Dual-lattice ordering and partial lattice reduction for SIC-based MIMO detection

This is the author's accepted manuscript. The final published article is available from the link below. Copyright @ 2009 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other users, including reprinting/ republishing this material for advertising or promotional purposes, creating new collective works for resale or redistribution to servers or lists, or reuse of any copyrighted components of this work in other works.In this paper, we propose low-complexity lattice detection algorithms for successive interference cancelation (SIC) in multi-input multi-output (MIMO) communications. First, we present a dual-lattice view of the vertical Bell Labs Layered Space-Time (V-BLAST) detection. We show that V-BLAST ordering is equivalent to applying sorted QR decomposition to the dual basis, or equivalently, applying sorted Cholesky decomposition to the associated Gram matrix. This new view results in lower detection complexity and allows simultaneous ordering and detection. Second, we propose a partial reduction algorithm that only performs lattice reduction for the last several, weak substreams, whose implementation is also facilitated by the dual-lattice view. By tuning the block size of the partial reduction (hence the complexity), it can achieve a variable diversity order, hence offering a graceful tradeoff between performance and complexity for SIC-based MIMO detection. Numerical results are presented to compare the computational costs and to verify the achieved diversity order

From Linear Equalization to Lattice-Reduction-Aided Sphere-Detector as an Answer to the MIMO Detection Problematic in Spatial Multiplexing Systems

ISBN 978-953-307-223-4International audienc

Energy Efficient VLSI Circuits for MIMO-WLAN

Mobile communication - anytime, anywhere access to data and communication services - has been continuously increasing since the operation of the first wireless communication link by Guglielmo Marconi. The demand for higher data rates, despite the limited bandwidth, led to the development of multiple-input multiple-output (MIMO) communication which is often combined with orthogonal frequency division multiplexing (OFDM). Together, these two techniques achieve a high bandwidth efficiency. Unfortunately, techniques such as MIMO-OFDM significantly increase the signal processing complexity of transceivers. While fast improvements in the integrated circuit (IC) technology enabled to implement more signal processing complexity per chip, large efforts had and have to be done for novel algorithms as well as for efficient very large scaled integration (VLSI) architectures in order to meet today's and tomorrow's requirements for mobile wireless communication systems. In this thesis, we will present architectures and VLSI implementations of complete physical (PHY) layer application specific integrated circuits (ASICs) under the constraints imposed by an industrial wireless communication standard. Contrary to many other publications, we do not elaborate individual components of a MIMO-OFDM communication system stand-alone, but in the context of the complete PHY layer ASIC. We will investigate the performance of several MIMO detectors and the corresponding preprocessing circuits, being integrated into the entire PHY layer ASIC, in terms of achievable error-rate, power consumption, and area requirement. Finally, we will assemble the results from the proposed PHY layer implementations in order to enhance the energy efficiency of a transceiver. To this end, we propose a cross-layer optimization of PHY layer and medium access control (MAC) layer

