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I'm looking at decoding an OFDM signal which consists of 6 carriers (or tones) which are BPSK modulated and a pilot tone which aids tuning. This is the first time I have worked with OFDM so I need to know if I'm approaching this in the right way.

The way I'm thinking of decoding it is to use the pilot tone to calibrate (as the receiver may be slightly mistuned) then to have six band pass filters to separate out each carrier which is then demodulated in the usual way. Can anyone see any problems with this ? or can you suggest a better way of doing this.

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    $\begingroup$ Are you sure that the carriers are BPSK modulated? QPSK or QAM might be in use. Also, there is typically more to OFDM demodulation than just demodulation of BPSK in six parallel channels, and you may also need to be concerned about things like cyclic prefix etc. I suggest doing some reading first and not trying to wing it based on what you know about BPSK modulation. $\endgroup$ – Dilip Sarwate Oct 4 '11 at 20:07
  • $\begingroup$ You could try this gaussianwaves.com/2010/10/… $\endgroup$ – user2105 Oct 12 '12 at 9:24
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One of the nice features of OFDM is that it allows a very simple structure for the modulator and demodulator: given a set of symbols (in general complex-valued, taken from a signal constellation such as BPSK, QPSK, or QAM) to map onto each carrier, the modulator can be implemented using an inverse discrete Fourier transform, typically implemented using an FFT. Each set of symbols (one per carrier) is transformed to yield an OFDM symbol, which is then sent to the channel. The DFT length will typically be chosen to be larger than the number of desired carriers to allow some "guard band" near the system Nyquist rate.

In addition to the above DFT-based structure, most OFDM systems also incorporate a cyclic prefix, which allows for simple implementation of an equalizer in the frequency domain. Equalization can provide improved link performance in multipath environments (e.g. many wireless communication scenarios). It can also be used to aid in synchronization, as described below.

The simple structure carries over to the receiver; an OFDM waveform can be demodulated using the inverse transform to that used at the transmitter, yielding the original symbol values. The inverse to the inverse DFT used at the transmitter is a "regular" (forward) DFT. Thus, you will often see OFDM receivers diagrammed with an "FFT" block at the front end. The output of the transform contains the symbol values mapped onto each of the carriers, including all of the unused ones that make up the guard band. The demodulator plucks out the (complex-valued) amplitudes of each of the carriers of interest and passes those on to any further decoding logic (equalization as described above, channel decoding, mapping to bits, etc.).

As usual, however, the answer isn't quite so simple; the above explanation overlooks some important issues that must be addressed for a practical system:

  • Timing synchronization: When you actually think about how you would build an OFDM receiver, one of the first problems you will run into is how to align the receiver's FFT frame with the stream of incoming samples. Synchronization with the OFDM signal's symbol timing is required to properly align the receiver's FFT operation with the appropriate time period in the observed sample stream.

    This can be implemented using a correlation-based approach. As stated previously, most OFDM waveforms include a cyclic prefix, which is a scheme of forceably adding some circular periodicity to the transmitted waveform. This can be exploited at the receiver to obtain symbol timing; the timing detector simply calculates the sliding autocorrelation of the observed symbol stream using a lag commensurate with the known period between the transmitted signal and its cyclic copy. The magnitude of the result will reach a peak at the instant that corresponds to the start of each OFDM symbol.

  • Frequency synchronization: Fine frequency synchronization is also key to robust OFDM reception, as frequency error causes intercarrier interference. Correction of frequency error can also be estimated using the timing synchronizer's correlator output. As stated previously, the autocorrelation of the observed stream at a lag equal to the cyclic prefix delay has a large magnitude at the start of each OFDM symbol. The phase of the correlator output provides a measure of the amount of phase drift over the course of each symbol time. This measure of "phase drift per unit time" can be recast as a measure of "frequency drift" instead. If the receiver can safely assume that the frequency error is constant over the course of a symbol time (which is reasonable for many cases), then the bulk frequency offset can be removed before calculating the DFT.

There can be even more problems to tackle for each of your carriers, depending upon the modulation used on each. For the simple case of BPSK, you may also need to worry about phase synchronization if you desire a coherent receiver. However, synchronization of timing and frequency are the key implementation details that often seemed to be glossed over in discussion of OFDM receiver structures.

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  • $\begingroup$ Its all fun and dandy until we introduce doppler... :-P $\endgroup$ – Spacey Nov 7 '11 at 3:48
  • $\begingroup$ Doppler shift (as well as all other sources of frequency offset) is what I'm talking about in the "Frequency synchronization" bullet above. There are very few cases where you have the luxury of not handling frequency offset in a receiver. How you attack the problem may differ based on your requirements and the topology of your system, but the problem is still there. $\endgroup$ – Jason R Nov 7 '11 at 13:45
  • $\begingroup$ I saw that, but I am pointing out that based on lots of the literature I have read, doppler spreading seems to be the nemesis of OFDM, more so than typical freq offsets based on clocks. Why that is I dont know. $\endgroup$ – Spacey Nov 7 '11 at 14:39
  • $\begingroup$ I would expect that the angle of the complex-valued auto correlation peak can only be used to fine-tune the frequency synchronization. What about larger shifts? What's the best practise in that regard? Isolated pilot tones? Thanks for the great answer! $\endgroup$ – sellibitze Sep 15 '12 at 15:35
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Normally OFDM is demodulated using FFTs. But if you have a very few number of carriers, you might be able to use a small number of orthogonal quadrature demodulators (1-bin DFTs, or complex-output Goertzel filters), depending the number of carriers vs. log(n) the length of each DFT frame (each frame of a length where the frequency of all carriers are orthogonal to one another and the pilot).

You will also need to find a way to synchronize the decoding frames so that they do not cross the encoding frames transition times (nor near the very beginning of each transition where multi-path problems are more likely).

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