channels. The algorithm is an extension of the iterative equalization algorithm by Reynolds and Wang (see Signal Processing, vol.81, no.5, p.989-995, 2001) for frequency-selective fading channels and of iterative multiuser detection for code-division multiple-access (CDMA) systems by Wang and Poor (see IEEE Trans. Commun., vol.47, p.1046-1061, 1999). The proposed algorithm is implemented as a MIMO detector consisting of a soft-input-soft-output (SISO) linear MMSE detector followed by SISO channel decoders for the multiple users. The detector first forms a soft replica of each composite interfering signal using the log likelihood ratio (LLR), fed back from the SISO channel decoders, of the transmitted coded symbols and subtracts it from the received signal vector. Linear adaptive filtering then takes place to suppress the interference residuals: filter taps are adjusted based on the minimum mean square error (MMSE) criterion. The LLR is then calculated for adaptive filter output. This process is repeated in an iterative fashion to enhance signal-detection performance. This paper also discusses the performance sensitivity of the proposed algorithm to channel-estimation error. A channel-estimation scheme is introduced that works with the iterative MIMO equalization process to reduce estimation errors.     

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.     

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.     

Iterative channel estimation for turbo equalization of time-varying frequency-selective channels

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.     

Structured set partitions and multilevel concatenated coding forpartial response channels

We present a systematic way to construct multilevel concatenated codes for partial response (PR) channels using: (1) a structured set partition (SSP) of multiple channel output sets and (2) a set of conventional block codes with different error correcting capabilities. A lower bound on the minimum squared Euclidean distance of the constructed codes is given. This bound is based on the interset minimal Euclidean distances of the SSP and the minimum Hamming distances of the used block codes. An example of SSP for the extended class 4 partial response channel (EPR4) is presented. Iterative suboptimal decoding, which combines Viterbi detection on the trellis of the PR channel with algebraic error detection/correction, can be applied to the constructed concatenated codes. Truncated versions of the iterative decoding scheme are simulated and compared with each other     

Bit-interleaved turbo equalization over static frequency-selective channels: constellation mapping impact

The purpose is to assess the performance of bit-interleaved turbo equalization (TE) over static frequency-selective channels. The asymptotic performance is therefore first pointed out, emphasizing the fundamental role played by the constellation mapping. This specific feature is then further analyzed using the extrinsic information-transfer chart technique, leading to an efficient optimization tool. This finally enables showing that bit-interleaved TE can outperform its symbol-interleaved counterpart.     

Cyclic delay diversity with frequency domain turbo equalization for uplink fast fading channels

Cyclic delay diversity (CDD) is an attractive diversity technique due to its low complexity and compatibility to existing wireless communication systems. This letter proposes a CDD with frequency domain turbo equalization (FDTE) for single carrier (SC) transmission, in order to achieve the full spatial diversity of frequency-selective multi-antenna channels. The frequency diversity inherent in SC is picked up from the increased channel selectivity of CDD. The noise or intersymbol interference enhanced by equalization for highly selective channels is then mitigated through applying FDTE at the receiver. Simulation results show that the performance of proposed system approaches the corresponding orthogonal spacetime block coding (STBC) system in slowly fading channels without any data rate loss, and considerably outperforms the STBC system in fast fading channels.     

LMMSE turbo equalization based on factor graphs

In this paper, a vector-form factor graph representation is derived for intersymbol interference (ISI) channels. The resultant graphs have a tree-structure that avoids the short cycle problem in existing graph approaches. Based on a joint Gaussian approximation, we establish a connection between the LLR (log-likelihood ratio) estimator for a linear system driven by binary inputs and the LMMSE (linear minimum mean-square error) estimator for a linear system driven by Gaussian inputs. This connection facilitates the application of the recently proposed Gaussian message passing technique to the cycle-free graphs for ISI channels. We also show the equivalence between the proposed approach and the Wang-Poor approach based on the LMMSE principle. An attractive advantage of the proposed approach is its intrinsic parallel structure. Simulation results are provided to demonstrate this property.     

Blind equalization of turbo trellis-coded partial-response continuous-phase modulation signaling over narrow-band Rician fading channels

In this paper, a blind maximum-likelihood channel estimation algorithm is developed for turbo trellis-coded/continuous-phase modulation (TTC/CPM) signals propagating through additive white Gaussian noise (AWGN) and Rician fading environments. We present CPM for TTC signals, since it provides low spectral occupancy and is suitable for power- and bandwidth-limited channels. Here, the Baum-Welch (BW) algorithm is modified to estimate the channel parameters. We investigate the performance of TTC/CPM for 16-CPFSK over AWGN and Rician channels for different frame sizes, in the case of ideal channel state information (CSI), no CSI, and BW estimated CSI.     

Joint MF combining and turbo equalization for wireless communications over ISI channels with diversity reception

A new method called joint Matched Filter (MF) combining and turbo equalization is proposed for wireless communications over Inter-Symbol Interference (ISI) channels with diversity reception. This method takes diversity combining and equalization as integrity and need just one turbo equalizer for all diversity branches. Computer simulations prove that our method can take advantage of turbo equalization and diversity reception to combat fading of wireless channels.     

Low complexity turbo equalization based on soft feedback interference cancellation

This letter presents a new soft feedback interference cancellation (SFIC) based equalizer suitable for iterative receivers applying turbo equalization. SFIC offers a very low computational complexity depending only linearly on the channel memory length. Despite its low complexity, SFIC shows a very good BER performance. Simulation results for the severely intersymbol interference distorted Proakis C channel show, that our approach performs within 0.5 dB to the powerful turbo equalization scheme based on MMSE linear filtering with time-varying coefficients and fails the mathematical optimum maximum a-posteriori (MAP) equalizer only by 1.2 dB.     

