<p> A multiple-input multiple-output (MIMO) communication system has the potential to provide reliable transmissions at high data rates. However, the computational cost of achieving this promising performance can be quite substantial. With an emphasis on practical implementations, the MIMO systems employing the low cost linear receivers are studied in this thesis. The optimum space-time block codes (STBC) that enable a linear receiver to achieve its best possible performance are proposed for various MIMO systems. These codes satisfy an intra and inter orthogonality property, and are called unitary trace-orthogonal codes. In addition, several novel transmission schemes are specially designed for linear receivers with the use of the proposed code structure. The applications of the unitary trace-orthogonal code are not restricted to systems employing linear receivers. The proposed code structure can be also applied to the systems employing other types of receivers where several originally intractable code design problems are successfully solved.</p> <p>The communication schemes presented in this thesis are outlined as follows: •For a MIMO system with N ≥ M, where M and N are the number of transmitter and receiver antennas, respectively, the optimal full rate linear STBC for linear receivers is proposed and named unitary trace-orthogonal code. The proposed code structure is proved to be necessary and sufficient to achieve the minimum detection error probability for the system. • When applied to a multiple input single output (MISO) communication system, a special linear unitary trace-orthogonal code, named the Toeplitz STBC, is proposed. The code enables a linear receiver to provide full diversity and to achieve the optimal tradeoff between the detection error and the data transmission rate. This is, thus far, the first code that possesses such properties for an arbitrary MISO system that employs a linear receiver. • In MIMO systems in which N ≥ M and the signals are transmitted at full symbol rate, the highest diversity gain achievable by linear receivers is analyzed and shown to be N - M + 1. To improve the performance of a linear receiver, a multi-block transmission scheme is proposed, in which signals are coded so that they span multiple independent channel realizations. An optimal full rate linear STBC for this system that minimizes the detection error probability is presented. The code is named multi-block unitary trace-orthogonal code. The resulting system has an improved diversity gain. Furthermore, by relaxing the code from the full symbol rate constraint, a special multi-block transmission scheme is proposed. This scheme achieves a much improved diversity gain than those with full symbol rate. • The unitary trace-orthogonal code can also be applied to a system that employs a maximum-likelihood (ML) receiver rather than the simple linear receiver. For such a system, a systematic design of full diversity unitary trace-orthogonal code is presented for an arbitrary data transmission rate. </p> <p>In summary, when a simple linear receiver is employed, unitary trace-orthogonal codes and their optimality properties are exploited for various multiple antenna communication systems. Some members from this code family can also enable an optimal performance of ML detection. </P> / Thesis / Doctor of Philosophy (PhD)

ITC/USA 2008 Conference Proceedings / The Forty-Fourth Annual International Telemetering Conference and Technical Exhibition / October 27-30, 2008 / Town and Country Resort & Convention Center, San Diego, California / Although multiple-input multiple-output (MIMO) systems have become increasingly popular, the existence of real time results to compare with those predicted by theory is still surprisingly limited. In this work the hardware description of a MIMO wireless communication system using orthogonal space time block codes (OSTBC) is discussed for two antennas at both the transmitter and receiver. A numerical example for a frequency flat time correlated channel is given to show the impact of channel estimation.

