Error-Rate Evaluation and Optimization for Space-Time Codes

This dissertation, "Error-rate Evaluation and Optimization for Space-time Codes" by Zhi, Zhang, 張治, was obtained from The University of Hong Kong (Pokfulam, Hong Kong) and is being sold pursuant to Creative Commons: Attribution 3.0 Hong Kong License. The content of this dissertation has not been altered in any way. We have altered the formatting in order to facilitate the ease of printing and reading of the dissertation. All rights not granted by the above license are retained by the author. Abstract: Abstract of thesis entitled Error-Rate Evaluation and Optimization for Space-Time Codes Submitted by Zhang Zhi for the degree of Doctor of Philosophy at The University of Hong Kong in August 2007 Error-rate evaluation and optimization are important issues for the study of Space-Time (S-T) codes. This thesis investigates the accuracy and efficiency of error-rate evaluation for S-T codes. The accuracy of the optimization and the convenience of using the optimized results over a range of signal-to-noise ratios (SNRs) are also investigated. An exact close-form Pair-wise Error Probability (PEP) is derived which is based on a proposed simple solution to determine the coefficients of the partial fraction expansion, thus eliminating the complexity to obtain any high order derivatives. The Union bound using the proposed exact PEP can produce accurate BER performance in moderate and high SNR regions. However the calculation needs to be repeated for every SNR value investigated because of the complicated mathematical structures involved in the proposed close-form PEP. To efficiently evaluate the error rate, an alternative power series representation for the exact PEP is proposed to reduce the computational load, which can produce accurate results within a certain region of convergence. When the exact Union bound (EUB) is used for S-T codes optimization, the results usually vary with SNR, which is inconvenient in practical use. Thus a Common function shared by different Union bounds is proposed and is used to optimize the S-T codes to produce SNR independent optimization results that have only minor error performance loss. A modified Union bound constructed from the Common function is subsequently derived to give an efficient error-rate evaluation of S-T codes. Numerical calculations show that the proposed modified Union bound (MUB) can achieve a good compromise between the evaluation accuracy and the computational load. The PEP based methods cannot give accurate results in low SNR regions due to the binary detection assumption in its definition. Thus, two methods using correct probability instead of error probability are proposed for error rate evaluation in low SNR region for S-T codes. One method has a similar computational load as the EUB but a tighter error-rate performance. The other method can give results nearly identical to that of simulations, but requires numerical integration. An expurgation condition is developed for S-T codes to simplify the two proposed methods. DOI: 10.5353/th_b3963421 Subjects: Space time codes Wireless communication systems