Introduction to OFDM – orthogonal Frequency division multiplexing

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In modulations, information is mapped on to changes in frequency, phase or amplitude (or a combination of them) of a carrier signal. Multiplexing deals with allocation/accommodation of users in a given bandwidth (i.e. it deals with allocation of available resource).
OFDM is a combination of modulation and multiplexing. In this technique, the given resource (bandwidth) is shared among individual modulated data sources. Normal modulation techniques (like AM, PM, FM, BPSK, QPSK, etc.., ) are single carrier modulation techniques, in which the incoming information is modulated over a single carrier. OFDM is a multicarrier modulation technique, which employs several carriers, within the allocated bandwidth, to convey the information from source to destination. Each carrier may employ one of the several available digital modulation techniques (BPSK, QPSK, QAM etc..,).

Why OFDM

OFDM is very effective for communication over channels with frequency selective fading ( different frequency components of the signal experience different fading). It is very difficult to handle frequency selective fading in the receiver , in which case, the design of the receiver is hugely complex. Instead of trying to mitigate frequency selective fading as a whole (which occurs when a huge bandwidth is allocated for the data transmission over a frequency selective fading channel), OFDM mitigates the problem by converting the entire frequency selective fading channel into small flat fading channels (as seen by the individual subcarriers). Flat fading is easier to combat (compared to frequency selective fading) by employing simple error correction and equalization schemes.

Difference between FDM and OFDM:

OFDM is a special case of FDM ( Frequency Division Multiplexing). In FDM, the given bandwidth is subdivided among a set of carriers. There is no relationship between the carrier frequencies in FDM. For example, consider that the given bandwidth has to be divided among 5 carriers (say a,b,c,d,e). There is no relationship between the subcarriers ; a,b,c,d and e can anything within the given bandwidth.

If the carriers are harmonics, say (b=2a,c=3a,d=4a,d=5a , integral multiple of fundamental component a ) then they become orthogonal. This is a special case of FDM, which is called OFDM (as implied by the word – ‘orthogonal’ in OFDM)

Designing OFDM Transmitter:

Consider that we want to send the following data bits using OFDM : D = {d0,d1,d2,…). The first thing that should be considered in designing the OFDM transmitter is the number of subcarriers required to send the given data. As a generic case, lets assume that we have N subcarriers. Each subcarriers are centered at frequencies that are orthogonal to each other (usually multiples of frequencies).

The second design parameter could be the modulation format that we wish to use. An OFDM signal can be constructed using anyone of the following digital modulation techniques namely BPSK, QPSK, QAM etc..,
The data (D) has to be first converted from serial stream into parallel stream depending on the number of sub-carriers (N). Since we assumed that there are N subcarriers allowed for the OFDM transmission, we name the subcarriers from 0 to N-1. Now, the Serial to Parallel converter takes the serial stream of input bits and outputs N parallel streams (indexed from 0 to N-1). These parallel streams are individually converted into the required digital modulation format (BPSK, QPSK, QAM etc..,). Lets call this output S0,S1,..SN. The conversion of parallel data (D) into the digitally modulated data (S) is usually achieved by a constellation mapper, which is essentially a look up table (LUT). Once the data bits are converted to required modulation format, they need to be superimposed on the required orthogonal subcarriers for transmission. This is achieved by a series of N parallel sinusoidal oscillators tuned to N orthogonal frequencies (f0,f1,…fN-1). Finally, the resultant output from the N parallel arms are summed up together to produce the OFDM signal.

The following figure illustrates the basic concept of OFDM transmission (note: In order to give a simple explanation to illustrate the underlying concept,the usual IFFT/FFT blocks that are used in actual OFDM system, are not used in the block diagram) .

OFDM Transmitter
OFDM Transmitter

Example:

The first example illustrates the concept of OFDM transmission with BPSK modulation as its underlying modulation format. The second example illustrates the OFDM transmission with pi/4 shifted QPSK modulation. Here 5 orthogonal subcarriers are assumed for the OFDM transmission.

See also:

(1) An OFDM Communication System – Implementation Details
(2) Role of Cyclic Prefix in OFDM
(3) Simulation of OFDM system in Matlab – BER Vs Eb/N0 for OFDM in AWGN channel

16 thoughts on “Introduction to OFDM – orthogonal Frequency division multiplexing”

  3. Hi Mathurathan. Excellent information here. Can I ask how the constellation mapper will work if the mapper does 64-QAM? Here, we can see that you have five parallel streams going into the mapper —- ie. d0, d1, d2, d3, d4. So does this mean that the 64-QAM mapper needs to collect six consecutive bits of d0 before it can generate a single complex value S0? And similarly, the 64-QAM mapper will need to collect six consecutive bits of d1 before it can generate S1? Thanks Mathurathan!