Faster-than-Nyquist signaling: on linear and non-linear reduced-complexity turbo equalization

In the framework of digital video broadcasting by satellite-second generation (DVB-S2), we analyze a faster-than-Nyquist (FTN) system based on turbo equalization and low-density parity-check (LDPC) codes. Truncated maximum a posteriori and minimum mean square error equalizers provide a reduced-complexity implementation of the FTN system. On the other hand, LDPC codes allow us to demonstrate attractive performance results over an additive white Gaussian noise channel while increasing spectral efficiency beyond the Nyquist rate and keeping a complexity comparable to that of a current DVB-S2 modem.     

Comparative study of turbo equalization schemes usingconvolutional, convolutional turbo, and block-turbo codes

Turbo equalizers have been shown to be successful in mitigating the effects of inter-symbol interference introduced by partial response modems and by dispersive channels for code rates of R⩽ 1/2. We comparatively studied the performance of a range of binary phase-shift keying turbo equalizers employing block-turbo codes, namely Bose-Chaudhuri-Hocquenghen (1960, 1959) turbo codes, convolutional codes, and convolutional turbo codes having high code rates, such as R=3/4 and R=5/6, over a dispersive five-path Gaussian channel and an equally weighted symbol-spaced five-path Rayleigh fading channel. These turbo equalization schemes were combined with an iterative channel estimation scheme in order to characterize a realistic scenario. The simulation results demonstrated that the turbo-equalized system using convolutional turbo codes was the most robust system for all code rates investigated     

Method to analyse convergence of turbo codes

The use of cross-entropy to analyse the convergence behaviour of a turbo decoder is proposed. Based on the new method, E/sub b//N/sub 0/ thresholds are predicted and compared with those predicted by existing techniques. Simulation results show that the new technique is effective and advantageous in practical applications.     

Double turbo equalization of continuous phase modulation with frequency domain processing

In this paper, a doubly-iterative linear receiver, equipped with a soft-information aided frequency domain minimum mean-squared error (MMSE) equalizer, is proposed for the combined equalization and decoding of coded continuous phase modulation (CPM) signals over long multipath fading channels. In the proposed receiver architecture, the front-end frequency domain equalizer (FDE) is followed by the soft-input, softoutput (SISO) CPM demodulator and channel decoder modules. The receiver employs double turbo processing by performing back-end demodulation/decoding iterations per each equalization iteration to improve the a priori information for the front-end FDE. As presented by the computational complexity analysis and simulations, this process provides not only a significant reduction in the overall computational complexity, but also a performance improvement over the previously proposed iterative and noniterative MMSE receivers.     

Selection of component codes for turbo coding based on convergence properties

The turbo decoding is a sub-optimal decoding, i.e. it is not a maximum likelihood decoding. It is important to be aware of this fact when the parameters for the scheme are chosen. This goes especially for the selection of component codes, where the selection often has been based solely on the performance at highSnr’s. We will show that it is important to base the choice on the performance at lowSnr’s. i.e. the convergence properties, as well. Further, the study of the performance with different component codes may lead to an understanding of the convergence process in the turbo decoder.     

A dynamic convergence analysis of blind equalization algorithms

Blind equalizers do not require a training sequence to start up or to restart after a communications breakdown, making them particularly useful in applications such as broadcast and point-to-multipoint networks. We study in parallel the dynamic convergence behavior of three blind equalization algorithms: the multimodulus algorithm (MMA), the constant modulus algorithm (CMA), and the reduced constellation algorithm (RCA). Using a conditional Gaussian approximation, we first derive the theoretical mean-squared-error (MSE) trajectory for MMA. This analysis leads to accurate but somewhat cumbersome expressions. Alternatively, we apply a Taylor series approximation to derive MSE trajectories for MMA, CMA, and RCA. This approach yields simpler but somewhat less accurate expressions. For the steady-state operation, however we derive even simpler formulas that accurately predict the asymptotic MSE values. We finally study the convergence rates of the three blind algorithms using their theoretical MSE trajectories, computer simulations, and a laboratory experiment     

Phase-noise effects on turbo trellis-coded over M-ary coherent channels

The effect of the phase noise on the performance of bandwidth-efficient coded modulation is studied. To this end, the average mutual information (AMI) for specific constellations such as 8-phase-shift keying and 16-quadrature amplitude modulation is calculated in the presence of carrier phase error caused by imperfect carrier tracking over an additive white Gaussian noise channel. The AMI not only quantifies the effect of the phase noise from an information-theoretic viewpoint, but also serves as an estimate for a permissible amount of the phase noise for a given signal-to-noise ratio. The bit-error rate (BER) performance of a near-optimal turbo trellis-coded modulation scheme is then investigated over such a channel. For this purpose, an optimal branch metric which best fits the channel characteristics is derived. Furthermore, simple branch metrics (referred to as suboptimal, simplified, and Gaussian metrics) are derived, which may offer the tradeoff between BER performance and computational complexity. Numerical analysis shows that a near-optimal coded-modulation scheme renders a transmission system more robust against phase noise than is the case with a conventional trellis-coded modulation scheme.     

Design and analysis of turbo codes on Rayleigh fading channels

The performance and design of turbo codes using coherent BPSK signaling on the Rayleigh fading channel is considered. In low signal-to-noise regions, performance analysis uses simulations of typical turbo coding systems. For higher signal-to-noise regions beyond simulation capabilities, an average upper bound is used in which the average is over all possible interleaving schemes. Fully interleaved and exponentially correlated Rayleigh channels are explored. Furthermore, the design issues relevant to turbo codes are examined for the correlated fading channel. Turbo interleaver design criteria are developed and architectural modifications are proposed for improved performance