Vladimir D. Trajkovic

Adaptive decision feedback turbo equalization and multiuser detection

The analysis of adaptive decision feedback turbo equalization is provided. The turbo detector is a reduced-complexity adaptive turbo equalizer where trellis-based channel equalization is replaced by the adaptive decision feedback equalizer (DFE). We show that for severe intersymbol interference (ISI) the turbo effect (waterfall region) starts at lower SNR relative to the detector applying conventional MMSE DFE coefficients assuming perfect feedback.

Adaptive decision aided turbo equalization of unknown channels using SOVA and MAP decoding algorithms

The computational complexity of a turbo equalizer with decision aided equalizer is analysed. We considered two different decoding algorithms named MAP and SOVA together with the adaptive equalization scheme. The channel is assumed to be unknown. The training sequence is provided in order to estimate the channel impulse response. The implementations of decoding algorithms require different computational complexities. Simulation results show that the same BER performance is obtained for different channels using both decoding algorithms although SOVA performs significantly less number of computations.

Implicit and explicit receiver training in flat fading channels modeled as finite state Markov processes

We study the effect of training method on the receiver bit error rate (BER) performance in constant envelope phase modulation schemes that are transmitted through flat fading channels. Here we propose a novel method for receiver training by sending information bits with unbalanced probabilities. We call this method implicit training and compare it with traditional (explicit) training scheme in which known periodic training sequences are sent to the receiver. The simulation results show superior performance of implicit training where the gain is 2 dB at information rate of 0.15 bits/channel use.

Turbo equalization using non-systematic and recursive systematic convolutional codes

A turbo equalization scheme using non-systematic (NSC) and recursive systematic convolutional (RSC) codes are analyzed. Although it is already known that RSC code is always better in terms of bit error rate (BER) than the best NSC code at any signal to noise ratio (SNR) [C. Berrou et al., 1993], in this paper it is shown that both types of convolutional codes, using the same generator polynomials, achieve the identical BER performance when used in the turbo equalization scheme. The simulation results are obtained over different discrete frequency selective channels introducing severe intersymbol interference (ISI) proving that the RSC codes do not outperform classical NSC codes in terms of BER for each channel in each turbo iteration. All BER results in the presence of ISI are compared with the BER results where the channel introduced no ISI so that the signal is corrupted just with additive white Gaussian noise (AWGN).

The performance of a low complexity decision aided turbo equalization using NSC and RSC codes

In this paper a low complexity adaptive Turbo equalization scheme using classical nonsystematic and recently proposed recursive systematic convolutional codes (NSC and RSC) has been analyzed. Although it was shown that at low signal to noise ratio (SNR), RSC outperforms the best NSC codes, in terms of bit error rate (BER), it is not the case when both codes are used in the proposed adaptive Turbo scheme. The results have been confirmed by simulations when the communication is performed over different communication channels and different code constraint lengths.

Novel exact low complexity MMSE turbo equalization

In this paper we analyze low complexity turbo equalization that combines interference canceling and soft-input soft-output (SISO) decoding. We derive a new, exact MMSE solution for the equalization part taking into account the cross-correlation between the linear equalizer output and the soft decisions in the turbo equalization feedback loop as well as the auto-correlation function of the decoder output. Also, this solution implicitly takes into account the error propagation in the feedback loop of the turbo equalizer. We also introduce a non-linear element in the feedback loop that suppresses less reliable soft decisions. The level of suppression depends on the reliability of a soft decision, which is directly proportional to its absolute value. The simulation results for a common scenario show that the proposed solution outperforms all previously known turbo equalizers of similar computational complexity.

Near-capacity turbo equalization using optimized turbo codes

In this paper we analyze a turbo equalization scheme that combines maximum a posteriori probability (MAP) equalization and turbo decoding. Our aim is to optimize the turbo equalizer in order to approach the information capacity limit for channels with severe inter-symbol interference (ISI). For this purpose, we perform an extensive search for turbo codes that give an SNR-BER performance closest to the channel information capacity limit. Our results show that the optimized turbo equalizer can approach the information capacity limit to within 0.7 dB. We also optimize the turbo equalizer in terms of the minimum number of required turbo decoding iterations. Our results show that a turbo decoder within a turbo equalization loop requires only a small number of iterations. Finally, our analysis reveals that when there are turbo codes with similar extrinsic information transfer characteristics, the computational complexity can be reduced by choosing the code with the smallest constraint length with no loss in SNR-BER performance.

Turbo Equalization With Irregular Turbo Codes

We analyze a turbo equalization system that combines maximum a posteriori probability (MAP) equalization with irregular turbo codes. Our goal is to approach the information capacity limit for severe inter-symbol interference (ISI) channels. To this end, we optimize the degree profile of irregular turbo codes by maximizing the minimum distance between the mutual information transfer functions for the MAP equalizer and decoder. We show that turbo equalizers employing such optimized irregular turbo codes can approach the information capacity limit of some severe ISI channels within 0.75 dB.

New Improved Decision Aided Turbo Equalization

In this paper we propose a new Turbo Equalization algorithm with Decision Aided Equalizer (DAE). The algorithm takes into account that the soft feedback decisions from the previous iteration contain errors that cannot be neglected. The proposed algorithm finds the error variance and recalculates DAE coefficients at each turbo iteration. The algorithm shows Bit Error Rate (BER) performance improvement relative to the conventional Turbo DAE for severe frequency-selective channels. The achieved improvement is 0.8 dB at BER of 10-5.

On the feedback error in adaptive turbo equalization

In this paper we analyze the decision feedback error propagation in the adaptive turbo equalization with a decision feedback loop. We derive the exact mathematical expression for the feedback error probability density function (pdf) with the assumption that the soft outputs of channel decoder are identical independent distributed (i.i.d) Gaussian random variables with known mean value and variance. We also find a new set of turbo equalizer coefficients based on the feedback error pdf and MMSE criterion. New turbo equalizer is shown to outperform the conventional one (assuming no feedback error propagation) in terms of bit error rate (BER). The achieved improvement is up to 4 dB for severe frequency-selective channels. The analysis is applicable to other turbo detection methods employing the feedback loop