    Reply

      • Thanks for your help and your time Mathurathan. Totally appreciated here. The information that you’ve shared is incredibly useful already. I purchased your ebook the other day. Very nice material in it. Amazing effort you put into it. Also, thanks for letting me know how the 64-QAM ties with the IFFT side of things. It was something that I didn’t understand before — not from your material, but just in general. I found there was some kind of lack of basic run-down by other people (other sources), where people have a hard time grasping the theory due to gaps missing. But the detail that you provide appears to be far better than what I’ve seen elsewhere. For example, I didn’t know whether the input to the IFFT (for 64-QAM) was merely a sequence of 6 unipolar binary bits, or a sequence of 6 bipolar bits. I think I incorrectly thought that the input to the IFFT was just 6 plain bits….like [1 0 1 0 0 1] or bipolar form [-1 1 -1 1 1 -1]. Then I noticed that the IFFT of these 6 bit sequences can have IFFT output sequences containing some values of zero (ie. 0 + j0)…. ie. some ‘zero’ elements. I figured that wasn’t going to down well with using the real and imaginary parts to modulate cos and sin waves (respectively). So I then focused on the definition of ‘constellation mapper’ for 64-QAM, which doesn’t seem to be clear from sources that I’ve found so far. I guessed that the mapper not only had the function of grabbing 6 consecutive data bits at a time, but the output would be a complex number (representing a vector) that is able to represent those 6 particular bits. But after that, I wondered — if the mapper only outputs one complex number (a single vector), then we’d be doing an IFFT of 1 single complex value. So this didn’t make sense to me. But then, I figured that maybe the real case is multiple 64-QAM mappers all operating in parallel. Each mapper taking in 6 bits at a time, and each one outputting a complex number. So if we had 5 mappers working in parallel, then we’d get 5 complex numbers coming out of this parallel system, where each complexer number is associated with 1 QAM symbol (and 1 QAM symbol is representing 6 particular binary bits). The input to the IFFT would be these 5 complex values for example. The IFFT output would also be 5 complex values, all in parallel. However, since the IFFT outputs are going to be tied to a time-changing ‘sequence’, then the parallel IFFT output (eg. 5 complex values) would then be pushed out (one at a time) in a time sequence fashion. In order to preserve the real and imaginary values of each complex value, we split each complex value into real and imaginary value, and operate on the real and imaginary values in a parallel fashion. The real value can be used to modulate a cos wave ( ie. multiply the real value with cos(wt) ), and the imaginary value can be used to modulate a sin wave. And since the modulated cos wave is a real-valued signal, just like the modulated sin wave, those two waveforms can be added together by summation. The summed modulated cos and sin waves (as a function of time) is the OFDM signal. I may still have the wrong idea about certain aspects of generating OFDM from IFFT. But this was the kind of thought-process that I was going through. The information you’ve provided seems to be the most user/student/scholar friendly —- as it really makes a tremendous attempt to teach and explain the details properly. Thanks Mathuranathan!

        Reply

  4. Hi Mathuranathan,

    Thanks for the possibility to discuss with you.

    Can we say that the “coding QAM” is integrated, included in the IFFT process of OFDM?… Or, is it a separated operation.

    I’m not expert of that.

    I would suppose it is included in the IFFT process. Is it possible to have some words, to allow a better understanding of how it is done?

    Best regards,
    Michel

    Reply

  5. Hi Mathuranathan,

    Is there really a difference between DMT and OFDM modulations. DMT is used for ADSL and G.fast for example. OFDM is not only used for wireless. We can find it for coaxial cable technologies, as DOCSIS and EPoC (a new IEEE specification based on DOCSIS).
    DMT and OFDM are both orthogonal with IFFT and FFT.
    Best regards, Michel

    Reply

    • The frequencies depend on the band allocation for the transmission.

      Given a frequency band for transmission, the carrier frequencies fi are related by fi = f0 + ifd, where f0 is the smallest carrier frequency, and fd is an integer multiple of the OFDM symbol rate 1/T. This property enables frequency bands to overlap without
      causing interference to each other. We can also observe the orthogonality of the OFDM subcarriers in frequency
      domain. Each OFDM symbol contains subcarriers of constant nonzero envelope over a T-second interval.
      https://uploads.disquscdn.com/images/bf2ddd01bdf7e87423a81d56e2c88ce5415a83b7c00bf39bc73d92a8ce36122c.png

      The OFDM spectrum is shown in the figure attached. We observe that at the maximum of each subcarrier spectrum all other subcarrier spectra have amplitude zero, thus we can demodulate each subcarrier without interference from others.

      Reply

      • Hi Mathuranathan,

        Many thanks for this adapted explanation. That’s really excellent for me, because I’m not an expert of this domain. I appreciate such a figure, with the different subcarrier amplitudes. Best regards.

        Reply

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