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I work on a VLC system in which 16-PAM symbols with complex pilot symbols are as ifft input. I made the ifft output real and positive. Now how should i use these ofdm symbols to modulate LED? Their apmlitude or their power are used to be multiplied by time domain response time of LED?

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  • $\begingroup$ Hi! Eventhough someone who works on the same problem might give you an answer, to increase your chance of getting a valuble response please consider the following: What is VLC for (Variable Length Coding?) and what is a LED (Light Emitting Diode?) and what is it to do with IFFT (Inverse FFT?) and what do you mean by making the ifft output as real and positive ? What is you overall goal, and what have you accomplished and where exactly are you stuck in? $\endgroup$ – Fat32 Jun 14 '16 at 11:42
  • $\begingroup$ VLC stands for Visible Light Communications. $\endgroup$ – Deve Aug 7 '16 at 7:55
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OFDM in general is a complex baseband technology, which means it produces an I and a Q signal, which have to be mixed with a carrier wave and it's 90° shifted version, and added up before it can be used to excite a real-valued emitter (like an antenna or an LED driver).

By "I made the IFFT output real" you probably mean that you supplied the IFFT with a symmetric signal? That's nice, because it circumvents the need for a carrier frequency, but it also inherently halves your available bandwidth! Also, I can't fight the feeling that the discrete Fourier transform is not really what you're looking for if you just want to produce a real signal – the discrete cosine transform might be better suited for you.

The core question here is why you want to use OFDM in the first place.

The main motivation for OFDM comes from something that is highly inherent to the RF channel: Channels of high bandwidth aren't flat, so the equalizer for something like 20MHz of WiFi channel gets really ugly. Here, you can gain a lot by dividing your channel into orthogonal subchannels, and equalize them with a much simpler equalizer individually. I wasn't aware the same problem applies to the monochromatic VLC channel!

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  • $\begingroup$ It is quite common to use OFDM with a complex conjugate symmetric input to produce a real valued signal for lowpass channels. A prominent example is the digital subscriber line (DSL). $\endgroup$ – Deve Aug 7 '16 at 7:57
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As a light emitting diode (LED) emits incoherent light, the phase $\phi(t)$ of the emitted electrical field component (in the equivalent baseband) $$E(t)=E_0(t) \mathrm e^{\mathrm j \phi(t)}\tag{1}\label{E}$$ is uncontrollable. Consequently, it can not be used for transmitting information. Only the amplitude $E_0(t)$ can be used for that purpose.

A VLC system using OFDM as modulation scheme and an LED as light source could be constructed as follows.

  • Create an IFFT input vector $X(k)$ exhibitting a conjugate complex symmetry to
  • obtain an IFFT output vector $x(n)$ which is real valued
  • convert $x(n)$ to an analog signal $\tilde x(t)$
  • add a constant bias $b$ to this signal so that $\tilde x_\mathrm b(t)=\tilde x(t)+b$ is positive
  • modulate the current $i_\mathrm L(t)$ driving the LED such that $i_\mathrm L(t)=I_0\tilde x_\mathrm b(t)$

The emitted optical power $P$ of the LED is approximately proportional to its driving current: $$P(t)=R_1 i_L(t).\tag{2}\label{P1}$$ Furthermore, $$ P(t) =R_2|E(t)|^2 \tag{3}\label{P2} $$ where $R_1$ and $R_2$ are proportionality constants. Inserting $\eqref{E}$ and $\eqref{P1}$ into $\eqref{P2}$ we get $$ \left|E_0(t)\right|=\sqrt{\frac{R_2}{R_1}I_0\tilde x_\mathrm b(t)}\tag{4}\label{E0} $$ From the above equation we can see, that only the magnitude of the electrical field can be controlled if the LED is modulated through its driving current. This is another reason why $\tilde x_\mathrm b$ should be real-valued and positive.

At the receiver, a photodiode is used to detect the incoming optical power. As its output current $i_\mathrm P(t)$ is again proportional to the optical power and thus to the square of the incident electrical field (take the square of $\eqref{E0})$, $i_\mathrm P(t)$ is a linear function of $\tilde x_\mathrm b$ which is very important for a communication system, especially if it uses OFDM.

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