Exact pairwise error probability for the MIMO block fading channel

In this work, we present a closed form of the exact pairwise error probability (PEP) for coded block Rayleigh fading channels with multiple transmit and receive antennas. Based on the values of the signal-to-noise ratio and the eigenvalue products in each block and each transmit antenna, where the eigenvalues are obtained from the product of the signal-difierence matrix and its complex conjugate transpose, we classify the calculation of PEP into two groups: the symmetric case in which the mentioned products are all equal and the asymmetric case. We provide a new technique to calculate the PEP in the symmetric case. In the asymmetric case, we apply the flnite integral form of Q-function and our results from the symmetric case to obtain the PEP.

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