Recently, there has been a renewed interest in code based cryptosystems. Amongst the reasons for this interest is that they have shown to be resistant to quantum at- tacks, making them candidates for post-quantum cryptosystems. In fact, the National Institute of Standards and Technology is currently considering candidates for secure communication in the post-quantum era. Three of the proposals are code based cryp- tosystems. Other reasons for this renewed interest include e cient encryption and decryption. In this dissertation, new code based cryptosystems (symmetric key and public key) are presented that use high rate codes and have small key sizes. Hence they overcome the drawbacks of code based cryptosystems (low information rate and very large key size). The techniques used in designing these cryptosystems include random bit/block deletions, random bit insertions, random interleaving, and random bit ipping. An advantage of the proposed cryptosystems over other code based cryp- tosystems is that the code can be/is not secret. These cryptosystems are among the rst with this advantage. Having a public code eliminates the need for permutation and scrambling matrices. The absence of permutation and scrambling matrices results in a signi cant reduction in the key size. In fact, it is shown that with simple random bit ipping and interleaving the key size is comparable to well known symmetric key cryptosystems in use today such as Advanced Encryption Standard (AES). The security of the new cryptosystems are analysed. It is shown that they are immune against previously proposed attacks for code based cryptosystems. This is because scrambling or permutation matrices are not used and the random bit ipping is beyond the error correcting capability of the code. It is also shown that having a public code still provides a good level of security. This is proved in two ways, by nding the probability of an adversary being able to break the cryptosystem and showing that this probability is extremely small, and showing that the cryptosystem has indistinguishability against a chosen plaintext attack (i.e. is IND-CPA secure). IND-CPA security is among the primary necessities for a cryptosystem to be practical. This means that a ciphertext reveals no information about the corresponding plaintext other than its length. It is also shown that having a public code results in smaller key sizes. / Graduate

The modeling of the soft-output decoding of a binary linear block code using a Binary Phase Shift Keying (BPSK) modulation system (with reduced noise power) is the main focus of this work. With this model, it is possible to provide bit error performance approximations to help in the evaluation of the performance of binary linear block codes. As well, the model can be used in the design of communications systems which require knowledge of the characteristics of the channel, such as combined source-channel coding. Assuming an Additive White Gaussian Noise channel model, soft-output Log Likelihood Ratio (LLR) values are modeled to be Gaussian distributed. The bit error performance for a binary linear code over an AWGN channel can then be approximated using the Q-function that is used for BPSK systems. Simulation results are presented which show that the actual bit error performance of the code is very well approximated by the LLR approximation, especially for low signal-to-noise ratios (SNR). A new measure of the coding gain achievable through the use of a code is introduced by comparing the LLR variance to that of an equivalently scaled BPSK system. Furthermore, arguments are presented which show that the approximation requires fewer samples than conventional simulation methods to obtain the same confidence in the bit error probability value. This translates into fewer computations and therefore, less time is needed to obtain performance results. Other work was completed that uses a discrete Fourier Transform technique to calculate the weight distribution of a linear code. The weight distribution of a code is defined by the number of codewords which have a certain number of ones in the codewords. For codeword lengths of small to moderate size, this method is faster and provides an easily implementable and methodical approach over other methods. This technique has the added advantage over other techniques of being able to methodically calculate the number of codewords of a particular Hamming weight instead of calculating the entire weight distribution of the code.

The modeling of the soft-output decoding of a binary linear block code using a Binary Phase Shift Keying (BPSK) modulation system (with reduced noise power) is the main focus of this work. With this model, it is possible to provide bit error performance approximations to help in the evaluation of the performance of binary linear block codes. As well, the model can be used in the design of communications systems which require knowledge of the characteristics of the channel, such as combined source-channel coding. Assuming an Additive White Gaussian Noise channel model, soft-output Log Likelihood Ratio (LLR) values are modeled to be Gaussian distributed. The bit error performance for a binary linear code over an AWGN channel can then be approximated using the Q-function that is used for BPSK systems. Simulation results are presented which show that the actual bit error performance of the code is very well approximated by the LLR approximation, especially for low signal-to-noise ratios (SNR). A new measure of the coding gain achievable through the use of a code is introduced by comparing the LLR variance to that of an equivalently scaled BPSK system. Furthermore, arguments are presented which show that the approximation requires fewer samples than conventional simulation methods to obtain the same confidence in the bit error probability value. This translates into fewer computations and therefore, less time is needed to obtain performance results. Other work was completed that uses a discrete Fourier Transform technique to calculate the weight distribution of a linear code. The weight distribution of a code is defined by the number of codewords which have a certain number of ones in the codewords. For codeword lengths of small to moderate size, this method is faster and provides an easily implementable and methodical approach over other methods. This technique has the added advantage over other techniques of being able to methodically calculate the number of codewords of a particular Hamming weight instead of calculating the entire weight distribution of the code.

