Turbo Detection Research Articles

A Novel Turbo Detector Design for a High-Speed SSVEP-Based Brain Speller

The past decade has witnessed the rapid development of brain-computer interfaces (BCIs). The contradiction between communication rates and tedious training processes has become one of the major barriers restricting the application of steady-state visual-evoked potential (SSVEP)-based BCIs. A turbo detector was proposed in this study to resolve this issue. The turbo detector uses the filter bank canonical correlation analysis (FBCCA) as the first-stage detector and then utilizes the soft information generated by the first-stage detector and the pool of identified data generated during use to complete the second-stage detection. This strategy allows for rapid performance improvements as the data pool size increases. A standard benchmark dataset was used to evaluate the performance of the proposed method. The results show that the turbo detector can achieve an average ITR of 130 bits/min, which is about 8% higher than FBCCA. As the size of the data pool increases, the ITR of the turbo detector could be further improved.

Turbo Detection Aided Autoencoder for Multicarrier Wireless Systems: Integrating Deep Learning Into Channel Coded Systems

A variety of deep learning schemes have endeavoured to integrate deep neural networks (DNNs) into channel coded systems by jointly designing DNN and the channel coding scheme in specific channels. However, this leads to limitations concerning the choice of both the channel coding scheme and the channel paramters. We circumvent these impediments and conceive a turbo-style multi-carrier auto-encoder (MC-AE) for orthogonal frequency-division multiplexing (OFDM) systems, which is the first one that achieves the flexible integration of DNN into any given channel coded systems while achieving an iteration gain. More explicitly, first of all, we design the MC-AE independently of both the channel coding arrangement and of the channel model, where the output layer of the MC-AE decoder is designed for both accepting and producing reliable soft-bit decisions. Owing to the fact that bit-dependency is imposed by the MC-AE mapping, our bespoke MC-AE decoder becomes capable of achieving a beneficial iteration gain, when the extrinsic information is exchanged between the soft-decision MC-AE decoder and the soft-decision channel decoder. Secondly, in order to be able to interpret the performance advantages of our MC-AE over the conventional OFDM, we map the MC-AE’s input-output relationship to an equivalent model-based representation. The associated theoretical analysis verifies the fact that during the process of data-driven signal reconstruction across OFDM’s subcarriers, a beneficial frequency diversity gain is achieved by the proposed MC-AE design. Finally, our simulation results demonstrate that the MC-AE is capable of achieving substantial performance advantages over both conventional OFDM and OFDM based index modulation (OFDM-IM) in channel coded systems.

OTFS Signaling for Uplink NOMA of Heterogeneous Mobility Users

We investigate a coded uplink non-orthogonal multiple access (NOMA) configuration in which groups of co-channel users are modulated in accordance with orthogonal time frequency space (OTFS). We take advantage of OTFS characteristics to achieve NOMA spectrum sharing in the delay-Doppler domain between stationary and mobile users. We develop an efficient iterative turbo receiver based on the principle of successive interference cancellation (SIC) to overcome the co-channel interference (CCI). We propose two turbo detector algorithms: orthogonal approximate message passing with linear minimum mean squared error (OAMP-LMMSE) and Gaussian approximate message passing with expectation propagation (GAMP-EP). The interactive OAMP-LMMSE detector and GAMP-EP detector are respectively assigned for the reception of the stationary and mobile users. We analyze the convergence performance of our proposed iterative SIC turbo receiver by utilizing a customized extrinsic information transfer (EXIT) chart and simplify the corresponding detector algorithms to further reduce receiver complexity. Our proposed iterative SIC turbo receiver demonstrates performance improvement over existing receivers and robustness against imperfect SIC process and channel state information uncertainty.

