A Common Function of Different Union Bounds for Optimization and BER Evaluation of Space–Time codes

Abstract

Optimizing Space-Time (S---T) codes, in terms of minimum error rates, based on Union bounds often produces results which vary with signal-to-noise ratio (SNR) and so are not easy to use. Error-rate evaluation of S---T codes using Union bounds sometimes requires very heavy computational loads and so is impractical. In this paper, a Common function shared by different Union bounds is derived and proposed for optimization of S---T codes. The Common function produces the optimization results which are SNR independent and so requires a substantially lower computation load. Results of Monte-Carlo simulation on two 2 × 2 rotation-based diagonal S---T codes (D codes) and two Linear-Dispersion codes (LDCs) show that the bit-error-rate (BER) performances using the optimization results based on the Common function, the exact Union bound (EUB) and Chernoff Union bound (CUB) are all nearly identical. The Common function is subsequently used to develop a modified Union bound (MUB) and modified Chernoff Union bound (MCUB). Results of numerical calculations show that the MUB can provide a good compromise between the accuracy and computational load for BER evaluation.