Deriving Bit Error Rates for different diveristy tecniques

[Ian_Brooks]

Homework Statement

Using the normal distribution for different modulation techniques over rayleigh fading , we have to derive SNR values for different Diversity techniques such as selection combining, Equal Gain Combining and Maximal Ratio Combining.

Now for Non-coherent BPSK I have to derive the Bit Error Rate for different diversity techniques.

I have the Probability of the Bit Error Rate - i need to find how I can find the Bit Error Rate from this. Apparently it involves a sum of another term and then a double integral that would give us the BER.

Can someone point me in the right direction in finding this so called sum and what I have to integrate it with? What would I be integrating the second term by for the double integral, as It can't be Signal To Noise Ration (SNR) of the signal.

Homework Equations

The Probability of a Bit Error Rate was found in terms of SNR (gamma).

The Attempt at a Solution

Too much to type up here.

 

[Valkarie]

The BER was found in terms of gamma (SNR) for Non-coherent BPSK.BER = 1/2 * erfc(sqrt(gamma/2)) + 1/2 * exp(-gamma) * erfc(sqrt(gamma/2 + 1))Now for different Diversity Techniques, we have to derive the SNR values for different Diversity techniques such as selection combining, Equal Gain Combining and Maximal Ratio Combining. For Selection Combining,SNR_SC = SNR_1 + SNR_2 + ... SNR_N For Equal Gain CombiningSNR_EGC = N * SNR_1For Maximal Ratio CombiningSNR_MRC = N * max(SNR_1, SNR_2, ... SNR_N)Now I have to find the Bit Error Rate for the different Diversity Techniques, which involves another sum and a double integral. The sum is - BER_SC/EGC/MRC = 1/2 * erfc(sqrt(gamma_SC/EGC/MRC/2)) + 1/2 * exp(-gamma_SC/EGC/MRC) * erfc(sqrt(gamma_SC/EGC/MRC/2 + 1))Where gamma_SC/EGC/MRC are the SNR values for the respective Diversity Techniques. Now I have to find the double integral term. I don't understand how to go about this. How do I know what to integrate with? Thanks.

 

[piercas]

I would suggest starting by researching the equations and methods for deriving Bit Error Rates for different diversity techniques. This may involve looking into the theory behind these techniques, as well as previous studies and experiments that have been conducted on them. You can also consult textbooks or research papers on the topic to gain a better understanding of the equations and methods involved.

Once you have a good understanding of the theory and equations, you can then start working on deriving the Bit Error Rates for the different diversity techniques. This may involve using mathematical tools such as integration and summation to solve the equations and obtain the desired results. It is important to carefully follow the steps and assumptions made in the derivation to ensure accuracy and validity of the results.

In terms of the second term and double integral mentioned in the content, it is likely that you would be integrating with respect to the fading distribution of the channel. This could be a Rayleigh or Rician distribution, depending on the specific scenario being studied. Again, it is important to carefully follow the steps and assumptions made in the derivation to ensure accuracy.

Lastly, it may be helpful to consult with a supervisor or colleague who has experience in this area, as they may be able to provide guidance and assistance in the derivation process. Good luck!