# Shannon Capacity of a GSM Channel in Fading Environment

In the previous post we calculated the Shannon Capacity of a 200kHz GSM channel in AWGN (Additive White Gaussian Noise). However, in a practical scenario the capacity is limited by time varying fading and interference. Let us consider a fading channel with four possible states corresponding to SNRs of 15dB, 10dB, 5dB and 0dB. The probability of these states is 0.50, 0.25, 0.15 and 0.10 respectively. The Shannon Capacity of such a channel is given as (assuming that the channel state information is known at the receiver):

C=Σ B*log2(1+SNRi)* p(SNRi)

C=B*(Σ log2(1+SNRi)* p(SNRi))

C=(200e3)*(log2(1+31.62)*0.50+log2(1+10.00)*0.25+log2(1+3.16)*0.15+log2(1+1)*0.10)

C=757.43kbps

Assuming that only one out of eight time slots is allocated to any user the Shannon Capacity of a GSM channel is reduced to 94.68kbps.

Note: The contribution of the high SNR states dominates the capacity of the channel. The contribution of the four states in terms of percentage capacity is given as 66.38%, 22.84%, 8.14% and 2.64%.

#### Author: John (YA)

John has over 20 years of Research and Development experience in the field of Wireless Communications. He has worked for a number of companies around the world including Qualcomm Inc. USA.

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