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LTE UL (SC-FDMA) Demodulation with DMRS Analysis - 1RB

 

This page is a kind of extension of previous tutorial : LTE UL(SC-FDMA) Demodulation (without DMRS Analysis). In the previous tutorial, we had two important factors as given.

    i) Timing Synchronization

    ii) Phase Compensation after demodulation

In this page, I will show you how to find items (actually both Phase and Amplitude compensation) from PUSCH DMRS data. The I/Q Data used here is also generated by a real hardware (Vector signal generator) and captured by Vector Signal Analyzer with special Sync signal. So you don't have to implement an algorithm for synchronization and a lot of compensation which is a too much for an example. If you are interested in working as beginner level of LTE DSP, this can be helpful or motivation as well.

 

Following is the result of the Matlab source code listed here. (A) shows the frequency domain result for each symbols within the first slot of subframe 0 and this is the case that is not compensated with DMRS. (B) is the I/Q plot (real and imaginary) representation of column (A). (C) shows the frequency domain result for each symbols within the first slot of subframe 0 after compensation (Equalization) with DMRS. (D) is the I/Q plot (real and imaginary) representation of column (C).

 

 

The data that I used in this example is from following LTE Configuration. If you don't consider the compensation process (Equalization Process), only the first four items would be important. The last three parameters are for DMRS analysis. The number of RB and StartRB is for both Demodulation and Compensation process.

  • System BandWidth = 5 Mhz
  • Sampling Rate = 7.68 Mhz
  • Number of RB = 1
  • Start RB = 0
  • Physical Cell ID = 0
  • Subframe Number = 0
  • Slot Number = 0

Following is the Matlab source code that produced the figure shown above. The code is designed intentionally long. I might have make it very short if I used for-loop, but it would look harder to understand. So I try to write every procedure step by step. Hopefully, this would be easier for you to follow even though it looks a little too lengthy.

     

    clear all;

     

    % you can download the data file in this example from here.

    % this is for reading the baseband IQ data of OFDM symbol in time domain.

    % detailed explantion for this three line and file format in this example is described in

    % Matlab : Read Number in Binary file page.

     

    fid = fopen('LTE_UL_5_1_CID_0_1RB_NoFilter.bin','r');

    [data,count] = fread(fid, 'single');

    fclose(fid);

     

     

    % This variable represents the first sample in the first SCFDM symbol.

    % How do I know this ? This is just a magic number I could figure out from the vector signal

    % analyzer. Just think this is just a given number. If you seriously want to work in this

    % area, try to implement the algorithm to find this number on your own.

     

    Offset = 280228;

     

    % Nfft represents the FFT size for the specified system bandwidth. 512 is the FFT size for

    % 5 Mhz System Bandwidth.

    Nfft = 512;

     

    % N_RB is the number of RB assinged to this signal. N_RE is the number of Resource Elements

    % in this signal and can be calculated from N_RB. This N_RE determines the IFFT size in

    % demodulation process (N_RE is the size of IFFT)

    N_RB = 1;

    N_RE = N_RB * 12;

     

    % SamplingScale is to figure out the number of samples in CP and OFDM Symbol for each specific system

    % Bandwidth from the 20 Mhz Bandwidth. Physical Layer Parameters - FDD, Downlink will help you understand

    % the meaning of each numbers here.

    SamplingScale = (double(Nfft)/2048);

    CP_LengthList = SamplingScale * [160;144;144;144;144;144;144];

    Symbol_LengthList = SamplingScale * [2048;2048;2048;2048;2048;2048;2048];

     

    % This is to generate a complex numbered sequence to shift the frequency of the I/Q signal by 7.5 Khz

    % the number of samples of this data is same as the number of samples of each SC-FDM symbol.

    Ts = 1.0/(7.68 * 10^6);

    t = linspace(0,Nfft-1,Nfft);

    t = t .* Ts;

    Fshift = 7.5 * 1000 ;

    FrequencyShift = exp(j*2*pi*Fshift*t);

     

    %%%%%%%%%%%%%%%%%%%%%%%%%%%%% Calculate Equalization Factor %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

     

    % This would be the main part of this tutorial. I would calculate Equalization Factor

    % basically by comparing the ideal DMRS generated from the Physical Cell ID, Number of RB,

    % Slot Number and the algorithm described in PUSCH DMRS page.

