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In Rayleigh fading channel(SISO), I know the instantaneous SER of QPSK for a given channel realization.

However, I do not know the exact average error probability.

It is very hard to calculate the average error probability because of the square of q function.

Are there any results on the exact average error probability of QPSK in Rayleigh fading channel?

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From Tse and Viswanath, "Fundamentals of Wireless Communication" (which I highly recommend): $$p_e = \frac{1}{2}\left(1-\sqrt{\frac{\text{SNR}}{2+\text{SNR}}}\right)$$ Note that this is the probability of symbol error.

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    $\begingroup$ Note that the authors make this book available for free: web.stanford.edu/~dntse/wireless_book.html . $\endgroup$
    – Marcus Müller
    Commented Apr 16, 2021 at 19:24
  • $\begingroup$ I know the book, however in the book the squared q function term is omitted for simplicity of derivation $\endgroup$
    – user56886
    Commented Apr 22, 2021 at 12:36

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