Relation between AWGN and bit rate

I want to get the value of the maximum rate of digital information to be transmitted by carrier modulation through an AWGN channel with a bandwidth of $$\ 100\ \mathrm{kHz} \$$ and $$\ N_o = 10^{-10}\ \mathrm{W/Hz}\$$. That is transmitted through the channel for four-phase PSK and four-frequency orthogonal FSK that is detected non-coherently.

I guess some initials that

4-Phase PSK is 4-PSK or QPSK.

4-Frequency orthogonal FSK is 4-orthogonal FSK or 4-ary FSK (M-ary FSK) in non-coherently detection.

Then

for 4-PSK: $$\ bit\ rate (f_b) = bandwidth \$$

and for 4-orthogonal FSK for non-coherent source: $$\ bit\ rate (f_b) = bandwidth/4 \$$

where,

$$\ bandwidth = ((f_b\cdot2^{N+1}/N)\ , N = log_2M\ \text{here}\ M = 4 \$$

But if the signal passes through the AWGN channel, how does it affect the bit rate? I couldn't find the relationship between bandwidth or bit rate and the value of $$\N_0\$$.

Is there any relation between Power Spectral Density and bandwidth or bit rate, and how do I calculate the bit rate from $$\N_0\$$ with bandwidth?

• You also need to know signal power (so you can calculate SNR) and to know the allowed bit-error-rate (BER) Commented Oct 24, 2022 at 18:11
• Are you sure the noise is specified as $N_0 = 10^{-10}{\rm W/Hz}$ and not $10^{-10}{\rm W/\sqrt{Hz}}$? Commented Oct 24, 2022 at 18:20
• @ThePhoton Yes. The noise is specified as $N_0 = 10^{-10} W/Hz$ Commented Oct 24, 2022 at 18:26

Is there any relation between Power Spectral Density and bandwidth or bit rate, and how do I calculate the bit rate from N0 with bandwidth?

There isn't.

Practically, the modulation scheme and bit rate you choose determines the bandwidth required at the receiver, and then the noise power spectral density will determine the noise power. From the noise power and signal power you will get the SNR. And from the SNR you will get the BER.

If you are free to choose an optimal encoding scheme then the Shannon-Hartley theorem gives the maximum achievable error-free bit rate (aka the channel capacity) as

$$C = B\log_2(1+{\rm SNR})$$

If you are free to increase the signal power, you can always increase the SNR and thereby increase the channel capacity.

Note that practically the optimal encoding scheme is not known, however we can achieve arbitrarily low BER at bit rates quite close to this limit, given enough computing power to implement an error-correcting code at the required rate.