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I am not a professional but I'm trying to figure out how OFDM works. It is clear to me that OFDM works with closely spaced subcarriers with orthogonal frequency. Each subcarrier gets modulated with a conventional digital modulation scheme, let say for the sake of this example QAM-4.

Lets say that I have a stream of data 0101 1100 1111 0100 broken up in four parts to be send with OFDM.

What confuses me is this. I know that QAM requires two carriers and uses symbols with two bits. Does this mean that fow every broken part of data stream, OFDM will actually use two subcarriers?

Quirik
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2 Answers2

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QAM does not require any subcarriers at all, it modulates the carrier signal at the carrier frequency.Both the in-phase (I) and the quadrature (Q) components in QAM are modulated at the carrier frequency, the only difference is that the carrier waves used for modulation are \$90^0\$ out of phase i.e the I-component is modulated with \$\cos(2\pi f_ct)\$ whilst the Q-component is modulated with \$\sin(2\pi f_ct)\$, where \$f_c\$ is the carrier frequency.So the use of QAM does not change the number of subcarriers used in a OFDM scheme.And for clarification in a M-QAM scheme, each symbol will represent \$\sqrt{M}\$ bits, a symbol does not necessarily have to represent 2 bits.

In OFDM, we have \$n\$ different subcarriers so instead of transmitting at the carrier frequency \$f_c\$ we will transmit at a set of frequencies \$\{f_i\} \text{ where } i = 1,..,n\$ and where all frequencies in \$\{f_i\}\$ are very close to \$f_c\$.So if for example we use 4 subcarriers and we have your bitstream of \$0101110011110100\$, we would first map the bitstream to parallel symbol streams \$S_{\# 3} S_{\# 2} S_{\# 1} S_{\# 0}\$ and transmit symbol \$S_{\# 0}\$ at \$f_0\$, \$S_{\# 1}\$ at \$f_1\$, ... e.t.c Because we have 4 subcarriers all 4 symbols will be transmitted in parallel.

KillaKem
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  • If I understood correctly, every symbol is transmited at different subcarrier frequency? What if the data stream was broken down in three parts? My guess is that since the amplitude and phase of the subcarrier is changed, we can transmit any symbol with any subcarrier? – Quirik Aug 10 '15 at 14:40
  • E.g. last bits of data stream are mapped to symbols 00, 01, 11, 11 and then ransmitted at f0, f1, f2, and f3 subcarrier frequencies? – Quirik Aug 10 '15 at 14:48
  • No, any symbol can be transmitted at any of the subcarrier frequencies.So even if you have 00 00 11 11 you will still transmit them at \$f_0\$, \$f_1\$, \$f_2\$ & \$f_3\$.The actual symbol to be transmitted has no connection to which frequency it will be transmitted on. – KillaKem Aug 13 '15 at 09:02
  • QAM will use one subcarrier frequency e.g. f0, and its I and Q component, which is 90 degrees out of phase to transmit symbol S0. Is this correct? – Quirik Dec 11 '15 at 15:35
  • QAM uses one carrier at \$f_c\$, you can't call it a subcarrier because there is only one frequency used in QAM modulation. – KillaKem Dec 12 '15 at 10:42
  • But in OFDM, isn't QAM used in every subchannel to send data? E.g. in subchannel 1, uses datastream 1 to modulate subcarrier 1; in subchannel 2 uses datastream 2 to modulate subcarrier 2, etc. as long as subcarriers frequencies are orthogonal. – Quirik Dec 12 '15 at 11:09
  • I must have misunderstood your earlier comment - Yes, in the context of QAM used in an OFDM scheme then QAM symbols will be transmitted over multiple subcarriers, after all OFDM is a multi-carrier scheme. – KillaKem Dec 12 '15 at 14:14
  • I am reffering to the following link https://www.gaussianwaves.com/2011/05/introduction-to-ofdm-orthogonal-frequency-division-multiplexing-2/ and the last illustration where it says "multiplying by orthogonal subcarriers"? What does this exactly mean? – Quirik Oct 05 '17 at 12:56
  • @Navi All that means is each stream will be multiplied the subcarrier associated with it. So for instance \$S_{\#0}\$ will be multiplied by \$\cos(2\pi f_0 t)\$, \$S_{\#1}\$ by \$cos(2\pi f_1 t)\$ and so on. Orthogonality just means subcarriers should not interfere with each other. – KillaKem Oct 05 '17 at 13:30
  • @Navi OFDM just splits one stream into multiple streams and then uses different subcarriers for each stream. If you are using OFDM with QAM or BPSK each of those individual streams will be independently modulated. – KillaKem Oct 05 '17 at 13:40
  • But where does, for example, QAM fit in and its I and Q component if each aubcarrier is multiplied by a complex number depending on combinations of bits? – Quirik Oct 05 '17 at 13:48
  • Or are we talking about two variants that can be used with OFDM. One is multiplication by subcarrier and other is using, e.g. QAM with I and Q component at each subcarrier frequency? – Quirik Oct 05 '17 at 14:00
  • @Navi Yes, if you are using QAM you will have an I and Q component with each and every subcarrier, with each subcarrier you will just modulate it like you would modulate normal QAM. – KillaKem Oct 05 '17 at 14:52
  • But on the link I was reffering to where each subcarrier is multiplied by a complex number, it is not actually a QAM, right? – Quirik Oct 05 '17 at 14:58
  • I mean, it only uses QPSK constellation to modulate subcarrier(s) but it is not actually a QPSK beacuse the carrier expression would contain I and Q component, not only sine? – Quirik Oct 05 '17 at 15:02
  • @Navi But the article has represented the signal to be sent as \$s(t) = (I + jQ) \sin(2\pi f_nt)\$, which is still a valid QAM signal. All what that basically means is send \$I\$ with \$sin(2\pi f t)\$ and send Q with \$j\sin (2\pi ft)\$ (which in practice just means \$\sin(2 \pi f_n t)\$ shifted by \$\pi/2\$ - which is basically \$\cos(2 \pi f_n t)\$). You can't really send a complex number (a + jb) because all signals in the real world are real. Complex numbers are just representations. – KillaKem Oct 05 '17 at 16:00
  • @Navi Remember when someone says they are going to send you two signals, \$s_1 = a\$ and then \$s_2 = ja\$. All they mean is that they will send you \$a\$ and then send you \$ja\$ (which is basically a signal 90 degrees out of phase with \$a\$). So in the QAM case, you send the sum of the in-phase component and the quadrature component (which is basically a component which is 90 degrees out of phase with the in-phase component). – KillaKem Oct 05 '17 at 16:17
  • Aaaa, I was confused then with a type of notation used in the article. Therefore, it is correct to write $$s(t)=Icos(2\pi f_nt)+Qsin(2\pi f_nt)$$ instead of just $$s(t)=(I+jQ)sin(2\pi f_nt)$$ – Quirik Oct 06 '17 at 07:45
  • @Navi The in-phase component (\$I\$) has to be in phase with the carrier. So if the carrier is \$\sin(2\pi f_nt)\$ then the in-phase portion needs to be of form \$I\sin(2\pi ft)\$ and if the carrier is specified to be \$\cos(2\pi f_nt)\$ then the in-phase portion of the signal has be \$I\cos(2 \pi f_nt)\$. If you specify the signal to be transmitted to be of form \$I\cos(2\pi f_nt) + Q\sin(2\pi f_nt)\$ then there is an implication that the carrier is of form \$\cos(2\pi f_nt)\$. So \$s(t) = (I + jQ)\sin(2\pi f_nt)\$ would be \$I\sin(2\pi f_nt) + Q\cos(2\pi f_n t)\$. – KillaKem Oct 06 '17 at 12:51
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The reason why OFDM is confusing is mainly because it is never fully presented. There are always gaps and holes in the details. For old-school OFDM, you see details of multiple orthogonal carriers (eg. a fundamental sinusoid and harmonics of it are all orthogonal), where each orthogonal carrier amplitude may be altered (eg. either make the amplitude equal to zero or make it a finite real constant value - which can be changed with time - this is using each carrier as a binary data-carrying component).

