Orthogonal Designs and a Cubic Binary Function

Orthogonal designs are fundamental mathematical notions used in the construction of space time block codes for wireless transmissions. Designs have two important parameters, the rate and the decoding delay; the main problem of the theory is to construct designs maximizing the rate and minimizing the decoding delay. All known constructions of CODs are inductive or algorithmic. In this paper, we present an explicit construction of optimal CODs. We do not apply recurrent procedures and do calculate the matrix elements directly. Our formula is based on a cubic function in two binary n-vectors. In our previous work (Comm. Math. Phys., 2010, and J. Pure and Appl. Algebra, 2011), we used this function to define a series of non-associative algebras generalizing the classical algebra of octonions and to obtain sum of squares identities of Hurwitz-Radon type

Structure theorem of square complex orthogonal design

Square COD (complex orthogonal design) with size $[n, n, k]$ is an $n \times n$ matrix $\mathcal{O}_z$, where each entry is a complex linear combination of $z_i$ and their conjugations $z_i^*$, $i=1,\ldots, k$, such that $\mathcal{O}_z^H \mathcal{O}_z = (|z_1|^2 + \ldots + |z_k|^2)I_n$. Closely following the work of Hottinen and Tirkkonen, which proved an upper bound of $k/n$ by making a crucial observation between square COD and group representation, we prove the structure theorem of square COD

Distributed Quasi-Orthogonal Space-Time coding in wireless cooperative relay networks

Cooperative diversity provides a new paradigm in robust wireless re- lay networks that leverages Space-Time (ST) processing techniques to combat the effects of fading. Distributing the encoding over multiple relays that potentially observe uncorrelated channels to a destination terminal has demonstrated promising results in extending range, data- rates and transmit power utilization. Specifically, Space Time Block Codes (STBCs) based on orthogonal designs have proven extremely popular at exploiting spatial diversity through simple distributed pro- cessing without channel knowledge at the relaying terminals. This thesis aims at extending further the extensive design and analysis in relay networks based on orthogonal designs in the context of Quasi- Orthogonal Space Time Block Codes (QOSTBCs). The characterization of Quasi-Orthogonal MIMO channels for cooper- ative networks is performed under Ergodic and Non-Ergodic channel conditions. Specific to cooperative diversity, the sub-channels are as- sumed to observe different shadowing conditions as opposed to the traditional co-located communication system. Under Ergodic chan- nel assumptions novel closed-form solutions for cooperative channel capacity under the constraint of distributed-QOSTBC processing are presented. This analysis is extended to yield closed-form approx- imate expressions and their utility is verified through simulations. The effective use of partial feedback to orthogonalize the QOSTBC is examined and significant gains under specific channel conditions are demonstrated. Distributed systems cooperating over the network introduce chal- lenges in synchronization. Without extensive network management it is difficult to synchronize all the nodes participating in the relaying between source and destination terminals. Based on QOSTBC tech- niques simple encoding strategies are introduced that provide compa- rable throughput to schemes under synchronous conditions with neg- ligible overhead in processing throughout the protocol. Both mutli- carrier and single-carrier schemes are developed to enable the flexi- bility to limit Peak-to-Average-Power-Ratio (PAPR) and reduce the Radio Frequency (RF) requirements of the relaying terminals. The insights gained in asynchronous design in flat-fading cooperative channels are then extended to broadband networks over frequency- selective channels where the novel application of QOSTBCs are used in distributed-Space-Time-Frequency (STF) coding. Specifically, cod- ing schemes are presented that extract both spatial and mutli-path diversity offered by the cooperative Multiple-Input Multiple-Output (MIMO) channel. To provide maximum flexibility the proposed schemes are adapted to facilitate both Decode-and-Forward (DF) and Amplify- and-Forward (AF) relaying. In-depth Pairwise-Error-Probability (PEP) analysis provides distinct design specifications which tailor the distributed- STF code to maximize the diversity and coding gain offered under the DF and AF protocols. Numerical simulation are used extensively to confirm the validity of the proposed cooperative schemes. The analytical and numerical re- sults demonstrate the effective use of QOSTBC over orthogonal tech- niques in a wide range of channel conditions