    % In this tutorial, I manually copied DMRS data using the algorithm described in PUSCH DMRS

    % with Physical Cell ID = 0, Number of RB = 1, Slot Number 0.

    DMRS = [0.7071-0.7071i  -0.9659+0.2588i  0.9659+0.2588i  -0.7071-0.7071i  -0.2588-0.9659i ...

            0.9659+0.2588i   0.7071+0.7071i  -0.9659+0.2588i   0.9659+0.2588i   0.7071+0.7071i ...

            0.9659-0.2588i   0.9659+0.2588i];

     

    % Taking the inverse of DMRS

    DMRS_Inv = 1 ./ DMRS;   

     

    % Taking out PUSCH DMRS Symbol from the slots and Demodulate.

    ChunkStart = Offset  ...

                + CP_LengthList(1) + Symbol_LengthList(1)  ...

                + CP_LengthList(2) + Symbol_LengthList(2)  ...

                + CP_LengthList(3) + Symbol_LengthList(3)  ...

                + CP_LengthList(4);

    ChunkLength = Symbol_LengthList(4);

     

    DataChunk = data((2.* ChunkStart)-1 : (2.*(ChunkStart+ChunkLength)-2));

    DataChunkI = DataChunk(1:2:length(DataChunk));

    DataChunkQ = DataChunk(2:2:length(DataChunk));

    DataChunkComplex = DataChunkI + j*DataChunkQ;

     

    DataChunkFFT = fftshift(fft(DataChunkComplex .* FrequencyShift'));

    DataChunkFFT_RE = DataChunkFFT(107:107+(N_RE-1));

     

    % Calculating Equalization Factor by multiplying DMRS_Inv with the demodulated DMRS.

    % Very important thing : For transposing DataChunkFFT_RE don't use ('). I need just mechanical

    % transposition of DataChunkFFT_RE to make the two vectors multiplicable, but if you use (')

    % it does not only transpose but also taking the complex conjugate of each element, meaning

    % it takes Hermitian transposition which would give you completely unexpected result in this

    % case. It took me a couple hours to realize this. (I am using Matlab 2014 for this page)

    EqFactor = DMRS_Inv .* transpose(DataChunkFFT_RE);

     

     

    %%%%%%%%%%%%%%%%%%%%%%%%%%%%%% Demodulation of symbol 0 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

     

    % This is to demoulate the symbol 0 within the slot 0 of Subframe 0.

    % ChuckStart here indicates the index(position) of the first sample within the binary file.

    % You would notice that I skip the first CP length. This is the same effect of removing the

    % first CP as described in CP removal described in RE Map to/from Antenna page.

    ChunkStart = Offset ...

                + CP_LengthList(1);

     

    % This variable indicates the number of samples within the first OFDM symbol excluding the CP

    ChunkLength = Symbol_LengthList(1);

     

    % This is to read I/Q data pair.

    DataChunk = data((2.* ChunkStart)-1 : (2.*(ChunkStart+ChunkLength)-2));

     

    % This is to separate I and Q into a separate array (vector)

    DataChunkI = DataChunk(1:2:length(DataChunk));

    DataChunkQ = DataChunk(2:2:length(DataChunk));

     

    % This is to combine I array and Q array into a complex number array.

    DataChunkComplex = DataChunkI + j*DataChunkQ;

     

    % This is to convert the time domain OFDM symbol into the frequency domain. Note that the data

    % is shifted in frequency domain. Unlike the previous example : PUSCH Demodulation (without

    % compensation with DMRS), I did fftshift() in this example. For me, it is easier to take out

    % the subcarries allocated for allocated RB. But if you think, the previous method is easier

    % for you, go for it.

