A Reliability-Based SNR Estimation Method in Turbo Detection Systems

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.

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.

The turbo equalization principle, based on Berrou's (1993) turbo principle, is a high performance receiver scheme to mitigate intersymbol interference (ISI) caused by a frequency selective channel. Several turbo equalization (TEQ) schemes, like Douillard's (1995) MAP/MLSE TEQ, Laot's (1997) TEQ scheme by means of soft ISI cancellation and turbo equalization based on MMSE linear equalization have been presented different in performance and computational complexity. One of these schemes, turbo equalization based on MMSE linear equalization achieves nearly MAP/MLSE performance, while reducing the computational complexity tremendously. We extend this receiver scheme to 16-QAM and present simulation results for different ISI channels.

Communication over HF-ionospheric channel requires the use of a performant receiver based on turbo equalization scheme. In this receiver, channel estimation can be improved for each iteration using soft information fed back from the decoder. We propose a turbo equalizer based on a soft-input Kalman estimator that can operate without channel impulse response knowledge. Performance analysis of the channel estimator is tested using four paths channel for two Doppler spread values and records of realistic channel. Simulation results show the convergence of the algorithm versus the frequency dispersion of the paths and compare the BER of the proposed Kalman based turbo equalizer with that of the conventional turbo equalizer. Results show that the proposed equalizer provide a significant gains in BER performance and convergence without the need for training data.

A multi-stage turbo equalization scheme based on the bit-level combining (BLC) is proposed for multiple-input multiple-output (MIMO) systems with hybrid automatic repeat request (HARQ). In the proposed multi-stage turbo equalization scheme, the minimum mean-square-error equalizer at each iteration calculates the extrinsic log-likelihood ratios for the transmitted bits in a subpacket and the subpackets are sequentially replaced at each iteration according to the HARQ rounds of received subpackets. Therefore, a number of iterations are executed for different subpackets received at several HARQ rounds, and the transmitted bits received at the previous HARQ rounds as well as the current HARQ round can be estimated from the combined information up to the current HARQ round. In addition, the proposed multi-stage turbo equalization scheme has the same computational complexity as the conventional bit-level combining based turbo equalization scheme. Simulation results show that the proposed multi-stage turbo equalization scheme outperforms the conventional BLC based turbo equalization scheme for MIMO systems with HARQ.

In this paper, an enhanced linear minimum mean square error (LMMSE) turbo equalization scheme is proposed for multiple-input multiple-output (MIMO) communication systems with bit-interleaved coded modulation (BICM) in the time domain and multiplexing in the space domain. The proposed turbo equalization scheme outperforms the conventional LMMSE turbo equalization by adopting two new signal processing techniques. First, it performs hybrid soft interference cancellation (HSOIC) by subtracting the soft decisions of the interfering symbols, and the soft decisions are calculated by using a hybrid of the a priori information at the equalizer input and the a posteriori information at the equalizer output. Second, it employs a novel block-wise reliability-based ordering scheme such that more “reliable” symbols are detected before the less “reliable” ones to reduce error propagation in HSOIC. The symbol reliability information is based on the symbol a priori probability, as a unique byproduct of turbo detection, thus can be obtained with very small overhead. A low-complexity approximation of the enhanced MIMO LMMSE turbo equalization is also proposed to balance the tradeoff between complexity and performance. The performance of the enhanced MIMO LMMSE turbo equalization has been verified through both numerical simulations and the undersea experimental data collected in the SPACE08 experiment launched near Martha's Vineyard, Edgartown, MA, in 2008.

The performance of turbo-codes relies on two major concepts: code concatenation so as to build a powerful global code and iterative decoding in order to efficiently approximate the optimal decoding process. A turbo equalization (TE) scheme based on convolutional code and normalized least mean square equalizer for coherent optical communication links is proposed and experimentally demonstrated. For counteracting PDM 16 QAM impairments in dispersion uncompensated coherent transmission links, the iterative TE technique is proved effective.

This paper presents a turbo equalization (TEQ) scheme, which employs a radial basis function (RBF)-based equalizer instead of the conventional trellis-based equalizer of Douillard et al. (1995). Structural, computational complexity, and performance comparisons of the RBF-based and trellis-based TEQs are provided. The decision feedback-assisted RBF TEQ is capable of attaining a similar performance to the logarithmic maximum a posteriori scheme in the context of both binary phase-shift keying (BPSK) and quaternary phase-shift keying (QPSK) modulation, while achieving a factor 2.5 and 3 lower computational complexity, respectively. However, there is a 2.5-dB performance loss in the context of 16 quadrature amplitude modulation (QAM), which suffers more dramatically from the phenomenon of erroneous decision-feedback effects. A novel element of our design, in order to further reduce the computational complexity of the RBF TEQ, is that symbol equalizations are invoked at current iterations only if the decoded symbol has a high error probability. This techniques provides 37% and 54% computational complexity reduction compared to the full-complexity RBF TEQ for the BPSK RBF TEQ and 16QAM RBF TEQ, respectively, with little performance degradation, when communicating over dispersive Rayleigh fading channels.

