The threshold value of SNR for a cellular communication is connected to the standard or the equipment you are using. e.g for GSM I think is 18 dB.

So you have to assume a value based on the equipment or standard for the cellular communication system you are dealing with.

Thanks.

Dear Khalid,

I wrote a short paper about outage probability last year, which may help you to set your threshold, and find the optimal outage probability: 

https://hal.archives-ouvertes.fr/hal-01418637/file/IET_ELetters_2016.pdf

Vincent

Dear Khaled,

This question is interesting! 

Adding to the colleagues above, there are formulas to estimate the outage probability for for wireless communication channels including the cellular communications.

It is so that the mobile Rayleigh or Rician radio channel is characterized by rapidly changing channel characteristics. As typically a certain minimum  or threshold signal level is needed for acceptable communication performance, the received signal will experience periods of sufficient signal strength for "non-fade intervals"and insufficient signal strength for "fades". During fades lower than the threshold the user experiences a signal outage.

Assuming a base station is radiating an average  Paverage wireless power at a distance r at the a receiver site with a power sensitivity of Ps. the power ps is the minimum receive power required to detect the revived signal without error. This power  is limited by the noise and interference at the receiver site. So, if Pavearge is greater or equal to Ps the received signal will be received with the acceptable level of error.

Unfortunately, the received power at the receiver is subjected to statistical variations because of multipath effect. These leads to the decrease of the received signal power below the threshold level causing outage of the reception.

The outage potability depends on on the time the received signal lasts below the threshold for specific total reception time.

One method to decrease the outage probability is to increase the fading margin when planning the link budget.

There are some fading models according to the wireless channel propagation such as Rayleigh, Rice Nakagami and others. These models give the probability distribution function of the fading signal amplitudes  and therefore one can calculate the outage probability  if the signal threshold is known. As pointed before, the threshold is calculated from the link budget and radio planning.

It is so that formally:

The outage probability Pout= Integral p(x) dx for x greater than xthreshold to infinity, where x is the received signal amlitude, p(x) is the probability distribution function of the signal amplitudes due to fading.

For more information please refer to the link:http://www.wirelesscommunication.nl/reference/chaptr04/outage/outage.htm

Best wishes

Dear Khalid,

You can check the following link, in which  the explanation of addressing  the problem of how to make reasonable approximations of the outage probability in numerical evaluations of interference-limited cellular radio systems, while restricting the complexity of calculations. The method is useful for Rician, Nakagami and Rayleigh channels.

http://www.wirelesscommunication.nl/reference/chaptr03/ricenaka/outage.htm

Defiantly, your assumption must be based on a threshold. If not, at least a generally accepted value.

Signal to noise Ratio (SNR) = Allocated Power (P) * the Singular value of each channel / the variance noice of the channels.