tailieunhanh - MIMO Systems Theory and Applications Part 2

Tham khảo tài liệu 'mimo systems theory and applications part 2', kỹ thuật - công nghệ, cơ khí - chế tạo máy phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả | Advanced MIMO Techniques Polarization Diversity and Antenna Selection 19 Thus Ry HRxHH Rb 31 The mutual information is expressed as I x yIH log2 det rceRy log2 det i Rb log2det Inr HRxHH Rb 32 For circularly symmetric Gaussian random vectors the mutual information is maximum and also expressed as CMIMO max I x y H bits s Hz 33 p x E xHx PT When no CSI Channel State Information is available at the transmitter equal power allocation is adopted. With the assumption that no correlation exits at the transmit side PT Rx NT ÌNt Pt is the total power available at the transmit side. The MIMO capacity is then expressed as Cmimo log2 det In YHH bits s Hz 34 NT Y is the SNR. MIMO capacity based on SVD CSI known at the receiver When CSI is available at the receiver SVD factorization is used and MIMO channel capacity could be easily derived. Let us first review the SVD technique. SVD is a factorization method for complex matrix which is widely used in signal processing. We take an N X M matrix A SVD theorem states A USVH 35 The eigenvectors of AAH make up the columns of U N X N which is an unitary matrix UUH In . The singular values in S N X M are square roots of eigenvalues from AAH or AHA. The singular values are the diagonal entries of the S matrix and are arranged in descending order. The eigenvectors of AH A make up the columns of V. V M X M is also a unitary matrix VVH Im . Calculating the SVD of the MIMO channel matrix H leads to the following factorization H USVH 36 We substitute H by its SVD decomposition. Hence the received signal is expressed as y USVH x b 37 20 MIMO Systems Theory and Applications Let y UH y x VH x b UH b 38 As U and V are unitary matrix variables x and b keep the same statistical densities as x and b. Therefore the channel model y Hx b could be also presented as y Sx b 39 y y1 . yNR T x x1 . xNt t S diag ÃĨ . ựXR 0 . 0 R min Nr Nt is the rank of the channel matrix H. Equation 1 can be rewritten as i V ix t b t i 1 . R y pi i R 1 . NR. 40 .

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