Cyclic division algebras: a tool for space-time coding

Multiple antennas at both the transmitter and receiver ends of a wireless digital transmission channel may increase both data rate and reliability. Reliable high rate transmission over such channels can only be achieved through Space–Time coding. Rank and determinant code design criteria have been proposed to enhance diversity and coding gain. The special case of full-diversity criterion requires that the difference of any two distinct codewords has full rank. Extensive work has been done on Space–Time coding, aiming at finding fully diverse codes with high rate. Division algebras have been proposed as a new tool for constructing Space–Time codes, since they are non-commutative algebras that naturally yield linear fully diverse codes. Their algebraic properties can thus be further exploited to improve the design of good codes. The aim of this work is to provide a tutorial introduction to the algebraic tools involved in the design of codes based on cyclic division algebras. The different design criteria involved will be illustrated, including the constellation shaping, the information lossless property, the non-vanishing determinant property, and the diversity multiplexing trade-off. The final target is to give the complete mathematical background underlying the construction of the Golden code and the other Perfect Space–Time block codes

A robust maximin approach for MIMO communications with imperfect channel state information based on convex optimization

This paper considers a wireless communication system with multiple transmit and receive antennas, i.e., a multiple-input-multiple-output (MIMO) channel. The objective is to design the transmitter according to an imperfect channel estimate, where the errors are explicitly taken into account to obtain a robust design under the maximin or worst case philosophy. The robust transmission scheme is composed of an orthogonal space–time block code (OSTBC), whose outputs are transmitted through the eigenmodes of the channel estimate with an appropriate power allocation among them. At the receiver, the signal is detected assuming a perfect channel knowledge. The optimization problem corresponding to the design of the power allocation among the estimated eigenmodes, whose goal is the maximization of the signal-to-noise ratio (SNR), is transformed to a simple convex problem that can be easily solved. Different sources of errors are considered in the channel estimate, such as the Gaussian noise from the estimation process and the errors from the quantization of the channel estimate, among others. For the case of Gaussian noise, the robust power allocation admits a closed-form expression. Finally, the benefits of the proposed design are evaluated and compared with the pure OSTBC and nonrobust approaches.Postprint (published version

Order-Theoretic Methods for Space-Time Coding: Symmetric and Asymmetric Designs

Siirretty Doriast

Feedback of channel state information in multi-antenna systems based on quantization of channel Gram matrices

