In mobile communications, using multiple transmit and receive antennas has shown considerable improvement over single antenna systems. The performance increase can be characterized by more reliable throughput obtained through diversity and the higher achievable data rate through spatial multiplexing. The combination of multiple-input multiple-output (MIMO) wireless technology with the IEEE 802.16e-2005 (WiMAX) standard has been recognized as one of the most promising technologies with the advent of next generation broadband wireless communications. The dissertation introduces a performance evaluation of modern multi-antenna coding techniques on a MIMO-WiMAX platform developed to be capable of simulating space-selective, time-selective and frequency-selective fading conditions, which are known as triply-selective fading conditions. A new concatenated space-time-frequency low-density parity check (LDPC) code is proposed for high performance MIMO systems, where it is shown that the newly defined coding technique outperforms a more conventional approach by concatenating space-time blocks with LDPC codes. The analysis of the coding techniques in realistic mobile environments, as well as the proposed STFC-LDPC code, can form a set of newly defined codes, complementing the current coding schemes defined in the WiMAX standard. / Dissertation (MEng)--University of Pretoria, 2009. / Electrical, Electronic and Computer Engineering / unrestricted

The aim of the dissertation was to design a realistic, low-complexity non-binary (NB) low density parity check (LDPC) coded space-time-frequency (STF) coded multiple-input multiple-output (MIMO) orthogonal frequency division multiplexing (OFDM) system with an iterative joint decoder and detector structure at the receiver. The goal of the first part of the dissertation was to compare the performance of different design procedures for NB-LDPC codes on an additive white Gaussian noise (AWGN) channel, taking into account the constraint on the code length. The effect of quantisation on the performance of the code was also analysed. Different methods for choosing the NB elements in the parity check matrix were compared. For the STF coding, a class of universal STF codes was used. These codes use linear pre-coding and a layering approach based on Diophantine numbers to achieve full diversity and a transmission rate (in symbols per channel use per frequency) equal to the number of transmitter antennas. The study of the system considers a comparative performance analysis of di erent ST, SF and STF codes. The simulations of the system were performed on a triply selective block fading channel. Thus, there was selectivity in the fading over time, space and frequency. The effect of quantisation at the receiver on the achievable diversity of linearly pre-coded systems (such as the STF codes used) was mathematically derived and verified with simulations. A sphere decoder (SD) was used as a MIMO detector. The standard method used to create a soft-input soft output (SISO) SD uses a hard-to-soft process and the max-log-map approximation. A new approach was developed which combines a Hopfield network with the SD. This SD-Hopfield detector was connected with the fast Fourier transform belief propagation (FFT-BP) algorithm in an iterative structure. This iterative system was able to achieve the same bit error rate (BER) performance as the original SISO-SD at a reduced complexity. The use of the iterative Hopfield-SD and FFT-BP decoder system also allows performance to be traded off for complexity by varying the number of decoding iterations. The complete system employs a NB-LDPC code concatenated with an STF code at the transmitter with a SISO-SD and FFT-BP decoder connected in an iterative structure at the receiver. The system was analysed in varying channel conditions taking into account the effect of correlation and quantisation. The performance of different SF and STF codes were compared and analysed in the system. An analysis comparing different numbers of FFT-BP and outer iterations was also done. AFRIKAANS : Die doel van die verhandeling was om ’n realistiese, lae-kompleksiteit nie-binˆere (NB) LDPC gekodeerde ruimte-tyd-frekwensie-gekodeerde MIMO-OFDM-sisteem met iteratiewe gesamentlike dekodeerder- en detektorstrukture by die ontvanger te ontwerp. Die eerstem deel van die verhandeling was om die werkverrigting van verskillende ontwerpprosedures vir NB-LDPC kodes op ’n gesommeerde wit Gausruiskanaal te vergelyk met inagneming van die beperking op die lengte van die kode. Verskillende metodes om die nie-bineêre elemente in die pariteitstoetsmatriks te kies, is gebruik. Vir die ruimte-tyd-frekwensiekodering is ’n klas universele ruimte-tyd-frekwensiekodes gebruik. Hierdie kodes gebruik lineêre pre-kodering en ’n laagbenadering gebaseer op Diofantiese syfers om volle diversiteit te bereik en ’n oordragtempo (in simbole per kanaalgebruik per frekwensie) gelyk aan die aantal senderantennes. Die studie van die sisteem oorweeg ’n vergelykende werkverrigtinganalisie van verskillende ruimte-tyd-, ruimte-freksensie- en ruimte-tyd-frekwensiekodes. Die simulasies van die sisteem is gedoen op ’n drievoudig selektiewe blokwegsterwingskanaal. Daar was dus selektiwiteit in die wegsterwing oor tyd, ruimte en frekwensie. Die effek van kwantisering by die ontvanger op die bereikbare diversiteit van lineêr pre-gekodeerde sisteme (soos die ruimte-tyd-frekwensiekodes wat gebruik is) is matematies afgelei en bevestig deur simulasies. ’n Sfeerdekodeerder (SD) is gebruik as ’n MIMO-detektor. Die standaardmetode wat gebuik is om ’n sagte-inset-sagte-uitset (SISO) SD te skep, gebruik ’n harde-na-sagte proses en die maksimum logaritmiese afbeelding-benadering. ’n Nuwe benadering wat ’n Hopfield-netwerk met die SD kombineer, is ontwikkel. Hierdie SD-Hopfield-detektor is verbind met die