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Adaptive Filtering Applications Part 11

Tham khảo tài liệu 'adaptive filtering applications part 11', kỹ thuật - công nghệ, cơ khí - chế tạo máy phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả | 292 Adaptive Filtering Applications consider the instantaneous ML channel estimates i.e. the estimates computed by using only the kth data block which is given by Kaiser et al. 2005 L ML H H_. mru hk yXk Xk J Xk yk. 25 For OSTBCs thanks to lemma 1 25 reduces to h kML hxk II2 X H yk -L2 X H yk. 26 v 7 II xk II Thus using 26 the channel estimate 24d can be rewritten as hk k Bk hk-1 k-1 Ak h kML . 27 Consequently the KF proposed in Loiola et al. 2009 updates the channel estimates through weighted sums of instantaneous maximum likelihood channel estimates. It is important to note that the weights are time-varying and optimally calculated in the MMSE sense for each data block. Considering communication systems where pilot sequences are periodically inserted between information symbols the algorithm in 24a - 24e can operate in both training and decision-directed DD modes. First when pilot symbols are available the matrix Xk in 24d is constructed from them. Once the transmission of pilot symbols is finished the algorithm enters in decision-directed mode and the matrix Xk is then formed by the decisions provided by the ML space-time decoder. Note that these decisions are based on the channel estimates generated by the algorithm in the previous iteration. 4. Steady-state Kalman channel estimator The measurement equation 11 represents a time-varying system since the matrix Xk changes at each transmitted data block. However in the Kalman channel estimator 24a - 24e only 24d has an explicit dependence on Xk. Because of the orthogonality of OSTBC codewords all other expressions in this recursive estimator depend only on the energy of the uncoded data block i.e. xfc 2. Now for constant modulus signal constellations such as M-PSK xfc 2 is a constant. In this case 24a - 24c and 24e are just functions of the initial estimate of Pk k the normalized Doppler rate the spatial correlation matrix a constant equal to the energy of the constellation symbols and the variance of the .