No-instruction-set-computer design experience of flexible and efficient architectures for digital communication applications: two case studies on MIMO turbo detection and universal turbo demapping

The emerging flexibility need in designing application-specific processors dedicated for modules of digital receiver imposes a new design metric, which is added to the requirements of efficiency and productivity. In order to cope with the emerging flexibility requirement combined with the best performance efficiency, many application-specific processor design approaches have been proposed and investigated. In general, available design approaches that adopt dynamic scheduling of instructions add an overhead due to the instruction decoding. To minimize this overhead, several approaches have been introduced, which opt static scheduling. In this context, No-Instruction-Set-Computer (NISC) concept has been introduced to design application-specific processors without an instruction set. NISC concept proposes that there is no need to first design and then use an instruction set when the hardware is programmed by its designers rather than its users. NISC designing approach offers a good compromise between flexibility, productivity, and quality for the design of a digital system. In our work, NISC approach is explored through the design of flexible and efficient architectures dedicated for digital communication applications which fulfill the requirements imposed by multiple emergent communication standards. This paper introduces briefly the NISC concept and the corresponding design methodology. Also, it provides an overview of the related design approach. In addition, the relevance of NISC in realizing flexible and efficient implementation in the domain of digital communication is demonstrated through two case studies on MIMO turbo detection and universal turbo demapping. Both designed NISC-based architectures have been compared to state-of-the-art ASIP-based architectures using similar computational resources and supporting same flexibility parameters. The obtained results show that the proposed NISC-based architectures provide a significant improvement in execution performance while having reduced implementation costs. The results also illustrates how the control memory requirements depend on the application and the devised architecture choices. In the detector module, the adopted re-usability of allocated resources imposes separate controlling of each component; hence, additional control signals are implied. Whereas for the demapper module, implemented hardware components are considered to perform specific operations and to deal with the same type of data; hence, the number of control signals can be reduced significantly.

Deep Neural Network Based Media Noise Predictors for Use in High-Density Magnetic Recording Turbo-Detectors

This article presents a combined Bahl–Cocke–Jelinek–Raviv (BCJR) and deep neural network (DNN) turbo-detection architecture for 1-D hard disk drive (HDD) magnetic recording. Simulated HDD readings based on a grain flipping probabilistic (GFP) model are input to a linear filter equalizer with a 1-D partial response (PR) target. The equalizer output is provided to the BCJR detector in order to minimize the intersymbol interference (ISI) due to the PR mask. The BCJR detector’s log-likelihood-ratio (LLR) outputs (along with the linear equalizer outputs) are then input to the DNN detector, which estimates the signal-dependent media noise. The media noise estimate is then fed back to the BCJR detector in an iterative manner. Several DNN media noise estimation architectures based on fully connected (FC) and convolutional neural networks (CNNs) are investigated. For GFP data at 48 nm track pitch and 11 nm bit length, the CNN-based BCJR-DNN turbo detector reduces the detector bit error rate (BER) by $0.334\times $ and the per bit computational time by $0.731\times $ compared to a BCJR detector that incorporates 1-D pattern-dependent noise prediction (PDNP). The proposed BCJR-DNN turbo detection architecture can be generalized for two-dimensional magnetic recording (TDMR).

On Orthogonal AMP in Coded Linear Vector Systems

Linear minimum mean square error (LMMSE) estimation based turbo detection has been extensively studied for coded linear systems since the seminal work of Wang and Poor (WP). The WP algorithm operates iteratively between a linear detector (LD) and a nonlinear detector (NLD): the LD suppresses the interference based on LMMSE filtering, and the NLD decodes the data by treating the output of the LD as an observation from an additive white Gaussian noise (AWGN) channel. In WP, the messages exchanged between LD and NLD are required to be extrinsic . For the NLD, the extrinsic message comes from the constraint imposed on feedforward error correction (FEC) codes. Therefore, WP does not work in an un-coded linear system. Recently, we proposed an orthogonal approximate message passing (OAMP) algorithm, which only requires the input/output error terms of LD and NLD to be orthogonal . We conjectured that for un-coded linear systems that involve certain large random matrices, the dynamics of OAMP can be accurately characterized by state evolution (SE). In this paper, we consider a coded linear system and develop an extrinsic message aided OAMP (EMA-OAMP) algorithm. Similar to the un-coded case, EMA-OAMP relaxes the requirements on output messages to be orthogonal instead of extrinsic. We derive an SE procedure to characterize the performance of OAMP in coded systems. We conjecture that this SE procedure is accurate, which is verified by simulation results. Under this conjecture, we show that EMA-OAMP can outperform WP under certain standard assumptions for iterative decoding. Extensive simulations results are provided to verify the advantages of OAMP in coded MIMO systems.

