Approved for public release, distribution is unlimited / This thesis investigates the simulation performance of multiple-input multiple-output (MIMO) systems utilizing Alamoutibased space-time block coding (STBC) technique. The MIMO communication systems using STBC technique employing both single- carrier modulation and orthogonal frequency division multiplexing (OFDM) are simulated in Matlab. The physical layer part of the IEEE 802.16a standard is used in constructing the simulated OFDM schemes. Stanford University Interim (SUI) channel models are selected for the wireless channel in the simulation process. The performance results of the simulated MIMO systems are compared to those of conventional single antenna systems. / Lieutenant Junior Grade, Turkish Navy

Multi-antenna wireless systems have become very popular due to their theoretically predicted higher spectral efficiencies and improved performance compared to single-antenna systems. Large-scale multiple-input multiple-output (MIMO) systems refer to wireless systems where communication terminals employ tens to hundreds of antennas to achieve in-creased spectral efficiencies/sum rates, reliability, and power efficiency. Large-scale multi-antenna systems are attractive to meet the increasing wireless data rate requirements, without compromising on the bandwidth. This thesis addresses key signal processing issues in large-scale MIMO systems. Specifically, the thesis investigates efficient algorithms for signal detection and channel estimation in large-scale MIMO systems. It also investigates ‘spatial modulation,’ a multi-antenna modulation scheme that can reduce the number of transmit radio frequency (RF) chains, without compromising much on the spectral efficiency. The work reported in this thesis is comprised of the following two parts: 1 investigation of low-complexity receiver algorithms based on Markov chain Monte Carlo (MCMC) technique, tabu search, and belief propagation for large-scale uplink multiuser MIMO systems, and 2 investigation of achievable rates and signal detection in generalized spatial modulation. 1. Receiver algorithms for large-scale multiuser MIMO systems on the uplink In this part of the thesis, we propose low-complexity algorithms based on MCMC techniques, Gaussian sampling based lattice decoding (GSLD), reactive tabu search (RTS), and factor graph based belief propagation (BP) for signal detection on the uplink in large-scale multiuser MIMO systems. We also propose an efficient channel estimation scheme based on Gaussian sampling. Markov chain Monte Carlo (MCMC) sampling: We propose a novel MCMC based detection algorithm, which achieves near-optimal performance in large dimensions at low complexities by the joint use of a mixed Gibbs sampling (MGS) strategy and a multiple restart strategy with an efficient restart criterion. The proposed mixed Gibbs sampling distribution is a weighted mixture of the target distribution and uniform distribution. The presence of the uniform component in the sampling distribution allows the algorithm to exit from local traps quickly and alleviate the stalling problem encountered in conventional Gibbs sampling. We present an analysis for the optimum choice of the mixing ratio. The analysis approach is to define an absorbing Markov chain and use its property regarding the expected number of iterations needed to reach the global minima for the first time. We also propose an MCMC based algorithm which exploits the sparsity in uplink multiuser MIMO transmissions, where not all users are active simultaneously. Gaussian sampling based lattice decoding: Next, we investigate the problem of searching the closest lattice point in large dimensional lattices and its use in signal detection in large-scale MIMO systems. Specifically, we propose a Gaussian sampling based lattice decoding (GSLD) algorithm. The novelty of this algorithm is that, instead of sampling from a discrete distribution as in Gibbs sampling, the algorithm iteratively generates samples from a continuous Gaussian distribution, whose parameters are obtained analytically. This makes the complexity of the proposed algorithm to be independent of the size of the modulation alpha-bet. Also, the algorithm is able to achieve near-optimal performance for different antenna and modulation alphabet settings at low complexities. Random restart reactive tabu search (R3TS): Next, we study receiver algorithms based on reactive tabu search (RTS) technique in large-scale MIMO systems. We propose a multiple random restarts based reactive tabu search (R3TS) algorithm that achieves near-optimal performance in large-scale MIMO systems. A key feature of the proposed R3TS algorithm is its performance based restart criterion, which gives very good performance-complexity tradeoff in large-dimension systems. Lower bound on maximum likelihood (ML) bit error rate (BER) performance: We propose an approach to obtain lower bounds on the ML performance of large-scale MIMO systems using RTS simulation. In the proposed approach, we run the RTS algorithm using the transmitted vector as the initial vector, along with a suitable neighborhood definition, and find a lower bound on number of errors in ML solution. We demonstrate that the proposed bound is tight (within about 0.5 dB of the optimal performance in a 16×16MIMO