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Recently, I've ventured into a new domain that I intend to incorporate into my work. After thorough research and consultation, I've found this model to calculate the data transmission rate (Capacity).

The data transmission rate for offloading task $ i \in I $ to server $v \in V $ (volunteer or cloud) is denoted as $ r_{iv}$. We calculate it as follows:

  • $B_i$: Wireless bandwidth of the corresponding end-device (Mbit/s).
  • $P_i$: Transmission power in dBm.
  • $d_{ij}$: Distance between the user device and server (either volunteer or cloud) in km or meters.

Noise Power

First, compute the noise power, $\omega_0$, in dBm: $$ \omega_0 = -174 + 10 \log_{10}(B_i) $$

Channel Gain

Next, the channel gain, $ h $, in dB is computed as: $$ h = 10 \log_{10} \left( \frac{\lambda^2}{(4\pi)^2} \right) - 20 \log_{10}(d_{ij}) $$ Where $ \lambda$ is the wavelength (e.g., 0.1 meters).

SNR in dB

The Signal-to-Noise Ratio (SNR) in dB is: $$ \text{SNR}_{\text{dB}} = P_i + h - \omega_0 $$

Conversion of SNR from dB to Linear Scale

$\text{SNR}_{\text{linear}} = 10^{\frac{\text{SNR}_{\text{dB}}}{10}}$

Transmission Rate

Finally, the transmission rate, $ r_{iv} $, is: $$ r_{iv} = B_i \log_2(1 + \text{SNR}_{\text{linear}}) $$

**Now, I believe there's an issue: In the formula for $\text{SNR}_{\text{dB}}$, we are adding $ \omega_0 $(measured in dBm) and $h$ (measured in dB). Can we directly sum these quantities due to their differing units? I would greatly appreciate any insights or feedback from you all. I've invested a significant amount of time in this endeavor and have done my utmost to ensure its accuracy and relevance.

It is like If we have 1 kg of apples and 1g of apples, we simply cannot sum up because 1 kg + 1 g = 2 ??? makes no sense.

You can sum up either kg or g: 1 kg + 0.001 kg = 1.001 kg 1000 g + 1 g = 1001 g

If $SNR_{db}$ is in dB, then $\omega$, which is in dBm has the wrong unit.

**

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1 Answer 1

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Yes, you can just add these quantities. $\omega_0$ is just a gain. In linear domain, this would be a factor, in logarithmic domain, this transforms to a summand.

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  • $\begingroup$ Sorry, I think the answer does not address the issue. If you have 1 kg of apples and 1g of apples, you simply cannot sum up because 1 kg + 1 g = 2 ??? makes no sense. You can sum up either kg or g: 1 kg + 0.001 kg = 1.001 kg 1000 g + 1 g = 1001 g If SNR_db is in dB, then omega, which is in dBm has the wrong unit. $\endgroup$ Oct 20, 2023 at 19:26
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    $\begingroup$ You need to take a look at the definition of "dB". It is NOT a physical unit. It is always a RATIO. "dBm" means "regarding 1 mW", "dB" means "regarding 1". Both are just factors. And they are expressed logarithmically, so, yes, you can just sum them up, which corresponds to a multiplication in linear domain. $\endgroup$
    – Max
    Oct 21, 2023 at 14:01
  • $\begingroup$ Great dear. Thanks $\endgroup$ Oct 22, 2023 at 14:59

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