Constant-Envelope Space-Time Shift Keying

From the power amplifier's perspective, the peak-to-average power ratio (PAPR) is of essential importance, especially for both single-RF and reduced-RF multiple-input multiple-output (MIMO) single-carrier schemes. In this context, many of the diversity-oriented index modulation schemes—including the full-RF space-time shift keying (STSK) and the single-RF asynchronous STSK (ASTSK) that invoke randomized signals—exhibit eroded energy-efficiency. To circumvent this problem, we propose a holistic signal construction approach for single-RF, reduced-RF, and full-RF MIMO setups, which always achieve both perfect 0 dB PAPR transmission and inter-channel interference (ICI) free signal detection. More explicitly, first of all , we conceive a new family of single-RF constant-envelope ASTSK (CE-ASTSK), which is capable of substantially outperforming conventional spatial modulation (SM) in both Rayleigh fading and Ricean fading associated with increasing line-of-sight (LoS) power. Second , we propose the new full-RF CE-STSK concept, which is capable of outperforming the orthogonal space-time block codes (STBCs) without either increasing PAPR or imposing ICI. This is particularly beneficial because the conventional linear dispersion code (LDC) approaches always compromise the orthogonality of STBC and hence impose ICI. Third , we also conceive the reduced-RF versions of CE-STSK, which outperform both generalized spatial modulation (GSM) and space-time block coded spatial modulation (STBC-SM). Finally , the proposed schemes are intrinsically amalgamated with turbo detection assisted channel coding, which further confirms the superiority of CE-ASTSK and CE-STSK over SM and STBC in the single-RF and full-RF modes, respectively.

Novel Detectors for Massive MU-MIMO Communications

The massive multi-user multiple-input multiple-output (MU-MIMO) can be adapted to meet the increasing requirement of data throughput services in wireless transmission systems. The combination of the Single Carrier Frequency Division Multiple Access (SC-FDMA) with the massive MU-MIMO technology can be employed for the uplink transmission to meet the requirement of data rates and error performance. In this paper, for practical implementation, we integrate multi-user detection, Kalman channel estimation and turbo equalization and propose turbo detectors to solve the problem of huge computation load of matrix inversion at receiver side. The proposed low-complexity detectors are based on Neumann series expansion, successive over-relaxation (SOR), and symmetric successive over-relaxation (SSOR) principles. Simulation examples in the uplink scenario are given for the proposed low-complexity turbo detectors to demonstrate the comparisons and effectiveness of the proposed schemes.

Computational Complexity Reduction of MMSE-IC MIMO Turbo Detection

High data rates and error-rate performance approaching close to theoretical limits are key trends for evolving digital wireless communication applications. To address the first requirement, multiple-input multiple-output (MIMO) techniques are adopted in emergent wireless communication standards and applications. On the other hand, turbo concept is used to alleviate the destructive effects of the channel and ensure error-rate performance close to theoretical limits. At the receiver side, the incorporation of MIMO techniques and turbo processing leads to increased complexity that has a severe impact on computation speed, power consumption and implementation area. Because of its increased complexity, the detector is considered critical among all receiver components. Low-complexity algorithms are developed at the cost of decreased performance. Minimum mean-squared error (MMSE) solution with iterative detection and decoding shows an acceptable tradeoff. In this paper, the complexity of the MMSE algorithm in turbo detection context is investigated thoroughly. Algorithmic computations are surveyed to extract the characteristics of all involved parameters. Consequently, several decompositions are applied leading to enhanced performance and to a significant reduction of utilized computations. The complexity of the algorithm is evaluated in terms of real-valued operations. The proposed decompositions save an average of [Formula: see text] and [Formula: see text] of required operations for 2 [Formula: see text] 2 and 4 [Formula: see text] 4 MIMO systems, respectively. In addition, the hardware implementation designed applying the devised simplifications and decompositions outperforms available state-of-the-art implementations in terms of maximum operating frequency, execution time, and performance.

