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

Mumbai university > Comp > SEM 8 > Mobile Communication

Marks: 10M

Year: Revised 2012

1 Answer
  • 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

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


    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,

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


    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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