Turbo Packet Combining for Broadband Space-Time BICM Hybrid-ARQ Systems with Co-Channel Interference

In this paper, efficient turbo packet combining for single carrier (SC) broadband multiple-input--multiple-output (MIMO) hybrid--automatic repeat request (ARQ) transmission with unknown co-channel interference (CCI) is studied. We propose a new frequency domain soft minimum mean square error (MMSE)-based signal level combining technique where received signals and channel frequency responses (CFR)s corresponding to all retransmissions are used to decode the data packet. We provide a recursive implementation algorithm for the introduced scheme, and show that both its computational complexity and memory requirements are quite insensitive to the ARQ delay, i.e., maximum number of ARQ rounds. Furthermore, we analyze the asymptotic performance, and show that under a sum-rank condition on the CCI MIMO ARQ channel, the proposed packet combining scheme is not interference-limited. Simulation results are provided to demonstrate the gains offered by the proposed technique.Comment: 12 pages, 7 figures, and 2 table

Transmission strategies for broadband wireless systems with MMSE turbo equalization

This monograph details efficient transmission strategies for single-carrier wireless broadband communication systems employing iterative (turbo) equalization. In particular, the first part focuses on the design and analysis of low complexity and robust MMSE-based turbo equalizers operating in the frequency domain. Accordingly, several novel receiver schemes are presented which improve the convergence properties and error performance over the existing turbo equalizers. The second part discusses concepts and algorithms that aim to increase the power and spectral efficiency of the communication system by efficiently exploiting the available resources at the transmitter side based upon the channel conditions. The challenging issue encountered in this context is how the transmission rate and power can be optimized, while a specific convergence constraint of the turbo equalizer is guaranteed.Die vorliegende Arbeit beschäftigt sich mit dem Entwurf und der Analyse von effizienten Übertragungs-konzepten für drahtlose, breitbandige Einträger-Kommunikationssysteme mit iterativer (Turbo-) Entzerrung und Kanaldekodierung. Dies beinhaltet einerseits die Entwicklung von empfängerseitigen Frequenzbereichs-entzerrern mit geringer Komplexität basierend auf dem Prinzip der Soft Interference Cancellation Minimum-Mean Squared-Error (SC-MMSE) Filterung und andererseits den Entwurf von senderseitigen Algorithmen, die durch Ausnutzung von Kanalzustandsinformationen die Bandbreiten- und Leistungseffizienz in Ein- und Mehrnutzersystemen mit Mehrfachantennen (sog. Multiple-Input Multiple-Output (MIMO)) verbessern. Im ersten Teil dieser Arbeit wird ein allgemeiner Ansatz für Verfahren zur Turbo-Entzerrung nach dem Prinzip der linearen MMSE-Schätzung, der nichtlinearen MMSE-Schätzung sowie der kombinierten MMSE- und Maximum-a-Posteriori (MAP)-Schätzung vorgestellt. In diesem Zusammenhang werden zwei neue Empfängerkonzepte, die eine Steigerung der Leistungsfähigkeit und Verbesserung der Konvergenz in Bezug auf existierende SC-MMSE Turbo-Entzerrer in verschiedenen Kanalumgebungen erzielen, eingeführt. Der erste Empfänger - PDA SC-MMSE - stellt eine Kombination aus dem Probabilistic-Data-Association (PDA) Ansatz und dem bekannten SC-MMSE Entzerrer dar. Im Gegensatz zum SC-MMSE nutzt der PDA SC-MMSE eine interne Entscheidungsrückführung, so dass zur Unterdrückung von Interferenzen neben den a priori Informationen der