# Outage definition based on rate and outage definition based on outage.. please help

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#### sabyaec0411

##### Newbie level 1 Hi. I am working on relay selection problem in outage restricted network.

When I read papers, outage in relayed network is defined in two ways,

(a) some papers say outage probability as the probability that SNR is below a threshold level,

(b) other papers say probability that transmission rate is greater than end-to-end support rate.

Does the definition of outage probability in (a) is same as the (b) with relationship [/NR]-1 as the SNR threshold, or if outage probability definition of (a) has its own significance. Lets say if I am not interested in end-to-end data rate, and consider SNR at the destination to be higher than a threshold value for successful reception of the signal, the outage probability definition according to (a) can be used. Please let me know if I am right or not.

Thanks.

#### David83

##### Advanced Member level 1 Hi. I am working on relay selection problem in outage restricted network.

When I read papers, outage in relayed network is defined in two ways,

(a) some papers say outage probability as the probability that SNR is below a threshold level,

(b) other papers say probability that transmission rate is greater than end-to-end support rate.

Does the definition of outage probability in (a) is same as the (b) with relationship [/NR]-1 as the SNR threshold, or if outage probability definition of (a) has its own significance. Lets say if I am not interested in end-to-end data rate, and consider SNR at the destination to be higher than a threshold value for successful reception of the signal, the outage probability definition according to (a) can be used. Please let me know if I am right or not.

Thanks.

They are both the same. For each SNR y there is a channel capacity. For the case of half-duplex relaying (single relay) it is (1/2)*log2(1+y). Now if the transmission rate R is greater than the channel capacity, i.e. R > (1/2)*log2(1+y), the system will be in outage. Solving the previous inequality with regard to y gives you that the system is in outage if

$\gamma< 2^{2R}-1=\gamma_{th}$

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