Energy Efficient Transmission Based on Grouped Spatial Modulation for Upstream DSL Systems

The digital Subscriber Line (DSL) remains an important component of heterogeneous networking, especially in historic city-centers, where using optical fibre is less realistic. Recently, the power consumption has become an important performance metric in telecommunication due to the associated environmental issues. In the recent bonding model, customer sites have been equipped with two/four copper pairs, which may be exploited for designing grouped spatial modulation (SM) aiming for reducing the power consumption and mitigating the stubborn crosstalk in DSL communications. Explicitly, we view the two pair copper pairs equipped for each user as a group and propose an energy efficient transmission scheme based on grouped SM strategy for the upstream DSL systems, which is capable of reducing the power consumption of the upstream transmitters by activating a single copper line of each user. More especially, in order to compensate for the potential bit-rate reduction imposed by reducing the number of activated lines, the proposed scheme implicitly delivers ``virtual bits" via activating/deactivating the lines in addition to the classic modulation scheme. This is particularly beneficial in the DSL context, because the cross-talk imposed by activating several lines may swamp the desired signal. Furthermore, a pair of near-optimal soft turbo detection schemes are proposed for exploiting the unique properties of the DSL channel in order to eliminate the error propagation problem of SM detection routinely encountered in wireless channels. Both the attainable energy-efficiency and the achievable Bit Error Ratio (BER) are investigated. Our simulation results demonstrate that the proposed group-based SM is capable of outperforming the vectoring scheme both in terms of its energy efficiency for all the examined loop lengths and transmit powers.

Low‐complexity graph‐based turbo equalisation for single‐carrier and multi‐carrier FTN signalling

We propose a novel turbo detection scheme based on the factor graph serial-schedule belief propagation equalization algorithm with low complexity for single-carrier faster-than-Nyquist (FTN) and multicarrier FTN signaling. In this work, the additive white Gaussian noise channel and multi-path fading channels are both considered. The iterative factor graph-based equalization algorithm can deal with severe intersymbol interference and intercarrier interference introduced by the generation of single-carrier and multi-carrier FTN signals, as well as the effect of multi-path fading. With the application of Gaussian approximation, the complexity of the proposed equalization algorithm is significantly reduced. In the turbo detection, Low density parity check code is employed. The simulation results demonstrate that the factor graph-based turbo detection method can achieve satisfactory performance with low complexity.

Iterative QR-Based SFSIC Detection and Decoder Algorithm for a Reed–Muller Space-Time Turbo System

An iterative QR-based soft feedback segment interference cancellation (QRSFSIC) detection and decoder algorithm for a Reed–Muller (RM) space-time turbo system is proposed in this paper. It forms the sufficient statistic for the minimum-mean-square error (MMSE) estimate according to QR decomposition-based soft feedback successive interference cancellation, stemmed from the a priori log-likelihood ratio (LLR) of encoded bits. Then, the signal originating from the symbols of the reliable segment, the symbol reliability metric, in terms of an a posteriori LLR of encoded bits which is larger than a certain threshold, is iteratively cancelled with the QRSFSIC in order to further obtain the residual signal for evaluating the symbols in the unreliable segment. This is done until the unreliable segment is empty, resulting in the extrinsic information for a RM turbo-coded bit with the greatest likelihood. Bridged by de-multiplexing and multiplexing, an iterative QRSFSIC detection is concatenated with an iterative trellis-based maximum a posteriori probability RM turbo decoder as if a principal Turbo detection and decoder is embedded with an iterative subordinate QRSFSIC detection and a RM turbo decoder, exchanging each other’s detection and decoding soft-decision information iteratively. These three stages let the proposed algorithm approach the upper bound of the diversity. The simulation results also show that the proposed scheme outperforms the other suboptimum detectors considered in this paper.

High Density Turbo TDMR Detection With Local Area Influence Probabilistic Model

This paper proposes probabilistic message-passing turbo detection algorithms for 2-D magnetic recording that locally estimate magnetic grain interactions with coded data bits, and thus iteratively assist channel decoding. Such local area influence probabilistic (LAIP) techniques are especially effective at densities ranging from about 4 magnetic grains per coded bit (GPB) down to about 1 GPB, where interaction between grains and bits is significant and occasionally a bit will not be written on any grain, and hence will effectively be “overwritten” by bits on surrounding grains. By modeling the interaction among grains, LAIP enables detection of both overwritten bits and wrong-sign non-overwritten bits so that their log-likelihood ratios are assigned small magnitudes for overwritten bits and correct signs for non-overwritten bits. Simulation results with a random Voronoi magnetic media model show that the LAIP-based detector can accurately detect both overwritten bits and severely influenced non-overwritten bits, and that higher user densities and lower bit error rates can be achieved compared with our previously proposed generalized belief propagation (GBP) detector presented at the 2015 Magnetic Recording Conference (TMRC 2015). In addition, the LAIP-based detector's computer run time is 10 000 times faster than the GBP-based detector.