system) at moderate to high SNRs. Factor graph using Gaussian approximation of interference (FG-GAI): Multiuser MIMO channels can be represented by graphical models that are fully/densely connected (loopy graphs), where conventional belief propagation yields suboptimal performance and requires high complexity. We propose a solution to this problem that uses a simple, yet effective, Gaussian approximation of interference (GAI) approach that carries out a linear per-symbol complexity message passing on a factor graph (FG) based graphical model. The proposed algorithm achieves near-optimal performance in large dimensions in frequency-flat as well as frequency-selective channels. Gaussian sampling based channel estimation: Next, we propose a Gaussian sampling based channel estimation technique for large-scale time-division duplex (TDD) MIMO systems. The proposed algorithm refines the initial estimate of the channel by iteratively detecting the data block and using that knowledge to improve the estimated channel knowledge using a Gaussian sampling based technique. We demonstrate that this algorithm achieves near-optimal performance both in terms of mean square error of the channel estimates and BER of detected data in both frequency-flat and frequency-selective channels. 2. Generalized spatial modulation In the second part of the thesis, we investigate generalized spatial modulation (GSM) in point-to point MIMO systems. GSM is attractive because of its ability to work with less number of transmit RF chains compared to traditional spatial multiplexing, without com-promising much on spectral efficiency. In this work, we show that, by using an optimum combination of number of transmit antennas and number of transmit RF chains, GSM can achieve better throughput and/or BER than spatial multiplexing. We compute tight bounds on the maximum achievable rate in a GSM system, and quantify the percentage savings in the number of transmit RF chains as well as the percentage increase in the rate achieved in GSM compared to spatial multiplexing. We also propose a Gibbs sampling based algorithm suited to detect GSM signals, which yields impressive BER performance and complexity results.

Communication over a wireless channel is a challenging task because of the inherent fading effects. Any wireless communication system employs some form of diversity improving techniques in order to improve the reliability of the channel. This thesis deals with efficient code design for two different spatial diversity techniques, viz, diversity by employing multiple antennas at the transmitter and/or the receiver, and diversity through cooperative commu- nication between users. In other words, this thesis deals with efficient code design for (1) multiple-input multiple-output (MIMO) channels, and (2) wireless relay channels. Codes for the MIMO channel are termed space-time (ST) codes and those for the relay channels are called distributed ST codes. The first part of the thesis focuses on ST code construction for MIMO fading channel with perfect channel state information (CSI) at the receiver, and no CSI at the transmitter. As a measure of performance we use the rate-diversity tradeoff and the Diversity-Multiplexing Gain (D-MG) Tradeoff, which are two different tradeoffs characterizing the tradeoff between the rate and the reliability achievable by any ST code. We provide two types of code constructions that are optimal with respect to the rate-diversity tradeoff; one is based on the rank-distance codes which are traditionally applied as codes for storage devices, and the second construction is based on a matrix representation of a cayley algebra. The second contribution in ST code constructions is related to codes with a certain nonvanishing determinant (NVD) property. Motivation for these constructions is a recent result on the necessary and sufficient conditions for an ST code to achieve the D-MG tradeoff. Explicit code constructions satisfying these conditions are provided for certain number of transmit antennas. The second part of the thesis focuses on distributed ST code construction for wireless relay channel. The transmission protocol follows a two-hop model wherein the source broadcasts a vector in the first hop and in the second hop the relays transmit a vector that is a transformation of the received vector by a relay-specific unitary transformation. While the source and relays do not have CSI, at the destination we assume two different scenarios (a) destina- tion with complete CSI (b) destination with only the relay-destination CSI. For both these scenarios, we derive a Chernoff bound on the pair-wise error probability and propose code design criteria. For the first case, we provide explicit construction of distributed ST codes with lower decoding complexity compared to codes based on some earlier system models. For the latter case, we propose a novel differential encoding and differential decoding technique and also provide explicit code constructions. At the heart of all these constructions is the cyclic division algebra (CDA) and its matrix representations. We translate the problem of code construction in each of the above scenarios to the problem of constructing CDAs satisfying certain properties. Explicit examples are provided to illustrate each of these constructions.