Novel Efficient Precoding Techniques for Multiuser MIMO Systems

In Multiuser MIMO (MU-MIMO) systems, precoding is essential to eliminate or minimize the multiuser interference (MUI). However, the design of a suitable precoding algorithm with good overall performance and low computational complexity at the same time is quite challenging, especially with the increase of system dimensions. In this thesis, we explore the art of novel low-complexity high-performance precoding algorithms with both linear and non-linear processing strategies. Block diagonalization (BD)-type based precoding techniques are well-known linear precoding strategies for MU-MIMO systems. By employing BD-type precoding algorithms at the transmit side, the MU-MIMO broadcast channel is decomposed into multiple independent parallel SU-MIMO channels and achieves the maximum diversity order at high data rates. The main computational complexity of BD-type precoding algorithms comes from two singular value decomposition (SVD) operations, which depend on the number of users and the dimensions of each user's channel matrix. In this thesis, two categories of low-complexity precoding algorithms are proposed to reduce the computational complexity and improve the performance of BD-type precoding algorithms. One is based on multiple LQ decompositions and lattice reductions. The other one is based on a channel inversion technique, QR decompositions, and lattice reductions to decouple the MU-MIMO channel into equivalent SU-MIMO channels. Both of the two proposed precoding algorithms can achieve a comparable sum-rate performance as BD-type precoding algorithms, substantial bit error rate (BER) performance gains, and a simplified receiver structure, while requiring a much lower complexity. Tomlinson-Harashima precoding (THP) is a prominent nonlinear processing technique employed at the transmit side and is a dual to the successive interference cancelation (SIC) detection at the receive side. Like SIC detection, the performance of THP strongly depends on the ordering of the precoded symbols. The optimal ordering algorithm, however, is impractical for MU-MIMO systems with multiple receive antennas. We propose a multi-branch THP (MB-THP) scheme and algorithms that employ multiple transmit processing and ordering strategies along with a selection scheme to mitigate interference in MU-MIMO systems. Two types of multi-branch THP (MB-THP) structures are proposed. The first one employs a decentralized strategy with diagonal weighted filters at the receivers of the users and the second uses a diagonal weighted filter at the transmitter. The MB-MMSE-THP algorithms are also derived based on an extended system model with the aid of an LQ decomposition, which is much simpler compared to the conventional MMSE-THP algorithms. Simulation results show that a better BER performance can be achieved by the proposed MB-MMSE-THP precoder with a small computational complexity increase