We introduced nested search methods to design (n, k) block codes for arbitrary channels by optimizing an appropriate metric spectrum in each iteration. For a given k, the methods start with a good high rate code, say k/(k + 1), and successively design lower rate codes up to rate k/2^k corresponding to a Hadamard code. Using a full search for small binary codes we found that optimal or near-optimal codes of increasing length can be obtained in a nested manner by utilizing Hadamard matrix columns. The codes can be linear if the Hadamard matrix is linear and non-linear otherwise. The design methodology was extended to the generic complex codes by utilizing columns of newly derived or existing unitary codes. The inherent nested nature of the codes make them ideal for progressive transmission. Extensive comparisons to metric bounds and to previously designed codes show the optimality or near-optimality of the new codes, designed for the fading and the additive white Gaussian noise channel (AWGN). It was also shown that linear codes can be optimal or at least meeting the metric bounds; one example is the systematic pilot-based code of rate k/(k + 1) which was proved to meet the lower bound on the maximum cross-correlation. Further, the method was generalized such that good codes for arbitrary channels can be designed given the corresponding metric or the pairwise error probability. In synchronous multiple-access schemes it is common to use unitary block codes to transmit the multiple users’ information, especially in the downlink. In this work we suggest the use of newly designed non-unitary block codes, resulting in increased throughput e&#64259;ciency, while the performance is shown not to be substantially sacri&#64257;ced. The non-unitary codes are again developed through suitable nested searches. In addition, new multiple-access codes are introduced that optimize certain criteria, such as the sum-rate capacity. Finally, the introduction of the asymptotically optimum convolutional codes for a given constraint length, reduces dramatically the search size for good convolutional codes of a certain asymptotic performance, and the consequences to coded code-division multiple access (CDMA) system design are highlighted.

Spatial diversity is an effective technique to combat the effects of severe fading in wireless environments. Recently, cooperative communications has emerged as an attractive communications paradigm that can introduce a new form of spatial diversity which is known as cooperative diversity, that can enhance system reliability without sacrificing the scarce bandwidth resource or consuming more transmit power. It enables single-antenna terminals in a wireless relay network to share their antennas to form a virtual antenna array on the basis of their distributed locations. As such, the same diversity gains as in multi-input multi-output systems can be achieved without requiring multiple-antenna terminals. In this thesis, a new approach to cooperative communications via distributed extended orthogonal space-time block coding (D-EO-STBC) based on limited partial feedback is proposed for cooperative relay networks with three and four relay nodes and then generalized for an arbitrary number of relay nodes. This scheme can achieve full cooperative diversity and full transmission rate in addition to array gain, and it has certain properties that make it alluring for practical systems such as orthogonality, flexibility, low computational complexity and decoding delay, and high robustness to node failure. Versions of the closed-loop D-EO-STBC scheme based on cooperative orthogonal frequency division multiplexing type transmission are also proposed for both flat and frequency-selective fading channels which can overcome imperfect synchronization in the network. As such, this proposed technique can effectively cope with the effects of fading and timing errors. Moreover, to increase the end-to-end data rate, this scheme is extended for two-way relay networks through a three-time slot framework. On the other hand, to substantially reduce the feedback channel overhead, limited feedback approaches based on parameter quantization are proposed. In particular, an optimal one-bit partial feedback approach is proposed for the generalized D-O-STBC scheme to maximize the array gain. To further enhance the end-to-end bit error rate performance of the cooperative relay system, a relay selection scheme based on D-EO-STBC is then proposed. Finally, to highlight the utility of the proposed D-EO-STBC scheme, an application to cognitive radio is studied.

