Diversity order of L i.ni.d MRC

[David83]

Hello,

How can I find the diversity order of a Rayleigh fading wireless system with 1 transmit antenna and L receive antennas where the channels are independent but not necessarily identically distributed channels? Any paper on this is appreciated.

Thanks

 

[pangpangfish]

For your system model, the diversity order is L, for any linear combining. One way to find the diversity order is to obtain an analytical expression for the asymptotic SER/BER expressions and the slope of the SER/BER curve on a log-log plot (versus average SNR) will be your diversity order. The wireless literature on this subject is rich.

Hello,

How can I find the diversity order of a Rayleigh fading wireless system with 1 transmit antenna and L receive antennas where the channels are independent but not necessarily identically distributed channels? Any paper on this is appreciated.

Thanks

 

[David83]

Can you point me to a one paper on this? Again, I need for the not identical channels case.

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Can you point me to a one paper on this? Again, I need for the not identical channels case.

 

[pangpangfish]

You can start with the book by Simon and Alouini. In your original post, you said Rayleigh. Do you mean all diversity branches have Rayleigh fading with different variance?

If you have a mixed fading model, say the first branch is Rayleigh and the second branch is Nakagami, then the diversity order will not be 2. My educated guess is that the diversity order will be 1+m for this scenario.

As long as you write down the asymptotic error rate expressions, you can pretty much read the diversity order from your expressions.

 

[David83]

You can start with the book by Simon and Alouini. In your original post, you said Rayleigh. Do you mean all diversity branches have Rayleigh fading with different variance?

If you have a mixed fading model, say the first branch is Rayleigh and the second branch is Nakagami, then the diversity order will not be 2. My educated guess is that the diversity order will be 1+m for this scenario.

As long as you write down the asymptotic error rate expressions, you can pretty much read the diversity order from your expressions.

All the channels are Rayleigh, but they have different variances. I can find the outage probability as a sum, but I could not find the diversity order from that formula!!

 

[pangpangfish]

This is quite simple. In order to apply the asymptotic analysis, you don't have to have fading channel with identical variance or mean. Your diversity order should be L.

 

[Shug]

The diversity gain should just be given by the sum of the variances on the Rayleigh random variables. This is also discussed here:

https://en.wikipedia.org/wiki/Diversity_gain

In that article they refer to the paper "Linear diversity combining techniques," which I cannot access right now, but the result seems to correspond to just summing the variances.