    DataChunkFFT = fftshift(fft(DataChunkComplex .* FrequencyShift'));

     

    % This is to take out the data samples which will be mapped to each resource element

    % within the symbol

    DataChunkFFT_RE = DataChunkFFT(107:107+(N_RE-1));

     

    % Taking the IFFT and normalize to get normalized I/Q

    DataChunkFFT_IFFT = ifft(DataChunkFFT_RE);

    DataChunkFFT_IFFT_Norm = DataChunkFFT_IFFT/max(abs(DataChunkFFT_IFFT));

     

    % Plot the normalized I/Q in frequency domain. This is the data before compensation

    subplot(7,6,[1 2]);

    plot(abs(DataChunkFFT_IFFT_Norm));xlim([1, length(DataChunkFFT_IFFT_Norm)]); ylim([0 1.2]);

    set(gca,'xticklabel',[]);set(gca,'yticklabel',[]);

    set(gca,'xtick',[]);set(gca,'ytick',[]);

     

    % Taking the IFFT and normalize to get normalized I/Q. This is a kind of duplicated process

    % of the steps right above.

    DataChunkFFT_RE = DataChunkFFT_RE ;

    DataChunkFFT_IFFT = ifft(DataChunkFFT_RE);

    DataChunkFFT_IFFT = DataChunkFFT_IFFT/max(abs(DataChunkFFT_IFFT));

    DataChunkFFT_IFFT = DataChunkFFT_IFFT;

    DataChunkFftMag = abs(DataChunkFFT_IFFT);

     

    subplot(7,6,3);

    plot(real(DataChunkFFT_IFFT),imag(DataChunkFFT_IFFT),'ro','MarkerFaceColor',[1 0 0],'MarkerSize',2);

    xlim([-1 1]);ylim([-1 1]);

    set(gca,'xticklabel',[]);set(gca,'yticklabel',[]);

    set(gca,'xtick',[]);set(gca,'ytick',[]);

     

    % Taking the IFFT and normalize to get normalized I/Q. But this one has an important

    % difference comparing with the processs shown above. In this step, you see 'EqFactor'

    % is multiplied before ifft(). Also, notice in this case I used "EqFactor'" rather than

    % transpose(EqFactor).

    DataChunkFFT_RE = DataChunkFFT_RE .* EqFactor' ;

    DataChunkFFT_IFFT = ifft(DataChunkFFT_RE);

    DataChunkFFT_IFFT = DataChunkFFT_IFFT/max(abs(DataChunkFFT_IFFT));

    DataChunkFFT_IFFT = DataChunkFFT_IFFT;

    DataChunkFftMag = abs(DataChunkFFT_IFFT);

     

    % Plotting the I/Q in frequency Domain

    subplot(7,6,[4 5]);

    plot(DataChunkFftMag);xlim([1, length(DataChunkFftMag)]); ylim([0 1.2]);

    set(gca,'xticklabel',[]);set(gca,'yticklabel',[]);

    set(gca,'xtick',[]);set(gca,'ytick',[]);

     

    % Plotting the I/Q in Constellation

    subplot(7,6,6);

    DataChunkFFT_Comp = DataChunkFFT_IFFT;

    DataChunkFFT_Comp = DataChunkFFT_Comp/max(abs(DataChunkFFT_Comp));

    plot(real(DataChunkFFT_Comp),imag(DataChunkFFT_Comp),'ro','MarkerFaceColor',[1 0 0],'MarkerSize',2);

    xlim([-1 1]);ylim([-1 1]);

    set(gca,'xticklabel',[]);set(gca,'yticklabel',[]);

    set(gca,'xtick',[]);set(gca,'ytick',[]);

     

    %%%%%%%%%%%%%%%%%%%%%%%%%%%%%% Demodulation of symbol 1 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

    % This is to demodulate the symbol 1 within the slot 0 of Subframe 0. Everything is same

    % as in the symbol 0 analysis except the 'ChunkStart. So I would not explain any further.

     

    ChunkStart = Offset ...

               + CP_LengthList(1) + Symbol_LengthList(1)  ...