Design and implimentationof Multi-user MIMO precoding algorithms

The demand for high-speed communications required by cutting-edge applications has put a strain on the already saturated wireless spectrum. The incorporation of antenna arrays at both ends of the communication link has provided improved spectral efficiency and link reliability to the inherently complex wireless environment, thus allowing for the thriving of high data-rate applications without the cost of extra bandwidth consumption. As a consequence to this, multiple-input multiple-output (MIMO) systems have become the key technology for wideband communication standards both in single-user and multi-user setups. The main difficulty in single-user MIMO systems stems from the signal detection stage at the receiver, whereas multi-user downlink systems struggle with the challenge of enabling non-cooperative signal acquisition at the user terminals. In this respect, precoding techniques perform a pre-equalization stage at the base station so that the signal at each receiver can be interpreted independently and without the knowledge of the overall channel state. Vector precoding (VP) has been recently proposed for non-cooperative signal acquisition in the multi-user broadcast channel. The performance advantage with respect to the more straightforward linear precoding algorithms is the result of an added perturbation vector which enhances the properties of the precoded signal. Nevertheless, the computation of the perturbation signal entails a search for the closest point in an in nite lattice, which is known to be in the class of non-deterministic polynomial-time hard (NP-hard) problems. This thesis addresses the difficulties that stem from the perturbation process in VP systems from both theoretical and practical perspectives. On one hand, the asymptotic performance of VP is analyzed assuming optimal decoding. Since the perturbation process hinders the analytical assessment of the VP performance, lower and upper bounds on the expected data rate are reviewed and proposed. Based on these bounds, VP is compared to linear precoding with respect to the performance after a weighted sum rate optimization, the power resulting from a quality of service (QoS) formulation, and the performance when balancing the user rates. On the other hand, the intricacies of performing an efficient computation of the perturbation vector are analyzed. This study is focused on tree-search techniques that, by means of an strategic node pruning policy, reduce the complexity derived from an exhaustive search and yield a close-to-optimum performance. To that respect, three tree-search algorithms are proposed. The xed-sphere encoder (FSE) features a constant data path and a non-iterative architecture that enable the parallel processing of the set of vector hypotheses and thus, allow for high-data processing rates. The sequential best-node expansion (SBE) algorithm applies a distance control policy to reduce the amount of metric computations performed during the tree traversal. Finally, the low-complexity SBE (LC-SBE) aims at reducing the complexity and latency of the aforementioned algorithm by combining an approximate distance computation model and a novel approach of variable run-time constraints. Furthermore, the hardware implementation of non-recursive tree-search algorithms for the precoding scenario is also addressed in this thesis. More specifically, the hardware architecture design and resource occupation of the FSE and K-Best xed-complexity treesearch techniques are presented. The determination of the ordered sequence of complexvalued nodes, also known as the Schnorr-Euchner enumeration, is required in order to select the nodes to be evaluated during the tree traversal. With the aim of minimizing the hardware resource demand of such a computationally-expensive task, a novel non-sequential and lowcomplexity enumeration algorithm is presented, which enables the independent selection of the nodes within the ordered sequence. The incorporation of the proposed enumeration technique along with a fully-pipelined architecture of the FSE and K-Best approaches, allow for data processing throughputs of up to 5 Gbps in a 4x4 antenna setup.Aplikazio abangoardistek beharrezko duten abiadura handiko komunikazioen eskaerak presio handia ezarri du dagoeneko saturatuta dagoen haririk gabeko