Low Complexity Turbo Equalization Research Articles

Joint ML Estimation of CFO and Channel, and a Low Complexity Turbo Equalization Technique for High Mobility OFDMA Uplinks

In this paper, we propose a pilot aided joint estimation technique for carrier frequency offsets (CFOs) and doubly selective channels (DSCs), and a low complexity turbo equalization (TE) scheme for orthogonal frequency division multiple access (OFDMA) uplink systems with high mobility users. We propose the use of Chebyshev polynomials of the first kind (CPF) for accurately representing the DSCs. As the exact solution to the estimation problem is computationally intensive, we make use of space alternating generalized expectation maximization (SAGE) algorithm, that replaces the complex multidimensional search with many one dimensional searches. We derive the exact Cramer-Rao bound (CRB) of the joint estimation problem and the mean squared error of the proposed estimation technique is shown to be closely comparable to it. The convergence characteristics are also studied and it is proved analytically that the proposed method converges. Additionally, we propose a low complexity turbo equalization method with iterative multiple access interference (MAI) cancellation, which uses the soft feedback symbol estimate for removing the MAI and self inter-carrier interference (ICI) in each iteration. Our proposed estimation and equalization technique can be applied to any type of carrier assignment scheme (CAS) in OFDMA and offers very good performance even at high mobile speeds.

Low Complexity Turbo-Equalization: A Clustering Approach

We introduce a low complexity approach to iterative equalization and decoding, or “turbo equalization”, which uses clustered models to better match the nonlinear relationship that exists between likelihood information from a channel decoder and the symbol estimates that arise in soft-input channel equalization. The introduced clustered turbo equalizer uses piecewise linear models to capture the nonlinear dependency of the linear minimum mean square error (MMSE) symbol estimate on the symbol likelihoods produced by the channel decoder and maintains a computational complexity that is only linear in the channel memory. By partitioning the space of likelihood information from the decoder based on either hard or soft clustering and using locally-linear adaptive equalizers within each clustered region, the performance gap between the linear MMSE turbo equalizers and low-complexity least mean square (LMS)-based linear turbo equalizers can be narrowed.

A low complexity approach to equalization for doubly selective channels

AbstractIn this manuscript, a low complexity scheme for linear and decision feedback equalization of doubly selective channels is introduced, and it is further extended to low complexity turbo equalization of doubly selective channels. The proposed low complexity scheme involves time‐varying equalizer design by explicitly solving for the equalizer at a few sparse points within the transmit block. The obtained equalizer coefficients at these uniformly spaced points within the transmit block are then interpolated to obtain the equalizer coefficients in the remainder of the block. This interpolation‐based approach to time‐varying equalizer design ensures a low design complexity. The performance of the proposed low complexity equalizer is assessed through numerical simulations. Furthermore, its effectiveness in a turbo equalization setup is studied by numerical simulations, which show the effectiveness of the proposed algorithm. Copyright © 2014 John Wiley & Sons, Ltd.

Spectrally Efficient Frame-Format-Aided Turbo Equalization With Channel Estimation

Chained turbo equalization (CHATUE) has been recently recognized as a low-complexity frequency-domain turbo equalization technique that eliminates the necessity of transmitting the cyclic prefix (CP), and hence allows for spectrally efficient signaling in wireless communications. However, two issues arise from the original version of CHATUE (referred to as CHATUE1) as a consequence of eliminating the CP, which are the noise enhancement and the latency due to the time-concatenated structure. This paper proposes a new version of CHATUE (referred to as CHATUE2) to solve the noise enhancement problem. CHATUE2 retrieves the circulant structure of the channel matrix, originally inherent within the CP transmission, by utilizing composite replica signals that combine the received signals and the soft reference signals replicated from the log-likelihood ratio (LLR) fed back from the decoder. For this purpose, this paper determines the optimal combining ratio based on the minimum-mean-square-error (MMSE) criterion. CHATUE2 is hence able to achieve an improvement in bit-error-rate (BER) performance over CHATUE1. In addition, this paper provides a solution to solving the latency problem by making a practical assumption on the training sequence (TR) transmission, which is required to perform channel estimation generally, in practical systems. Furthermore, this paper proposes a new channel estimation technique, i.e., chained turbo estimation (CHATES), which improves the spectrum efficiency and asymptotically achieves the Cramer–Rao bound (CRB). CHATES assumes that the TR length is exactly equal to the channel impulse response (CIR) length, although the conventional technique requires twice as long or even longer TR lengths. Numerical results show that CHATUE2 with CHATES achieves a gain of 1 dB over conventional turbo equalization with a CP at a BER of $\hbox{10}^{-5}$ in realistic propagation scenarios represented by channel sounding measurement data and in model-based frequency-selective fading channels.