Fast-Decodable Asymmetric Space-Time Codes from Division Algebras

Multiple-input double-output (MIDO) codes are important in the near-future wireless communications, where the portable end-user device is physically small and will typically contain at most two receive antennas. Especially tempting is the 4 x 2 channel due to its immediate applicability in the digital video broadcasting (DVB). Such channels optimally employ rate-two space-time (ST) codes consisting of (4 x 4) matrices. Unfortunately, such codes are in general very complex to decode, hence setting forth a call for constructions with reduced complexity. Recently, some reduced complexity constructions have been proposed, but they have mainly been based on different ad hoc methods and have resulted in isolated examples rather than in a more general class of codes. In this paper, it will be shown that a family of division algebra based MIDO codes will always result in at least 37.5% worst-case complexity reduction, while maintaining full diversity and, for the first time, the non-vanishing determinant (NVD) property. The reduction follows from the fact that, similarly to the Alamouti code, the codes will be subsets of matrix rings of the Hamiltonian quaternions, hence allowing simplified decoding. At the moment, such reductions are among the best known for rate-two MIDO codes. Several explicit constructions are presented and shown to have excellent performance through computer simulations.Comment: 26 pages, 1 figure, submitted to IEEE Trans. Inf. Theory, October 201

Técnicas de igualização adaptativas com estimativas imperfeitas do canal para os futuros sistemas 5G

Wireless communication networks have been continuously experiencing an exponential growth since their inception. The overwhelming demand for high data rates, support of a large number of users while mitigating disruptive interference are the constant research focus and it has led to the creation of new technologies and efficient techniques. Orthogonal frequency division multiplexing (OFDM) is the most common example of a technology that has come to the fore in this past decade as it provided a simple and generally ideal platform for wireless data transmission. It’s drawback of a rather high peak-to-average power ratio (PAPR) and sensitivity to phase noise, which in turn led to the adoption of alternative techniques, such as the single carrier systems with frequency domain equalization (SC-FDE) or the multi carrier systems with code division multiple access (MC-CDMA), but the nonlinear Frequency Domain Equalizers (FDE) have been of special note due to their improved performance. From these, the Iterative Block Decision Feedback Equalizer (IB-DFE) has proven itself especially promising due to its compatibility with space diversity, MIMO systems and CDMA schemes. However, the IB-DFE requires the system to have constant knowledge of the communication channel properties, that is, to have constantly perfect Channel State Information (CSI), which is both unrealistic and impractical to implement. In this dissertation we shall design an altered IB-DFE receiver that is able to properly detect signals from SC-FDMA based transmitters, even with constantly erroneous channel states. The results shall demonstrate that the proposed equalization scheme is robust to imperfect CSI (I-CSI) situations, since its performance is constantly close to the perfect CSI case, within just a few iterations.Redes sem fios têm crescido de maneira contínua e exponencial desde a sua incepção. A tremenda exigência para altas taxas de dados e o suporte para um elevado número de utilizadores sem aumentar a interferência disruptiva originada por estes são alguns dos focos que levaram ao desenvolvimento de técnicas de compensação e novas tecnologias. “Orthogonal frequency division multiplexing” (OFDM) é um dos exemplos de tecnologias que se destacaram nesta última década, visto ter fornecido uma plataforma para transmissão de dados sem-fio eficaz e simples. O seu maior problema é a alta “peak-to-average power ratio” (PAPR) e a sua sensibilidade a ruído de fase que deram motivo à adoção de técnicas alternativas, tais como os sistemas “single carrier” com “frequency domain equalization” (SC-FDE) ou os sistemas “multi-carrier” com “code division multiple access” (MC-CDMA), mas equalizadores não lineares no domínio de frequência têm sido alvo de especial atenção devido ao seu melhor desempenho. Destes, o “iterative block decision feedback equalizer” (IB-DFE) tem-se provado especialmente promissor devido à sua compatibilidade com técnicas de diversidade no espaço, sistemas MIMO e esquemas CDMA. No entanto, IB-DFE requer que o sistema tenha constante conhecimento das propriedades dos canais usados, ou seja, necessita de ter perfeito “channel state information” (CSI) constantemente, o que é tanto irrealista como impossível de implementar. Nesta dissertação iremos projetar um recetor IB-DFE alterado de forma a conseguir detetar sinais dum transmissor baseado em tecnologia SC-FDMA, mesmo com a informação de estado de canal errada. Os resultados irão então demonstrar que o novo esquema de equalização proposto é robusto para situações de CSI imperfeito (I-CSI), visto que o seu desempenho se mantém próximo dos valores esperados para CSI perfeito, em apenas algumas iterações.Mestrado em Engenharia Eletrónica e Telecomunicaçõe