espektruan. Komunikazio loturaren bi muturretan antena array-en erabilerak eraginkortasun espektral eta dagarritasun handiagoez hornitu du berez konplexua den haririk gabeko ingurunea, modu honetan banda zabalera gehigarririk gabeko abiadura handiko aplikazioen garapena ahalbidetuz. Honen ondorioz, multiple-input multiple output (MIMO) sistemak banda zabaleko komunikazio estandarren funtsezko teknologia bihurtu dira, erabiltzaile bakarreko ezarpenetan hala nola erabiltzaile anitzeko inguruneetan. Erabiltzaile bakarreko MIMO sistemen zailtasun garrantzitsuena hartzailean ematen den seinalearen detekzio fasean datza. Erabiltzaile anitzeko sistemetan, aldiz, erronka nagusiena datu jasotze ez kooperatiboa bermatzea da. Prekodi kazio teknikek hartzaile bakoitzaren seinalea kanalaren egoera orokorraren ezagutzarik gabe eta modu independiente baten interpretatzea ahalbidetzen dute estazio nagusian seinalearen pre-ekualizazio fase bat inposatuz. Azken aldian, prekodi kazio bektoriala (VP, ingelesez vector precoding) proposatu da erabiltzaile anitzeko igorpen kanalean seinalearen eskuratze ez kooperatiboa ahalbidetzeko. Perturbazio seinale baten erabilerak, prekodi katutako seinalearen ezaugarriak hobetzeaz gain, errendimenduaren hobekuntza nabarmen bat lortzen du prekodi kazio linearreko teknikekiko. Hala ere, perturbazio seinalearen kalkuluak sare in nitu baten puntu hurbilenaren bilaketa suposatzen du. Problema honen ebazpenaren konplexutasuna denbora polinomialean ez deterministikoa dela jakina da. Doktoretza tesi honen helburu nagusia VP sistemetan perturbazio prozesuaren ondorioz ematen diren zailtasun teoriko eta praktikoei irtenbide egoki bat ematea da. Alde batetik, seinale/zarata ratio handiko ingurunetan VP sistemen errendimendua aztertzen da, beti ere deskodetze optimoa ematen dela suposatuz. Perturbazio prozesuak VP sistemen errendimenduaren azterketa analitikoa oztopatzen duenez, data transmisio tasaren hainbat goi eta behe borne proposatu eta berrikusi dira. Borne hauetan oinarrituz, VP eta prekodi kazio linealaren arteko errendimendu desberdintasuna neurtu da hainbat aplikazio ezberdinen eremuan. Konkretuki, kanalaren ahalmen ponderatua, zerbitzu kalitatearen formulazio baten ondorioz esleitzen den seinale potentzia eta erabiltzaileen datu transmisio tasa orekatzean lortzen den errendimenduaren azterketa burutu dira. Beste alde batetik, perturbazio bektorearen kalkulu eraginkorra lortzeko metodoak ere aztertu dira. Analisi hau zuhaitz-bilaketa tekniketan oinarritzen da, non egitura sinple baten bitartez errendimendu ia optimoa lortzen den. Ildo horretan, hiru zuhaitz-bilaketa algoritmo proposatu dira. Alde batetik, Fixed-sphere encoder-aren (FSE) konplexutasun konstateak eta arkitektura ez errekurtsiboak datu prozesaketa abiadura handiak lortzea ahalbidetzen dute. Sequential best-node expansion (SBE) delako algoritmo iteratiboak ordea, distantzia kontrol politika baten bitartez metrika kalkuluen kopurua murriztea lortzen du. Azkenik, low-complexity SBE (LC-SBE) algoritmoak SBE metodoaren latentzia eta konplexutasuna murriztea lortzen du ordezko distantzien kalkuluari eta exekuzio iraupenean ezarritako muga aldakorreko metodo berri bati esker. Honetaz gain, prekodi kazio sistementzako zuhaitz-bilaketa algoritmo ez errekurtsiboen hardware inplementazioa garatu da. Zehazki, konplexutasun nkoko FSE eta K-Best algoritmoen arkitektura diseinua eta hardware baliabideen erabilera landu dira. Balio konplexuko nodoen sekuentzia ordenatua, Schnorr-Euchner zerrendapena bezala ezagutua, funtsezkoa da zuhaitz bilaketan erabiliko diren nodoen aukeraketa egiteko. Prozesu honek beharrezkoak dituen hardware baliabideen eskaera murrizteko, konplexutasun bajuko algoritmo ez sekuentzial bat proposatzen da. Metodo honen bitartez, sekuentzia ordenatuko edozein nodoren aukeraketa independenteki egin ahal da. Proposatutako zerrendapen metodoa eta estruktura fully-pipeline baten bitartez, 5 Gbps-ko datu prozesaketa abiadura lortu daiteke FSE eta K-Best delako algoritmoen inplementazioan.La demanda de comunicaciones de alta velocidad requeridas por las aplicaciones más vanguardistas ha impuesto una presión sobre el actualmente saturado espectro inalámbrico. La incorporación de arrays de antenas en ambos extremos del enlace de comunicación ha proporcionado una mayor e ciencia espectral y abilidad al inherentemente complejo entorno