Soft-Decision Multiple-Symbol Differential Sphere Detection and Decision-Feedback Differential Detection for Differential QAM Dispensing with Channel Estimation in the Face of Rapidly Fading Channels

Turbo detection performed by exchanging extrinsic information between the soft-decision QAM detector and the channel decoder is beneficial for the sake of exploring the bit dependency imposed both by modulation and by channel coding. However, when the soft-decision coherent QAM detectors are provided with imperfect channel estimates in rapidly fading channels, they tend to produce potentially unreliable LLRs that deviate from the true probabilities, which degrades the turbo detection performance. Against this background, in this paper, we propose a range of new soft-decision multiple-symbol differential sphere detection (MSDSD) and decision-feedback differential detection (DFDD) solutions for differential QAM (DQAM), which dispense with channel estimation in the face of rapidly fading channels. Our proposed design aims for solving the two inherent problems in soft-decision DQAM detection design, which have also been the most substantial obstacle in the way of offering a solution for turbo detected MSDSD aided differential MIMO schemes using QAM: 1) how to facilitate the soft-decision detection of the DQAM’s amplitudes, which—in contrast to the DPSK phases—do not form a unitary matrix, and 2) how to separate and streamline the DQAM’s soft-decision amplitude and phase detectors. Our simulation results demonstrate that our proposed MSDSD aided DQAM solution is capable of substantially outperforming its MSDSD aided DPSK counterpart in coded systems without imposing a higher complexity . Moreover, our proposed DFDD aided DQAM solution is shown to outperform the conventional solutions in literature. Our discussions on the important subject of coherent versus noncoherent schemes suggest that compared to coherent square QAM relying on realistic imperfect channel estimation, MSDSD aided DQAM may be deemed as a better candidate for turbo detection assisted coded systems operating at high Doppler frequencies.

Main-Branch Structure Iterative Detection Using Approximate Message Passing for Uplink Large-Scale Multiuser MIMO Systems

The emerging large-scale/massive multi-input multioutput (MIMO) system combined with orthogonal frequency division multiplexing (OFDM) is considered a key technology for its advantage of improving the spectral efficiency. In this paper, we introduce an iterative detection algorithm for uplink large-scale multiuser MIMO-OFDM communication systems. We design a Main-Branch structure iterative turbo detector using the Approximate Message Passing algorithm simplified by linear approximation (AMP-LA) and using the Mean Square Error (MSE) criterion to calculate the correlation coefficients between main detector and branch detector for the given iteration. The complexity of our method is compared with other detection algorithms. The simulation results show that our scheme can achieve better performance than the conventional detection methods and have the acceptable complexity.

Reduced-Complexity Soft-Decision Multiple-Symbol Differential Sphere Detection

Unlike a generic PSK/QAM detector, which may visit a constellation diagram only once, a depth-first Sphere Decoder (SD) has to re-visit the same constellation diagram multiple times. Therefore, in order to prevent the SD from repeating the detection operations, the Schnorr-Euchner search strategy of Schnorr and Euchner may be invoked for optimizing the nodes' search-order, where the ideal case is for the SD to visit the constellation nodes in a zigzag fashion. However, when the hard-decision Multiple-Symbol Differential Sphere Detection (MSDSD) of Lampe et al. is invoked for using multiple receive antennas $N_R\ge 1$ , the Schnorr-Euchner search strategy has to visit and sort all the $M\textrm{PSK}$ constellation points. A similar situation is encountered for the soft-decision MSDSD of Pauli et al. , when the a priori LLRs gleaned from the channel decoder are taken into account. In order to tackle these open problems, in this paper, we propose a correlation process for the hard-decision MSDSD of Lampe et al. and a reduced-complexity design for the soft-decision MSDSD of Pauli et al. , so that the Schnorr-Euchner search strategy always opts for visiting the $M\textrm{PSK}$ constellation points in a zigzag fashion. Our simulation results demonstrate that a substantial complexity reduction is achieved by our reduced-complexity design without imposing any performance loss . Explicitly, up to 88.7% complexity reduction is attained for MSDSD $(N_w=4)$ aided D16PSK. This complexity reduction is quite substantial, especially when the MSDSD is invoked several times during turbo detection. Furthermore, in order to offer an improved solution and a comprehensive study for the soft-decision MSDSD, we also propose to modify the output of the SD to harmonize its operation with the near-optimum Approx-Log-MAP. Then the important subject of coherent versus noncoherent is discussed in the context of coded systems, which suggests that MSDSD aided DPSK is an eminently suitable candidate for turbo detection assisted coded systems operating at high Doppler frequencies.

