0
$\begingroup$

I have an OFDM system. I would like to introduce a fractional delay of (0.25 samples). Therefore:

  1. I increase the sampling rate of the OFDM signal by a factor of 4 (via frequency domain zero padding (FDZP)).
  2. and then I shift the signal by simply adding 1 zero at the beginning of the signal.
  3. and then I downsample the signal by a factor of 4. So that the fractional delay will be (1/4 = 0.25)

However, I have noticed, that by doing this, after equalization and phase correction (due to this introduced timing offset), the EVM performance of high-frequency subcarriers is lower than low-frequency subcarriers, and I don't know the reason (see Figs. 2 & 3 & 4). Even before equalization, I can see that the constellation of high-frequency subcarriers suffers more noise compared with low-frequency subcarriers (see Figs. 5 & 6) To verify my code, at the receiver, I measured STO by observing the phase rotation of the received constellation, I can see that the STO is almost 0.25 samples for all subcarriers (except subcarrier -N/2 which is at the Nyquist frequency). (see Fig. 1).

I cannot understand why the EVM performance is subcarrier dependent. I expected all subcarriers to have the same EVM (should be low) as STO is less than the length of the cyclic prefix. Please help me to identify the problem. I suspect that this is caused by the oversampling method I used which is frequency-domain zero padding (FDZP), but I was told that FDZP does not introduce noise and all subcarriers should be equally effected. I would be very grateful if someone explains why EVM performance is subcarrier dependent. Here is my code, it is very simple

%% OFDM system with channel estimation: clear all;clc; %% define parameters Nsymbol = 3000; %OFDM symbols to be simulated; Nsc = 128; %length of OFDM symbols; M = 16; %Constellation Order; Ncp = 4; %Cyclic Prefix length; Ncs = 4; %cyclic suffix; Npilot = 100; %training sequence for equalization %% data generation Data=randi ([0 M-1],Nsc,Nsymbol+Npilot); %% mapping Tx_QAM=qammod(Data,M,'UnitAveragePower',true); %% inverse discret Fourier transform (IFFT) OFDM_Sig_no_cp=ifft(Tx_QAM); %% Adding Cyclic Prefix & Suffix OFDM_Sig_with_cp_cs=[OFDM_Sig_no_cp((Nsc-(Ncp)+1):end,:);OFDM_Sig_no_cp;OFDM_Sig_no_cp(1:Ncs,:)]; %% parallel to serail OFDM_Sig=reshape(OFDM_Sig_with_cp_cs,1,(Nsymbol+Npilot)*(Nsc+Ncp+Ncs)); %% adding fractional STO STO = 0.25; osf = 4; % Oversample the signal by a factor of osf by FDZP L = length(OFDM_Sig); OFDM_Sig_f = fft(OFDM_Sig); OFDM_Sig_f = [OFDM_Sig_f(1:L/2) zeros(1,(osf-1)*L) OFDM_Sig_f(L/2+1:end)]; OFDM_Sig_osf = osf*ifft(OFDM_Sig_f); % apply STO OFDM_Sig_osf_STO = circshift(OFDM_Sig_osf,STO*osf); % downsample the signal OFDM_Sig_STO = OFDM_Sig_osf_STO(1:osf:end); %% Receiver %% serial to parallel Rx_OFDM_Sig = reshape(OFDM_Sig_STO,Nsc+Ncp+Ncs,Nsymbol+Npilot); Rx_OFDM_cp_removed = Rx_OFDM_Sig(Ncp+1:end,:); % remove cyclic prefix Rx_OFDM_cs_removed = Rx_OFDM_cp_removed(1:end-Ncs,:); % remove cyclic suffix %% Discret Fourier transform (FFT) Rx_QAM = fft(Rx_OFDM_cs_removed); %% LS channel estimation & Equalization TxP = Tx_QAM(:,1:Npilot); % trnasmitted pilots RxP = Rx_QAM(:,1:Npilot); % received pilots Hpilot_LS = mean(RxP./TxP,2); % LS channel estimation Rx_QAM = Rx_QAM(:,Npilot+1:end); % remove pilot sequence of the received signal Tx_QAM = Tx_QAM(:,Npilot+1:end); % remove pilot sequence of the transmitted signal Rx_QAM_EQ = (Rx_QAM)./repmat(Hpilot_LS,1,Nsymbol); %% measure STO by estimating phase offset Phase = mean((angle(Rx_QAM./Tx_QAM)),2); SC_index = [0:Nsc/2-1 -Nsc/2:1:-1]; Phase2 = (Phase./2/pi*Nsc); estimated_STO = -1*Phase2./SC_index.'; %this is the STO measured by observing the phase rotation due to STO figure(1);plot(fftshift(SC_index), fftshift(estimated_STO),'linewidth',3) grid on xlabel('subcarrier index') ylabel('Measured STO by observing phase rotation due to STO') title('Fig.1') %% measuring EVM for cc = 1:Nsc EVM = lteEVM(Rx_QAM_EQ(cc,:),Tx_QAM(cc,:)); EVM_per_SC_rms(cc) = EVM.RMS; EVM_per_SC_dB(cc) = 20*log10(EVM_per_SC_rms(cc)); end figure(2);plot(fftshift(SC_index), fftshift(EVM_per_SC_dB),'linewidth',3) grid on xlabel('subcarrier index') ylabel('EVM (dB)') title('Fig.2') %% plotting original received signal % SC0 figure(3);plot(Rx_QAM(1,:),'.') title('Fig.3 Original Received Constellation of Subcarrier 0 (before Equalization)') % SC0 figure(4);plot(Rx_QAM(64,:),'.') title('Fig.4 Original Received Constellation of Subcarrier 63 (before Equalization)') %% plotting received signal % SC0 figure(5);plot(Rx_QAM_EQ(1,:),'.') title('Fig.5 Original Received Constellation of Subcarrier 0 (after Equalization)') % SC0 figure(6);plot(Rx_QAM_EQ(64,:),'.') title('Fig.6 Original Received Constellation of Subcarrier 63 (after Equalization)')