inalámbrico, permitiendo así el desarrollo de aplicaciones de alta velocidad de transmisión sin un consumo adicional de ancho de banda. Consecuentemente, los sistemas multiple-input multiple output (MIMO) se han convertido en la tecnología clave para los estándares de comunicación de banda ancha, tanto en las con guraciones de usuario único como en los entornos multiusuario. La principal di cultad presente en los sistemas MIMO de usuario único reside en la etapa de detección de la señal en el extremo receptor, mientras que los sistemas multiusuario en el canal de bajada se enfrentan al reto de habilitar la adquisición de datos no cooperativa en los terminales receptores. A tal efecto, las técnicas de precodi cación realizan una etapa de pre-ecualización en la estación base de tal manera que la señal en cada receptor se pueda interpretar independientemente y sin el conocimiento del estado general del canal. La precodifi cación vectorial (VP, del inglés vector precoding) se ha propuesto recientemente para la adquisición no cooperativa de la señal en el canal de difusión multiusuario. La principal ventaja de la incorporación de un vector de perturbación es una considerable mejora en el rendimiento con respecto a los métodos de precodi cación lineales. Sin embargo, la adquisición de la señal de perturbación implica la búsqueda del punto más cercano en un reticulado in nito. Este problema se considera de complejidad no determinística en tiempo polinomial o NP-complejo. Esta tesis aborda las di cultades que se derivan del proceso de perturbación en sistemas VP desde una perspectiva tanto teórica como práctica. Por un lado, se analiza el rendimiento de VP asumiendo una decodi cación óptima en escenarios de alta relación señal a ruido. Debido a que el proceso de perturbación di culta la evaluación analítica del rendimiento de los sistemas de VP, se proponen y revisan diversas cotas superiores e inferiores en la tasa esperada de transmisión de estos sistemas. En base a estas cotas, se realiza una comparación de VP con respecto a la precodi cación lineal en el ámbito de la capacidad suma ponderada, la potencia resultante de una formulación de calidad de servicio y el rendimiento obtenido al equilibrar las tasas de transmisión de los usuarios. Por otro lado, se han propuesto nuevos procedimientos para un cómputo e ciente del vector de perturbación. Estos métodos se basan en técnicas de búsqueda en árbol que, por medio de diferentes políticas de podado, reducen la complejidad derivada de una búsqueda exhaustiva y obtienen un rendimiento cercano al óptimo. A este respecto, se proponen tres algoritmos de búsqueda en árbol. El xed-sphere encoder (FSE) cuenta con una complejidad constante y una arquitectura no iterativa, lo que permite el procesamiento paralelo de varios vectores candidatos, lo que a su vez deriva en grandes velocidades de procesamiento de datos. El algoritmo iterativo denominado sequential best-node expansion (SBE) aplica una política de control de distancias para reducir la cantidad de cómputo de métricas realizadas durante la búsqueda en árbol. Por último, el low-complexity SBE (LC-SBE) tiene por objetivo reducir la complejidad y latencia del algoritmo anterior mediante la combinación de un modelo de cálculo aproximado de distancias y una estrategia novedosa de restricción variable del tiempo de ejecución. Adicionalmente, se analiza la implementación en hardware de algoritmos de búsqueda en árbol no iterativos para los escenarios de precodi cación. Más especí camente, se presentan el diseño de la arquitectura y la ocupación de recursos de hardware de las técnicas de complejidad ja FSE y K-Best. La determinación de la secuencia ordenada de nodos de naturaleza compleja, también conocida como la enumeración de Schnorr-Euchner, es vital para seleccionar los nodos evaluados durante la búsqueda en árbol. Con la intención de reducir al mínimo la demanda de recursos de hardware de esta tarea de alta carga computacional, se presenta un novedoso algoritmo no secuencial de baja complejidad que permite la selección independiente de los nodos dentro de la secuencia ordenada. La incorporación de la técnica de enumeración no secuencial junto con la arquitectura fully-pipeline de los algoritmos FSE y K-Best, permite alcanzar velocidades de procesamiento de datos de hasta 5 Gbps para un sistema de 4 antenas receptoras

