Talk:Orthogonal frequency-division multiplexing

Better description of Orthogonal in this context

This article does a pretty poor job of explaining the orthogonality condition in OFDM. it says

"Conceptually, OFDM is a specialized FDM, the additional constraint being: all the carrier signals are orthogonal to each other."

This makes little sense, because the concept of all FDM is that different carriers are orthogonal, and for this reason you can put different data on different carriers. In TDM/TDMA, you use orthogonal time slots; In FDM/FDMA you use orthogonal frequency slots; in CDM/CDMA you use orthogonal Spreading codes. — Preceding unsigned comment added by 65.216.151.126 (talk) 18:41, 14 January 2016 (UTC)

I think what is important is that the subcarriers are orthogonal over a symbol period, which is by design.

A proof that the described channel spacing gives orthogonality would be helpful. 86.141.10.180 (talk) 20:18, 4 July 2017 (UTC)HG

OFDMA

OFDMA links here. Should they be merged?--Gbleem 21:36, 14 December 2005 (UTC)

     NO! OFDMA is a multiple access scheme which relies on OFDM.

Doppler: "(...) sender or the receiver is moving at a high speed (...)"

I removed this sentence from the text. I am not 100% sure, but is seems very unlikely to me that normal speeds (car, train, plane, etc) would affect this, especially when we talk about frequencies around 5 GHz. I wrote a small thesis about OFDM in uni and I cannot recall any major issued with moving receivers/senders. Please correct me if anyone has more accurate information. --83.109.152.151 22:12, 20 December 2005 (UTC)

Well, at least according to recent tests by Digita in Finland, mobile use at speeds of "over 200 km/h" is no problem for Flash-OFDM operating at 450 MHz. --80.222.254.10 16:01, 22 December 2005 (UTC)

Okay, I'm removing that statement for now. R6144 01:52, 23 December 2005 (UTC)

As the Doppler frequency offset is proporcional to the carrier frequency, the offset would be different for every subcarrier thus causing loss of orthogonality Danielcohn 03:20, 1 May 2006 (UTC)

I put the sentence back since it is a problem in for example DVB-T, but I added that "Several techniques for ICI suppression are suggested, but they may increase the receiver complexity substantially." I have seen several papers on very complex equalizers for this purpose. Are there a simpler method? Can the sample rate be adopted, based on the pilot carriers?Someone said that modern DVB-T receivers are less sensitive to doppler. Howcome? Mange01 10:17, 13 October 2006 (UTC)

The problem comes from the combination of Multipath and Doppler. Consider the simple case of travelling into the direction of a steady transmitter. This slightly increases the frequency observed by the receiver. If at the same time there is a reflection of the tranmitted signal coming from the back of the driver, than the frequency shifts to a slightly lower frequency. So one tone results into two simultanious tones received. This corrupts the orthogonality and so the carrier breaks through to all the other carriers and thus introduces distortions. This is THE failure mechanism. The closer the intercarrier spacing the higher the distortions. —The preceding unsigned comment was added by 161.85.127.152 (talk) 14:47, 6 December 2006 (UTC).

Thnx for a helpful comment. User:Oli Filth has now incorporated it into the text. HOwever, in modern OFDM based systems such as DVB-H, the dopper shift does not seem to be a problem. It would be interesting to know which ICI cancellation algorithm that is used in practice. Mange01 23:00, 6 December 2006 (UTC)

The robustness against multipath can be improved by extending the guard interval duration. Usually the length of OFDM symbol will be scaled too to keep the guard overhead relatively the same. The carrier-spacing is then reciprocal with the symbol duration (1/T) and thus becomes smaller by better multi-path robustness. However the Doppler robustness will decrease at the same time, so there is a trade-off between multi-path and doppler robustness. In DVB-T they just forgot to define one intermediate intercarrier spacing. This gap appeared to be a good compromise between doppler and multi-path robustness. So they included that carrier spacing in the DVB-H standard. (PS: I'm the same writer as talk:161.85.127.152)

Reorganization - and GA nomination

This is a very understandable article and I'd love to see it promoted to good article. I did not pass it this time because:

• The lead is too short.
• The article has structural/formatting problems.

Some suggestions on how to improve the article's structure/formatting:

• The "Digital radio and television" heading has no content beneath it and should be removed.
• The table dominates the "Wireless LAN" section.
• The "OFDM feature abstract" is a list not a section consider making it an inset for the "Characteristics" section.
• The "Ideal encoder" and "Mathematical Description" (should be "Mathematical description") sections should probably come before "Usage".
• The "History" section seems tacked on, maybe it could also be made an inset.

Examples of how to do insets are available in the Columbine high school massacre article. Please renominate once the above problems are fixed.

Cedars 00:09, 14 April 2006 (UTC)

I have restructured the text by removing overlapping text; moving the list of key features (which I divided into advantages and disadvantages) to the top; moving the list of applications to the top and adding a numerical example in blockquote; and dividing the section "Characteristics and principles of operation" into sub-sections.

I have clearified why OFDM is considered a modulation scheme as opposed to a MA scheme, and added references to OFDMA and MC-CDMA. I have also corrected som incorrect statements, for example that OFDM would be sensitive to time synchronization errors.

(Someone else has addressed most of Cedars suggestions, except using insets.) Mange01 12:29, 13 October 2006 (UTC)

Multipath resistance only when coded?

