Decoding by Embedding: Correct Decoding Radius and DMT Optimality

The closest vector problem (CVP) and shortest (nonzero) vector problem (SVP) are the core algorithmic problems on Euclidean lattices. They are central to the applications of lattices in many problems of communications and cryptography. Kannan's \emph{embedding technique} is a powerful technique for solving the approximate CVP, yet its remarkable practical performance is not well understood. In this paper, the embedding technique is analyzed from a \emph{bounded distance decoding} (BDD) viewpoint. We present two complementary analyses of the embedding technique: We establish a reduction from BDD to Hermite SVP (via unique SVP), which can be used along with any Hermite SVP solver (including, among others, the Lenstra, Lenstra and Lov\'asz (LLL) algorithm), and show that, in the special case of LLL, it performs at least as well as Babai's nearest plane algorithm (LLL-aided SIC). The former analysis helps to explain the folklore practical observation that unique SVP is easier than standard approximate SVP. It is proven that when the LLL algorithm is employed, the embedding technique can solve the CVP provided that the noise norm is smaller than a decoding radius $\lambda_1/(2\gamma)$, where $\lambda_1$ is the minimum distance of the lattice, and $\gamma \approx O(2^{n/4})$. This substantially improves the previously best known correct decoding bound $\gamma \approx {O}(2^{n})$. Focusing on the applications of BDD to decoding of multiple-input multiple-output (MIMO) systems, we also prove that BDD of the regularized lattice is optimal in terms of the diversity-multiplexing gain tradeoff (DMT), and propose practical variants of embedding decoding which require no knowledge of the minimum distance of the lattice and/or further improve the error performance.Comment: To appear in IEEE Transactions on Information Theor

FPGA Implementation of Sphere Detector for Spatial Multiplexing MIMO System

Multiple Input Multiple Output (MIMO (techniquesuse multiple antennas at both transmitter and receiver forincreasing the channel reliability and enhancing the spectralefficiency of wireless communication system.MIMO Spatial Multiplexing (SM) is a technology that can increase the channelcapacity without additional spectral resources. The implementation of MIMO detection techniques become a difficult missionas the computational complexity increases with the number oftransmitting antenna and constellation size. So designing detection techniques that can recover transmitted signals from SpatialMultiplexing (SM) MIMO with reduced complexity and highperformance is challenging. In this survey, the general model ofMIMO communication system is presented in addition to multipleMIMO Spatial Multiplexing (SM) detection techniques. These detection techniques are divided into different categories, such as linear detection, Non-linear detection and tree-search detection.Detailed discussions on the advantages and disadvantages of each detection algorithm are introduced. Hardware implementation of Sphere Decoder (SD) algorithm using VHDL/FPGA is alsopresente

Successive interference cancellation aided sphere decoder for multi-input multi-output systems

In this paper, sphere decoding algorithms are proposed for both hard detection and soft processing in multi-input multi-output (MIMO) systems. Both algorithms are based on the complex tree structure to reduce the complexity of searching the unique minimum Euclidean distance and multiple Euclidean distances, and obtain the corresponding transmit symbol vectors. The novel complex hard sphere decoder for MIMO detection is presented first, and then the soft processing of a novel sphere decoding algorithm for list generation is discussed. The performance and complexity of the proposed techniques are demonstrated via simulations in terms of bit error rate (BER), the number of nodes accessed and floating-point operations (FLOPS)