Intersymbol interference cancellation in CDMA 1xEVDO network

SUMMARYThis paper presents the BER performance of the physical layer of the code division multiple access 1x Evolution Data Only (EVDO) standard for different data transmission formats, and shows the improvement on the BER performance of the EVDO system over intersymbol interference channel by adapting the low complexity turbo equalization scheme at the receiver. The radio frequency, channel condition, and mobile user data speeds were extracted from a mobile user with a drive experiment on a live wireless EVDO network. Then, the real data were utilized to simulate the actual mobile user's data speeds in our simulations to show the overall BER performance of the EVDO system application. The simulation results are shown over Gaussian and Proakis A channels and the results indicate that significant intersymbol interference cancellation is obtained with an adapted code division multiple access system and the advantages of turbo equalization on the EVDO system are discussed in this research. Copyright © 2012 John Wiley & Sons, Ltd.

Reduced-Complexity Receivers for Strongly Narrowband Intersymbol Interference Introduced by Faster-than-Nyquist Signaling

We propose new M-algorithm BCJR (M-BCJR) algorithms for low-complexity turbo equalization and apply them to severe intersymbol interference (ISI) introduced by faster than Nyquist signaling. These reduced-search detectors are evaluated in simple detection over the ISI channel and in iterative decoding of coded FTN transmissions. In the second case, accurate log likelihood ratios are essential and we introduce a 3-recursion M-BCJR that provides this. Focusing signal energy by a minimum phase conversion before the M-BCJR is also essential; we propose an improvement to this older idea. The new M-BCJRs are compared to reduced-trellis VA and BCJR benchmarks. The FTN signals carry 4-8 bits/Hz-s in a fixed spectrum, with severe ISI models as long as 32 taps. The combination of coded FTN and the reduced-complexity BCJR is an attractive narrowband coding method.

Frequency-Domain Turbo Equalization with Soft Successive Interference Cancellation for Single Carrier MIMO Underwater Acoustic Communications

This paper proposes a low-complexity frequency-domain turbo equalizer (FDTE) combined with phase rotation compensation and soft successive interference cancellation (SSIC) for single carrier multiple-input multiple-output (MIMO) underwater acoustic (UWA) communications. Different from existing time-domain turbo equalizers in MIMO UWA systems, the proposed receiver implements low-complexity turbo equalization in the frequency domain to combat severe inter-symbol interference (ISI) and employs a layered structure to cope with unbalanced MIMO channels. Soft, rather than hard, successive interference cancellation (SIC) is employed in the layered iterative turbo detection to alleviate co-channel interference (CCI), and phase compensation is utilized within the layered FDTE to mitigate phase rotation. The proposed scheme was evaluated by the SPACE08 experiment conducted in a shallow area of the Atlantic Ocean in October 2008. The 2-transducer 12-hydrophone MIMO system communicated with quaternary phase shift keying (QPSK) and 8-phase shift keying (8PSK) modulation schemes over 200 m and 1000 m ranges, where the proposed FDTE-SSIC scheme achieved low bit error rates (BERs) with only a few iterations. Simulation results also demonstrated that the proposed FDTE-SSIC receiver provided lower BER than one-layer FDTE receivers with comparable complexity.

