By analogy with CDMA and the rich literature on low correlation sequences and allied cyclic codes.
Dear Dr. Patrick Solé, Yes, in an OFDM system the real time domain system is related to the real frequency constellation point x, as Y = Ax, where A is the real representation of the Inverse Fast Fourier Transform. (IFFT).
In my view, there is no deep mathematical problem hidden in OFDMA itself. It is simply a coding technique like others and there is no mathematical depth beyond manipulating few matrices (or a transform). On the other hand, the deep mathematical problem might be hidden where one may apply OFDMA. One needs to devise what mathematical model one can use for the problem where one is applying these coding techniques.
Dear Dr. Ash Mohammad Abbas, Thanks, for the answer. For sake of personal query I want to know how can we differentiate between deep mathematics and surface level mathematics.
In academics, our views can be different. I tried to answer the original question. The question was: Is there any deep mathematical problem hidden in OFDMA? In my view, it was no. In the view of some body else, it may be yes. I respect your views.
Dear Dr. Ash Mohammad Abbas, Good, continue to interact I like the way " In my view, it was no. In the view of some body else, it may be yes". I respect your views." Hope to meet you there in my "ALMA-MATTER" where I got "educated".
I came across your interactions on RG and noted, you are a positive and an enthusiastic researcher. Wishing you all the best. Good Luck. We will keep more interactions.
Dear All, thanks for your attempted answers. Of course if the answer is NO I have to take your word for it. If it is YES I expect a clear cut problem with a context free formulation. Eg no need to be an engineer to understand the paradigm of low correlation sequences. Some of my colleagues claimed that the problem of optimizing the flow thru an OFDMA system was a hard problem but they could not identify the mathematical bottlenecks...
Well if you are looking for a real open problem in OFDM system to work on and contribute, there is a really hard problem which is still unexplored too much. since the biggest problem in OFDMA is PAPR (peak to average power ratio) which makes it improper for power efficient and mobile applications, In my opinion the biggest challenge in OFDM system to find the capacity of an OFDM system under PAPR constraint ! this problem is kinda statistical and information theory and still not well explored. however i am not sure this problem can be well manipulated by a person who is not well experienced in information theory and OFDM system.
@Behrad, I already have an article on PAPR reduction. One of my many papers with Dima Zinoviev...
MR2773903 Indexed
Solé, Patrick; Zinoviev, Dmitrii
Galois rings and pseudo-random sequences. (English summary) Cryptography and coding, 16–33,
Lecture Notes in Comput. Sci., 4887, Springer, Berlin, 2007.
PAPR concept is not new at all. however taking it as a constraint in resource allocation to maximize performance (such as Capacity) is an open problem !
Dear Dr. Patrick Solé, Why not to re-orient and explore towards correlational property.
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