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In a previous post (here), we discussed in brief, Orthogonal Frequency Division Multiplexing (OFDM) transmission. Let us know probe bit more into the motivation of cyclic prefix (aka guard interval) associated with each OFDM symbol.
What is cyclic prefix?
Let us consider one subcarrier (subcarrier +1 specified in IEEE 802.11a specification) alone. In the figure shown below, the blue line corresponds to the original sinusoidal where one cycle of the sinusoidal is of duration 64 samples ( with 20MHz sampling), corresponding to subcarrier of frequency 312.5kHz.
Figure: Sinuosoidal with cyclic prefix
To add the cyclic prefix, 16 samples () from the end of the sinusoidal are appended to the beginning of the sinusoidal (shown in green colour). As can be seen, appending of cyclic prefix does not cause any discontinuities and we still have the original sinusoidal of frequency 312.5kHz.
Further, after adding cyclic prefix, as the sinusoidal is of duration , we now have a bigger window for choosing one period of the sinuosidal. Ofcourse, depending on which set of
is chosen, the phase needs to be corrected, but that will be a trivial operation in a typical implementation.
Effect of passing a sinusoidal through a multipath channel
Let us consider a simple multipath channel of the form
.
Let the transmit symbol be a single sinusoidal .
The received signal is
.
As can be seen from the above equation, after passing through the multipath channel, the received signal is the original sinusoidal albeit with modifications in amplitude and phase.
Use of cyclic prefix in multipath channel
Cyclic prefix acts as a buffer region where delayed information from the previous symbols can get stored. The receiver has to exclude samples from the cyclic prefix which got corrupted by the previous symbol when choosing the samples for an OFDM symbol. Further, from the previous section, we learned that a sinusoidal added with a delayed version of the same sinusoidal does not affect the frequency of the sinusoidal (it only affects the amplitude and phase).
Figure: OFDM symbol with multipath
Given so, for demodulating the received symbol, the receiver can chose samples from a region which is not affected by the previous symbol. As shown in the figure above, the samples can be chosen from the blue-arrow region OR the orange-arrow region OR somewhere inbetween.
Note:
When the pertinent samples of an OFDM symbol is taken (as explained above), the orthogonality aspect in OFDM is not affected by the multipath channel i.e. eventhough the individual subcarriers undergo phase and amplitude change, as the frequency is not affected, there is no interference between the subcarriers.
Cons of cyclic prefix
Ofcourse, the flipside of adding cyclic prefix is the loss in data rate as we are conveying redundant information.
Choosing the cyclic prefix duration
Given that transmission of cyclic prefix reduces the data rate, the system designers will want to minimize the cyclic prefix duration. Typically, cyclic prefix duration is determined by the expected duration of the multipath channel in the operating environment. For example, for the indoor wireless multipath channel, the typically expected multipath channel is of around duration, hence determining the cyclic prefix chosen per the IEEE 802.11a specification.
Summary
1. Passing a sinsuodial through a multipath channel does not affect the frequency of the sinusoidal.
2. As the multipath channel does not change the frequency of the sinusoidal, multipath channel does not affect orthogonality of the subcarriers (only if the receiver chooses samples which correspond only to the delay-added versions of the samples of the current symbol).
3. Transmission of cyclic prefix reduces the data rate, hence the cyclic prefix duration should not be much more than the duration of the maximum expected multipath channel.
References
[802.11A] Wireless LAN Medium Access Control (MAC) and Physical (PHY) Layer specifications – High speed physical layer in 5GHz band
Hope this helps.
Krishna
Related posts
- BER for BPSK in OFDM with Rayleigh multipath channel
- BPSK BER with OFDM modulation
- Understanding an OFDM transmission
- Frequency offset estimation using 802.11a short preamble
- Peak to Average Power Ratio for OFDM
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{ 15 comments… read them below or add one }
we want the apt meaning of cyclic prefix in multiband OFDM
@ venkatesh:
May I point you to a nice article on CommsDesign from Anuj Batra et al (Texas Instruments).
URI: http://tinyurl.com/yvfvu3
As explained in the artcle, in multband OFDM, the transmission of an OFDM symbol of bandwidth 500MHz is performed on three channels (with the transmissions seperated in time).