Why does the article claim that multipath resistance exists only when combining OFDM with coding schemes? Multipath resistance is added by the fact that OFDM allows using longer symbols and therefore decreasing inefficiency caused by GI.Danielcohn 01:35, 22 June 2006 (UTC)

OFDM uses a cyclic prefix guard interval to convert a frequency-selective channel to a set of frequency-nonselective fading channels. As a consequence, intersymbol interference is avoided. The thing is, however, OFDM does not have frequency diversity. With coding, OFDM achieves diversity and performs well in multipath. ---sct

"Ideal encoder" section

I believe that the Ideal encoder section is in severe need of revision. I'll make these changes at some point in the near future; just wondering if anyone had any thoughts before I do.

Scrambling

Firstly, I don't think that it's necessary to include scrambling (shown as multiplication by $(-1)^{k}$ in the diagram) in a hypothetical "ideal" encoder. Secondly, it is shown as occurring in the time-domain, which is completely incorrect (see section 17.3.2.1 in the 802.11a spec, for instance). Thirdly, the reason given, "in order to have a null mean value", is also incorrect.

Inter-symbol interference

In the second paragraph, orthogonality of the sub-carriers results in zero inter-carrier interference, not zero inter-symbol interference, and only in the case when a cyclic prefix is used, which is not mentioned or illustrated.

Diagram

The blocks marked "ROM" are clearly meant to represent constellation mapping, but what does "ROM" stand for?

In my opinion, it would be better to replace the "impulse generator" and $H_{t}(f)$ blocks with "DAC".

It's also debatable whether illustrating frequency-domain zero-padding is necessary for an "ideal" encoder.

Oli Filth 17:47, 20 August 2006 (UTC)

All fixed. Oli Filth 13:50, 2 September 2006 (UTC)

Why does the "Transmitter" diagram show the IFFT block having only two outputs? Better start from the beginning again. Correct me if I'm wrong. My thoughts are --- a set of complex numbers (which could also be considered as a set of 'vectors', where each complex number can represent a 'vector', and each individual vector could be a single QAM 'symbol') is presented at the input to the IFFT. N complex numbers in parallel presented to the input of the IFFT. Even though the input to the IFFT is N complex values in parallel, we can imagine that set of numbers represent a made-up (ad-hoc) discrete frequency spectrum. A fabricated spectral picture. If we have N discrete spectral components, then the first component is expected to be the DC component, at zero frequency -- so basically the complex number for the DC value should be 0+j0 at DC (or for f = 0 Hz) because we don't want any DC component. The remainder of the components (ie. 'N - 1' of them) will be spaced evenly apart. The actual frequency spacing will later be determined by the parallel to sequential output of the IFFT system [ie. recall FFT takes N points of time-domain signal and converts to N points in frequency domain, with constant frequency spacing equal to (1/time_gap)/N or (1/sampling_period)/N or sampling_frequency/N (between components), so the time sequence spacing in the discrete time-domain will determine frequency spacing in the discrete frequency domain, and we will have full control of the time sequence spacing]. Perhaps the very first complex number (which we might purposely make to represent the DC component of our fabricated spectrum) should be zero, while the remaining 'N-1' complex-valued components should all have the same non-zero complex value (for redundancy and transmission reliability purposes. which means the set of N elements into the IFFT could be [X(0) X(1) X(2) X(3) ...... X(N-1)], with X(0) equal to zero, while X(1) = X(2) = X(3) = ..... X(N-1). X(0) is purposely set to be zero, this is to set the DC component of our ad-hoc spectrum to be zero. The rest of the components X(1), X(2) etc could all be the same complex value, which basically means that each of our non-DC fabricated spectral components are all "replicas" for purposes of redundancy. That is, if we were to transmit a time-domain equivalent of this 'spectrum', and the communications channel doesn't allow some of our spectral components to get through, then it is not a problem because we know that the same information will come through the other frequency 'channels'. So, back to the IFFT process. For N inputs to the IFFT, there should be N outputs (instead of just two outputs). The "Transmitter" diagram is currently showing just two outputs, because somebody decided to skip some important information. It should be N parallel outputs from the IFFT. And if there is meant to be N outputs for the IFFT, then what do we do with these N individual outputs? Each of these N individual outputs is typically a complex number, right? So, we then need to treat these N complex values as a complex time-domain sequence. This base-band time-domain sequence is the base-band OFDM signal sequence (in discrete time form). It's a sequence of complex numbers, which is all good and nice inside a computer. But what if we want to transmit and receive the complex number data is the fastest way possible? One way of transmitting complex numbers is by individually using the 'real part' and 'imaginary part' to modulate orthogonal carrier signals --- eg. cos(wt) carrier and sin(wt) carrier. The modulated carriers might be r(t).cos(wt) and i(t).sin(wt), where r(t) and i(t) are the real and imaginary analog values. The SUM of the two modulated carriers r(t).cos(wt) + i(t).sin(wt) is a real-valued time-domain signal (not complex signal), and it is an OFDM signal that we can transmit through a wire, or even wirelessly if the carriers cos(wt) and sin(wt) have a suitable frequency, noting that both carriers have identical frequency but are out of phase by 90 degrees. I'm really thinking that if somebody is going to explain this IFFT method of generating OFDM, then they should take a few extra steps to explain the method properly, otherwise it confuses everybody. If somebody going to teach somebody something on Wiki (or anywhere for that matter), then teach it without putting in cryptic or confusing diagrams etc. Make important areas clear for everybody to have a chance to understand. KorgBoy (talk) 08:53, 19 February 2018 (UTC)

Image Effects

The up and down mixing described would give rise to images, is OFDM actually symetrical about it's base carrier (this is implied by the article but not explicitly stated) or is it purely above the carrier (effectively SSB, and so requiring image rejection mixers and so on? Scruffy brit 12:15, 3 April 2007 (UTC)

The up-mixing does not give rise to images (assuming a perfect mixer). OFDM is not (in general) symmetrical around its centre frequency, although it may appear that way on a spectrum analyser (as each sub-carrier generally has an identical power spectrum).