               + CP_LengthList(2) ;

    ChunkLength = Symbol_LengthList(2);

     

    DataChunk = data((2.* ChunkStart)-1 : (2.*(ChunkStart+ChunkLength)-2));

    DataChunkI = DataChunk(1:2:length(DataChunk));

    DataChunkQ = DataChunk(2:2:length(DataChunk));

    DataChunkComplex = DataChunkI + j*DataChunkQ;

     

    DataChunkFFT = fftshift(fft(DataChunkComplex .* FrequencyShift'));

     

    DataChunkFFT_RE = DataChunkFFT(107:107+(N_RE-1));

    DataChunkFFT_IFFT = ifft(DataChunkFFT_RE);

    DataChunkFFT_IFFT_Norm = DataChunkFFT_IFFT/max(abs(DataChunkFFT_IFFT));

     

    subplot(7,6,[7 8]);

    plot(abs(DataChunkFFT_IFFT_Norm));xlim([1, length(DataChunkFFT_IFFT_Norm)]); ylim([0 1.2]);

    set(gca,'xticklabel',[]);set(gca,'yticklabel',[]);

    set(gca,'xtick',[]);set(gca,'ytick',[]);

     

    DataChunkFFT_RE = DataChunkFFT_RE ;

    DataChunkFFT_IFFT = ifft(DataChunkFFT_RE);

    DataChunkFFT_IFFT = DataChunkFFT_IFFT/max(abs(DataChunkFFT_IFFT));

    DataChunkFFT_IFFT = DataChunkFFT_IFFT;

    DataChunkFftMag = abs(DataChunkFFT_IFFT);

     

    subplot(7,6,9);

    plot(real(DataChunkFFT_IFFT),imag(DataChunkFFT_IFFT),'ro','MarkerFaceColor',[1 0 0],'MarkerSize',2);

    xlim([-1 1]);ylim([-1 1]);

    set(gca,'xticklabel',[]);set(gca,'yticklabel',[]);

    set(gca,'xtick',[]);set(gca,'ytick',[]);

     

    DataChunkFFT_RE = DataChunkFFT_RE .* EqFactor' ;

    DataChunkFFT_IFFT = ifft(DataChunkFFT_RE);

    DataChunkFFT_IFFT = DataChunkFFT_IFFT/max(abs(DataChunkFFT_IFFT));

    DataChunkFFT_IFFT = DataChunkFFT_IFFT;

    DataChunkFftMag = abs(DataChunkFFT_IFFT);

     

    subplot(7,6,[10 11]);

    plot(DataChunkFftMag);xlim([1, length(DataChunkFftMag)]); ylim([0 1.2]);

    set(gca,'xticklabel',[]);set(gca,'yticklabel',[]);

    set(gca,'xtick',[]);set(gca,'ytick',[]);

     

    subplot(7,6,12);

    DataChunkFFT_Comp = DataChunkFFT_IFFT;

    DataChunkFFT_Comp = DataChunkFFT_Comp/max(abs(DataChunkFFT_Comp));

    plot(real(DataChunkFFT_Comp),imag(DataChunkFFT_Comp),'ro','MarkerFaceColor',[1 0 0],'MarkerSize',2);

    xlim([-1 1]);ylim([-1 1]);

    set(gca,'xticklabel',[]);set(gca,'yticklabel',[]);

    set(gca,'xtick',[]);set(gca,'ytick',[]);

     

     

    %%%%%%%%%%%%%%%%%%%%%%%%%%%%%% Demodulation of symbol 2 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

    % This is to demodulate the symbol 2 within the slot 0 of Subframe 0. Everything is same

    % as in the symbol 0 analysis except the 'ChunkStart. So I would not explain any further.

     

    ChunkStart = Offset  ...

                + CP_LengthList(1) + Symbol_LengthList(1)  ...

                + CP_LengthList(2) + Symbol_LengthList(2)  ...

                + CP_LengthList(3);

    ChunkLength = Symbol_LengthList(3);

     

    DataChunk = data((2.* ChunkStart)-1 : (2.*(ChunkStart+ChunkLength)-2));

    DataChunkI = DataChunk(1:2:length(DataChunk));

    DataChunkQ = DataChunk(2:2:length(DataChunk));

    DataChunkComplex = DataChunkI + j*DataChunkQ;

     

    DataChunkFFT = fftshift(fft(DataChunkComplex .* FrequencyShift'));

     

    DataChunkFFT_RE = DataChunkFFT(107:107+(N_RE-1));

    DataChunkFFT_IFFT = ifft(DataChunkFFT_RE);

    DataChunkFFT_IFFT_Norm = DataChunkFFT_IFFT/max(abs(DataChunkFFT_IFFT));