Efficient detection algorithms for Multiple-Input Multiple-Output (MIMO) systems

[EN] In the last ten years, one of the most significant technological developments that will lead to the new broadband wireless generation is the communication via Multiple-Input Multiple-Output (MIMO) systems. MIMO systems are known to provide an increase of the maximum rate, reliability and coverage of current wireless communications. Maximum-Likelihood (detection over Gaussian MIMO channels is shown to get the lowest Bit Error Rate for a given scenario. However, it has a prohibitive complexity which grows exponentially with the number of transmit antennas and the size of the constellation. Motivated by this, there is a continuous search for computationally efficient optimal or suboptimal detectors. In this work, we carry out an state of the art review of detection algorithms and propose the combination of a suboptimal MIMO detector called K-Best Sphere Decoder with a channel matrix condition number estimator to obtain a versatile combined detector with predictable performance and suitable for hardware implementation. The effect of the channel matrix condition number in data detection is exploited in order to achieve a decoding complexity lower than the one of already proposed algorithms with similar performance. Some practical algorithms for finding the 2-norm condition number of a given channel matrix and for performing the threshold selection are also presented and their computational costs and accuracy are discussed[ES] Uno de los desarrollos tecnol'ogicos m'as significativos de la ' ultima d'ecada que llevar'an a la nueva generaci'on de banda ancha en movilidad es la comunicaci'on mediante sistemas de m' ultiples entradas y m' ultiples salidas (MIMO). Los sistemas MIMO proporcionan un notable incremento en la capacidad, fiabilidad y cobertura de las comunicaciones inal'ambricas actuales. Se puede demostrar que la detecci'on 'optima o dem'axima verosimilitud (ML) en canales MIMO Gaussianos proporciona la m'¿nima tasa de error de bit (BER) para un escenario dado pero tiene el inconveniente de que su complejidad crece exponencialmente con el n'umero de antenas y el tama¿no de la constelaci'on utilizada. Por este motivo, hay una cont'¿nua b' usqueda de detectores 'optimos o sub'optimos que sean m'as eficientes computacionalmente. En este trabajo, se ha llevado a cabo una revisi 'on del estado del arte de los principales algoritmos de detecci'on para sistemas MIMO y se ha propuesto la combinaci'on de un detector MIMO sub'optimo conocido como K-Best Sphere Decoder con un estimador del n'umero de condici'on de la matriz de canal, para conseguir un detector combinado basado en umbral con complejidad predecible y adecuado para implementaci'on en hardware. Se ha explotado el efecto del n'umero de condici'on en la detecci'on de datos para disminuir la complejidad de los algoritmos de detecci 'on existentes sin apenas alterar sus prestaciones. Por ' ultimo tambi'en se presentan distintos algoritmos pr'acticos para encontrar el dos n'umero de condici'on as'¿ como para realizar la selecci 'on del umbral.Roger Varea, S. (2008). Efficient detection algorithms for Multiple-Input Multiple-Output (MIMO) systems. http://hdl.handle.net/10251/12200Archivo delegad

Implementation aspects of list sphere decoder algorithms for MIMO-OFDM systems

A list sphere decoder (LSD) can be used to approximate the optimal maximum a posteriori (MAP) detector for the detection of multiple-input multiple-output (MIMO) signals. In this paper, we consider two LSD algorithms with different search methods and study some algorithm design choices which relate to the performance and computational complexity of the algorithm. We show that by limiting the dynamic range of log-likelihood ratio, the required LSD list size can be lowered, and, thus, the complexity of the LSD algorithm is decreased. We compare the real and the complex-valued signal models and their impact on the complexity of the algorithms. We show that the real-valued signal model is clearly the less complex choice and a better alternative for implementation. We also show the complexity of the sequential search LSD algorithm can be reduced by limiting the maximum number of checked nodes without sacrificing the performance of the system. Finally, we study the complexity and performance of an iterative receiver, analyze the tradeoff choices between complexity and performance, and show that the additional computational cost in LSD is justified to get better soft-output approximation.TekesFinnish Funding Agency for Technology and InnovationNokiaNokia Siemens Networks (NSN)ElekrobitUninor

Design and Implementation of Efficient Algorithms for Wireless MIMO Communication Systems

En la última década, uno de los avances tecnológicos más importantes que han hecho culminar la nueva generación de banda ancha inalámbrica es la comunicación mediante sistemas de múltiples entradas y múltiples salidas (MIMO). Las tecnologías MIMO han sido adoptadas por muchos estándares inalámbricos tales como LTE, WiMAS y WLAN. Esto se debe principalmente a su capacidad de aumentar la máxima velocidad de transmisión , junto con la fiabilidad alcanzada y la cobertura de las comunicaciones inalámbricas actuales sin la necesidad de ancho de banda extra ni de potencia de transmisión adicional. Sin embargo, las ventajas proporcionadas por los sistemas MIMO se producen a expensas de un aumento sustancial del coste de implementación de múltiples antenas y de la complejidad del receptor, la cual tiene un gran impacto sobre el consumo de energía. Por esta razón, el diseño de receptores de baja complejidad es un tema importante que se abordará a lo largo de esta tesis. En primer lugar, se investiga el uso de técnicas de preprocesado de la matriz de canal MIMO bien para disminuir el coste computacional de decodificadores óptimos o bien para mejorar las prestaciones de detectores subóptimos lineales, SIC o de búsqueda en árbol. Se presenta una descripción detallada de dos técnicas de preprocesado ampliamente utilizadas: el método de Lenstra, Lenstra, Lovasz (LLL) para lattice reduction (LR) y el algorimo VBLAST ZF-DFE. Tanto la complejidad como las prestaciones de ambos métodos se han evaluado y comparado entre sí. Además, se propone una implementación de bajo coste del algoritmo VBLAST ZF-DFE, la cual se incluye en la evaluación. En segundo lugar, se ha desarrollado un detector MIMO basado en búsqueda en árbol de baja complejidad, denominado detector K-Best de amplitud variable (VB K-Best). La idea principal de este método es aprovechar el impacto del número de condición de la matriz de canal sobre la detección de datos con el fin de disminuir la complejidad de los sistemasRoger Varea, S. (2012). Design and Implementation of Efficient Algorithms for Wireless MIMO Communication Systems [Tesis doctoral no publicada]. Universitat Politècnica de València. https://doi.org/10.4995/Thesis/10251/16562Palanci