The down-mixing does indeed give rise to an image at $2f_{c}$, hence the need for a low-pass filter after the mixing operation. This is shown in the diagram and explained in the article text. Oli Filth 12:42, 3 April 2007 (UTC)

Sorry, "Symetrical" wasn't the right term;-) But a OFDM signal does have modulation results on both sides of the carrier? Scruffy brit 11:05, 4 April 2007 (UTC)

Yes, in general. But this isn't due to mixing images. It's because the baseband OFDM spectrum straddles DC. Oli Filth 11:38, 4 April 2007 (UTC)

Flash-OFDM 450MHZ Data Network

In 9th October 2006, Finland has licenced the 450MHz band to an operator for building a nation-wide Flash-ODSM data network. Press release in Finnish: [1]. Could this be added to the main article?

I think Flash-OFDM deserves a separate article. Mange01 (talk) 06:53, 5 September 2008 (UTC)

Suggestion: OFDM standard comparison table

I suggest a table that summarizes the most crucial features of common OFDM systems. I have made a similar table for two broadcasting systems in the publication http://ieeexplore.ieee.org/iel5/49/20698/00957306.pdf?arnumber=957306.

Examples of features are:

• Standard name.
• Ratified year.
• Frequency band [GHz].
• Channel bandwidth [MHz].
• Number of subcarriers.
• Subcarrier spacing [kHz].
• Net bit rate [Mbps].
• Link spectrum efficiency [bit/s/Hz].
• Symbol length [s].
• Guard interval [s].
• Subcarriermodulation scheme.
• Inner FEC.
• Outer FEC (if any).
• Sub-carrier adaptive transmission (if any). Yes/no.
• Multiple access scheme (if any). Example: OFDMA uplink.
• Maximum travelling speed.
• Time interleaving depth [ms] (if larger than the symbol).
• Requied carrier-to-interference ratio (for AWGN without fading). Example: 5dB for BER 10^-5.

Mange01 13:11, 13 October 2006 (UTC)

Failed GA

This is a very promising article, but it is let down by an extreme scarcity of citations, and by a number of lists that would read better if converted to prose. Once these improvements have been made, please feel free to renominate the article. MLilburne 20:20, 2 December 2006 (UTC)

Merge with DAB really a good idea?

It has been suggested for a while that DAB COFDM section should be merged into the OFDM article, but none of us commented on the suggestion. Now it is accomplished, but I'm not sure that it was such a good idea.

Anyway, some of the merged text is overlapping with the old OFDM text, or is generic, not specific for DAB, and should therefor be removed or moved up in the article.

Secondly, Wikipedia now warns that the article has become longer than 30kB. Is that a recommended maximum length?

Should every application of OFDM be described as detailed as DAB in this article? In case the article should be extended with something, I would prefer more illustrations, and a comparison table summarizing the features of several systems.

Whats your vote? Should the merge be reverted?

Mange01 23:37, 2 December 2006 (UTC)

I completely agree; the verbatim insertion of the text from the DAB article completely disrupted this article, introduced a lot of repetition and redundancy, and also brought over a lot of the errors that were present in the DAB article. I have removed this addition, and have pasted the inserted text here; I'm not going to attempt to re-edit the DAB article; it's a complete mess; I'll leave that for someone else to sort out! Oli Filth

Removed text

Modulation

The modulation used in DAB is Coded Orthogonal Frequency Division Multiplexing (COFDM). According to this acronym the three properties of COFDM are: 'C' for coding; 'O' for orthogonal modulation and 'FDM' for frequency division multiplexing. These are described here.

Coding

Coding refers to convolutional coding and means that the original data carried over the multiplex is deliberately manipulated by splitting it into small blocks and adding some intelligently designed redundant information to each, thus generating a data 'overhead'. The overhead bits added to each block are determined according to rules applied to the true data content of the block. After demodulation at the receiver the digital signal processor examines both the actually received data and overhead bits and regenerates what it believes to be the original data based on a set of statistical rules known as an algorithm. The regenerated data may include a number of data bit corrections. The algorithm used in DAB is known as a Viterbi algorithm, and is an example of a maximum likelihood algorithm. This works by maintaining a history of demodulated bit sequences, building up a view of their probabilities and then using these to finally select either a 0 or 1 for the bit under consideration. This type of coding is also known as an example of forward error correction (FEC).

To some extent the types of errors most likely to be present with DAB can be mathematically predicted and therefore corrected for. The addition of FEC requires extra information to be transmitted at the same time as the original traffic data and therefore requires an increased channel capacity, needing extra bandwidth, compared to if it had been uncoded. DAB carries different 'strengths' of FEC, a stronger one being used for the control of critical features in the receiver.

Orthogonal

Orthogonal is the mathematical term applied to two RF sinusoidal signals when their phase relationship is precisely 90 degrees. Alternatively they may be said to be in 'quadrature'. In DAB the sub-carrier frequency spacing is chosen to be the reciprocal of the active symbol period. Under this condition the DAB modulation results in successive sub-carriers having a quadrature relationship with each other. The frequency spectra components of one modulated sub-carrier will therefore integrate to zero at the corresponding components from both of the adjacent sub-carriers. This has two advantages: (a) the modulated sub-carrier spectra will efficiently occupy the allocated bandwidth with a degree of controlled overlapping and (b) simple I-Q demodulation to zero intermediate frequency (zero-IF) can be used in the receiver without needing the costly hardware overhead of many bandpass filters to extract the sub-carriers.

