MIMO Channel Capacity of Static Channels Zhe Chen Department of Electrical and Computer Engineering Tennessee Technological University Cookeville, TN38505 December 2008
Contents Introduction Parallel Decomposition of the MIMO Channel MIMO Channel Capacity Static Channels Summary 2
Introduction to MIMO MIMO (Multiple Input Multiple Output) transmits two or more data streams in the same channel at the same time, using multi-antennas at transmitter and receiver. Main features Can achieve high throughput without consuming extra radio frequency Can achieve high link reliability of wireless communication Main technical fields of MIMO Radio wave propagation Coding and information theory Signal processing 3
Narrowband MIMO Model y = Hx + n x represents the Mt-dimensional transmitted symbol n is the Mr-dimensional noise vector H is the Mr * Mt matrix of channel gains y represents the Mr-dimensional received symbol 4
Parallel Decomposition of the MIMO Channel (1 Decompose a MIMO channel into a number of parallel independent channels Singular value decomposition (SVD) of H is is the rank of H, U: matrix, V: matrix is an diagonal matrix of singular values of H.,, 5
Parallel Decomposition of the MIMO Channel (2 Transmit precoding & receiver shaping Parallel decomposition of the MIMO channel 6
MIMO Channel Capacity Static Channels (1) Channel capacity is defined as: If y and x are zero-mean circularly-symmetric y complex Gaussian random vectors, then So the MIMO channel capacity is: The optimization relative to Rx will depend on whether or not H is known at the transmitter. 7
MIMO Channel Capacity Static Channels (2) If channel is known at transmitter (with CSIT and CSIR) By substituting the SVD of channel into the MIMO channel capacity formula, we get the MIMO capacity with CSIT and CSIR: is the SNR associated with the i th channel at full power. Solving the optimization leads to a water-filling power allocation for the MIMO channel: The resulting capacity is then: for some cutoff value. 8
MIMO Channel Capacity Static Channels (3) If channel is unknown at transmitter If the distribution of H follows the zero-mean spatially white channel gain model, the best strategy is to allocate equal power to each transmit antenna. The mutual information of the channel can be expressed as: The appropriate capacity definition is capacity with outage: (the probability that the transmitted data will not be received correctly) 9
Summary Parallel decomposition of the MIMO channel and MIMO channel capacity of static channels are introduced. MIMO channels can provide very high data rates without requiring increased signal power or bandwidth. MIMO systems offer a promising solution for future generation wireless networks. 10
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