Kanaldekodierung auch weiche Entscheidungen der vorherigen Detektions-schritte berücksichtigt werden. Durch die zusätzlich interne Entscheidungsrückführung erzielt der PDA SC-MMSE einen wesentlichen Gewinn an Performance in räumlich unkorrelierten MIMO-Kanälen gegenüber dem SC-MMSE, ohne dabei die Komplexität des Entzerrers wesentlich zu erhöhen. Der zweite Empfänger - hybrid SC-MMSE - bildet eine Verknüpfung von gruppenbasierter SC-MMSE Frequenzbereichsfilterung und MAP-Detektion. Dieser Empfänger besitzt eine skalierbare Berechnungskomplexität und weist eine hohe Robustheit gegenüber räumlichen Korrelationen in MIMO-Kanälen auf. Die numerischen Ergebnisse von Simulationen basierend auf Messungen mit einem Channel-Sounder in Mehrnutzerkanälen mit starken räumlichen Korrelationen zeigen eindrucksvoll die Überlegenheit des hybriden SC-MMSE-Ansatzes gegenüber dem konventionellen SC-MMSE-basiertem Empfänger. Im zweiten Teil wird der Einfluss von System- und Kanalmodellparametern auf die Konvergenzeigenschaften der vorgestellten iterativen Empfänger mit Hilfe sogenannter Korrelationsdiagramme untersucht. Durch semi-analytische Berechnungen der Entzerrer- und Kanaldecoder-Korrelationsfunktionen wird eine einfache Berechnungsvorschrift zur Vorhersage der Bitfehlerwahrscheinlichkeit von SC-MMSE und PDA SC-MMSE Turbo Entzerrern für MIMO-Fadingkanäle entwickelt. Des Weiteren werden zwei Fehlerschranken für die Ausfallwahrscheinlichkeit der Empfänger vorgestellt. Die semi-analytische Methode und die abgeleiteten Fehlerschranken ermöglichen eine aufwandsgeringe Abschätzung sowie Optimierung der Leistungsfähigkeit des iterativen Systems. Im dritten und abschließenden Teil werden Strategien zur Raten- und Leistungszuweisung in Kommunikationssystemen mit konventionellen iterativen SC-MMSE Empfängern untersucht. Zunächst wird das Problem der Maximierung der instantanen Summendatenrate unter der Berücksichtigung der Konvergenz des iterativen Empfängers für einen Zweinutzerkanal mit fester Leistungsallokation betrachtet. Mit Hilfe des Flächentheorems von Extrinsic-Information-Transfer (EXIT)-Funktionen wird eine obere Schranke für die erreichbare Ratenregion hergeleitet. Auf Grundlage dieser Schranke wird ein einfacher Algorithmus entwickelt, der für jeden Nutzer aus einer Menge von vorgegebenen Kanalcodes mit verschiedenen Codierraten denjenigen auswählt, der den instantanen Datendurchsatz des Mehrnutzersystems verbessert. Neben der instantanen Ratenzuweisung wird auch ein ausfallbasierter Ansatz zur Ratenzuweisung entwickelt. Hierbei erfolgt die Auswahl der Kanalcodes für die Nutzer unter Berücksichtigung der Einhaltung einer bestimmten Ausfallwahrscheinlichkeit (outage probability) des iterativen Empfängers. Des Weiteren wird ein neues Entwurfskriterium für irreguläre Faltungscodes hergeleitet, das die Ausfallwahrscheinlichkeit von Turbo SC-MMSE Systemen verringert und somit die Zuverlässigkeit der Datenübertragung erhöht. Eine Reihe von Simulationsergebnissen von Kapazitäts- und Durchsatzberechnungen werden vorgestellt, die die Wirksamkeit der vorgeschlagenen Algorithmen und Optimierungsverfahren in Mehrnutzerkanälen belegen. Abschließend werden außerdem verschiedene Maßnahmen zur Minimierung der Sendeleistung in Einnutzersystemen mit senderseitiger Singular-Value-Decomposition (SVD)-basierter Vorcodierung untersucht. Es wird gezeigt, dass eine Methode, welche die Leistungspegel des Senders hinsichtlich der Bitfehlerrate des iterativen Empfängers optimiert, den konventionellen Verfahren zur Leistungszuweisung überlegen ist

Channel estimation for SISO and MIMO OFDM communications systems.