Space-Time Block Coding is an efficient communication technique used in multiple-input multiple-output wireless systems. The complexity with which a Space-Time Block Code (STBC) can be decoded is important from an implementation point of view since it directly affects the receiver complexity and speed. In this thesis, we address the problem of designing low complexity decoding techniques for STBCs, and constructing STBCs that achieve high rate and full-diversity with these decoders. This thesis is divided into two parts; the first is concerned with the optimal decoder, viz. the maximum-likelihood (ML) decoder, and the second with non-ML decoders. An STBC is said to be multigroup ML decodable if the information symbols encoded by it can be partitioned into several groups such that each symbol group can be ML decoded independently of the others, and thereby admitting low complexity ML decoding. In this thesis, we first give a new framework for constructing low ML decoding complexity STBCs using codes over the Klein group, and show that almost all known low ML decoding complexity STBCs can be obtained by this method. Using this framework we then construct new full-diversity STBCs that have the least known ML decoding complexity for a large set of choices of number of transmit antennas and rate. We then introduce the notion of Asymptotically-Good (AG) multigroup ML decodable codes, which are families of multigroup ML decodable codes whose rate increases linearly with the number of transmit antennas. We give constructions for full-diversity AG multigroup ML decodable codes for each number of groups g > 1. For g > 2, these are the first instances of g-group ML decodable codes that are AG or have rate more than 1. For g = 2 and identical delay, the new codes match the known families of AG codes in terms of rate. In the final section of the first part we show that the upper triangular matrix R encountered during the sphere-decoding of STBCs can be rank-deficient, thus leading to higher sphere-decoding complexity, even when the rate is less than the minimum of the number of transmit antennas and the number receive antennas. We show that all known AG multigroup ML decodable codes suffer from such rank-deficiency, and we explicitly derive the sphere-decoding complexities of most known AG multigroup ML decodable codes. In the second part of this thesis we first study a low complexity non-ML decoder introduced by Guo and Xia called Partial Interference Cancellation (PIC) decoder. We give a new full-diversity criterion for PIC decoding of STBCs which is equivalent to the criterion of Guo and Xia, and is easier to check. We then show that Distributed STBCs (DSTBCs) used in wireless relay networks can be full-diversity PIC decoded, and we give a full-diversity criterion for the same. We then construct full-diversity PIC decodable STBCs and DSTBCs which give higher rate and better error performance than known multigroup ML decodable codes for similar decoding complexity, and which include other known full-diversity PIC decodable codes as special cases. Finally, inspired by a low complexity essentially-ML decoder given by Sirianunpiboon et al. for the two and three antenna Perfect codes, we introduce a new non-ML decoder called Adaptive Conditional Zero-Forcing (ACZF) decoder which includes the technique of Sirianunpiboon et al. as a special case. We give a full-diversity criterion for ACZF decoding, and show that the Perfect codes for two, three and four antennas, the Threaded Algebraic Space-Time code, and the 4 antenna rate 2 code of Srinath and Rajan satisfy this criterion. Simulation results show that the proposed decoder performs identical to ML decoding for these five codes. These STBCs along with ACZF decoding have the best error performance with least complexity among all known STBCs for four or less transmit antennas.