tailieunhanh - Mobile and Wireless Communications-Physical layer development and implementation 2012 Part 6

Tham khảo tài liệu 'mobile and wireless communications-physical layer development and implementation 2012 part 6', kỹ thuật - công nghệ, cơ khí - chế tạo máy phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả | Sequential Blind Beamforming for Wireless Multipath Communications in Confined Areas 91 hij sinc -j 1 i K P j p 43 where K represents the inverse resolution over Ts of the estimated delay t . The theoretical elements of the t -th row of the matrix H are therefore identical to the samples of the truncated sinc function with delay equal to ti i 1 i K. 44 For the time delay estimation process only the estimated time delay ti k is adapted in our approach and it is used as an index to obtain the vector ht from a lookup table. As mentioned previously this lookup table is a two-dimensional matrix called H of size Kx 2P 1 that contains samples of the sinc function with delay ranging from 0 to K - 1 K. For a given vector t with theoretically delayed value elements ti given by 44 the i-th row is computed as follows i Ti-K 1. 45 So at each iteration the integer part of ti K 1 is used to locate the i-th row of the matrix H . ht that is used to delay the signal yMCMA k using yh k hỊ1 u k 46 where u k is given by u k yMCMA k yMCMA k 2p 1 T. 47 The estimated fractional time delay is obtained by using the gradient descent of the instantaneous squared error ịehị2 surface to locate the global minimum . using LMS So et al. 1994 . The estimated gradient is equal to the derivative of ịehị2 with respect to t . The FTDE algorithm may be summarized as follows. The complex error signal eh k is given by eh k yFD k yh k yFD k n -psinc n tyyMcMA k ri 48 where yFD .k W D Ji x1_D k 49 x1_D k x4 k P 1 . 50 xe1 k is delayed by P 1 . Ts to be aligned with the output of the filter H . yh k that has latency depending on its order value M 2P 1 as shown in Figure 10. The estimated time delay can be adapted by minimizing the cost function given by J t WFD E eh k 2 E yFD k yh k 2 . 51 The constrained LMS algorithm becomes t k 1 t k y4 J t Wfd 52 where y4 is a small positive step size. By differentiating the instantaneous error surface eh k 2 with respect to the estimated time delay we have 92 .