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In the book “Fundamentals of Wireless communication”by Tse and Vishwanath, Can someone help with the how the integration helps derive equation 3.8 ?

The equation is

$$ p_e= \mathbb P\left\{\left\lvert y[1] \right\rvert^2 > \left\lvert y[0]\right\rvert^2\mathbf x_A\right\} = \left[ 2+\frac{a^2}{N_0} \right]^{-1}. $$

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    $\begingroup$ It's really necessary that you add the equation to your question (plus some context). Not everybody has access to the book, and there might be different editions with different equation numbers. $\endgroup$
    – Matt L.
    Feb 9, 2022 at 17:52
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    $\begingroup$ If you will just read the two sentences immediately preceding Eq.(3.8), you will find that $|y[1]|^2$ and $|y[0]|^2$ are independent exponential random variables with specified means. Can you write down the direct integration that needs to be done in order to compute $p_e$? Can you evaluate the integral for yourself as Tse and Viswanath state they did in arriving at the expression on the right side of Eq. (3.8)? This is far too much of a homework problem without any attempt on your part of trying to find the solution for yourself. This is not a do-my-homework-for-me site... -1 $\endgroup$
    – Dilip Sarwate
    Feb 9, 2022 at 21:01

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