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Theory and applications of ofdm and cdma wideband wireless communications phần 3

Chúng tôi lập luận rằng chỉ có kết quả đầu ra thu đối với những kích thước một biểu tượng đã được truyền đi có liên quan quyết định và những người khác có thể được bỏ qua bởi vì họ là thống kê độc lập, quá. Trong ví dụ của chúng tôi, điều này có nghĩa là chúng ta có thể bỏ qua r3 sản lượng thu. Vì vậy, chúng tôi hy vọng rằng P (s1, s2 | r1, r2, r3) = P (s1, s2 | r1, r2) | 74 MOBILE RADIO CHANNELS This equation allows an interesting interpretation of the optimum receiver. First the receive symbols rk are multiplied by the inverse of the complex channel coefficient ck ake7W. This means that by multiplying with c-1 the channel phase shift pk is back rotated and the receive symbol is divided by the channel amplitude ak to adjust the symbols to their original size. We may regard this as an equalizer. Each properly equalized receive symbol will be compared with the possible transmit symbol sk by means of the squared Euclidean distance. These individual decision variables for each index k must be summed up with weighting factors given by ck 2 the squared channel amplitude. Without these weighting factors the receiver would inflate the noise for the very unreliable receive symbols. If a deep fade occurs at the index k the channel transmit power ck 2 may be much less than the power of the noise. The receive symbol rk is nearly absolutely unreliable and provides us with nearly no useful information about the most likely transmit vector s. It would thus be much better to ignore that very noisy receive symbol instead of amplifying it and using it like the more reliable ones. The factor ck 2 just takes care of the weighting with the individual reliabilities. As in Subsection 1.4.2 we may use another form of the maximum likelihood condition. Replacing the vector s by Cs in Equation 1.78 we obtain s arg max i stCtr - 1 Cs 2 2.30 There is one difference to the AWGN case in the first term before cross-correlating with all possible transmit vectors s the receive vector r will first be processed by multiplication with the matrix Ơ. This operation performs a back rotation of the channel phase shift yk for each receive symbol rk and a weighting with the channel amplitude ak . The resulting vector ơr c ri . . . cKrK must be cross-correlated with all possible transmit vectors. The second term takes the different energies of the transmit vectors Cs into .