## Probability of Error for BPSK over Rayleigh channel with Maximal Ratio Combiner

Aside from deriving BER for BPSK over rayleigh channel, I also got another assignment to derive the equation of probability of error (BER) for BPSK over rayleigh channel with maximal ratio combiner (mrc). After searching here and there, I found the solution in Digital Communications by Proakis page 825. But just like the previous assignment, Proakis didn’t derive the equation in detail. Even Mr. Google couldn’t help me this time ðŸ˜¦ So I tried to solve it myself, but I’m stuck. So I posted here my unfinished work, maybe you can help me figuring it out.

For a certain value of time, the bit error rate probability is

where . is the instantaneous SNR on the th channel.

When , and

where (average SNR per channel). So the characteristic function is

Since the fading on K channels is mutually statistically independent

Using inverse fourier transform,

So, the Bit error rate (error probability)

To solve equation above, use integration by parts.

By definition,

which is another way of rewriting the usual

Let .

And by definition

So we have

Let also

So

Probability of error becomes

And somehow the equation becomes

where

So that’s it. Anybody can help me on the last part of the derivation? You can download the pdf version of that equation here.

I am sorry. I don’t know

amir said this on December 3, 2008 at 10:49 am |