Frequency division multiplexing

Frequency division multiplexing (FDM) is the process where two or more basic information channel bandwidths or basebands are shifted in frequency and added to others to form an aggregate wider bandwidth containing the information from all of the constituent basebands. To avoid mutual interference, their bandwidths would normally require shifting (translating) in frequency and no two translated basebands would occupy any part of the same frequency spectrum. In the context of DAB, FDM refers to the manner in which the modulated sub-carriers are assembled across the allocated frequency range.

Modulation type

DAB uses a digital modulation type known as differential quadrature phase shift keying (DQPSK), which is an incoherent modulation scheme. DQPSK differs from the more common quadrature phase shift keying (QPSK) in that the modulated carrier phase for the current symbol being detected depends on its phase relative to that phase detected for the previous one. In QPSK it is just the absolute phase of the modulated carrier that determines the associated symbol. A differential modulation scheme can be more resillient to the typical fading scenarios of DAB. The modulation scheme also incorporates a form of Gray coding in that only one bit changes on moving from one symbol state to an adjacent one. For a constant phase progression, the consecutive set of symbols are represented by the bit pairs 00, 01, 11 and 10.

Time interleaving

DAB uses data buffering which enables the data symbols to be transmitted over the RF path in a different time-order than they were generated the audio source (studio). At the receiver they are re-assembled and returned to the original time-order before conversion back to analog signals to feed the receiver audio output. This process is called time interleaving. Typical multipath interference experienced in a moving vehicle is regular over time so an intelligent choice of time interleaving to some degree 'averages' out the resulting error bursts over time. This data buffering and other processing contributes to a delay, typically of a few seconds, between the studio source and the receiver. This is much longer than the equivalent delay for am FM broadcast channel which would typically be a fraction of a second. For most broadcasts such a delay would be unimportant but it does mean that, for example, real-time reference signals for setting clocks such as those re-broadcast by the BBC on DAB from their national FM service are actually quite inaccurate.

Frequency interleaving

DAB also uses frequency interleaving, a similar technique to time interleaving but applied to the sub-carriers centre frequencies in the RF spectrum instead. The data stream from the studio is deliberately not modulated serially onto sub-carriers across the frequency range, but instead in a more random way. Multipath and other forms of selective fading generally affect a relatively narrow part of the RF multiplex bandwidth at any one time so frequency interleaving would tend to average out 'bursts' of errors resulting from these.

This is some good stuff

This is some good text! Put it back! -143.215.155.26 (talk) 05:17, 21 March 2009 (UTC)

DMT vs OFDM

On a somewhat related topic, i question whether the redirect to OFDM from DMT (http://en.wiki.x.io/w/index.php?title=Discrete_multitone_modulation&diff=next&oldid=10618564 ) is optimum. Certainly DMT and OFDM share many characteristics, but the common use of the DMT term in wireline, as well as in the standards reference in ANSI T1.413 http://en.wiki.x.io/wiki/ANSI_T1.413_Issue_2 suggest they should remain distinct topics. Particularly as there are non-trivial differences between the two techniques, that also in fact form some of the basis of T1.413 - such as the Cioffi/Amati patented bit loading / tone swapping algorithm which allows better throughput in copper specific interference such as the ISI found in bridged taps. Because in copper the noise is stationary and the channel is time invariant, DMT is much better able to adapt to the communication medium than OFDM would. In any case, this may not be the best place to discuss the validity of a redirect, but because it does involve technical details relevant to this article, I felt to introduce the idea for comments here first. Duedilly 23:47, 10 February 2007 (UTC)

To add some further detail to the consideration of differences between OFDM and DMT (and whether DMT should redirect to OFDM), here are more distinction points:

• DMT is a real-valued baseband multiplex s(n), whereas OFDM is a complex-valued baseband multiplex s(n);
• DMT has the channel known at the transmitter, whereas with OFDM, the channel is unknown at the transmitter;
• DMT is used in wireline communications (lowpass channel), whereas OFDM is used in wireless communications (passband channel)
• (from http://www.ist-muse.eu/Documents/AutumnSchool2006/track2/Track2%20ofdmnutshell_print.pdf )

Duedilly 19:48, 11 February 2007 (UTC)

There is nothing about OFDM which precludes it from being baseband, wireline, or pre-equalised/rate-adaptive. It would be a bit like trying to state that 802.11a is distinct from OFDM because it uses PRBS-based scrambling, or that DVB is distinct from OFDM because it uses scattered pilots. IMHO, "DMT" really just describes a particular implementation, which just so happens to be baseband, wireless and pre-equalised and rate-adpative. Oli Filth 22:09, 11 February 2007 (UTC)

DMT is discussed in the section "Adaptive transmission", as well as in the ADSL section. I would like to encourage to you elaborate on the bit loading/tone swapping algorithm there. A VDSL section should also be created. A separate DMT article would not be a good idea. Mange01 07:37, 14 February 2007 (UTC)

