tailieunhanh - Space-Time Coding phần 4

Kể từ khi tại mỗi thời điểm t là chỉ có nhiều nhất một giá trị riêng khác không, Dt1, các biểu thức (2,81) có thể được đại diện bởibiểu thị tập hợp các trường hợp thời gian chúng tôi nhận đượcđiểm kinh nghiệm | Performance Analysis of Space-Time Codes 73 eigenvalue element which is equal to the squared Euclidean distance between the two space-time symbols Xt and Xt. riT DI IV. _ V. 2 _ x I yi _ i 2 o 7QA t lxt xt I xt xt I i 1 The eigenvector of C xt xt corresponding to the nonzero eigenvalue Dt is denoted by vt1. Let us define hj as hj hj hj . htj nT Equation can be rewritten as L nR iT j2 Y YA A A A I ot 2 r i H Q1 dh X X 2_ Pj i Dt where j hj vi Since at each time t there is at most only one nonzero eigenvalue D1 the expression can be represented by _ IR_ j2 v Vi I pt 2 TA1 dh X X P 1 Dt IR_ E E fj 1 2 - xt -XI2 tep x x j 1 where p x X denotes the set of time instances t 1 2 . L such that xt - xt 0. Substituting into we get P X X H 2 exp nR - E E fj 1 2 xt - XtI24N p tep x X j 1 Comparing with it is obvious that j 1 are also independent complex Gaussian random variables with variance 1 2 per dimension and fj 1 follows a Rician distribution with the pdf i pt IX __ OIZ t I pt 12 prj 1 T l Ị I pt I F j 1 Ì OCX p pj 1 2 pj 1 exp I pj 1 Kt 0 I 2 pj 1 VKt I where j 1 j 1 j 2 j iT 1 Kt I hi Pht . ht vt I The conditional pairwise error probability upper bound can be averaged over independent Rician-distributed variables fj 1 . If we define 8h as the number of space-time symbols in which the two codewords X and X differ then at the right hand side of inequality there are 8HnR independent random variables. As before we will distinguish two cases in the analysis depending on the value of 8HnR. The term 8H is also called the space-time symbol-wise Hamming distance between the two codewords. 74 Space-Time Coding Performance Analysis and Code Design The Pairwise Error Probability Upper Bound for Large HnR Provided that the value of 8HnR for a given code is large . 8HnR 4 according to the central limit theorem the expression d2 X X in can be approximated by a Gaussian random .