I am new to communication systems and am working on a model for task offloading on edge computing. One key parameter I'm aiming to determine is the data transmission rate. While I am familiar with Shannon's capacity formula, I've noticed that some resources incorporate channel gain, especially with respect to distance, and some not. This has introduced some confusion for me.

System Setup:

-Distance Range: From a few meters to several kilometers.

-Devices: Regular phones or laptops (as edge devices) and cloud servers.

Known Parameters:

Transmission Power

White Gaussian Noise Power

Path Loss Exponent

Points of Confusion:

Some resources suggest that the channel gain is a function that multiplies with distance. How is this typically modeled? I've also come across references where the noise power is multiplied by the bandwidth. How does this impact the overall transmission rate calculation? Questions:

With the known parameters and points of confusion, what are the well-known approaches to determine the transmission rate for such a system setup?

-How does Shannon's formula or other related formulas adapt when incorporating channel gain affected by varying distances?

-Are there specific models or formulas that consider channel gain with distance before determining transmission rate?

-Are there any other specific considerations I should be aware of, given the distances and the type of devices involved?

After reviewing numerous resources, I've found these formulas that seem to align with my model for determining the transmission rate. I would appreciate any feedback or suggestions

I would greatly appreciate any insights, references, or clarifications on this matter.

Also please on the comments let me how I make my post clear for expert Thank you!

• My strong advice: if you're new to this field, and you're studying networks and not the physical layer, IGNORE Shannon's theorem. It does not apply. Ignore textbooks that mention it -- most networking textbooks misunderstand and misuse the theorem.
– MBaz
Oct 9, 2023 at 22:23
• @MBaz. Thanks for the comments. I have update the post. Do you mean this above formula that I should ignore. Or it looks fine Oct 10, 2023 at 13:17
• Hard to tell. It is a capacity, though, so a (not necessarily realistic) upper bound on the actual rate. The authors seem a bit careless with the details (for example, $\sigma^2_{uu}$ is not noise, but its variance). They assume a fading channel, something you didn't state in your question.
– MBaz
Oct 10, 2023 at 14:07
• @MBaz Yes, It is a capacity. Please take a look at the answer below. Let me know if it's correct, or if I should delete it. Oct 10, 2023 at 14:21

Shannon has no role to play here. My advice is to follow these steps.

1. Figure out the bit rate of the link. Not the information rate -- the actual raw number of bits that are transmitted per second.

2. Figure out the length (in bits) of an average frame.

3. Figure out the rate and the probability of bit error of the modulation/error-correcting code combo in use by the devices.

4. Using the path-loss exponent model, figure out the average received power and from there the average per-bit SNR (assuming a certain noise level in the receiver's front-end).

5. Finally, figure out the probability that a frame is received with non-corrected errors. This frame will have to be retransmitted after some sort of ARQ protocol, reducing your information rate.

6. Tweak the parameters until you get an acceptable information rate.

This process will give you a first-order estimate of the rate that can be achieved. As you learn more, you will find out how to improve this model -- even to the point of understanding the role of channel capacity in a problem like this. It's also, in my opinion, not something that a newcomer to this field can attempt in a couple of days. I'd recommend to start by reading some textbooks such as Goldsmith (at least the first 2 or 3 chapters).

I developed this model, but I believe it currently presents the capacity rather than the actual rate. I've taken care to introduce each parameter meticulously.

• I think you're missing temperature in the noise power calculation. I'd also include the receiver's noise figure. The channel gain calculation seems to assume the exponent is two (free space), but in general it will be different (depends on the environment). You may also want to include the antenna gain, if they're not isotropic.
– MBaz
Oct 10, 2023 at 17:27
• @MBaz. Thanks for these valuable information. I will incorporate them one by one. Oct 11, 2023 at 8:33