FFT-BP-algoritme in iteratiewe strukture. Hierdie iteratiewe sisteem was in staat om dieselfde bisfouttempo te bereik as die oorspronklike SISO-SD, met laer kompleksiteit. Die gebruik van die iteratiewe Hopfield-SD en FFT-BP-dekodeerdersisteem maak ook daarvoor voorsiening dat werkverrigting opgeweeg kan word teen kompleksiteit deur die aantal dekodering-iterasies te varieer. Die volledige sisteem maak gebruik van ’n QC-NB-LDPC-kode wat met ’n ruimte-tyd-frekwensiekode by die sender aaneengeskakel is met ’n SISO-SD en FFT-BP-dekodeerder wat in ’n iteratiewe struktuur by die ontvanger gekoppel is. Die sisteem is onder ’n verskeidenheid kanaalkondisies ge-analiseer met inagneming van die effek van korrelasie en kwantisering. Die werkverrigting van verskillende ruimte-frekwensie- en ruimte-tyd-frekwensiekodes is vergelyk en in die sisteem ge-analiseer. ’n Analise om ’n wisselende aantal FFT-BP en buite-iterasies te vergelyk, is ook gedoen. Copyright / Dissertation (MEng)--University of Pretoria, 2010. / Electrical, Electronic and Computer Engineering / unrestricted

This work deals with the design of MT transmit, MR receive antenna MIMO (Multiple Input Multiple Output) communication system where the transmitter performs a linear operation on data. This linear precoding model includes systems which involve signal shaping for achieving higher data rates, uncoded MIMO Multicarrier and Single-Carrier systems and, the more recent, MIMO-OFDM (Orthogonal Frequency Division Multiplexing) systems employing full diversity Space-Frequency codes. The objective of this work is to design diversity centric and rate centric linear precoded MIMO systems whose performance is better than the existing designs. In particular, we consider MIMO-OFDM systems, Zero Padded MIMO systems and MIMO systems with limited rate feedback. Design of full diversity MIMO-OFDM systems of rate symbol per channel use (1 s/ pcu) : In literature, MIMO-OFDM systems exploiting full diversity at a rate of 1 s/ pcu are based on a few specific Space-Frequency (SF)/ Space-Time-Frequency (STF) codes. In this work, we devise a general parameterized framework for the design of MIMO-OFDM systems employing full diversity STF codes of rate 1 s/ pcu. This framework unifies all existing designs and provides tools for the design of new systems with interesting properties and superior performance. Apart from rate and diversity, the parameters of the framework are designed for a low complexity receiver. The parameters of the framework usually depend on the channel characteristics (number of multipath, Delay Profile (DP)). When channel characteristics are available at the transmitter, a procedure to optimize the performance of STF codes is provided. The resulting codes are termed as DP optimized codes. Designs obtained using the optimization are illustrated and their performance is shown to be better than the existing ones. To cater to the scenarios where channel characteristics are not available at the transmitter, a complete characterization of a class of full diversity DP Independent (DPI) STF codes is provided. These codes exploit full diversity on channels with a given number of multipath irrespective of their characteristics. Design of DP optimized STF codes and DPI codes from the same framework highlights the flexibility of the framework. Design of Zero Padded (ZP) MIMO systems : While the MIMO-OFDM transmitter needs to precode data for exploiting channel induced multipath diversity, ZP MIMO systems with ML receivers are shown to exploit multipath diversity without any precoding. However, the receiver complexity of such systems is enormous and hence a study ZP MIMO system with linear receivers is undertaken. Central to this study involves devising low complexity receivers and deriving the diversity gain of linear receivers. Reduced complexity receiver implementations are presented for two classes of precoding schemes. An upper bound on the diversity gain of linear receivers is evaluated for certain precoding schemes. For uncoded systems operating on a channel of length L, this bound is shown to be MRL_MT +1 for uncoded transmissions, i.e, such systems tend to exploit receiver and multipath diversities. On the other hand, MIMO-OFDM systems designed earlier have to trade diversity with receiver complexity. These observations motivate us to use ZP MIMO systems with linear receivers for channels with large delay spread when receiver complexity is at a premium. Design examples highlighting the attractiveness of ZP systems when employed on channels with large delay spread are also presented. Efficient design of MIMO systems with limited feedback : Literature presents a number of works that consider the design of MIMO systems with partial feedback. The works that consider feedback of complete CSI, however, do not provide for an efficient system design. In this work, we consider two schemes, Correlation matrix feedback and Channel information feedback that convey complete CSI to the transmitter. This CSI is perturbed due to various impairments. A perturbation analysis is carried out to study the variations in mutual information for each of the proposed schemes. For ergodic channels, this analysis is used to design a MIMO system with a limited rate feedback. Using a codebook based approach, vector quantizers are designed to minimize the loss in ergodic capacity for each of the proposed schemes. The efficiency of the design stems from the ability to obtain closed-form expression for centroids during the iterative vector quantizer design. The performance of designed vector quantizers compare favorably with the existing designs. The vector quantizer design for channel information feedback is robust in the sense that the same codebook can be used across all operating SNR. Use of vector quantizers for improving the outage performance is also presented.