To enable the transmitter (and receiver) to switch channels there is small gap of 9.5ns (called as guard interval) where there is no information transmitted.
Further, as in typical ofdm implementations, there is a cylcically rotated version of each ofdm symbol appended to tbe beginning of the symbol (called as cylcic prefix). Ref: Fig2.
The chosen value of cylcic prefix should ideally be longer than maximum expected channel delay (to avoid inter symbol interference). However, long cyclic prefix implies a loss in data rate. Based on simulations, cylcic prefix duration of 60.6ns is chosen. (Ref: Fig4)
Hope this helps. Kindly revert for clarifications.
Hello Krishna, thanks for ur nice work on OFDM.
I have run ur simulation of ofdm in rayleigh multipath channel with and without cyclic prefix. But I dont get any difference in the result.why? where actually this thing work?
How can I use the doppler shift in the rayleigh simulation?
is there any problem if we use the Matlab build-in function chan = rayleighchan(ts,fd) as channel estimation?
@Masum: My replies:
1. Its surprising that you were able to obtain similiar performance with and without cyclic prefix in a multipath channel. How many taps were your channel. And what was your cyclic prefix duration?
2. Sorry, I have not tried modeling doppler.
3. I have not used rayleighchan() function. Hence unable to comment.
hello…
we didn get the exact meaning of cyclic prefix..hw can i implement it in ofdm channel.if possible can u plz provide us the code.
@sona: Cylcic prefix is inserted by just copy pasting last N samples of a symbol to the beginning of the symbol. The post simulating BER with OFDM in Rayleigh multipath channel discuss insertion of cyclic prefix. Please refer
http://www.dsplog.com/2008/08/26/ofdm-rayleigh-channel-ber-bpsk/
Hope this helps.
what is the advantage of cyclic prefix, over zero padding?
@srikanth: I have not studied the topic, but a quick googlig gave me the paper
Cyclic Prefixing or Zero Padding for Wireless Multicarrier Transmissions? – Bertrand Muquet, Zhengdao Wang, Georgios B. Giannakis,
Marc de Courville and Pierre Duhamel, IEEE TRANSACTIONS ON COMMUNICATIONS, VOL. 50, NO. 12, DECEMBER 2002
Some key points:
1) the presence of zeros between the symbols ensure that there is no inter symbol interference. Hence channel becoming 0 is less likely and we are better off.
2) I think the receiver equalization is bit more complex, but did not understand that aspect well.
I would urge you to refer to the above paper for further details.
Hi
I have a little doubt about correct position of fft window. In different articles and papers it is mentioned that fft window should be aligned with the strongest multipath signal.
You have aligned it with your first multipath component in the above figure. What if strongest multipath components are delayed relative to the first arriving paths.
In other words suppose this is my channel impulse response
h=[0.1 1 0.2 0 0.3]
How can I extract the info using the signal delayed by one sample. Because first copy of signal is difficult to be found at the reciever due to noise and synchronization issues.
@jenna: Well, as long as the multipath does not cause ISI, its best to collect all the copies of the received signal.
If for some reason, you dont want to pickup the pre-cursor taps, its also fine. Just make sure that the channel estimation is also done on the preamble which is extracted in the same way. That will take care of the phase rotation due to the channel.
pls do you have the matlab code show the effect of the cyclic prefix in the ofdm system .pls advaise me
@bakkar: Please look at the post on BER for BPSK in OFDM with Rayleigh multipath channel.
http://www.dsplog.com/2008/08/26/ofdm-rayleigh-channel-ber-bpsk/
In that you can see that though there is multipath, there is no intersymbol interference, thanks to the cyclic prefix.
dear sir,
i’m working on UWB -MB-OFDM .can u plz help me giving any channel estimation code used in both multi band and single band.
@BIKRAMADITYA DAS: Well, I do not have any codes for channel estimation. But I would guess, it would be some thing like
- send a known transmit sequence x
- assume the channel is h
- the received signal y = hx+n
- as x is known at the receiver, the estimate of h is = y/x = h + n/x
I’m working on ofdm.very useful website.thanks