I have already coded the phased array antenna radiation pattern for my university project with Matlab. I will probably do this again for my master's thesis (phased array patch antenna).
Is there any difference between coding this in C++ or Matlab？It seems to me that the difference is not that much, as it is all about mathematic formulas.
is there any difference between coding via the C++ and matlab？
It's two pretty different programming languages.
The ways you implement something in Matlab and C++ will be very different (or your C++ will be pretty bad).
Also, the tooling that Matlab offers on one hand is terribly bad (really. The matlab editor as is is an atrocity, and the fact that Matlab code never comes with any unit testing framework is a testament to how sub-par a lot of matlab code is, in terms of software quality. It really is.)
If you don't know how to program C++ yet, you will need to learn it; that takes time.
It makes sense to get a good, modern book, as the way you'd want to write C++ has changed a lot in the last couple of years. Don't get a book that teaches C. Don't get a book that promises results after N days. The oldest you should go is Lippman's "C++ Primer", 5th edition. If you already know programming in a larger context using "proper languages" (like, something interfacing with multiple libraries in Python, or Rust, or Go, NOT matlab scripts that do one thing from top to bottom and call three self-written functions or e.g., isolated PHP scripts), Stroustroup's "A Tour of C++" 2nd or 3rd edition will do. If Matlab is the language you feel most at home in, stick with "C++ Primer". Your university library should be able to get you a copy of the newest edition – ask them, and tell them it's considered the reference textbook on C++.
Your statement
it seems to me that the difference is not that much
is what I, as a repeat supervisor of student theses, would call "classic student overconfidence". Not a bad thing to be optimistic! But writing a complicated simulator in a language that has way fewer math tools built in than Matlab has is not as straightforward as you seem to think.
The fact that someone asks you to reimplement some Matlab as C++ as your master thesis is a strong indication that your supervisor doesn't think it'll be trivial to you: It would be a terrible waste of a master student to let them just do trivial code translation in their thesis. And the demand for a C++ version indicates your Matlab version isn't good enough in some aspect – probably speed. So, you'll be asked to not just deliver some mostly working C++, but actually an fast implementation. Not an easy task to beat Matlab at linear algebra! What C++ allows you to do much nicer is fast control structures and reasoning about complex objects, isolating them and allow for much better parallelization.
But that requires an algorithmic understanding of your problem that probably goes beyond what you've done in a project – which is fine, it's a Master thesis after all, so you will be given time to understand, implement and refine.
Have fun! C++ is a mighty, and sometimes daunting language, but the more "modern" you stay in style (i.e. the more you avoid copied-since-the-1990s answers from the internet), the easier, safer and better to parallelize you get.
MATLAB is easier than C++. Learning C++ may take a while although the effort usually pays off. If you just need to write algorithms for mathematical formulae or equations, you can use C instead of C++ or just use C-style C++ which may work well for your thesis. If you have lot of time, you can learn C++ with a primer book and The C++ programming language book and implement your project in C++. If you don't have time, implementing your project in C-style C++ may be best.
Here's a slightly different perspective. In the early 70's, we (my company, not me personally) wrote pattern code in Fortran. We also wrote some E&M field solvers in Fortran to analyze high voltage breakdown.
After maybe 20 years of that, we started using MatLab to do the pattern analysis. We would take in the reams of data that came out of of our near field range systems and process it to determine the antenna beam pattern that was being created.
Recently, a lot of the recent grads (<10 years) have moved on to using Python to analyze and predict antenna patterns. But MLab is still used to process antenna range data.
I am not aware of anyone that wrote C (or C++) code to do this. One advantage Mlab had was the wealth of visualization tools that came with the program.
