The outage probability that the recieve SNR is greater than SNR_{th}

Hi everyone

How can calcuates the outage probability P_out = Pr (SNR is less than SNR_{th} ) for system has 10 users and the minimum rate should be greater than 3 and under Religh fading channel. I would be thankful for any information.

Answer 1

[vidyesh]

Hi A_SD,

It is my understanding that you want to calculate the outage probability () of 10 users when minimum rate () is greater than 3 and is known under Rayleigh channel.

Since 'R_min' is equal to 3, outage probability is equal to the probability that capacity is less than or equal to R_min.

From the Shannon-Hartley theorem we can define capacity for Rayleigh channel as

h represents the fading channel coefficient.

Therefore, .

The probability distribution of rayleigh fading channel is

Note that this is the outage probability for 1 user.

For all 10 users it will be .

For atleast 1 user out of 10 it will be .

Hope this helps.

[A_SD]

@vidyesh thank you so much for your kind reply!

Could we do it with SNR instead of the rate like P_out = P (SNR less than SNR_ threshold)?

[vidyesh]

Indeed, we can express in terms of SNR. However, in this formulation, the SNR will be that at the receiver, which is influenced by the channel coefficient. Consequently, the final expression for will closely resemble our current equation.

[Alexa]

@vidyesh Do you think the P_out is convex or noncovex probelm?