tailieunhanh - Spatial Multiplexing and Channel Modeling

So far we have only considered single-input multi-output (SIMO) and multi-input single-output (MISO) channels. They provide diversity and power gains but no degree-offreedom (.) gain. gain is most useful in the high SNR regime. MIMO channels have a potential to provide gain. We would like to understand how the gain depends on the physical environment and come up with statistical models that capture the properties succinctly. | 7. MIMO I: Spatial Multiplexing and Channel Modeling Main Story So far we have only considered single-input multi-output (SIMO) and multi-input single-output (MISO) channels. They provide diversity and power gains but no degree-of-freedom (.) gain. gain is most useful in the high SNR regime. MIMO channels have a potential to provide gain. We would like to understand how the gain depends on the physical environment and come up with statistical models that capture the properties succinctly. We start with deterministic models and then progress to statistical ones. Capacity of AWGN Channel Capacity of AWGN channel If average transmit power constraint is watts and noise psd is watts/Hz, MIMO Capacity via SVD Narrowband MIMO channel: is by , fixed channel matrix. Singular value decomposition: are complex orthogonal matrices and real diagonal (singular values). Spatial Parallel Channel Capacity is achieved by waterfilling over the eigenmodes of H. . | 7. MIMO I: Spatial Multiplexing and Channel Modeling Main Story So far we have only considered single-input multi-output (SIMO) and multi-input single-output (MISO) channels. They provide diversity and power gains but no degree-of-freedom (.) gain. gain is most useful in the high SNR regime. MIMO channels have a potential to provide gain. We would like to understand how the gain depends on the physical environment and come up with statistical models that capture the properties succinctly. We start with deterministic models and then progress to statistical ones. Capacity of AWGN Channel Capacity of AWGN channel If average transmit power constraint is watts and noise psd is watts/Hz, MIMO Capacity via SVD Narrowband MIMO channel: is by , fixed channel matrix. Singular value decomposition: are complex orthogonal matrices and real diagonal (singular values). Spatial Parallel Channel Capacity is achieved by waterfilling over the eigenmodes of H. (Analogy to frequency-selective channels.) Rank and Condition Number At high SNR, equal power allocation is optimal: where k is the number of nonzero i2 's, . the rank of H. The closer the condition number: to 1, the higher the capacity. Example 1: SIMO, Line-of-sight h is along the receive spatial signature in the direction := cos : nr –fold power gain. Example 2: MISO, Line-of-Sight h is along the transmit spatial signature in the direction := cos : nt – fold power gain. Example 3: MIMO, Line-of-Sight Rank 1, only one degree of freedom. No spatial multiplexing gain. nr nt – fold power gain Beamforming Patterns The receive beamforming pattern associated with er( 0): Beamforming pattern gives the antenna gain in different directions Line-of-Sight: Power Gain Energy is focused along a narrow beam. Power gain but no degree-of-freedom gain. Example 4: MIMO, Tx Antennas Apart hi is the receive spatial signature from Tx antenna i along direction i = cos ri:

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