This dissertation deals with the proper design of efficient feedback strategies for Multiple-Input Multiple-Output (MIMO) communication systems. MIMO systems outperform single antenna systems in terms of achievable throughput and are more resilient to noise and interference, which are becoming the limiting factors in the current and future communications. Apart from the clear performance advantages, MIMO systems introduce an additional complexity factor, since they require knowledge of the propagation channel in order to be able to adapt the transmission to the propagation channel’s characteristics and achieve optimum performance. This channel knowledge, also known as Channel State Information (CSI), is estimated at the receiver and sent to the transmitter through a limited feedback link. In this dissertation, first, the minimum channel information necessary at the transmitter for the optimum precoding design is identified. This minimum information for the optimum design of the system corresponds to the channel Gram matrix. It is essential for the design of optimized systems to avoid the transmission of redundant feedback information. Following this idea, a quantization algorithm that exploits the differential geometry of the set of Gram matrices and the correlation in time present in most propagation channels is developed in order to greatly improve the feedback performance. This scheme is applied first to single-user MIMO communications, then to some particular multiuser scenarios, and finally it is extended to general multiuser broadcast communications. To conclude, the feedback link sizing is studied. An analysis of the tradeoff between size of the forward link and size of the feedback link isformulated and the radio resource allocation problem, in terms of transmission energy, time, and bandwidth of the forward and feedback links is presented.En un mundo cada vez más interconectado, donde hay una clara tendencia hacia un mayor número de comunicaciones inalámbricas simultáneas (comunicaciones M2M: Machine to Machine, redes de sensores, etc.) y en el que las necesidades de capacidad de transmisión de los enlaces de comunicaciones aumentan de manera vertiginosa (audio, video, contenidos multimedia, alta definición, etc.) el problema de la interferencia se convierte en uno de los factores limitadores de los enlaces junto con los desvanecimientos del nivel de señal y las pérdidas de propagación. Por este motivo los sistemas que emplean múltiples antenas tanto en la transmisión como en la recepción (los llamados sistemas MIMO: Multiple-Input Multiple-Output) se presentan como una de las soluciones más interesantes para satisfacer los crecientes requisitos de capacidad y comportamiento relativo a interferencias. Los sistemas MIMO permiten obtener un mejor rendimiento en términos de tasa de transmisión de información y a su vez son más robustos frente a ruido e interferencias en el canal. Esto significa que pueden usarse para aumentar la capacidad de los enlaces de comunicaciones actuales o para reducir drásticamente el consumo energético manteniendo las mismas prestaciones. Por otro lado, además de estas claras ventajas, los sistemas MIMO introducen un punto de complejidad adicional puesto que para aprovechar al máximo las posibilidades de estos sistemas es necesario tener conocimiento de la información de estado del canal (CSI: Channel State Information) tanto en el transmisor como en el receptor. Esta CSI se obtiene mediante estimación de canal en el receptor y posteriormente se envía al transmisor a través de un canal de realimentación. Esta tesis trata sobre el diseño del canal de realimentación para la transmisión de CSI, que es un elemento fundamental de los sistemas de comunicaciones del presente y del futuro. Las técnicas de transmisión que consideran activamente el efecto de la interferencia y el ruido requieren adaptarse al canal y, para ello, la realimentación de CSI es necesaria. En esta tesis se identifica, en primer lugar, la mínima información sobre el estado del canal necesaria para implementar un diseño óptimo en el transmisor, con el fin de evitar transmitir información redundante y obtener así un sistema más eficiente. Esta información es la matriz de Gram del canal MIMO. Seguidamente, se desarrolla un algoritmo de cuantificación adaptado a la geometría diferencial del conjunto que contiene la información a cuantificar y que además aprovecha la correlación temporal existente en los canales de propagación inalámbricos. Este algoritmo se implementa y evalúa primero en comunicaciones MIMO punto a punto entre dos usuarios, después se implementa para algunos casos particulares con múltiples usuarios, y finalmente se amplía para el caso general de sistemas broadcast multi-usuario. Adicionalmente, esta tesis también estudia y optimiza el dimensionamiento del canal de realimentación en función de la cantidad de recursos radio disponibles, en términos de ancho de banda, tiempo y potencia de transmisión. Para ello presenta el problema de la distribución óptima de dichos recursos radio entre el enlace de transmisión de datos y el enlace de realimentación para transmisión de información sobre estado del canal como un problema de optimización

Explicit Space-Time Codes Achieving The Diversity-Multiplexing Gain Tradeoff

A recent result of Zheng and Tse states that over a quasi-static channel, there exists a fundamental tradeoff, referred to as the diversity-multiplexing gain (D-MG) tradeoff, between the spatial multiplexing gain and the diversity gain that can be simultaneously achieved by a space-time (ST) block code. This tradeoff is precisely known in the case of i.i.d. Rayleigh-fading, for T>= n_t+n_r-1 where T is the number of time slots over which coding takes place and n_t,n_r are the number of transmit and receive antennas respectively. For T < n_t+n_r-1, only upper and lower bounds on the D-MG tradeoff are available. In this paper, we present a complete solution to the problem of explicitly constructing D-MG optimal ST codes, i.e., codes that achieve the D-MG tradeoff for any number of receive antennas. We do this by showing that for the square minimum-delay case when T=n_t=n, cyclic-division-algebra (CDA) based ST codes having the non-vanishing determinant property are D-MG optimal. While constructions of such codes were previously known for restricted values of n, we provide here a construction for such codes that is valid for all n. For the rectangular, T > n_t case, we present two general techniques for building D-MG-optimal rectangular ST codes from their square counterparts. A byproduct of our results establishes that the D-MG tradeoff for all T>= n_t is the same as that previously known to hold for T >= n_t + n_r -1.Comment: Revised submission to IEEE Transactions on Information Theor