Thanks Oli and Mange. I notice there is an entry for ITU_G.992.1 and wonder why DMT would not more likely redirect to that? (or even to an ANSI T1E1.413 entry, which predates and was the basis for the adopted ITU standard). I think your idea though to further clarify the ADSL section is good, though obviously not all ADSL is FDM - technologies like CAP and DWMT and other DFT implemented filter bank modulation schemes, (both perfect, and particularly the imperfect, due to frequency overlap with low cross-channel interference which are decidedly NOT like PO-FDM) have a rightful place of discussion near DMT - which would likely not be appropriate in this entry. I agree that these may all have evolved from a common ancestor and have filled different niches, but am not yet convinced of the value of reducing them to a single OFDM entry. I am traveling soon, but will look forward to discussing specifics and considering the best approach for further elucidation of these topics, and will also look to get some feedback from Cioffi and others involved in ANSI DSL standards to help. We might also consider adding discussion of expected "multicarrier" CDMA implementations of OFDM using spread spectrum. Duedilly 19:43, 16 February 2007 (UTC)

If found Discrete Multi-Tone page (an orphan page), should this be merged to this page, or at least redirect? I'm no expert on this field. Memming 22:04, 11 April 2007 (UTC)

Sub-carrier

What is meant with a sub-carrier in OFDM and what is its difference compared to a normal carrier? --Abdull 10:40, 6 March 2007 (UTC)

More explanation of the cyclic prefix purpose

I was wondering about this, won't it be nice if we also show that the cyclic prefix serves to make the effect of the channel become circular convolution for the OFDM symbol? Then, we mention that circular convolution becomes just multiplication when the DFT is taken.

Something like The OFDM symbol $[d_{0},d_{1},\ldots d_{N_{c}-1}]^{T}$ is prefixed with the $L-1$ length cyclic prefix and becomes $[d_{N_{c}-L+1},d_{N_{c}-L+2}\ldots d_{N_{c}-2},d_{N_{c}-1},d_{0},d_{1},\ldots d_{N_{c}-1}]^{T}$. Then, after convolution with the channel, which happens as

$y[m]=\sum _{l=0}^{L}h_{l}x[m-l]\quad 0\leq m\leq N_{c}$

which is circular convolution, as $x[m-k]$ becomes $x[(m-k)\mod N_{c}]$. So, taking the DFT, we get:

$Y[k]=H[k]\cdot X[k]$.

Of course, the noise etc. has to be accounted for. Note that another thign one could mention is that the distribution of the noise, if it is isotropic complex Gaussian, remains identical under the DFT operation.

Just my suggestions to make it more clear... Kumar Appaiah 12:32, 11 March 2007 (UTC)

I suggest that some of this stuff would be well worth putting in the Cyclic prefix article, which is essentially just a stub right now. I keep meaning to flesh that article out myself, but I never get round to it. I don't think we want any more maths in the OFDM article, as it's already overly-long. Oli Filth 13:05, 11 March 2007 (UTC)

Oli, thanks for the suggestion. I am heading to Cylic prefix to make a start! Kumar Appaiah 14:24, 11 March 2007 (UTC)

Overview

I think a critical clarification needed in the summary at the start of the article is that the difference between OFDM and FDM is that with OFDM we're simultaneously transmitting on all the sub-channel frequencies, whereas FDM transmits on each frequency sequentially. Ceri Reid68.200.109.154 17:24, 29 March 2007 (UTC)

FDM tramsits simultaneously on all frequencies as well (otherwise it would be TDM!). Oli Filth 18:18, 29 March 2007 (UTC)

Yes, the orthoganal part allows much closer spacing without the guardband that would be needed between conventional channels on different frequencies (such as on FM radio), without the interference being destructive. --Lindosland (talk) 16:52, 28 January 2008 (UTC)

OFDM Chipset

Can any one help of the best chipset available in the market for Baseband OFDM chipset that could be used in an OFDM modem for not that high data bit rate?, the RF part not necessary for building the OFDM modem only baseband part. Thanks Matalal 13:17, 4 April 2007 (UTC) —The preceding unsigned comment was added by Matalal (talk • contribs) 10:19, 4 April 2007 (UTC).

More Images!!!

Hi, the article is good, but it is sometimes harder to perceive things for the person not already in WiFi field.

A good drawing explaining guard interval and cyclic prefix would not be obsolete, for sure. Also one explaining orthogonality. Keep up the good work! -- Mtodorov 69 08:28, 19 April 2007 (UTC)

Overlap between "Example of applications" and "Usage"

Section 1, "Example of applications", was originally part of the ingress, as a summary of the "Usage" section. Someone perhaps found the ingress too long, and moved it into a separate section, but now we have two sections with overlapping content.

What is the solution to the problem?

Mange01 18:44, 7 October 2007 (UTC)

Changes to article lead

I've mostly reverted today's additions to the article lead, for the following reasons:

1. "OFDM is a modern method of modulation ..." - Define "modern"! OFDM has been around since the 60s.
2. "... adopted primarily for digital radio television broadcasting ..." - Somewhat misleading. WiFi, WiMax, ADSL, DAB all use OFDM as well.
3. "It is analogous to the AM and FM systems of modulation used for analogue radio and television broadcasting ..." - I know what you're getting at, but in light of the point above, is meaningless.
4. "Typically each bit in each stream lasts for around a millisecond ..." - This is only true for 8K DVB, and only if we're talking about symbols, not bits.

The example is highly relevant, since, as I understand it, a key benefit of OFDM has been the possibility of operating all transmitters across a country on one set of frequencies. 50 miles is a typical distance between such transmitters, and hence 1ms was a design criterion for such applications used in deciding on the number of carriers. This issue is something the non-engineer can readily appreciate the value of. What is transmitted on a carrier is surely 'bits' in the basic sense of 'binary digits' ie on-off representation. I don't see a need to complicate things with symbols, when the average person is familiar with bits.--Lindosland (talk) 20:56, 28 January 2008 (UTC)

1. "... when the many adjacent frequencies interfere with each other, they do so in a way that is not destructive ..." - Again, I know what you're getting at. However, it's not that they're not destructive, it's that they don't "interfere" at all!

