I'm looking two papers https://ieeexplore.ieee.org/abstract/document/9370130 and https://ieeexplore.ieee.org/abstract/document/8855846.

In the first paper, achievable rate is

enter image description here

w_n is bandwidth. p_n is transmit power. h is channel gain.

And in second paper, achievable rate is

enter image description here

P is transmit power. H is channel gain.

What I curious is the difference between two same formula, the presence of bandwidth.

In first formula, there is bandwidth, however in second formula, there is no bandwidth in there(in the fraction part, denominator). What's the difference?

  • 1
    \$\begingroup\$ \$w_i\$ seems to be the bandwidth term in the second formula, so what's the question about? \$\endgroup\$ Jun 7, 2022 at 11:13
  • \$\begingroup\$ the question is that there is no bandwidth in second formula(in the fraction part, denominator) \$\endgroup\$
    – new_be
    Jun 7, 2022 at 11:15
  • \$\begingroup\$ Please clarify your specific problem or provide additional details to highlight exactly what you need. As it's currently written, it's hard to tell exactly what you're asking. \$\endgroup\$
    – Community Bot
    Jun 7, 2022 at 11:37
  • \$\begingroup\$ @MarcusMüller sorry for my misclarifing my problem \$\endgroup\$
    – new_be
    Jun 8, 2022 at 2:45

1 Answer 1


\$N_0\$ is the noise density, something that gives power per bandwidth, and since power is energy per time, and time is the inverse qunatity to bandiwdth, \$N_0\$ is an energy.

It makes no sense to divide a power \$P_i\lvert H_i\rvert^2\$ by an energy, and add it to 1, because you can't add a dimensionless number 1 to something that is a bandwidth.

In other words, the second formula can't be correct.

(If you want a hint: Look at where these two papers were published: One paper was published on the IEEE Communications Letters, which is a highly-reknown peer-reviewed journal, and the other had both the words "international" but stress on "in China" in its name, which says it's a regional conference, not a peer-reviewed journal, who tries to attract a wider publishers' audience, with lesser focus on publishing the best works.)

  • \$\begingroup\$ thanks a alot!! I solved my problem \$\endgroup\$
    – new_be
    Jun 8, 2022 at 2:43

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