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While implementing CPM, FSK, and PSK, The formula to analyze the Bit rate is

$$ R_{b} = R_{s} \log_{2} \left( M \right) \tag{1} \label{1} $$

If the values of $M = \left[2 \, 4 \, 8 \right]$ then $R_{b}$ would remain the same for all the different modulation schemes. But while analyzing the BER over different values of SNR the CPM, FSK, and PSK show different behaviors.

So while calculating the bit rate why do we not consider the channel requirements or the BER impacting the transmission? Similarly, the $R_{b}$ is actually the theoretical bit rate of any modulation scheme. How can we calculate the effective bit rate of a modulation scheme based on the conditions of channel?

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It seems you're confused between two rates.

The equation you refer to, i.e. $R_b=R_s\cdot \log_2(M)$, is the raw bit rate at the transmitter and is indeed indifferent to modulation kind (but is directly related the the size of the constellation). $R_s$ is the rate at which the transmitter emits symbols, and $R_b$ its rate of emitting bits.

The second rate is what is usually referred to as throughput, and is a much more complicated size. As you state yourself, it depends on the channel, but not only on it. It also depends on the error correction code (ECC) used, which adds more redundancy. In a practical system, there are even more overheads such as training signals / pilots, kernel margins, ISI guard time, and perhaps more.

When designing a system, both rates are important. The second rate, i.e. the throughput is the datarate as far as an end used is concerned. The first is importaant for designers, for instance to decide on the clock needed for the digital part, and for sample rates at ADC and DACs.

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  • $\begingroup$ Yes, I want to calculate the throughput at the end. Is there a specific formula or method to calculate it? Any helping link or any material related to it would be appreciated Thanks $\endgroup$ Commented Aug 31, 2024 at 16:55
  • $\begingroup$ @FatimaHaider I’m unaware of such a standard closed form formula and it depends on how realistic you want to be. As a first approximation you can use the raw data rate times the ECC code rate, but already then you’re analyzing not only the modulation but also specific codes. As I’ve said, this doesn’t spend only on modulation. $\endgroup$ Commented Aug 31, 2024 at 21:33
  • $\begingroup$ I understand it now, and your help was handy. Thank You $\endgroup$ Commented Sep 1, 2024 at 15:02
  • $\begingroup$ However, there is one more thing that I would like to confirm. If we get the Rb i.e. the data rate from the above formula without considering other factors can we use Reff = Rb*(1-BER) to get the loss that will be caused through channel conditions? $\endgroup$ Commented Sep 1, 2024 at 15:05
  • $\begingroup$ @FatimaHaider only if you ignore other factors such as error correction code rate, training signals and other realistic overheads. As I said, the data from user point of view depends on many things. If you find the question answered please mark it as such. $\endgroup$ Commented Sep 1, 2024 at 18:38

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