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Recent Advances in Signal Processing 2011 Part 12

Tham khảo tài liệu 'recent advances in signal processing 2011 part 12', kỹ thuật - công nghệ, cơ khí - chế tạo máy phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả | 372 Recent Advances in Signal Processing yi --- ywi represent the respective input and output signals. All signals from the Tx antennas arriving at one Rx antenna must be added to generate the corresponding Rx output. Fig. 3. Structure of a MIMO simulator. Equation 6 can be simplified to gain insight considering only linear arrays located as shown in the Fig. 2 along y direction. With this approach the channel impulse response of the system is measured in the positions rRx for signals transmitted along positions rTx If Tx _Rx - jVỉt- itf - ik-simv rTx - ik-simp rRx h t T r r Aĩờ t-tĩ eJl Jle 70 W7 e 70 . 8 ỉ 1 Or in its general form as Lf h t T rTx rRx A -T e-j t- Te . 9 ỉ 1 2.2 Simplified channel description by use of angle domains Taking the Fourier transform of 9 with respect to rTx and rRx we reach the spatial channel expressed in the wavenumber domain as is explained in detail in Durgin 2003 if hit.T kTx .k l V A.fiir - T. fi kTx - kTx fiikRx - kRx 1 e- v t- e 10 r 4 I t T Z1 ỉCz T T ỉ 4v ỉ 4v ỉ e . X J ỉ 1 In the last expression it could be considered that all shifts in the wavenumbers should be positive however eq. 10 is utilized in accordance with expressions commonly found in literature. This can be used without lose of generality as the final expression does not depend on this sign. Instead of using an expression that depends on the wavenumber the most common expressions found are channel impulse responses CIR given in terms of the AoD and the AoA. By supposing that the entire propagation scenario lies in a plane with only the azimuth angle taken into consideration a 2-dimensional propagation environment we arrive to the following form of the angular dependant CIR h l 7 - 7 Alổ z-zl ổ pT-vT PR-q R e-j -j 11 ỉ 1 where vTx and vRx are the azimuth angle variables as shown in Fig. 2 while tpR and tpR represents the azimuth AoD and AoA of the ỉ-path respectively. Equation 11 is rather simple but can be made even simpler by taking its Fourier transform with .