written 7.6 years ago by | • modified 7.6 years ago |

Mumbai university > Comp > SEM 8 > Mobile Communication

**Marks:** 10M

**Year:** Revised 2012

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Derive the relationship between S/I (Signal to Interference) and cluster size N.

written 7.6 years ago by | • modified 7.6 years ago |

Mumbai university > Comp > SEM 8 > Mobile Communication

**Marks:** 10M

**Year:** Revised 2012

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written 7.6 years ago by |

Signal to noise ratio depends upon radius (R) of a cell and interference due to co-channel cells. Signal to noise ratio is given by

$\frac{S}{I} = \frac{S}{∑_{i=1}^io Ii}$

Where,

io= total number of co-channels

Ii= interference due to i^th co-channel cell

S= desired signal power from base station

We know that as the distance between transmitter and receiver increases, average received signal strength deceases. The average received power Pr at distanced from transmitting antenna is given by,

$Pr = Po (\frac{d}{do})^{-n}$

Where,

Po= power received at reference point at distance do

d= distance between transmitting antenna and desired point

do= distance between transmitting antenna and reference point

n= path loss exponent

Signal strength S inversely depends on radius of a cell $S ∝ R^{-n}$ and interference I is inversely proportional to minimum safe distance D, $I ∝D^{-n}$

$ ∴ \frac{S}{I} = \frac{R^{-n}}{∑_{i=1}^io D^{-n}}$

Every cell has co-channel at same distance hence total distance will be D,

$\frac{S}{I} = \frac{R^{-n}}{io D}$

$ ∴ \frac{S}{I} = \frac{(\frac{D}{R})^n}{io}$

$ ∴ \frac{S}{I} = \frac{\sqrt{3N}^n}{io} .....( D/R=\sqrt{3N})$

Above equation gives us the relation between signal to noise ratio (S/I) and cluster size (N).

According to FCC S/I should be greater than 18 db.

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