Self-Iterating Soft Equalizer

This paper proposes an extrinsic information transfer (EXIT) chart analysis and an asymptotic bit error rate (BER) prediction method to speed up the design of high rate RCM-LDGM hybrid codes over AWGN and fast Rayleigh channels. These codes are based on a parallel concatenation of a rate compatible modulation (RCM) code with a low-density generator matrix (LDGM) code. The decoder uses the iterative sum-product algorithm to exchange information between the variable nodes (VNs) and the two types of constituent check nodes: RCM-CN and LDGM-CN. The novelty of the proposed EXIT chart procedure lies on the fact that it mixes together the analog RCM check nodes with the digital LDGM check nodes, something not possible in previous multi-edge EXIT charts proposed in the literature.

In this paper, we analyze an orthogonal frequency division multiplexing (OFDM) system employing combined space- time-frequency (STF) codes and an iterative receiver with extrinsic information transfer (EXIT) charts and bit-error rate plots. As STF codes, we examine orthogonal space-time block codes (OSTBCs), cyclic delay diversity, and discontinuous Doppler diversity. We present a combined STF code for eight transmit antennas with rate one. Another contribution of this work is the EXIT chart analysis demonstrating that EXIT charts are not always a suitable tool to analyze the performance of iterative receivers for STF coded OFDM systems. Further, error floors due to the mapping can be removed even for correlated channels by differential encoding and code doping the bits before the modulator.

Low Power Wide Area (LPWA) networks aim at connecting low cost devices with high constraints on the link budget. Focusing on the physical layer, the combination of Frequency Shift Keying (FSK) modulation and coding in the same process has been shown efficient when associated to a turbo receiver. This paper considers the optimization of Turbo-FSK parameters for the LPWA context using the EXtrinsic Information Transfer (EXIT) Chart analysis. After adapting the metric to the FSK waveforms, EXIT chart performance results are extended and compared to short packet lengths using extensive Bit Error Rate (BER) computations.

In minimum mean squared error (MMSE) based turbo equalization, the decoder's extrinsic information is used as the MMSE equalizer's prior information. In order to improve the performance, the combined prior information which consists of the whole decoder's extrinsic information and the partial decoder's full information in the last iteration, is used by the MMSE equalizer. Meanwhile, the MMSE equalizer is lead by matched filter as a preprocessor to reduce the complexity. The extrinsic information transfer (EXIT) chart analysis and simulation results show that the performance of the proposed scheme is much better than that of the conventional turbo equalizer.

This study presents a low-complexity soft-interference cancellation equaliser (SICE) for the turbo detection of multiple-input–multiple-output systems operating in time dispersive channels. The SICE contains three time-invariant linear filters: a feedforward filter, a causal feedback filter and an anti-causal feedback filter. The feedforward filter is designed to suppress the intersymbol interference because of channel time dispersion and the multiplexing interference from multiple transmit antennas. The causal (or anti-causal) feedback filter is developed to remove the residual interference caused by the symbols transmitted before (or after) the symbol under detection. The filters are designed by analysing the statistical properties of soft decisions. The performance of the proposed SICE is verified through both extrinsic information transfer (EXIT) chart analysis and computer simulations. The EXIT chart analysis shows that, because of the inclusion of the anti-causal soft decision, the SICE performance approaches the ideal matched filter bound as the iteration progresses. Consequently, the proposed SICE achieves significant performance gains over conventional equalisers.

A frequency division multiplexing technique, nonorthogonal frequency division multiplexing (n-OFDM), is proposed in [1]– [2] to enhance the efficiency of bandwidth utilization. This paper reveals that the smaller the frequency separation, the larger sum capacity can be achieved compared with the conventional OFDM technique. However, n-OFDM system introduces inter-carrier interference (ICI) at the transmitter because the orthogonality between the subcarriers no longer holds. Moreover, since the channel covariance matrix of n-OFDM has high condition number when the overlapping factor, 1 − α, is large, conventional linear detectors suffers from severe noise enhancement. To solve this problem, this paper proposes the use of soft cancellation- minimum mean-squared error (SCMMSE) turbo equalization. Binary constellation constrained mutual information (CCMI) is calculated by utilizing the area property for the EXtrinsic Information Transfer (EXIT) chart of the SC-MMSE equalizer. Results of the EXIT chart analysis and bit-error-rate (BER) simulations in additive white Gaussian noise (AWGN) channel are presented.

Turbo equalization schemes based on minimum mean square error (MMSE) criteria available in the literature for multiple-input multiple-output (MIMO) systems are computationally expensive, as they require a relatively large matrix inversion. In this paper, we propose a low complexity turbo equalization (TE) scheme with successive interference cancellation for orthogonal frequency division multiplexing (OFDM) based MIMO receiver systems (TE-SIC-MIMO). TE-SIC-MIMO leverages on the soft feedback symbol estimate to selectively remove the intercarrier interference (ICI) and co-antenna interference (CAI) from the received data, thus turning the system matrix into an easily invertible form. Extrinsic Information Transfer (EXIT) chart analysis supplemented with numerical simulation results shows that TE-SIC-MIMO performance under static and rapidly time varying multipath conditions is mostly on par with MMSE turbo equalization scheme available in the literature, that is based on a sub-matrix of the system matrix at signal-to-noise ratios (SNR) of practical interest. However, the computation complexity of TE-SIC-MIMO turns out to be much lesser than the TE scheme considered.

