As we all know, by adding cyclic prefix, OFDM signals can be able to tackle with both ISI and ICI. But how does the reflected signal affect the demodulation (FFT/DFT) on the same sub-carrier? In MATLAB simulation (without adding any noise, and only one reflected signal was introduced), the demodulated constellations are clustered around the target points as the figure below shows. Can this effect be explained or is there any equalisation method to reverse this distortion?
Dear Wentao,
Your constellation diagram shows that the basic modulation for every subcarrier is 4-QAM. The QAM vectors are superimposed by a discrete circular constellation resulting from the reflected delayed copy of the transmitted signal.
So, The received symbols can be expressed by :
r= An exp j phin ( 1 + a expj n dw Tau) where, An is amplitude of the symbol of carrier n, phin is the phase of the symbol of the carrier n , dw is the separation frequency between subcarrier and Tau the delay time of the reflected copy as well as a is the strength of the reflected copy with reference to the original signal.
The mathematical expression describes an original constellation vector superimposed on it a circular term with discrete points of the phases n dw Tau, where n an integer having a value from 1 to n= no. of subcarriers say 64.
Such multipath effect is corrected for by by frequency domain equalizer where the the channel frequency response is estimated bu pilot carriers. And the received signal in the frequency domain is corrected for by dividing the received vector on the the frequency response of the estimated channel at that frequency. That is the corrections takes place after the FFT operation of the received symbol.
wish you success
Dear Wentao,
Your constellation diagram shows that the basic modulation for every subcarrier is 4-QAM. The QAM vectors are superimposed by a discrete circular constellation resulting from the reflected delayed copy of the transmitted signal.
So, The received symbols can be expressed by :
r= An exp j phin ( 1 + a expj n dw Tau) where, An is amplitude of the symbol of carrier n, phin is the phase of the symbol of the carrier n , dw is the separation frequency between subcarrier and Tau the delay time of the reflected copy as well as a is the strength of the reflected copy with reference to the original signal.
The mathematical expression describes an original constellation vector superimposed on it a circular term with discrete points of the phases n dw Tau, where n an integer having a value from 1 to n= no. of subcarriers say 64.
Such multipath effect is corrected for by by frequency domain equalizer where the the channel frequency response is estimated bu pilot carriers. And the received signal in the frequency domain is corrected for by dividing the received vector on the the frequency response of the estimated channel at that frequency. That is the corrections takes place after the FFT operation of the received symbol.
wish you success
Dear Sir,
The whole idea of OFDM, is to have better performance for multipath.
The idea is that the delta-T, the time difference, of the 'straight' signal and the 'reflected' signal arriving at the receiver is less than the overlap.
If this is the case, there is no ISI (inter symbol interference) in the frequency domain, meaning the equalizer just needs to adjust gain. (Multipath still introduces amplitude distortion.)
The equalizer is then in the frequency domain, and all it does is to multiply the various carriers with complex numbers that undo the amplitude distortion.
For adjusting the equalizer, there are basically 3 methods:
- Adjust on the preamble symbols
- Decision feedback
- Adjust using pilots.
All of them have pro's and con's.
- You start to adjust on the preamble symbols. (In case of modulation systems like WiFi - eg 802.11n OFDM).
- Then, after starting demodulation, its either decision-feedback or pilots.- For decision feedback, the signal is run through the detector and error corrector,
the reconstructed signal based on detected bits is subtracted from the received signal, and the remainder is used as an error signal to adjust the equalizer.
- This is a very robust system when used in conjunction with Viterbi error corrector,
but for the newer LDPC (low density parity codes), I dont think it can work, as the
decode latency is too high, and may make the system unstable. (The advantage
of the Viterbi error corrector is its low latency.)
- Pilots can be used if decision feedback does not work. WIth pilots, some carriers are not modulated, and used (in a simpler way as above), to correct the equalizer.
(You dont need to reconstruct the pilot, as its value is known beforehand.)
Problem with pilots is you need interpolation for equalizer settings between the pilots, and this may not be accurate. Advantage of pilots is they are compatible with LDPC codes, but of course they need energy too, and make the advantage of LDPC over Viterbi smaller.
Cheers,
Henri.
Dear Sir,
I think the Henri's answer is good.
The whole idea of OFDM, is to have better performance for multipath.
The idea is that the delta-T, the time difference, of the 'straight' signal and the 'reflected' signal arriving at the receiver is less than the overlap.
If this is the case, there is no ISI (inter symbol interference) in the frequency domain, meaning the equalizer just needs to adjust gain. (Multipath still introduces amplitude distortion.)
The equalizer is then in the frequency domain, and all it does is to multiply the various carriers with complex numbers that undo the amplitude distortion.
For adjusting the equalizer, there are basically 3 methods:
- Adjust on the preamble symbols
- Decision feedback
- Adjust using pilots.
All of them have pro's and con's.
- You start to adjust on the preamble symbols. (In case of modulation systems like WiFi - eg 802.11n OFDM).
- Then, after starting demodulation, its either decision-feedback or pilots.- For decision feedback, the signal is run through the detector and error corrector,
the reconstructed signal based on detected bits is subtracted from the received signal, and the remainder is used as an error signal to adjust the equalizer.
- This is a very robust system when used in conjunction with Viterbi error corrector,
but for the newer LDPC (low density parity codes), I dont think it can work, as the
decode latency is too high, and may make the system unstable. (The advantage
of the Viterbi error corrector is its low latency.)
- Pilots can be used if decision feedback does not work. WIth pilots, some carriers are not modulated, and used (in a simpler way as above), to correct the equalizer.
(You dont need to reconstruct the pilot, as its value is known beforehand.)
Problem with pilots is you need interpolation for equalizer settings between the pilots, and this may not be accurate. Advantage of pilots is they are compatible with LDPC codes, but of course they need energy too, and make the advantage of LDPC over Viterbi smaller.
Interference from the multi-path signal. - ResearchGate. Available from: https://www.researchgate.net/post/Interference_from_the_multi-path_signal2 [accessed Oct 15, 2015].
there is no need for correction at such low levels of qam as the vectors are so far from each other, you only need to play about with the signal to fix these when getting to levels such as 4096 qam where the vectors are so close to each other when distortion problems are amplified even with smaller vector moves
The explanation of professor Zekry completely describes your problem. The reason why you get such clean circles is because the phase of the reflection is linearly changing for each carrier. You can indeed correct this using a frequency domain equalizer (FEQ). For each carrier, this FEQ is a complex number, i.e. a multiplication and a phase change.
Hi
This Constellation show a 4-QAM constellation-Coherent Interference. for more information you can refer to the "Digital communication book".
Good Luck
Dear all,
Thank you for your answers. This problem has been addressed and explained in full details in Section 3.4 of the following journal paper in Ultrasonics. Hope it helps.
Article Evaluation of multiple-channel OFDM based airborne ultrasoni...
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