In the past decade, cooperative communications has been emerging as a pertinent technology for the current and upcoming generations of mobile communication infrastructure. The indispensable benefits of this technology have motivated numerous studies from both academia and industry on this area. In particular, cooperative communications has been developed as a means of alleviating the effect of fading and hence improve the reliability of wireless communications. The key idea behind this technique is that communication between the source and destination can be assisted by several intermediate nodes, so-called relay nodes. As a result, cooperative communication networks can enhance the reliability of wireless communications where the transmitted signals are severely impaired because of fading. In addition, through relaying transmission, communication range can be extended and transmit power of each radio terminal can be reduced as well. The objective of this thesis is to analyze the system performance of cooperative relay networks integrating advanced radio transmission techniques and using the two major relaying protocols, i.e., decode-and-forward (DF) and amplify-and-forward (AF). In particular, the radio transmission techniques that are considered in this thesis include multiple-input multiple-output (MIMO) systems and orthogonal space-time block coding (OSTBC) transmission, adaptive transmission, beamforming transmission, coded cooperation, and cognitive radio transmission. The thesis is divided into an introduction section and six parts based on peer-reviewed journal articles and conference papers. The introduction provides the readers with some fundamental background on cooperative communications along with several key concepts of cognitive radio systems. In the first part, performance analysis of cooperative single and multiple relay networks using MIMO and OSTBC transmission is presented wherein the diversity gain, coding gain, outage probability, symbol error rate, and channel capacity are assessed. It is shown that integrating MIMO and OSTBC transmission into cooperative relay networks provides full diversity gain. In the second part, the performance benefits of MIMO relay networks with OSTBC and adaptive transmission strategies are investigated. In the third part, the performance improvement with respect to outage probability of coded cooperation applied to opportunistic DF relay networks over conventional cooperative networks is shown. In the fourth part, the effects of delay of channel state information feedback from the destination to the source and co-channel interference on system performance is analyzed for beamforming AF relay networks. In the fifth part, cooperative diversity is investigated in the context of an underlay cognitive AF relay network with beamforming. In the sixth part, finally, the impact of the interference power constraint on the system performance of multi-hop cognitive AF relay networks is investigated.

One of the facets of the mobile or wireless environment is that errors quite often occur in bursts. Thus, strong codes are required to provide protection against such errors. This in turn motivates the employment of decoding algorithms which are simple to implement, yet are still able to attempt to take the dependence or memory of the channel model into account in order to give optimal decoding estimates. Furthermore, such algorithms should be able to be applied for a variety of channel models and signalling alphabets. The research presented within this thesis describes a number of algorithms which can be used with linear block codes. Given the received word, these algorithms determine the symbol which was most likely transmitted, on a symbol-by-symbol basis. Due to their relative simplicity, a collection of algorithms for memoryless channels is reported first. This is done to establish the general style and principles of the overall collection. The concept of matrix diagonalisation may or may not be applied, resulting in two different types of procedure. Ultimately, it is shown that the choice between them should be motivated by whether storage space or computational complexity has the higher priority. As with all other procedures explained herein, the derivation is first performed for a binary signalling alphabet and then extended to fields of prime order. These procedures form the paradigm for algorithms used in conjunction with finite state channel models, where errors generally occur in bursts. In such cases, the necessary information is stored in matrices rather than as scalars. Finally, by analogy with the weight polynomials of a code and its dual as characterised by the MacWilliams identities, new procedures are developed for particular types of Gilbert-Elliott channel models. Here, the calculations are derived from three parameters which profile the occurrence of errors in those models. The decoding is then carried out using polynomial evaluation rather than matrix multiplication. Complementing this theory are several examples detailing the steps required to perform the decoding, as well as a collection of simulation results demonstrating the practical value of these algorithms.

As the demand of high data rate is increasing, a lot of research is being conducted in the field of wireless communication. A well-known channel coding technique called Space-Time Coding has been implemented in the wireless Communication systems using multiple antennas to ensure the high speed communication as well as reliability by exploiting limited spectrum and maintaining the power. In this thesis, Space-Time Coding is discussed along with other related topics with special focus on Alamouti Space-Time Block Code. The Alamouti Codes show good performance in terms of bit error rate over Rayleigh fading channel. The performance of Altamonte’s code and MIMO capacity is evaluated by using MATLAB simulation.