Block Transmissions over Doubly Selective Channels: Iterative Channel Estimation and Turbo Equalization

Modern wireless communication systems require high transmission rates, giving rise to frequency selectivity due to multipath propagation. In addition, high-mobility terminals and scatterers induce Doppler shifts that introduce time selectivity. Therefore, advanced techniques are needed to accurately model the time- and frequency-selective (i.e., doubly selective) channels and to counteract the related performance degradation. In this paper, we develop new receivers for orthogonal frequency-division multiplexing (OFDM) systems and single-carrier (SC) systems in doubly selective channels by embedding the channel estimation task within low-complexity block turbo equalizers. Linear minimum mean-squared error (MMSE) pilot-assisted channel estimators are presented, and the soft data estimates from the turbo equalizers are used to improve the quality of the channel estimates.

Frequency-Domain Turbo Equalization and Multiuser Detection for DS-UWB Systems

One of the major challenges in direct sequence-ultra wideband (DS-UWB) receiver design is intersymbol interference (ISI). Several equalization schemes to eliminate ISI in DS-UWB systems have been proposed in the literature. It was shown that frequency-domain (FD) equalization techniques can offer better trade off between performance and complexity compared to time- domain equalization schemes for DS-UWB systems on highly dispersive channels. In this paper, we derive low-complexity FD minimum mean square error turbo equalization schemes for single-user binary phase shift keying (BPSK) and quaternary bi-orthogonal keying (4BOK) DS-UWB systems. For multiuser DS-UWB systems, we combine FD turbo equalization schemes with soft interference cancelation to obtain multiuser FD turbo detectors. The bit error rate performance gain due to turbo detection is shown to be significant, particularly for multiuser DS-UWB systems.

Improved BDFE Using A Priori Information for Turbo Equalization

Turbo equalization improves communication system performance by iteratively exchanging information between soft-input soft-output (SISO) equalizer and SISO channel decoder. The trellis-based maximum a posteriori probability (MAP) algorithm serves as the optimum SISO equalizer for turbo equalization. However, MAP algorithm is unsuitable for systems with large modulation constellation size and severe inter-symbol interference (ISI) due to its prohibitively high computational complexity. In this paper, an improved SISO block decision feedback equalizer (BDFE) is proposed for low complexity turbo equalization. Unlike other sub-optimum equalizers which perform symbol by symbol detection, the proposed equalizer generates the soft output for each data bit by collecting information from a sequence of samples as in MAP algorithm. The sequence-based equalization is enabled by using not only soft a priori input from channel decoder, but also hard a priori information obtained from BDFE in previous iteration. The combination of soft a priori information and hard a priori information renders better performance with less iterations compared to other sub-optimum algorithms. In addition, the computational complexity of the proposed algorithm is on the same order as conventional SISO BDFE algorithm, and is much lower compared to the trellis-based MAP algorithm.

Max-SINR ISI/ICI-Shaping Multicarrier Communication Over the Doubly Dispersive Channel

For communication over doubly dispersive channels, we consider the design of multicarrier modulation (MCM) schemes based on time-frequency shifts of prototype pulses. We consider the case where the receiver knows the channel state and the transmitter knows the channel statistics (e.g., delay spread and Doppler spread) but not the channel state. Previous work has examined MCM pulses designed for suppression of inter-symbol/inter-carrier interference (ISI/ICI) subject to orthogonal or biorthogonal constraints. In doubly dispersive channels, however, complete suppression of ISI/ICI is impossible, and the ISI/ICI pattern generated by these (bi)orthogonal schemes can be difficult to equalize, especially when operating at high bandwidth efficiency. We propose a different approach to MCM pulse design, whereby a limited expanse of ISI/ICI is tolerated in modulation/demodulation and treated near-optimally by a downstream equalizer. Specifically, we propose MCM pulse designs that maximize a signal-to-interference-plus-noise ratio (SINR) which suppresses ISI/ICI outside a target pattern. In addition, we propose two low-complexity turbo equalizers, based on minimum mean-squared error and maximum likelihood criteria, respectively, that leverage the structure of the target ISI/ICI pattern. The resulting system exhibits an excellent combination of low complexity, low bit-error rate, and high spectral efficiency.

