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4.2. Statistical Channel Capacity with Partial CSI
- Definition: Capacity under statistical channel state information (CSI) rather than perfect CSI is expressed as:
[ C_\textstat = \max_p_X \mathbbE_\Theta\big[ I(X;Y|\Theta) \big] ]
where ( \Theta ) is a random channel matrix. - Theorem: For i.i.d. Rayleigh fading MIMO channels, the optimal input distribution remains Gaussian, but the power allocation depends on the distribution of the singular values of ( \Theta ). The proof uses Jensen’s inequality and a convexity argument on the mutual information functional.
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- Introduction to Statistical Communication Theory: This topic covers the basics of statistical communication theory, including probability, random variables, and stochastic processes.
- Signal Detection Theory: This topic deals with the detection of signals in noise, including hypothesis testing and decision theory.
- Estimation Theory: This topic covers the estimation of parameters and signals in communication systems.
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