This paper presents a straightforward and efficient reduced-complexity radial basis function (RBF)assisted decision-feedback equalizer (DFE)-based turbo equalization (TEQ) scheme, which utilizes the a priori information provided by the channel decoder to significantly reduce the computational complexity of the RBF-based DFE. The proposed scheme is capable of achieving a close performance to the Jacobian RBF DFE TEQ in the context of both binary phase-shift keying (BPSK) modulation and 4 quadrature amplitude modulation (QAM), when communicating over dispersive Rayleigh fading channels. Furthermore, it attains a factor 3 and 4.38 lower computational complexity associated with the addition/subtraction operations compared to the Jacobian RBF DFE TEQ for BPSK and 4 QAM, respectively. In addition, the complexity reduction factor associated with the multiplication/division/exp(-)/ln(-) operations is 1.14 and 2.53 for BPSK and 4 QAM, respectively.

In this paper, a joint channel estimation and turbo equalization scheme is proposed with low complexity and high accuracy for doubly selective fading channels. Based on the traditional data frame, by adding several pre-training sequences, the spectral efficiency is improved in the proposed two stage scheme. In the first stage, with the adaptive subblock-wise inverse QR recursive least square (IQR-RLS) filter, more trustworthy estimated values of the channel coefficients are generated with a non-priori model compared with the first order autoregressive (AR) modeling extended Kalman filter (EKF), based on complex exponential basis expansion models (CE-BEMs). Particularly, the calculation of operations is significantly reduced. In the second stage, a turbo equalizer is provided by utilizing a non-linear Kalman filter, which has a remarkable improvement in BER performance over EKF. Furthermore, complexity analysis is presented and illustrates the advantage of the proposed scheme. Finally, simulation results demonstrate the validity of the proposed scheme.

We propose novel techniques to reduce the complexity of the well-known Bahl, Cocke, Jelinek, and Raviv (BCJR) algorithm when it is employed as a detection algorithm in turbo equalization schemes. In particular, by also considering an alternative formulation of the BCJR algorithm, which is more suitable than the original one for deriving reduced-complexity techniques, we describe three reduced-complexity algorithms, each of them particularly effective over one of the three different classes of channels affected by intersymbol interference (minimum-phase, maximum-phase, and mixed-phase channels). The proposed algorithms do not explore all paths on the trellis describing the channel memory, but they work only on the most promising ones, chosen according to the maximum a posteriori criterion. Moreover, some optimization techniques improving the effectiveness of the proposed solutions are described. Finally, we report the results of computer simulations showing the impressive performance of the proposed algorithms, and we compare them with other solutions in the literature.

In this paper we consider a soft-input soft-output equalizer, for MIMO intersymbol interference channels, used in a turbo equalization scheme. We derive the equalizer on the basis of a cyclic factor graph representation and the sum-product algorithm, with two different message schedules (serial and parallel). In the sum-product algorithm we use Gaussian messages, which results in a low-complexity LMMSE equalizer implementation. Computer simulations show that, for the turbo equalization application, the proposed equalizer has a good bit error rate performance compared with the optimal MAP equalizer, while achieving a remarkable reduction in complexity.

In this paper we propose a novel turbo equalizer based on the expectation propagation (EP) algorithm. Optimal equalization is computationally unfeasible when high-order modulations and/or large memory channels are used. In these scenarios, low-cost and suboptimal equalizers, such as those based on the linear minimum mean square error (LMMSE), are commonly used. The LMMSE-based equalizer can be efficiently implemented with a Kalman smoother (KS), i.e., a forward and backward Kalman filtering whose predictions are merged in a posterior smoothing step. Recently, it was shown that applying EP at the forward and backward stages of a KS equalizer could significantly improve its performance. In this paper, we investigate applying EP at the smoothing level instead. Also, we propose some further modifications to better exploit the information coming from the channel decoder in turbo equalization schemes. Overall, we remarkably reduce the computational complexity while highly improving the performance in terms of bit error rate.

In this paper, we propose a low-complexity soft-input/soft-output (SISO) intersymbol interference (ISI) channel detector based on soft interference cancellation (SIC) and instantaneous minimum-mean-square-error (MMSE) filtering, where the present evaluated equalizer's soft output is fed back and used for SIC in order to achieve a performance gain. To avoid computationally intensive matrix inversion for calculating MMSE filter coefficients, iterative algorithms such as the steepest descent (SD) method are used to find an approximate solution. Simulation results show that the proposed receiver converges quickly to the MMSE solution even using a simple 2-step SD approach. Moreover, it outperforms the powerful linear turbo equalization (LE) scheme over the severely ISI-distorted Proakis C channel.

Orthogonal frequency division multiplexing is a multicarrier modulation scheme proving robustness against Inter-symbol interference and offers high data rates. We investigate MIMO-OFDM system and propose novel SNR estimation algorithms by utilizing the information about the channel quality. Semi blind training symbols are adapted for analyzing parameters of adaptive transmission and periodic structure of the preamble is utilized for computationally efficient of SNR estimation. Theoretical analysis and simulation results illustrate the performance of proposed estimators with Normalized Mean Square Error.