Turbo equalization with nonlinear Kalman filtering for time-varying frequency-selective fading channels

In this paper, we present a low complexity turbo equalization receiver for data transmission over time-varying frequency-selective fading channels. In the receiver, an adaptive equalizer using nonlinear Kalman filters with delay is coupled with a soft-in soft-cut (SISO) decoder to perform the reception process iteratively. The proposed adaptive equalizer jointly optimizes the estimates for channel taps and data symbols in each iteration with the assistance of a priori information for the data symbols supplied by the SISO decoder. In this way, the correlation between the estimates of data symbols and channel taps is taken into account in the equalization process. This correlation is usually ignored in many other turbo equalizers with separated channel estimation and data equalization. The complexity of the proposed equalizer does not grow exponentially with the modulation constellation size, and is usually lower than that of many maximum a posteriori equalizers with joint channel estimation and data detection. Performance comparison with different types of turbo equalizers over different channel conditions by Monte Carlo simulations demonstrates the advantage of the proposed turbo equalizer for fast time-varying fading channels

Parallel-Trellis Turbo Equalizers for Sparse-Coded Transmission over SISO and MIMO Sparse Multipath Channels

This paper describes a low-complexity turbo equalizer for coded sparse multipath channels whose length can span hundreds of symbol intervals. First, for single-input-single-output (SISO) systems, an existing parallel-trellis framework, which consists of a bank of identical regular trellises, is exploited to construct the maximum a posteriori (MAP) equalizer in the turbo equalizer. This MAP equalizer, when combined with prefiltering, can equalize a broad selection of sparse multipath channels, including those with nonminimum phase, by using only M-state trellises, where M is the constellation size. For multiple-input-multiple-output (MIMO) systems, a MIMO prefilter and a bank of M-state parallel-trellis MAP equalizers are deployed according to a layering structure. The total number of states needed is only N <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">T</sub> M, where N <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">T</sub> is the number of transmit antennae. For both SISO and MIMO systems, a class of binary convolutional and turbo codes having sparse generator polynomials are chosen as the coding schemes. These codes partially integrate channel interleaving with encoding, which allows a simple channel interleaver with low latency and memory storage requirement to be employed. The MAP decoders for these codes can also be implemented with the same parallel-trellis framework as the MAP equalizers. Overall, parallel processing is supported throughout the turbo equalizers. The amount of computational time reduction when compared to a turbo equalizer using a single-trellis MAP equalizer and decoder is proportional to the number of trellises in the parallel-trellis MAP equalizer and decoder. The performance of the parallel-trellis turbo equalizers is evaluated on static and Rayleigh fading sparse multipath channels via Monte Carlo simulations

Low Complexity Turbo Equalization for High Data Rate Wireless Communications

Soft interference cancellers (SICs) have been proposed in the literature as a means for reducing the computational complexity of the so-called turbo equalization receiver architecture. Soft-input-soft output (SISO) equalization algorithms based on linear filters have a tremendous complexity advantage over trellis-diagram-based SISO equalizers, especially for high-order modulations and long-delay spread frequency selective channels. In this paper, we modify the way in which the SIC incorporates soft information. In existing literature the input to the cancellation filter is the expectation of the symbols based solely on the apriori probabilities coming from the decoder, whereas here we propose to use the conditional expectation of those symbols, given both the apriori probabilities and the received sequence. This modification results in performance gains at the expense of increased computational complexity, as compared to previous SIC-based schemes. However, by introducing an approximation to the aforementioned algorithm a linear complexity SISO equalizer can be derived. Simulation results for an 8-PSK constellation and hostile radio channels have shown the effectiveness of the proposed algorithms in mitigating the intersymbol interference (ISI).

Reduced-Complexity Turbo Equalization for Turbo Coded MIMO/OFDM Systems

This paper derives a low-complexity turbo equalization algorithm for turbo coded multiple input multiple output/orthogonal frequency division multiplexing systems. This algorithm consists of soft-output decision-feedback equalization with a probabilistic data association algorithm and a soft-input soft-output turbo channel decoder using iterative operations. In each iteration, extrinsic information extracted from the probabilistic data association algorithm detector and from the channel decoder is used as the prior information for the next iteration to realize iterative channel equalization and channel decoding. Our simulation results show that the algorithm improves the signal noise ratio around 1 dB with bit error rate reaching 10 −6 when the E b/N O = 4 dB compared to minimum mean square error and match filter, and can greatly reduce the intersymbol interference at a low overall complexity of O(N 3) after 2 iterations.