Thesis (Ph.D.)-University of KwaZulu-Natal, Durban, 2010.Telecommunications in the current information age is increasingly relying on the wireless link. This is because wireless communication has made possible a variety of services ranging from voice to data and now to multimedia. Consequently, demand for new wireless capacity is growing rapidly at a very alarming rate. In a bid to cope with challenges of increasing demand for higher data rate, better quality of service, and higher network capacity, there is a migration from Single Input Single Output (SISO) antenna technology to a more promising Multiple Input Multiple Output (MIMO) antenna technology. On the other hand, Orthogonal Frequency Division Multiplexing (OFDM) technique has emerged as a very popular multi-carrier modulation technique to combat the problems associated with physical properties of the wireless channels such as multipath fading, dispersion, and interference. The combination of MIMO technology with OFDM techniques, known as MIMO-OFDM Systems, is considered as a promising solution to enhance the data rate of future broadband wireless communication Systems. This thesis addresses a major area of challenge to both SISO-OFDM and MIMO-OFDM Systems; estimation of accurate channel state information (CSI) in order to make possible coherent detection of the transmitted signal at the receiver end of the system. Hence, the first novel contribution of this thesis is the development of a low complexity adaptive algorithm that is robust against both slow and fast fading channel scenarios, in comparison with other algorithms employed in literature, to implement soft iterative channel estimator for turbo equalizer-based receiver for single antenna communication Systems. Subsequently, a Fast Data Projection Method (FDPM) subspace tracking algorithm is adapted to derive Channel Impulse Response Estimator for implementation of Decision Directed Channel Estimation (DDCE) for Single Input Single Output - Orthogonal Frequency Division Multiplexing (SISO-OFDM) Systems. This is implemented in the context of a more realistic Fractionally Spaced-Channel Impulse Response (FS-CIR) channel model, as against the channel characterized by a Sample Spaced-Channel Impulse Response (SS)-CIR widely assumed by other authors. In addition, a fast convergence Variable Step Size Normalized Least Mean Square (VSSNLMS)-based predictor, with low computational complexity in comparison with others in literatures, is derived for the implementation of the CIR predictor module of the DDCE scheme. A novel iterative receiver structure for the FDPM-based Decision Directed Channel Estimation scheme is also designed for SISO-OFDM Systems. The iterative idea is based on Turbo iterative principle. It is shown that improvement in the performance can be achieved with the iterative DDCE scheme for OFDM system in comparison with the non iterative scheme. Lastly, an iterative receiver structure for FDPM-based DDCE scheme earlier designed for SISO OFDM is extended to MIMO-OFDM Systems. In addition, Variable Step Size Normalized Least Mean Square (VSSNLMS)-based channel transfer function estimator is derived in the context of MIMO Channel for the implementation of the CTF estimator module of the iterative Decision Directed Channel Estimation scheme for MIMO-OFDM Systems in place of linear minimum mean square error (MMSE) criterion. The VSSNLMS-based channel transfer function estimator is found to show improved MSE performance of about -4 MSE (dB) at SNR of 5dB in comparison with linear MMSE-based channel transfer function estimator

Turbo Decoding and Detection for Wireless Applications

A historical perspective of turbo coding and turbo transceivers inspired by the generic turbo principles is provided, as it evolved from Shannon’s visionary predictions. More specifically, we commence by discussing the turbo principles, which have been shown to be capable of performing close to Shannon’s capacity limit. We continue by reviewing the classic maximum a posteriori probability decoder. These discussions are followed by studying the effect of a range of system parameters in a systematic fashion, in order to gauge their performance ramifications. In the second part of this treatise, we focus our attention on the family of iterative receivers designed for wireless communication systems, which were partly inspired by the invention of turbo codes. More specifically, the family of iteratively detected joint coding and modulation schemes, turbo equalization, concatenated spacetime and channel coding arrangements, as well as multi-user detection and three-stage multimedia systems are highlighted