Low‐complexity soft‐interference cancellation turbo equalisation for multi‐input–multi‐output systems with multilevel modulations

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.

Two-Tier Channel Estimation Aided Near-Capacity MIMO Transceivers Relying on Norm-Based Joint Transmit and Receive Antenna Selection

We propose a norm-based joint transmit and receive antenna selection (NBJTRAS) aided near-capacity multiple-input–multiple-output (MIMO) system relying on the assistance of a novel two-tier channel estimation scheme. Specifically, a rough estimate of the full MIMO channel is first generated using a low-complexity, low-training-overhead minimum mean square error based channel estimator, which relies on reusing a modest number of radio frequency (RF) chains. NBJTRAS is then carried out based on this initial full MIMO channel estimate. The NBJTRAS aided MIMO system is capable of significantly outperforming conventional MIMO systems equipped with the same modest number of RF chains while dispensing with the idealized simplifying assumption of having perfectly known channel state information (CSI). Moreover, the initial subset channel estimate associated with the selected subset MIMO channel matrix is then used for activating a powerful semi-blind joint channel estimation and turbo detector–decoder, in which the channel estimate is refined by a novel block-of-bits selection based soft-decision aided channel estimator (BBSB-SDACE) embedded in the iterative detection and decoding process. The joint channel estimation and turbo detection–decoding scheme operating with the aid of the proposed BBSB-SDACE channel estimator is capable of approaching the performance of the near-capacity maximum-likelihood (ML) turbo transceiver associated with perfect CSI. This is achieved without increasing the complexity of the ML turbo detection and decoding process.

Optimising the activation cycle of Turbo Decoders using three‐dimensional extrinsic information transfer charts

In this study, activation cycle of turbo detection system is investigated using three-dimensional extrinsic information transfer charts. Turbo detection typically employs an iterative process of information transfer with a fixed activation schedule. In the proposed work, the activation cycle of different component decoders is adapted for each signal-to-noise ratio value using information obtained from extrinsic information transfer charts. The objective is to reach the desired reliability of estimates at a lower complexity and for that purpose an exhaustive tree search-based message passing algorithm has been adopted. The results are validated by showing that the optimum activation cycles are similar to that of fixed scheduler with matched component decoders. The resulting bit error rate curves closely approach and in some cases excel the results obtained for the fixed activation while operating at only a fraction of their complexity.

Simplified Parallel Interference Cancelation for Underdetermined MIMO Systems

In this paper, a low-complexity detection scheme is proposed for an underdetermined multiple-input-multiple-output (UD-MIMO) wireless communication system that employs N transmit antennas and M< Nreceive antennas. The proposed scheme combines a simplified parallel interference cancelation (S-PIC) with the block decision feedback equalization (BDFE) algorithm. To account for the extra (N − M )-dimension in the transmitted signal, the UD-MIMO system is partitioned into two subsystems: one with (N − M ) transmit antennas and the other one with M transmit antennas. The interference from the first subsystem to the second one is canceled in parallel, and BDFE is performed over the second subsystem. Unlike conventional PIC methods that exhaustively search all the Q (N −M ) sequences in the first subsystem, with Q being the constellation size, the proposed scheme explores only a small number of candidate sequences in the first subsystem; thus, it achieves significant complexity reduction. Two new candidate sequence selection methods are proposed. In the first iteration, the candidate sequences used for PIC are selected by exploring the statistical properties of the received signals. In the second iteration and beyond, the set containing the candidate sequences is constructed by utilizing the soft informa- tion generated from the previous iteration. The proposed scheme provides a balanced tradeoff between computational complexity and bit error rate (BER) performance. Index Terms—Block decision feedback equalization (BDFE), parallel interference cancelation (PIC), turbo detection, under- determined multiple-input multiple-output (UD-MIMO), wireless communication.