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P (Eq. 74)
were pNI is the probability of Non Interference (NI) of the receiver.
When a C/I criterion is considered, pNI is defined as:
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| body | ${{p}_{NI}}=P\left( \left. \frac{dRSS}{iRS{{S}_{comp}}}>\frac{C}{I} \right|dRSS>sens \right)$ |
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(Eq. 75)
since by definition P(A|B)=P(A∩B)/P(B), pNI becomes:
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| body | ${{p}_{NI}}=\frac{P\left( \frac{dRSS}{iRS{{S}_{comp}}}>\frac{C}{I},\quad \quad dRSS>sens \right)}{P\left( dRSS>sens \right)}$ |
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(Eq. 76)
with 
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| body | $iRS{{S}_{comp}}=\sum\limits_{j=1}^{P}{iRS{{S}_{j}}}$ |
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where P is the number of interferers (i.e. active transmitters).
Monte Carlo method is applied individually to the numerator and to the denominator of the expression of pNI . The result obtained is an estimation of pNI by using the following equations (p’NI):
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| body | $p{{'}_{NI}}=\frac{\frac{1}{M}\sum\limits_{i=1}^{M}{{{1}_{\left\{ \frac{dRSS(i)}{iRS{{S}_{comp}}(i)}>\frac{C}{I},\quad \quad dRSS(i)>sens \right\}}}}}{\frac{1}{M}\sum\limits_{i=1}^{M}{{{1}_{\left\{ dRSS(i)>sens \right\}}}}}=\frac{\sum\limits_{i=1}^{M}{{{1}_{\left\{ \frac{dRSS(i)}{iRS{{S}_{comp}}(i)}>\frac{C}{I},\quad \quad dRSS(i)>sens \right\}}}}}{\sum\limits_{i=1}^{M}{{{1}_{\left\{ dRSS(i)>sens \right\}}}}}$ |
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(Eq. 77)
with M the number of events (or snapshots) and where
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| body | ${{1}_{\left\{ condition \right\}}}=\left\{ \begin{matrix} 1, & \text{if condition is satisfied} \\ 0, & \text{else} \\ \end{matrix} \right.$ |
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(Eq. 78)Similarly, when a C/(I+N) criterion is considered, pNI is defined as:
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| body | ${{p}_{NI}}=\frac{P\left( \frac{dRSS}{iRS{{S}_{comp}}+N}>\frac{C}{I+N},\quad \quad dRSS>sens \right)}{P\left( dRSS>sens \right)}$ |
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(Eq. 79)
When a (I+N)/N criterion is considered, pNI is defined as:
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| body | ${{p}_{NI}}=\frac{P\left( \frac{iRS{{S}_{comp}}+N}{N}>\frac{I+N}{N},\quad \quad dRSS>sens \right)}{P\left( dRSS>sens \right)}$ |
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(Eq. 80)
When a I/N criterion is considered, pNI is defined as:
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| body | ${{p}_{NI}}=\frac{P\left( \frac{iRS{{S}_{comp}}}{N}>\frac{I}{N},\quad \quad dRSS>sens \right)}{P\left( dRSS>sens \right)}$ |
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(Eq. 81)