Architectures multi-Asip pour turbo récepteur flexible

Rapidly evolving wireless standards use modern techniques such as turbo codes, Bit Interleaved coded Modulation (BICM), high order QAM constellation, Signal Space Diversity (SSD), Multi-Input Multi-Output (MIMO) Spatial Multiplexing (SM) and Space Time Codes (STC) with different parameters for reliable high rate data transmissions. Adoption of such techniques in the transmitter can impact the receiver architecture in three ways: (1) the complex processing related to advanced techniques such as turbo codes, encourage to perform iterative processing in the receiver to improve error rate performance (2) to satisfy high throughput requirement for an iterative receiver, parallel processing is mandatory and finally (3) to allow the support of different techniques and parameters imposed, programmable yet high throughput hardware processing elements are required. In this thesis, to address the high throughput requirement with turbo processing, first of all a study of parallelism on turbo decoding is extended for turbo demodulation and turbo equalization. Based on the results acquired from the parallelism study a flexible high throughput heterogeneous multi-ASIP NoC based unified turbo receiver is proposed. The proposed architecture fulfils the target requirements in a way that: (a) Application Specific Instruction-set Processor (ASIP) exploits metric generation level parallelism and implements the required flexibility, (b) throughputs beyond the capacity of single ASIP in a turbo process are achieved through multiple ASIP elements implementing sub-block parallelism and shuffled processing and finally (c) Network on Chip is used to handle communication conflicts during parallel processing of multiple ASIPs. In pursuit to achieve a hardware model of the proposed architecture two ASIPs are conceived where the first one, namely EquASIP, is dedicated for MMSE-IC equalization and provides a flexible solution for multiple MIMO techniques adopted in multiple wireless standards with a capability to work in turbo equalization context. The second ASIP, named as DemASIP, is a flexible demapper which can be used in MIMO or single antenna environment for any modulation till 256-QAM with or without iterative demodulation. Using available TurbASIP and NoC components, the thesis concludes on an FPGA prototype of heterogeneous multi-ASIP NoC based unified turbo receiver which integrates 9 instances of 3 different ASIPs with 2 NoCs.Les normes de communication sans fil, sans cesse en évolution, imposent l'utilisation de techniques modernes telles que les turbocodes, modulation codée à entrelacement bit (BICM), constellation MAQ d'ordre élevé, diversité de constellation (SSD), multiplexage spatial et codage espace-temps multi-antennes (MIMO) avec des paramètres différents pour des transmissions fiables et de haut débit. L'adoption de ces techniques dans l'émetteur peut influencer l'architecture du récepteur de trois façons: (1) les traitement complexes relatifs aux techniques avancées comme les turbocodes, encourage à effectuer un traitement itératif dans le récepteur pour améliorer la performance en termes de taux d'erreur (2) pour satisfaire l'exigence de haut débit avec un récepteur itératif, le recours au parallélisme est obligatoire et enfin (3) pour assurer le support des différentes techniques et paramètres imposées, des processeurs de traitement matériel flexibles, mais aussi de haute performance, sont nécessaires. Dans cette thèse, pour répondre aux besoins de haut débit dans un contexte de traitement itératif, tout d'abord une étude de parallélisme sur le turbo décodage a été étendue aux applications de turbo démodulation et turbo égalisation. Partant des résultats obtenus à partir de l'étude du parallélisme, un récepteur itératif unifié basé sur un modèle d'architecture multi-ASIP hétérogène intégrant un réseau sur puce (NoC) a été proposé. L'architecture proposée répond aux exigences visées d'une manière où: (a) le concept de processeur à jeu d'instruction dédié à l'application (ASIP) exploite le parallélisme du niveau de génération de métriques et met en oeuvre la flexibilité nécessaire, (b) les débits au-delà de la capacité d'un seul ASIP dans un processus itératif sont obtenus au moyen de multiples ASIP implémentant le parallélisme de sous-blocs et le traitement combiné et enfin (c) le concept de réseau sur puce (NoC) est utilisé pour gérer les conflits de communication au cours du traitement parallèle itératif multi-ASIP. Dans le but de parvenir à un modèle matériel de l'architecture proposée, deux ASIP ont été conçus où le premier, nommé EquASIP, est dédié à l'égalisation MMSE-IC et fournit une solution flexible pour de multiples techniques multi-antennes adoptés dans plusieurs normes sans fil avec la capacité de travailler dans un contexte de turbo égalisation. Le deuxième ASIP, nommé DemASIP, est un démappeur flexible qui peut être utilisé dans un environnement multi-antennes et pour tout type de modulation jusqu'à MAQ-256 avec ou sans démodulation itérative. En intégrant ces ASIP, en plus des NoC et TurbASIP disponibles à Télécom Bretagne, la thèse conclut sur un prototype FPGA d'un récepteur itératif unifié multi-ASIP qui intègre 9 coeurs de 3 différents types d'ASIP avec 2 NoC