A Low-Complexity Turbo Equalizer for OFDM Communication Systems

With the growing demand for mobile communications, multicarrier (MC) schemes are receiving an increasing amount of attention, primarily because they handle frequency selective channels better than ordinary single-carrier schemes. However, despite offering several advantages, MC systems have certain weak points. One is their high sensitivity to interchannel interference (ICI). The influence of Doppler shift and ICI are the focus of this paper. Newly proposed B3G/4G systems are developed for data transmission rates higher than those of the IEEE 801.11 It is then necessary that the bandwidth of the subcarrier be small. Moreover, for a higher carrier frequency and mobile speed, the influence of the Doppler shift will be large; therefore, the influence of ICI becomes severer. Using a Markov chain approach, we synthesized a turbo equalizer (TE) that minimizes ICI when interference affects the arbitrary number M of adjacent subchannels. This approach shows the complexity of the proposed algorithm exhibits linear growth with respect to M and independence with respect to the total number of subchannels in the multicarrier system. The proposed ICI cancellation scheme can also be effective in the case of multiple Doppler frequency offsets. This makes the proposed approach attractive for practical implementations.

Low complexity turbo equalization based on soft feedback interference cancelation

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.

A MIMO-OFDM Receiver Employing the Low-Complexity Turbo Equalization in Multipath Environments with Delay Difference Greater than the Guard Interval

When the multipath delay difference exceeds the guard interval (GI), the performance of MIMO-OFDM transmission suffers severely from both the inter-symbol interference (ISI) from the adjacent OFDM symbols and the inter-carrier interference (ICI) within the same symbol. This paper therefore proposes a MIMO-OFDM receiver employing the low-complexity turbo equalization. The proposed receiver initially separates the data streams and suppresses ICI by linear processing. In the iterative processing, it cancels the other data streams as well as ISI and ICI. The MIMO-OFDM turbo equalizer consists of an ISI canceller, an ICI canceller, an optimal detection filter, and a MAP detector. The proposed receiver can improve the transmission performance by exploiting the log-likelihood ratio that the decoding process produces for canceling both ISI and ICI and separating of the spatially multiplexed streams. Computer simulations, which apply the wireless LAN to MIMO, demonstrate that the proposed receiver can provide excellent performance in the severe multipath channels where the delay difference is greater than GI.

Application of turbo codes to tactical communications

A practical multifunctional system comprising a turbo decoder, low complexity turbo equalizer and turbo synchronizer is developed to compensate for frequency-selective channels with fading. The combined synchronizer, equalizer and decoder are based on a turbo scheme where soft extrinsic information is exchanged between these processes and between iterations. The turbo codes are based on Partial Unit Memory Codes, which may be constructed with higher free distance than equivalent recursive systematic convolutional codes and can achieve better performance than the latter. The purely digital multifunctional receiver is targeted for end-applications such as combat-radio and radio-relay, providing robust communication at low signal-to-noise ratio with performance approaching the Shannon limit. This paper presents design considerations for the multifunctional turbo-based receiver as well as simulation results for its performance in combat-radio communications channels.

Application of turbo codes to tactical communications

A practical multifunctional system comprising a turbo decoder, low complexity turbo equalizer and turbo synchronizer is developed to compensate for frequency-selective channels with fading. The combined synchronizer, equalizer and decoder are based on a turbo scheme where soft extrinsic information is exchanged between these processes and between iterations. The turbo codes are based on Partial Unit Memory Codes, which may be constructed with higher free distance than equivalent recursive systematic convolutional codes and can achieve better performance than the latter. The purely digital multifunctional receiver is targeted for end-applications such as combat-radio and radio-relay, providing robust communication at low signal-to-noise ratio with performance approaching the Shannon limit. This paper presents design considerations for the multifunctional turbo-based receiver as well as simulation results for its performance in combat-radio communications channels.