# Fade Margin Calculation in GSM

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• Cell area probability (CAP ) is the percentage of the cell area that has signal strength greater than the receiver sensitivity.
• CAP is dependent on the radio environment, primarily the standard deviation of the log normal faded signal (s) and the propagation loss constant (n)
• The CAP is calculated using the following equaion

PCA=½ ( 1+ erf (a) + exp (2ab+1/b2)(1 – erf(ab+1/b)))

Where:

PCA = Cell area probability

B = 10nLog10(e) / sÖ2

s = Standard deviation of received signal

N = Propagation constant

• The outdoor fade margin depends on the standard deviation of the lognormal shadowing and the propagation constant
• The propagation constant depends on the environment and the frequency.
• For urban areas propagation constant varies from 2.7 to 5 , with a typical value of 5 for both 850 Mhz and 1900 Mhz.
• Standard deviation also varies on environment and frequency , and may vary slightly with frequency.
• The urban areas have higher standard deviation than rural areas.Typical value ranges from 5-12dB with a typical value of 8dB
• Outdoor fade margin can be calculated using a plot of the CAP       equation.
• The next figure shows the CAP plot for a propagation constant of 3.5 and standard deviation of 5, 8 and 12.

From the figure fade margin to be applied to the Link Budget may be selected depending on the standard of the received signal.