Frequency Domain Hybrid-ARQ Chase Combining for Broadband MIMO CDMA Systems

In this paper, we consider high-speed wireless packet access using code division multiple access (CDMA) and multiple-input multiple-output (MIMO). Current wireless standards, such as high speed packet access (HSPA), have adopted multi-code transmission and hybrid-automatic repeat request (ARQ) as major technologies for delivering high data rates. The key technique in hybrid-ARQ, is that erroneous data packets are kept in the receiver to detect/decode retransmitted ones. This strategy is refereed to as packet combining. In CDMA MIMO-based wireless packet access, multi-code transmission suffers from severe performance degradation due to the loss of code orthogonality caused by both interchip interference (ICI) and co-antenna interference (CAI). This limitation results in large transmission delays when an ARQ mechanism is used in the link layer. In this paper, we investigate efficient minimum mean square error (MMSE) frequency domain equalization (FDE)-based iterative (turbo) packet combining for cyclic prefix (CP)-CDMA MIMO with Chase-type ARQ. We introduce two turbo packet combining schemes: i) In the first scheme, namely "chip-level turbo packet combining", MMSE FDE and packet combining are jointly performed at the chip-level. ii) In the second scheme, namely "symbol-level turbo packet combining", chip-level MMSE FDE and despreading are separately carried out for each transmission, then packet combining is performed at the level of the soft demapper. The computational complexity and memory requirements of both techniques are quite insensitive to the ARQ delay, i.e., maximum number of ARQ rounds. The throughput is evaluated for some representative antenna configurations and load factors to show the gains offered by the proposed techniques.Comment: Submitted to IEEE Transactions on Vehicular Technology (Apr 2009

Channel Coding in Molecular Communication

This dissertation establishes and analyzes a complete molecular transmission system from a communication engineering perspective. Its focus is on diffusion-based molecular communication in an unbounded three-dimensional fluid medium. As a basis for the investigation of transmission algorithms, an equivalent discrete-time channel model (EDTCM) is developed and the characterization of the channel is described by an analytical derivation, a random walk based simulation, a trained artificial neural network (ANN), and a proof of concept testbed setup. The investigated transmission algorithms cover modulation schemes at the transmitter side, as well as channel equalizers and detectors at the receiver side. In addition to the evaluation of state-of-the-art techniques and the introduction of orthogonal frequency-division multiplexing (OFDM), the novel variable concentration shift keying (VCSK) modulation adapted to the diffusion-based transmission channel, the lowcomplex adaptive threshold detector (ATD) working without explicit channel knowledge, the low-complex soft-output piecewise linear detector (PLD), and the optimal a posteriori probability (APP) detector are of particular importance and treated. To improve the error-prone information transmission, block codes, convolutional codes, line codes, spreading codes and spatial codes are investigated. The analysis is carried out under various approaches of normalization and gains or losses compared to the uncoded transmission are highlighted. In addition to state-of-the-art forward error correction (FEC) codes, novel line codes adapted to the error statistics of the diffusion-based channel are proposed. Moreover, the turbo principle is introduced into the field of molecular communication, where extrinsic information is exchanged iteratively between detector and decoder. By means of an extrinsic information transfer (EXIT) chart analysis, the potential of the iterative processing is shown and the communication channel capacity is computed, which represents the theoretical performance limit for the system under investigation. In addition, the construction of an irregular convolutional code (IRCC) using the EXIT chart is presented and its performance capability is demonstrated. For the evaluation of all considered transmission algorithms the bit error rate (BER) performance is chosen. The BER is determined by means of Monte Carlo simulations and for some algorithms by theoretical derivation

