Multiple-input multiple-output (MIMO) technique in communication system has been widely researched. Compared with single-input single-output (SISO) communication, its properties of higher throughput, more e?cient spectrum and usage make it one of the most significant technology in modern wireless communications. In MIMO system, sphere detection is the fundamental part. The purpose of traditional sphere detection is to achieve the maximum likelihood (ML) demodulation of the MIMO system. However, with the development of advanced forward error correction (FEC) techniques, such as the Convolutional code, Turbo code and LDPC code, the sphere detection algorithms that can provide soft information for the outer decoder attract more interests recently. Considering the computing complexity of generating the soft information, it is important to develop a high-speed VLSI architecture for MIMO detection. The first part of this thesis is about MIMO sphere detection algorithms. Two sphere detection algorithms are introduced. The depth first Schnorr-Euchner (SE) algorithm which generates the ML detection solution and the width first K-BEST algorithm which only generates the nearly-ML detection solution but more efficient in implementation are presented. Based on these algorithms, an improved nearly-ML algorithm with lower complexity and limited performance lose, compared with traditional K-BEST algorithms, is presented. The second part is focused on the hardware design. A 4*4 16-QAM MIMO detection system which can generate both soft information and hard decision solution is designed and implemented in FPGA. With the fully pipelined and parallel structure, it can achieve a throughput of 3.7 Gbps. In this part, the improved nearly-ML algorithm is implmented as a detector to generat both the hard output and candidate list. Then, a soft information calculation block is designed to succeed the detector and produce the log-likelihood ratio (LLR) values for every bit as the soft output.

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.