Question

1. Given channel has a data rate of 1.5Mbps where the bandwidth is 130kHz. What is the signal to noise level in dB?

Answer 1

As the channel is noisy, so the theoretical highest data rate for this noisy channel is represented by:

Capacity = bandwidth * log2(1 + SNR)

This is known as Shanon Capacity.

Here, Capacity is the maximum bitrate possible for the noisy channel in bits per second, bandwidth is the bandwidth of the channel in Hz and SNR is Signal to Noise Ratio in dB (i.e. decibels).

1 Megabits per second (Mbps) = 1,000,000 bits per second (bps)

So, 1.5Mbps = 1.5 * 106 bps

and 130KHz = 130 * 103 Hz

Putting the values in the given equation:

=> 1.5 * 106 = 130 * 103 * log2( 1+SNR)

=> 150/13 = log2( 1+SNR)

=> 1+SNR = 2150/13

=> 1 + SNR = 2974.562

=> SNR = 2973.562 dB