Self-interference cancellation for full-duplex MIMO transceivers

PhD ThesisIn recent years, there has been enormous interest in utilizing the full-duplex (FD) technique with multiple-input multiple-output (MIMO) systems to complement the evolution of fifth generation technologies. Transmission and reception using FD-MIMO occur simultaneously over the same frequency band and multiple antennas are employed in both sides. The motivation for employing FD-MIMO is the rapidly increasing demand on frequency resources, and also FD has the ability to improve spectral efficiency and channel capacity by a factor of two compared to the conventional half-duplex technique. Additionally, MIMO can enhance the diversity gain and enable FD to acquire further degrees of freedom in mitigating the self-interference (SI). The latter is one of the key challenges degrading the performance of systems operating in FD mode due to local transmission which involves larger power level than the signals of interest coming from distance sources that are significantly more attenuated due to path loss propagation phenomena. Various approaches can be used for self-interference cancellation (SIC) to tackle SI by combining passive suppression with the analogue and digital cancellation techniques. Moreover, active SIC techniques using special domain suppression based on zero-forcing and null-space projection (NSP) can be exploited for this purpose too. The main contributions of this thesis can be summarized as follows. Maximum-ratio combining with NSP are jointly exploited in order to increase the signal-to-noise ratio (SNR) of the desired path and mitigate the undesired loop path, respectively, for an equalize-and-forward (EF) relay using FD-MIMO. Additionally, an end-to-end performance analysis of the proposed system is obtained in the presence of imperfect channel state information by formulating mathematically the exact closed-form solutions for the signal-to-interference-plus-noise ratio (SINR) distribution, outage probability, and average symbol-error rate for uncoded M-ary phase-shift keying over Rayleigh fading channels and in the presence of additive white Gaussian noise (AWGN). The coefficients of the EF-relay are designed to attain the minimum mean-square error (MMSE) between the transmission symbols. Comparison of the results obtained with relevant state-of-the-art techniques suggests significant improvements in the SINR figures and system capacity. Furthermore, iterative detection and decoding (IDD) are proposed to mitigate the residual self-interference (SI) remaining after applying passive suppression along with two stages of SI cancellation (SIC) filters in the analogue and digital domains for coded FD bi-directional transceiver based multiple antennas. IDD comprises an adaptive MMSE filter with log-likelihood ratio demapping, while the soft-in soft-out decoder utilizes the maximum a posteriori (MAP) algorithm. The proposed system’s performance is evaluated in the presence of AWGN over non-selective (flat) Rayleigh fading single-input multiple-output (SIMO) and MIMO channels. However, the results of the analyses can be applied to multi-path channels if orthogonal frequency division multiplexing is utilised with a proper length of cyclic prefix in order to tackle the channels’ frequency-selectivity and delay spread. Simulation results are presented to demonstrate the bit-error rate (BER) performance as a function of the SNR, revealing a close match to the SI-free case for the proposed system. Furthermore, the results are validated by deriving a tight upper bound on the performance of rate-1=2 convolutional codes for FD-SIMO and FD-MIMO systems for different modulation schemes under the same conditions, which asymptotically exhibits close agreement with the simulated BER performance.Ministry of Higher Education and Scientific Research (MoHESR), and the University of Mosul and to the Iraqi Cultural Attache in London for providing financial support for my PhD scholarship

Doctor of Philosophy

dissertationMultiple-input and multiple-output (MIMO) technique has emerged as a key feature for future generations of wireless communication systems. It increases the channel capacity proportionate to the minimum number of transmit and receive antennas. This dissertation addresses the receiver design for high-rate MIMO communications in at fading environments. The emphasis of the thesis is on the cases where channel state information (CSI) is not available and thus, clever channel estimation algorithms have to be developed to bene t from the maximum available channel capacity. The thesis makes four distinct novel contributions. First, we note that the conventional MCMC-MIMO detector presented in the prior work may deteriorate as SNR increases. We suggest and show through computer simulations that this problem to a great extent can be solved by initializing the MCMC detector with regulated states which are found through linear detectors. We also introduce the novel concept of staged-MCMC in a turbo receiver, where we start the detection process at a lower complexity and increase complexity only if the data could not be correctly detected in the present stage of data detection. Second, we note that in high-rate MIMO communications, joint data detection and channel estimation poses new challenges when a turbo loop is used to improve the quality of the estimated channel and the detected data. Erroneous detected data may propagate in the turbo loop and, thus, degrade the performance of the receiver signi cantly. This is referred to as error propagation. We propose a novel receiver that decorrelates channel estimation and the detected data to avoid the detrimental e ect of error propagation. Third, the dissertation studies joint channel estimation and MIMO detection over a continuously time-varying channel and proposes a new dual-layer channel estimator to overcome the complexity of optimal channel estimators. The proposed dual-layer channel estimator reduces the complexity of the MIMO detector with optimal channel estimator by an order of magnitude at a cost of a negligible performance degradation, on the order of 0.1 to 0.2 dB. The fourth contribution of this dissertation is to note that the Wiener ltering techniques that are discussed in this dissertation and elsewhere in the literature assume that channel (time-varying) statistics are available. We propose a new method that estimates such statistics using the coarse channel estimates obtained through pilot symbols. The dissertation also makes an additional contribution revealing di erences between the MCMC-MIMO and LMMSE-MIMO detectors. We nd that under the realistic condition where CSI has to be estimated, hence the available channel estimate will be noisy, the MCMC-MIMO detector outperforms the LMMSE-MIMO detector with a signi cant margin