Low-Complexity Algorithms for Channel Estimation in Optimised Pilot-Assisted Wireless OFDM Systems

Orthogonal frequency division multiplexing (OFDM) has recently become a dominant transmission technology considered for the next generation fixed and mobile broadband wireless communication systems. OFDM has an advantage of lessening the severe effects of the frequency-selective (multipath) fading due to the band splitting into relatively flat fading subchannels, and allows for low-complexity transceiver implementation based on the fast Fourier transform algorithms. Combining OFDM modulation with multilevel frequency-domain symbol mapping (e.g., QAM) and spatial multiplexing (SM) over the multiple-input multiple-output (MIMO) channels, can theoretically achieve near Shannon capacity of the communication link. However, the high-rate and spectrumefficient system implementation requires coherent detection at the receiving end that is possible only when accurate channel state information (CSI) is available. Since in practice, the response of the wireless channel is unknown and is subject to random variation with time, the receiver typically employs a channel estimator for CSI acquisition. The channel response information retrieved by the estimator is then used by the data detector and can also be fed back to the transmitter by means of in-band or out-of-band signalling, so the latter could adapt power loading, modulation and coding parameters according to the channel conditions. Thus, design of an accurate and robust channel estimator is a crucial requirement for reliable communication through the channel, which is selective in time and frequency. In a MIMO configuration, a separate channel estimator has to be associated with each transmit/receive antenna pair, making the estimation algorithm complexity a primary concern. Pilot-assisted methods, relying on the insertion of reference symbols in certain frequencies and time slots, have been found attractive for identification of the doubly-selective radio channels from both the complexity and performance standpoint. In this dissertation, a family of the reduced-complexity estimators for the single and multiple-antenna OFDM systems is developed. The estimators are based on the transform-domain processing and have the same order of computational complexity, irrespective of the number of pilot subcarriers and their positioning. The common estimator structure represents a cascade of successive small-dimension filtering modules. The number of modules, as well as their order inside the cascade, is determined by the class of the estimator (one or two-dimensional) and availability of the channel statistics (correlation and signal-to-noise power ratio). For fine precision estimation in the multipath channels with statistics not known a priori, we propose recursive design of the filtering modules. Simulation results show that in the steady state, performance of the recursive estimators approaches that of their theoretical counterparts, which are optimal in the minimum mean square error (MMSE) sense. In contrast to the majority of the channel estimators developed so far, our modular-type architectures are suitable for the reconfigurable OFDM transceivers where the actual channel conditions influence the decision of what class of filtering algorithm to use, and how to allot pilot subcarrier positions in the band. In the pilot-assisted transmissions, channel estimation and detection are performed separately from each other over the distinct subcarrier sets. The estimator output is used only to construct the detector transform, but not as the detector input. Since performance of both channel estimation and detection depends on the signal-to-noise power vi ratio (SNR) at the corresponding subcarriers, there is a dilemma of the optimal power allocation between the data and the pilot symbols as these are conflicting requirements under the total transmit power constraint. The problem is exacerbated by the variety of channel estimators. Each kind of estimation algorithm is characterised by its own SNR gain, which in general can vary depending on the channel correlation. In this dissertation, we optimise pilot-data power allocation for the case of developed low-complexity one and two-dimensional MMSE channel estimators. The resultant contribution is manifested by the closed-form analytical expressions of the upper bound (suboptimal approximate value) on the optimal pilot-to-data power ratio (PDR) as a function of a number of design parameters (number of subcarriers, number of pilots, number of transmit antennas, effective order of the channel model, maximum Doppler shift, SNR, etc.). The resultant PDR equations can be applied to the MIMO-OFDM systems with arbitrary arrangement of the pilot subcarriers, operating in an arbitrary multipath fading channel. These properties and relatively simple functional representation of the derived analytical PDR expressions are designated to alleviate the challenging task of on-the-fly optimisation of the adaptive SM-MIMO-OFDM system, which is capable of adjusting transmit signal configuration (e.g., block length, number of pilot subcarriers or antennas) according to the established channel conditions

Joint signal detection and channel estimation in rank-deficient MIMO systems

L'évolution de la prospère famille des standards 802.11 a encouragé le développement des technologies appliquées aux réseaux locaux sans fil (WLANs). Pour faire face à la toujours croissante nécessité de rendre possible les communications à très haut débit, les systèmes à antennes multiples (MIMO) sont une solution viable. Ils ont l'avantage d'accroître le débit de transmission sans avoir recours à plus de puissance ou de largeur de bande. Cependant, l'industrie hésite encore à augmenter le nombre d'antennes des portables et des accésoires sans fil. De plus, à l'intérieur des bâtiments, la déficience de rang de la matrice de canal peut se produire dû à la nature de la dispersion des parcours de propagation, ce phénomène est aussi occasionné à l'extérieur par de longues distances de transmission. Ce projet est motivé par les raisons décrites antérieurement, il se veut un étude sur la viabilité des transcepteurs sans fil à large bande capables de régulariser la déficience de rang du canal sans fil. On vise le développement des techniques capables de séparer M signaux co-canal, même avec une seule antenne et à faire une estimation précise du canal. Les solutions décrites dans ce document cherchent à surmonter les difficultés posées par le medium aux transcepteurs sans fil à large bande. Le résultat de cette étude est un algorithme transcepteur approprié aux systèmes MIMO à rang déficient