I think the seminal paper "Capacity of Multi-antenna Gaussian Channels" by E. Telatar provides a nice derivation of the MIMO capacity. Check out Sections 3.1 and 3.2 in http://ipg.epfl.ch/~leveque/Projects/telatar.pdf
I think the seminal paper "Capacity of Multi-antenna Gaussian Channels" by E. Telatar provides a nice derivation of the MIMO capacity. Check out Sections 3.1 and 3.2 in http://ipg.epfl.ch/~leveque/Projects/telatar.pdf
The question needs to be more specific. In other words, what is the type of the communication under consideration? Do you want to compute the capacity for fixed channel gains? Do the receiver has the channel state information? If the channel is not constant and it is random variable, how does it change (quasi state, ..) and what kind of distributions for the channel coefficients. The channel capacity is different in terms of the results and the approach.
Most of the researchers uses the Shannon capacity formula, which is a function of SNR. The Shannon capacity considers the input and the output of the digital communication systems to the system be is continuous-values with Gaussian distribution. However, in these systems (i.e., digital communication systems), the input to the systems is represented as discrete-values, since the transmitter maps a binary sequence to symbols, and the output can be represented as discrete-values
or a continuous-values depends on the decoder (i.e., the output is discrete-values
for the hard decoder and the output is continuous-values for the soft decoder).
The channel capacity for the discrete-input discrete-output system can be calculated using either the conventional method or the log-likelihood ratio.
The conventional method is symbol-based, in which the input to the system is considered to be symbols. while the LLR method is bit-based, in which the input to the system is considered to be bits. However, the capacity of the LLR method is equal to the capacity of the conventional method only when BPSK or 4-QAM is used, because the LLR method depends on the constellation ordering (e.g. Gray coding order, binary order).