A typical analog telephone line has an SNR of 30 dB. An ADSL modem used to provi

Question

A typical analog telephone line has an SNR of 30 dB. An ADSL modem used to provide Internet
services utilizes the telephone line and has a downstream bandwidth of approximately 962 KHz.
(a) What is the maximum theoretical downstream rate in Mbps of an ADSL modem?
(b) What if the SNR is reduced to 10 dB?

D5 (5 pts) A typical analog telephone line has an SNR of 30 dB. An ADSL modem used to provide Internet services utilizes the telephone line and has a downstream bandwidth of approximately 962 KHz (a) What is the maximum theoretical downstream rate in Mbps of an ADSL modem? (b) What if the SNR is reduced to 10 dB?

Explanation / Answer

a) According to Shannon theorem which specifies the maximum data rate in a noisy channel as B*log2(1+S/N) where B is the bandwidth, S/N is the signal-to-noise ratio. Usually, S/N is given in "decibel", not just a ratio. decibel is calculated by dB=10 * log10(S/N)
Therefore, we get S/N first by 30dB=10log10(S/N) ==> S/N=10^3=1000

Substitude S/N into Shannon's theorem, we get the maximum bps as 962k * log2(1+S/N) ==>

962 * log21001kbps=9588.47 kbps

b) if SNR is reduced to 10DB then the maximum rate also decrease by those times

then S/N ratio would be 10

and then  the maximum bps as 962k * log2(1+S/N) ==>

962k * log2(1+S/N) ==> 962k * log2(11) ==> 3327.973 kbps

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