Question

(please pay attention to this fact that in Shannon calculation, SNR has to be in absolute units).

Calculate the Nyquist capacity of a channel whose bandwidth is 5MHz with the following logical levels:

1.) 8 2.) 16 3.) 64 4.) 256 5.) 1024

Answer 1

Nyquist capacity of a channel whose bandwidth is B and the number of signal levels per symbol M:

= 2Blog₂M

1) Here, bandwidth = 5MHz and M = 8

Nyquist capacity of a channel = 2 x 5 x 1000000 x log₂8  

= 10000000 x 3 = 30000000 bps = 30 Mbps

2) Here, bandwidth = 5MHz and M = 16

Nyquist capacity of a channel = 2 x 5 x 1000000 x log₂16

= 10000000 x 3 = 40000000 bps = 40 Mbps

3)  Here, bandwidth = 5MHz and M = 64

Nyquist capacity of a channel = 2 x 5 x 1000000 x log₂ 64

= 10000000 x 6 = 60000000 bps = 60 Mbps

4) Here, bandwidth = 5MHz and M = 256

Nyquist capacity of a channel = 2 x 5 x 1000000 x log₂256

= 10000000 x 8 = 80000000 bps = 80 Mbps

5) Here, bandwidth = 5MHz and M = 1024

Nyquist capacity of a channel = 2 x 5 x 1000000 x log₂1024

= 10000000 x 10 = 100000000 bps = 100 Mbps

  

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