However, I've retained a mention of SFNs. Oli Filth^(talk) 19:32, 28 January 2008 (UTC)

I don't agree with the revert. The important thing is 'in simple terms' which qualifies what follows. The analogy with FM and AM is entirely appropriate for the average reader (who usually cannot destinguish AM from Medium wave). By all means improve what I wrote, but I think it was a good attempt, which I made because of a call for a 'simple explanation' at the DVB-T article talk page. A simple explanation can never be the whole truth, but is still needed on Wikipedia, especially for a subject as obscure to most people as this one, which they might come across when reading about digital TV. --Lindosland (talk) 20:08, 28 January 2008 (UTC)

I've reverted but with changes in line with your comments. I really think the lead, as it stood, was pitched at a much too technical level. I welcome the highly technical, but the lead should contain something for the non-engineer too, and this is actually a topic very relevant to non-engineers who are curious about modern developments in broadcasting etc. --Lindosland (talk) 20:24, 28 January 2008 (UTC)

I would further point out that this article failed to meet 'good article criteria'. One of these is that, 'The lead should be capable of standing alone as a concise overview of the article, establishing context, summarizing the most important points, explaining why the subject is interesting or notable.' A lead that fails to mention the relevance of OFDM in terms of DAB DTV and Wi-Fi is surely failing badly, considering that these are THE major developments of the last decade that almost everyone is aware of. --Lindosland (talk) 21:04, 28 January 2008 (UTC)

I agree with the fact that articles should be tractable by the non-specialist, so I'll have a go at working on your updated changes! I'll summarise the rationale for my revisions here:

1. I've worked the material into the existing paragraphs, as the article lead is not the place to have discrete "simple" and "more in-depth" versions which overlap in scope. Instead, it should serve as a "single-threaded" summary to the article, which should all be readable in one chunk!
2. Merge the "OFDM is a method of modulation that is proving well suited ..." and "analogous with AM..." sentences with the existing usage sentence ("OFDM has developed into a popular scheme ...") to eliminate redundancy, and rewrite to avoid singling-out TV as particularly prominent. I've removed the specific standard names to avoid acronym overload, and because they're listed in the very next section of the article.
3. Remove the "OFDM works by splitting the wide-band digital signal..." sentence, as this was redundant (see the first paragraph of the existing lead).
4. Move the discussion of non-interfering sub-carriers into the first paragraph, where it seemed to fit more closely with the existing material.
5. Remove the 8K DVB-specific values, as they're too specific, and either way, are unnecessary for describing the principle in the lead. Disclaiming this with "Typically (by way of example only, as in broadcast TV and Radio)" wasn't making this any clearer. Replaced with a more concise discussion of SFNs at the end of the existing paragraph. Note also that there are several numerical examples we could put in the lead, like the examples at OFDM#Guard interval for elimination of inter-symbol interference and OFDM#Simplified equalization, which are arguably more important than SFN (as these were the original reasons that OFDM became attractive). But we don't, for the sake of clarity and brevity (the whole point of a summary!).

I hope that you'll mostly agree with my revision of your additions; if not, let's carry on the discussion here. Regards, Oli Filth^(talk) 21:35, 28 January 2008 (UTC)

Thank you for your contributions Lindosland. However, I support Oli's revert. Some of these details might be discussed later in the article. The OFDM article is a quite well-written article, but the ingress is still a little bit long and should be more focused on the key issues rather than extended. I therefor suggest that the following is removed from the ingress: "several applications traditionally served by single-carrier methods such as AM, FM, QAM or PSK. These include". It might be moved down in the article. Mange01 (talk) 21:57, 28 January 2008 (UTC)

Hello. The lead as it stands is now a combination of Lindosland's additions, and my revisions of these changes. The particular sentence you've quoted is my re-working of Lindosland's version, but I'm happy for it to be removed, as the lead is indeed somewhat lengthy. I do think that some mention of "digital TV", "wireless networking" should be retained in the lead, though. Oli Filth^(talk) 22:02, 28 January 2008 (UTC)

Thanks, I'm reasonably happy with what you have done, though I still think a comparison with AM and FM in the intro would help as these are terms that have been absorbed into popular culture, while 'modulation' means nothing to many people. --Lindosland (talk) 21:59, 31 January 2008 (UTC)

New changes to the article lead and structure

In the changes made 23 February 2008 to the article, the paragraph which explains the primary advantages of OFDM was moved down from the article lead into a separate section. I reverted those changes for the following reasons:

• It does not make sense to both have a section on "Advantages" and "Summary of advantages", which are highly overlapping with each other. Both are summaries of certain issues discussed in the "Characteristics..." section.
• I suggest that major changes to the article lead and structure should be discussed at the talk page. There has already been a discussion on this talk page, where we have tried to agree on a compromise regarding short lead. Is it desirable to make it even shorter? Perhaps it is possible, but I would prefer a discussion first.

Mange01 (talk) 17:43, 23 February 2008 (UTC)

Survey: bit/s/Hz, (bit/s)/Hz or bit·s⁻¹·Hz⁻¹ as Spectral efficiency unit?

Please vote at Talk:Eb/N0#Survey on which unit to be used at Wikipedia for measuring Spectral efficiency. For a background discussion, see Talk:Spectral_efficiency#Bit/s/Hz and Talk:Eb/N0#Bit/s/Hz. Mange01 (talk) 07:21, 16 April 2008 (UTC)

Modulation or multiplex?

