I'm still new in OFDM and reading about it, but I have a question.

In OFDM system, when having $N$ data symbol assigned to sub-carriers, $N$ should be orthogonal with each others, which means $NN=0$. That's ok. What's about that matrices $N$ itself?

Is there any property in OFDM saying that $N N^H$ should equal $I$ (where $I$ is the identity matrix)?

  • $\begingroup$ I'm a bit confused by your notation. You say you have $N$ data symbols, so $N$ seems to be a natural number. But then, you say that $N$ should be orthogonal to something, thus implyting that $N$ is a vector. Also, you say that $NN=0$ ($N$ orthogonal to itself), which doesn't make any sense. Please clarify your question so we can help you out. $\endgroup$ – Tendero Sep 3 '18 at 14:16
  • $\begingroup$ @Tendero I modified the question .. could you please re check and help .. $\endgroup$ – Fatima_Ali Sep 3 '18 at 15:51

You're conflating two different definitions of orthogonal.

  • Orthogonal in the OFDM sense means that the subcarriers are mutually orthogonal to one another from the perspective of a correlator-based receiver (the optimum receiver for the AWGN channel).

  • An orthogonal matrix $\mathbf{A}$ is one whose columns are all unit vectors that are jointly orthogonal to one another, such that $\mathbf{AA^H} = I$.

These two concepts aren't related; there is no constraint on the modulation applied to the various subcarriers in an OFDM symbol. The orthogonality is imposed via careful choice of the symbol period and subcarrier spacing, typically implemented using DFTs since it conveniently provides the desired time/frequency grid.

  • $\begingroup$ Ok .. thank you for that clarification... let me explain the question in another way, suppose that we have F which is $N$ by $N$ DFT, does $F F^H$ have any special results in OFDM? $\endgroup$ – Fatima_Ali Sep 4 '18 at 6:17
  • $\begingroup$ It’s not clear what you’re asking. $\endgroup$ – Jason R Sep 4 '18 at 11:37

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