Bit-interleaved coded modulation with iterative decoding (BICM-ID) is investigated for bandwidth efficient transmissions, where the error performance can be improved by employing a suitable symbol mapping. This paper first introduces a low-complexity regular mapping optimization for BICM-ID and 8PSK, for the purpose of finding the optimal mapping. Furthermore, the irregular mapping optimization is proposed for a closer approach to the channel capacity. The extrinsic information transfer (EXIT) chart analysis is aided for the proposed optimization algorithms to provide design guidelines of mappings. The bit error rate (BER) results demonstrate that the BICM-ID system with the proposed optimal irregular mapping outperforms the other mappings used for comparison, and yields about 0.5dB away from the channel capacity over the additive white Gaussian noise (AWGN) channel.

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.

This paper presents an optimized turbo equalizer based on Laot's turbo equalization scheme by means of soft intersymbol interference (ISI) cancellation. Due to Berrou's turbo-principle, common turbo equalization schemes use the extrinsic information as a-priori input for the equalizer. In contrast to this, we propose the use of the full soft output channel decoder's information for the turbo interference canceller. The performance of this improved turbo equalizer by means of soft interference cancellation is evaluated in the environment of two channels, which introduce severe ISI. Simulation results show that the proposed turbo equalizer achieves a performance gain of up to 4 dB compared to Laot's original approach. The performance gain is achieved without any increase of computational complexity. Moreover, we apply a modified extrinsic information transfer (EXIT) chart to the proposed turbo equalizer and illustrate the convergence advantages in comparison to Laot's approach.

In this paper we derive a novel extrinsic information transfer (EXIT) function for a channel estimator that uses both pilot symbols and soft decoding information. We consider a CDMA system with forward error correction that employs iterative multiuser detection based on soft interference cancellation and single user decoding. The J function is useful in convergence analysis as it provides a mapping between mutual information and variance. J functions are derived for both the flat-fading Rayleigh channel and channel estimate, allowing the a priori inputs to the channel estimator, interference canceller and decoder to be modeled. Algorithms for obtaining the EXIT functions for the three receiver blocks are proposed. We then combine the EXIT functions to create an EXIT chart that can be used to predict the behaviour of the overall receiver. Simulations are run for a 3GPP-like receiver in a mobile environment with a vehicle speed of 100 km/h. It is found that under these conditions, the detector trajectory closely matches our proposed EXIT chart.

A number of turbo equalization (TE) methods with reduced complexity have recently been introduced, in which the maximum a posteriori probability (MAP) equalizer is replaced by suboptimal and low complexity ones. These methods can save the computational complexity significantly, but with sacrificed system performance. In this paper, the authors first use the extrinsic information transfer (EXIT) chart tool to visually explain why these suboptimal methods have the worse performance. Then, the authors propose a novel iterative method for TE which takes advantage of both parallel and serial concatenation turbo-like schemes. In the novel iterative method, the EXIT chart switches between the two schemes as a balance. The transmitter side is also changed correspondingly by utilizing the concept of repetition code to acquire a structure similar to turbo codes. It is shown from both analytical and simulation results that the proposed iterative method for TE results in the excellent system performance while its realization complexity is kept relatively low.

EXtrinsic Information Transfer (EXIT) chart is a graphical tool for analysis of low density parity check (LDPC) and other codes with iterative decoding. In this paper, we propose the design of LDPC codes for coded modulation schemes by application of linear programming with conditions derived from EXIT charts. Points on the EXIT curve for bit and check node operations are first computed either using analysis or by simulation. The entire EXIT curve is then obtained by linear interpolation. Finally, the EXIT curves are optimized to obtain the maximum possible rate for the code under a given threshold condition. To demonstrate the design procedure, we consider the cases of M-PAM and 8-PSK over the additive white Gaussian noise (AWGN) channel. The optimization method presented is versatile, and can be extended to other constellations and situations easily.

In this letter, the concept of multiple serially-concatenated codes is invoked in the context of stochastic resonance (SR), where the achievable performance is improved by increasing noise power. More specifically, the receiver's iterative decoding process is characterized with the aid of extrinsic information transfer (EXIT) charts, such that the SR effect induced by a non-linear component is taken into account. Our simulation results demonstrate that although the SR demodulator's log-likelihood ratio (LLR) outputs are not Gaussian distributed, the corresponding EXIT trajectory matches the prediction from the associated inner- and outer-codes' EXIT curves, while reaching the perfect convergence point in terms of mutual information. Therefore, an infinitesimally low bit-error ratio (BER) is attained by appropriately designing the channel code's parameters based on EXIT charts.

This paper focuses on the signal constellation shaping in LDPC coded modulation system. A novel constellation is presented by combining geometric shaping with probabilistic shaping based on quadrature amplitude modulation (QAM)constellation. With the shaped signal constellation, the signal mapping is optimized by using the extrinsic information transfer (EXIT) chart analysis. We further consider the nonbinary LDPC coded-modulation by combining with the proposed constellation shaping. Numerical results reveal that the proposed constellation can get the shaping gain without increasing the complexity of detection.