enter image description here enter image description here enter image description here enter image description here enter image description here enter image description here

Improve this question
$\endgroup$
7
  • 1
    $\begingroup$ I didn't read through your entire code processing but where do you do timing offset correction? Phase and Delay are not the same thing: phase is the rotation of the symbols while delay is a time offset; so I am suspecting that you may not have implemented yet an STO correction? (Or you have an issue with your correction approach?) $\endgroup$ Commented May 10, 2022 at 12:12
  • $\begingroup$ @DanBoschen, applied timing offset (STO = 0.25 samples) is less than the length of cyclic prefix, so it does not cause ISI or ICI. It just causes phase offset (rotation of the received constellation). My problem is that I see some noise (even before correcting the timing offset-induced phase offset) at high-frequency subcarriers as can be seen in Fig.4 compared with low-frequency subcarriers as shown in Fig.3 $\endgroup$ Commented May 10, 2022 at 12:28
  • 2
    $\begingroup$ that is a different phase rotation for every subcarrier (proportional to each subcarrier rather than a constant rotation for each). If you are doing that correction then you are correcting for STO. I suspect the issue may be in doing that- I suggest confirming your correction is a linear phase versus subcarrier index. For a 1/4 sample offset the phase will go linearly from 0 to pi/2 over each of the subcarriers $\endgroup$ Commented May 10, 2022 at 13:42
  • 1
    $\begingroup$ @DanBoschen I have double-checked, yes the phase rotation is linear and proportional to the subcarrier index, $\endgroup$ Commented May 11, 2022 at 8:46
  • 1
    $\begingroup$ It's convolved with a Dirichlet Kernel which is the aliased Sinc function but I don't see how it would treat any of the bins differently. What I am suspicious of if taking the FFT of the time domain sequence with the CP added which has now condensed that whole vector in the time domain into the frequency range given by the original waveform without CP in the frequency range (since there is no change of sampling rate or your used of time for the 1/4 sample delay). Can you try introducing your quarter sample delay using the original (frequency domain) waveform without CP? then add CP to that $\endgroup$ Commented May 11, 2022 at 13:09

1 Answer 1

Reset to default
1
$\begingroup$

I believe the distortion is from using the FFT of the complete OFDM symbol including the CP to introduce time delay with a zero-padded FFT. Even before zero-padding is added the FFT result will no longer be at the original subcarrier spacing. The waveform will be interpolated and delayed but in the receiver the CP is removed prior to taking the FFT, which then no longer matches the modified frequency domain waveform.

To not introduce distortion, do the FDZP on the OFDM waveform prior to adding the CP, re-index that result for the 1/4 sample time offset and then extract the CP from that to emulate a delayed time domain waveform. Alternatively if it is desired to emulate a delay on the time domain waveform representing the transmitter output, this can be done with fractional delay filters using a continuous stream of the OFDM waveform as it will be transmitted, or could be done symbol by symbol if the impulse response of the interpolation filter can be less than the CP and achieve sufficient distortion rejection. If there is access to the OFDM waveform prior to IFFT and CP insertion, that approach would be the easier of these two methods.

Improve this answer
$\endgroup$

Start asking to get answers

Find the answer to your question by asking.

Ask question

Explore related questions

See similar questions with these tags.