Effect of sampling frequency changes in OFDM

[thavamaran]

[MODDERATOR NOTE: The OP has a follow up question. I added it to the end of this thread.]

 

[thavamaran]

Hi guys, I have this question, I know in OFDM system, when you upconvert the signal with certain carrier frequency with certain sampling frequency and when you downconvert it, if the carrier frequency is same, but the sampling is not, then you will have a sampling frequency offset and that will cause unsyncronized problem, like you will get a phase rotation or shifted constellation.

But how actually this sampling difference causes the intermixing in subcarrier or even changes the phase of the signal? In theoretical perspective, I don't really get it. Please someone explain it to me, I went through books, and still I don't get the idea. thank you very much!

 

[anorlunda]

ping @sophiecentaur , @berkeman . Do you know about Orthogonal frequency-division multiplexing?

 

[sophiecentaur]

ping @sophiecentaur , @berkeman . Do you know about Orthogonal frequency-division multiplexing?

Not a lot of detail but I know it involves sending a multiplex of many signals (i.e. a wide and signal) as lower bandwidth signals on a set of different carriers. The system has been used by BBC Digital Audio Broadcasting, as an example. It avoids the multi path problems of a single carrier with very wide band modulation. The wiki article gives a description. (Hope this link insert works with my iPhone)

 

[sophiecentaur]

There are two aspects to digital signaling. There is the sampling and coding and there is the modulation. Coding can involve bit rate reduction or change of sample rate etc. In COFDM the spacing of the carriers is chosen to optimize the system and the transmitted signal is processed as a whole at both ends.
Afaiaa the ‘orthogonality’ is a way of using the gaps between the ‘fingers’ of the spectrum of each of the signals as a space to fit other signals.
I remember reading the word “codulation” to describe this kind of signaling.

 

[Svein]

https://en.wikipedia.org/wiki/Ortho...ion_multiplexing#OFDM_system_comparison_table

 

[tech99]

Hi guys, I have this question, I know in OFDM system, when you upconvert the signal with certain carrier frequency with certain sampling frequency and when you downconvert it, if the carrier frequency is same, but the sampling is not, then you will have a sampling frequency offset and that will cause unsyncronized problem, like you will get a phase rotation or shifted constellation.

But how actually this sampling difference causes the intermixing in subcarrier or even changes the phase of the signal? In theoretical perspective, I don't really get it. Please someone explain it to me, I went through books, and still I don't get the idea. thank you very much!

To demodulate just one of the carriers, first divide it into two paths. Mix one path with a local carrier which has the exact frequency. This will give you a data stream. Then mix the second path with the same local carrier but 90 degrees shifted in phase. This gives a second data stream. The two data streams are decoded using logic gates to obtain one stream which is faster.
If the data is not just 1 and 0s, but is "QAM", it has a number fof voltage levels, and a further decoding step is needed. The stream is "analogue-like", and is applied to a simple A to D convereter (imagine a function like a bar graph IC). The four or more parallel bits are then decoded along with those from the quadrature stream using logic gates. This gives an even faster original stream.

 

[Baluncore]

OFDM is used for digital TV broadcasting.
Say for example you want to transmit 8000 bits in the next 1 msec. You make a complex array of 4096 data bit pairs, you distribute the 96 unused elements and make them fixed reference phasor values. Now compute the FFT of the block, I & Q up-convert and transmit it for the next one millisec. Propagation time wanders and different parts of the spectrum have different delays.
Down convert the signal to I and Q digital signals, each a phasor. Reverse the FFT, which provides conversion gain and spreads pulse interference, so any short noise pulses during reception will lower the signal to noise ratio, but should not wipe out any data bits.
You do NOT know the exact timing due to propagation delay but you do know which the reference channels are, so you can untwist the phasors, to quantise and recover the constellation of data bits from the complex data frame.

 

[sophiecentaur]

But how actually this sampling difference causes the intermixing in subcarrier or even changes the phase of the signal?

The sampling issue is not related to the data channel. Once you have a data stream, phase errors will just compromise the channel noise performance ( ‘eye pattern’)

 

[anorlunda]

MODERATOR NOTE: I moved this follow up question from a new thread the OP posted.]

Hi guys, I am designing my OFDM system, actually have designed, I am using 128 subcarriers, 72 of it carriers my data, and 56 are zero padded, 27 subcarriers of zeros at the beginning which are at DC, then 36 subcarries of data, then 2 subcarries of zeros in the middle, then again with 36 subcarriers of data, at the end another 27 subcarries with zeros.

So 27 beginning, 2 in the middle and 27 at the end (Nyquist frequency). Correct me if I padded it wrongly.

Then now I am having problem at the end of my constellation, I have a phase shift because I am using a nonlinear laser model in between the channel, so to do the channel estimation now, I need to add Pilot symbol. I went through a few books and papers, but I still don't get the idea of Pilot symbol.

Can anyone rigorously explain to me why pilot tone, how to include them in subcarrier and a bit of explanation on that, please, thank you very much.

 

[Baluncore]

Will you re-transmit the end 25% so that your symbol frame receiver does not have to be perfectly synchronised, and so multipath reflections are not such a problem?

Why do you have so many nulls at the ends of your transform?
If some of those channel phasors were to be alternated between 0° and 180° for every symbol frame, you could quickly estimate your symbol framing error as a proportion of the symbol frame time.

How would you know if your receiver down conversion LO was accurate? If some of those early adjacent bits were given a low self-correlation constant pattern, then it would form a pilot that identifies the exact channel numbers with the unique pattern, you can then correct your down conversion carrier and not get your phasor channels shifted sideways by one or two.