Questions about reproducing results of a paper on Communication Systems and Wireless Communication I'm trying to reproduce the results of a paper on Device-to-Device Communication, channel assignment and mode selection (G. Yu, L. Xu, D. Feng, R. Yin, G. Y. Li and Y. Jiang, "Joint Mode Selection and Resource Allocation for Device-to-Device Communications," Nov. 2014.).

I have a couple of questions on the noise spectral density, how to generate the channel taps, and finally the throughput of the entire system. 

It is mentioned the following in the paper: 


  "All links are assumed to experience independent block fading.
  Hence, the instantaneous channel gain of the interference
  link between CU m and the receiver of D2D pair k can be
  expressed as
  $$h_{k,m} = Gβ_{k,m}d^{−\alpha}_{k, m},$$ 
  where G is the path loss constant, α is the path loss exponent,
  $β_{k,m}$ denotes the channel fading component, and $d_{k,m}$ is the
  distance between CU m and the receiver of D2D pair k.
  Similarly, we can express the channel gain between CU m and
  the eNB as $h^C_{m,B}$, the channel gain between D2D pair k as $h^D_k$,
  and the channel gain between the transmitter of D2D pair k and
  the eNB as $h^D_{k,B}$."


Towards the last section, we have the following relevant simulation parameters:


Noise Spectral Density: -174 dBm / Hz.
Path Loss Model (for Cellular Links): $128.1 + 37.6 \times \log_{10}(d[km])$.
Log Normal Shadowing: 10 dB.
Uplink Bandwidth: 3 MHz.


Now my questions are related to the channel model:


How do I convert from the Path Loss Model combined with the Shadowing Effect of 10 dB to the first mentioned equation ($h_{k,m} = Gβ_{k,m}d^{−\alpha}_{k, m}$) ?
When I convert the noise spectral density from dBm/Hz to dBm, should
I divide the value by the number of Uplink channels, which is 20 ?
And if so, should I do that in the dB or Watts units ?
Let's tackle this piece by piece:

Path loss

Your path loss model gives the path loss in dB. Convert to linear scale. You can directly read $\alpha$ and $G$ from the result. 

Haven't read that paper (paywalled), but it looks to me like your shadowing should be part of the fading  $\beta$. Make sure your channel model is compatible with the one used in the paper at all! There's no guarantee that different sources use channel models that are.

Power Spectral Density to Power

Well, assuming white noise (check that assumption is correct for this paper!), the noise power in a channel is of course bandwidth of that channel times noise power spectral density.


  should I do that in the dB or Watts units ? 


dB is not a unit!

Generally, the actual units don't matter, as long as you do all the calculations correctly, so it really doesn't matter whether you're working in W or (MeV per minute).

Your first question, however, points to you not being 100% familiar with what dB and dBm are. I strongly recommend reading the Wikipedia article on decibel if that is the case!