OFDM is listed under "modulation techniques", while OFDMA is listed under "multiplex techniques".

However, the OFDM article begins with "OFDM ... is a frequency-division multiplexing (FDM) scheme", which is in my opinion correct, and contrasts with the classification as a modulation technique. Fpoto (talk) 12:55, 28 May 2008 (UTC)

The ingress continues: OFDM " is a frequency-division multiplexing (FDM) scheme utilized as a digital modulation method." I don't agree totally with the first part of this sentence. OFDM rather involves or is based on FDM, but it is by definition a modulation scheme, since it includes inverse multiplexing that translates one bit stream into several. See section 3.6 for further arguments:

"OFDM in its primary form is considered as a digital modulation technique, and not a multi-user channel access technique, since it is utilized for transferring one bit stream over one communication channel using one sequence of OFDM symbols. However, OFDM can be combined with multiple access using time, frequency or coding separation of the users."

The december 2007 version of the ingress was i.m.o. more correct: "OFDM is a digital multi-carrier modulation scheme, which uses a large number of closely-spaced orthogonal sub-carriers". I have noticed that the new version of the ingress has caused confusion among my students. The OFDM literature is pretty clear on that OFDM is a modulation scheme, but many non-professionals are confused, since the M in OFDM means multiplexing.

You question that OFDMA is mentioned in the multiplexing template. You have a point here. OFDMA is a multiple access scheme rather than a multiplex scheme, at least from the name, but multiplexing and multiple access are related. If several transmitters are sending using different sub-carriers, it is a multiple access scheme, and should be called OFDMA and not OFDM. The downlink case is more complicated. If one transmitter is sending to several receivers using separate sub-carriers, it is multiplexing rather than multiple access, but I would still call it OFDMA since it is based on the same principles, especially if there is an OFDMA uplink backchannel controlled by the same algorithm or protocol. But a agree that the picture is not totally clear. What about ADSL - why do we call it OFDM and not OFDMA?

I would not accept OFDM in the multiplexing template, from the above reasons. I would understand if you remove OFDMA from it. Mange01 (talk) 20:42, 28 May 2008 (UTC)

I understand your point here. However, I have a couple of reservations about describing OFDM primarily as a "modulation method":

1. the underlying modulation used (QPSK, QAM16, etc.), i.e. what we traditionally understand "modulation" to mean, is not part of the definition of OFDM.
2. The argument that OFDM "includes inverse multiplexing" is really a matter of perspective. What it's really doing is mapping incoming bits to physical symbols, and so has more in common with techniques such as interleaving and traditional multiplexing. The only difference is that here, the physical symbols occupy a two-dimensional space (time+frequency), rather than just one-dimensional. Oli Filth^(talk) 17:59, 2 June 2008 (UTC)

Cleanup of article needed

Sections seem to be out of order or jumbled up somehow. --KJRehberg (talk) 21:16, 23 June 2008 (UTC)

Flash-OFDM / F-OFDM section reads like an advertisement

Removed text that celebrated the virtues of Flash-OFDM to the point of reading like a cheap advertorial. I'm not at all sure the section should stay at all as it completely fails to explain just what sets this ``flash thing apart from the rest, beyond expanding the acronym. 85.178.66.163 (talk) 23:44, 1 October 2008 (UTC)

I further trimmed it down, rewrote in past tense a little, updated it with some sources, and removed inline links. It still seems notable, but of historical interest now that other standards seem to be battling it out. W Nowicki (talk) 21:26, 23 July 2011 (UTC)

Idealized system model and constellation mapping

Can someone tell me what constellation mapping does with the incoming bits? If the constellation mapping was QAM, would the constellation mapping convert the incoming bits into a sinusoidal signal, with varying amplitude and phase (this signal would be digital)? Thank you in advance WielkiZielonyMelon (talk) 15:34, 6 February 2009 (UTC)

For example, if 64QAM is used, every 6 bit data will be converted to a complex value by the constellation mapping. For example, 011101 might be converted to 5 - i2, corresponding to a vector with horizontal value 5 and vertical value -2. This is the fourier coefficient for one of the sub-carriers. After the inverse fourier transform, this coefficient will correspond to a cosine wave with amplitude 5, plus a sine wave with amplitude 2, at this specific sub-carrier frequency. Mange01 (talk) 23:09, 7 February 2009 (UTC)

Magne01, thank you very much, I have hurried a little and forgot, that the entry of IFFT is in FREQUENCY DOMAIN, and the exit of the IFFT is in TIME DOMAIN. Anyway, thank you for explanation! WielkiZielonyMelon (talk) 10:15, 9 February 2009 (UTC)

DAB, HD Radio, other radio schemes

This article contains too much DAB-specific information that doesn't mesh well with the other information here. The DAB information belongs in an article about DAB technical aspects. If we had this much information about other specific COFDM-based services, this article would be huge and incomprehensible.

Also, none of this DAB-specific information is complemented by discussion of HD Radio (which has as many multiplexes as DAB does now!), DRM, etc.

-143.215.155.26 (talk) 05:20, 21 March 2009 (UTC)

Section: Channel coding and interleaving

The last paragraph and sentence states that "...[Turbo codes and LDPC codes] only perform close to the Shannon limit for the AWGN channel ... [therefore] concatenated them with either RS or BCH codes to improve performance further...".

I was under the impression that RS/BCH was concatenated with LDPC/Turbo codes in order to clean up resilient errors from their error floor???

