Problem statement is ready to review

[XingzhiMac]

Hello Dr. @smiths

I would like you to review my problem statement at https://github.com/XingzhiMac/CAS741-Proj/blob/master/docs/ProblemStatement/ProblemStatement.tex

Thanks very much.

[smiths]

Great start @XingzhiMac. I only have a few comments/questions on your problem statement, as follows:

• Your problem statement is clear on the inputs and outputs, but I find that I need a bit more information on how the outputs will be calculated. I don't want details (the presentation should remain abstract), but I need more information to judge feasibility. Is there a standard equation you are using? I believe (?) that you mentioned ray tracing. Will you be using ray tracing?
• Unless you have a constraint that you need to use Windows and Python, this information should not be included in your problem statement (keep it abstract)
• With respect to portability, why limit the system to Windows? Since you are planning on using Python, it shouldn't be hard to run it on different OSes. Is there a reason for this constraint?

Once you address these concerns, I'll close the issue and approve your problem statement.

[XingzhiMac]

Hi Dr. @smiths , here are my answers to the above questions/comments:

1. How to calculate the outputs? The output (received signal strength) will be the strength of a combined signal. This combined signal is the sum of the Line-Of-Sight (LOS) signal and first-order reflected signals. For the LOS signal, we can calculate its strength as a function of the distance between the signal source and the sampling point by free-space path loss model (https://en.wikipedia.org/wiki/Free-space_path_loss) derived from Friis Equation of Transmission (http://www.antenna-theory.com/basics/friis.php). For each 1st-order reflected signal, we can first mirror the signal source in the reflection plane (in this project each wall is a potential plane of reflection) by Image-Source Method (https://reuk.github.io/wayverb/image_source.html) and then use the distance between the mirrored signal source and the sampling point to find the unaugmented signal strength by free-space path loss model. The last step is to multiply the unaugmented signal strength by the coefficient of reflectivity of the wall to get the "real" reflected signal strength. Since all of these radio signals are in sinusoidal form, we need to consider each signal's phase when we add them together. Making the LOS signal a reference (phase angle = 0), we can determine the phase angle of each reflected signal by phase difference formula (https://byjus.com/physics/relation-between-phase-difference-and-path-difference/). Now we have both strength and phase angle for each signal, calculating the combined signal then becomes a basic complex number addition problem. I made a number of assumptions in this method (e.g. we only consider direct reflections, walls have no thickness, 2nd or higher-order reflections are negligible). I think it is better for me to discuss them further in Requirements, not here.

2. Keep the problem statement abstract. Thanks for your comment. I have updated the file and removed the lines about Python and Windows.

3. Is there a reason for limiting the system to windows? No. Thanks for pointing out this mistake of mine. I have reasons to make it compatible with Windows, but not to limit it on windows.

Thanks very much!

[smiths]

Sounds good @XingzhiMac. Your problem statement is approved.