# 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.

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!