Section: Linear transmitter power amplifier

There are techniques to reduce the PAPR: Active Constellation Extension (ACE), and Tone Reservation.

Could somebody comment on these points? Cheers, Nageh (talk) 12:07, 5 June 2009 (UTC)

Move the comparison table to a template that can be embedded in several articles?

Would it be a good idea to move the comparison table to a template, and embed it in the end of articles about each of the compared systems? For example template:ofdm sytem comparison table. The table should be collapsible. Mange01 (talk) 19:08, 11 May 2010 (UTC)

What is the crest factor?

We know it is high, but how high? OFDM is typically 12 dB, what would it be for COFDM? I am surprised this most critical parameter for Tx design is treated so lightly. — Preceding unsigned comment added by 75.99.58.122 (talk) 15:39, 24 January 2012 (UTC)

As you requested, I added an equation for calculating the crest factor to the article (with an example value).

In theory, if one were to hypothetically one were build a OFDM system without coding, and compare it to a COFDM system using the same subchannel modulation and the same number of non-zeroed subchannels, that hypothetical OFDM system would have exactly same crest factor.

In practice, practically all "OFDM" protocols are actually COFDM, so I suspect that "12 dB" value is actually the crest factor of some COFDM system. --DavidCary (talk) 18:07, 9 January 2013 (UTC)

Optical OFDM

Press release here on low-cost OOFDM claims it can extend subscriber FTTH capacities by 2000 fold (e.g. 20 Gb/s vice 10 Mb/s) without significant cost increase. Seems like it might be worth some discussionin the article. See WO2011051448 A4  or the Beeb for additional details. LeadSongDog come howl! 20:24, 6 November 2012 (UTC)

f-DPSK

Today I'm reading a paper by Martin Hoch ("Comparison of PLC G3 and PRIME".) which mentions "t-DPSK" and "f-DPSK".

I came to this Wikipedia article looking for a better explanation of "f-DPSK" and "t-DPSK". Dear Wikipedia editors, if you know what these things are, please add them to this article. --DavidCary (talk) 18:07, 9 January 2013 (UTC)

I know nothing about it... but why to this article (and not DPSK)? Nageh (talk) 12:02, 10 January 2013 (UTC)

Good point. Let me repost this question there.

I thought this might be relevant to OFDM because I haven't seen either term ever used in any non-OFDM system. --DavidCary (talk) 18:17, 19 January 2013 (UTC)

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Needs Updates Urgently

There is little mention of LTE/4G applications and significance, also new WiFi standards. Not in the table. Much that has happened within last few years, and it is a lot, is missing from discussions. Also in my opinion, DAB topics should have been kept separate, it does not make a good article all jumbled in. — Preceding unsigned comment added by 137.71.23.54 (talk) 19:47, 9 February 2017 (UTC)

OFDM vs COFDM

In a brief review of the article, nowhere do we say where the term COFDM comes from or what it means. We use it, but we don't define it. That's bad. We should fix that. I'm going to add a little note to the first paragraph based on a cite I found. Anyone who wants to improve it should.—chbarts (talk) 08:25, 16 April 2017 (UTC)

Caveat

This was added to the article by 79.123.76.94. It looks like it belongs here at least until it can be refined a bit. ~Kvng (talk) 14:03, 17 December 2018 (UTC)

So far in this article, little mention has been made of the importance of "frequency synchronisation" whatever that means. Perhaps it is better to use the term "Coherency". When a (C)OFDM signal is exchanged over a radio frequency channel, approximately 95% of the resources used in the hardware, and therefore in its design, must be devoted to this function, which is not shown on any block diagram depicting the system as a whole. What must be done is the following:

The received data must be converted numerically to the best available approximation of the transmitted data. This is upstream of any error correction or demodulation, it is essentially an analog function which must be applied to the data as it is acquired from the receiver. Without this, the data is meaningless and scrambled.

- First, the start of a frame must be detected, under any reasonable condition of frequency of phase shift.

- Then, the frequency and phase of the transmitted signal must be deduced from analysis of a transmitted reference signal. The received signal is then both corrected for deviation of baseband frequency and phase. It is restored to the form in which it was transmitted.

Only at this point is it possible to proceed with the processing of the data stream as shown in the block diagrams in this article. The processing elements required to do this would, if illustrated at the same level of detail, cover about five pages.

Firstly, the detection of the beginning of a transmission. For the elaboration, downstream, of a phase reference signal, it must be detected within a certain tolerance of time. This is usually specified as a fraction of the guard interval, which, itself, might be short. The requirement is to pass a guarded version of the phase reference symbol on for further processing. The quality of detection of the beginning of a transmission required is subject to debate, but at early stages of development, it is convenient for this to be somewhat more reliable than the data itself, in the sense that data incapable of being decoded should be, nonetheless, received for analysis. Time-frequency analysis of a mixed tone frame reference symbol, possibly at a resolution of as little as a single sample of data, may be required in order to do this. A time-frequency analysis of transform length N requires N parallel channels, at delays of a single sample, of, in practice, FFT analysis.

At this point, the reference signal can be streamed to a function which calculates the channel impulse response. This compares the received reference symbol with delayed versions of itself to determine time and frequency offsets. These can then be applied to the buffered, received payload following the phase reference signal to restore it to the form in which it was transmitted. This requires further parallel FFT channels together with significant numerical elaboration of their contents.

As stated, coherency reconstruction, together with the buffering needed to accommodate its latency, is a significant element of any OFDM transceiver, and I would advise caution if budgeting hardware resources to the implementation of such a device.