And then, you see new-school method of 'OFDM', which involves a sequence of QAM vectors (or QAM complex numbers) - a sequence of these, where each complex number in that sequence is a QAM symbol. This sequence can merely be imagined to be a make-believe 'frequency domain sequence'.

This is the main thing. We merely imagine that our data begins with a made-up 'frequency domain' sequence. It merely exists on 'paper' to begin with. This sequence of complex numbers goes into a IFFT processing unit. So basically an IFFT is applied to that sequence of complex numbers. Cyclic prefixing is then applied to the IFFT sequence (to deal with multipath effects later during wireless transmission). After cyclic-prefixing is applied, the resulting sequence is longer than the original IFFT sequence (because appending a cyclic prefix obviously leads to a longer sequence). At this point, it is then necessary to think of a way of sending this new longer sequence (such as wirelessly) - keeping in mind that each 'value' of this longer sequence is a complex number.

Each complex number has a real part and imaginary part. So this is where we can clock out these complex numbers - one number at a time. The rate of clocking out these stored complex values needs to be known and precise, and this rate needs to be known at the receiving side too. The real part of each number can modulate a single sinusoid broadcast carrier. The imaginary part of each number can modulate a 90-degrees phase-shifted version of that same single sinusoid carrier. This is quadrature modulation. These quadrature waveforms can then be added (summed) and then transmitted (eg. wirelessly). Now, sources do say that this transmitted waveform is supposed to be 'OFDM'. But it is really just quadrature modulation.

And - at the receiving side, quadrature demodulation is then carried out, in order to acquire the two (in-phase and quadrature) waveforms, and then some procedures then need to be carried out, such as finding pairs of repeated sequence patterns seen in the incoming waveforms --- this is for the purpose of synchronisation, and the beginning of procedures for channel estimation, followed by data recovery.

There are always a bunch of details left out in discussions about OFDM. I have only mentioned some details. But hopefully it helps people to get closer toward understanding OFDM and also differences between old-school multi-carrier OFDM and the new-school (IFFT) method.

One extra note is - the classical (old-school) method and the IFFT method are quite different. They can be compared - but they are two different kettles of fish.

Kenny
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