     

    subplot(7,6,[13 14]);

    plot(abs(DataChunkFFT_IFFT_Norm));xlim([1, length(DataChunkFFT_IFFT_Norm)]); ylim([0 1.2]);

    set(gca,'xticklabel',[]);set(gca,'yticklabel',[]);

    set(gca,'xtick',[]);set(gca,'ytick',[]);

     

    DataChunkFFT_RE = DataChunkFFT_RE ;

    DataChunkFFT_IFFT = ifft(DataChunkFFT_RE);

    DataChunkFFT_IFFT = DataChunkFFT_IFFT/max(abs(DataChunkFFT_IFFT));

    DataChunkFFT_IFFT = DataChunkFFT_IFFT;

    DataChunkFftMag = abs(DataChunkFFT_IFFT);

     

    subplot(7,6,15);

    plot(real(DataChunkFFT_IFFT),imag(DataChunkFFT_IFFT),'ro','MarkerFaceColor',[1 0 0],'MarkerSize',2);

    xlim([-1 1]);ylim([-1 1]);

    set(gca,'xticklabel',[]);set(gca,'yticklabel',[]);

    set(gca,'xtick',[]);set(gca,'ytick',[]);

     

    DataChunkFFT_RE = DataChunkFFT_RE .* EqFactor' ;

    DataChunkFFT_IFFT = ifft(DataChunkFFT_RE);

    DataChunkFFT_IFFT = DataChunkFFT_IFFT/max(abs(DataChunkFFT_IFFT));

    DataChunkFFT_IFFT = DataChunkFFT_IFFT;

    DataChunkFftMag = abs(DataChunkFFT_IFFT);

     

    subplot(7,6,[16 17]);

    plot(DataChunkFftMag);xlim([1, length(DataChunkFftMag)]); ylim([0 1.2]);

    set(gca,'xticklabel',[]);set(gca,'yticklabel',[]);

    set(gca,'xtick',[]);set(gca,'ytick',[]);

     

    subplot(7,6,18);

    DataChunkFFT_Comp = DataChunkFFT_IFFT;

    DataChunkFFT_Comp = DataChunkFFT_Comp/max(abs(DataChunkFFT_Comp));

    plot(real(DataChunkFFT_Comp),imag(DataChunkFFT_Comp),'ro','MarkerFaceColor',[1 0 0],'MarkerSize',2);

    xlim([-1 1]);ylim([-1 1]);

    set(gca,'xticklabel',[]);set(gca,'yticklabel',[]);

    set(gca,'xtick',[]);set(gca,'ytick',[]);

     

    %%%%%%%%%%%%%%%%%%%%%%%%%%%%%% Demodulation of symbol 3 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

    % This is to demodulate the symbol 3 within the slot 0 of Subframe 0. The symbol 3(the fourth

    % symbol in LTE UL slot is special. It is special symbol carrying PUSCH DMRS data, it does

    % not carry any user data. It just carries special reference signal based on Zad-off Chu

    % sequence. This signal does not go through transformation procoding when it is transmitted

    % so this does not go through IFFT process when it is demodulated. But I am still using the

    % variable xxxx_IFFT in this step as I used for other symbols.

     

    ChunkStart = Offset  ...

                + CP_LengthList(1) + Symbol_LengthList(1)  ...

                + CP_LengthList(2) + Symbol_LengthList(2)  ...

                + CP_LengthList(3) + Symbol_LengthList(3)  ...

                + CP_LengthList(4);

    ChunkLength = Symbol_LengthList(4);

     

    DataChunk = data((2.* ChunkStart)-1 : (2.*(ChunkStart+ChunkLength)-2));

    DataChunkI = DataChunk(1:2:length(DataChunk));

    DataChunkQ = DataChunk(2:2:length(DataChunk));

    DataChunkComplex = DataChunkI + j*DataChunkQ;

     

    DataChunkFFT = fftshift(fft(DataChunkComplex .* FrequencyShift'));

     

    DataChunkFFT_RE = DataChunkFFT(107:107+(N_RE-1));

    DataChunkFFT_RE_Norm = DataChunkFFT_RE/max(abs(DataChunkFFT_RE));

     

    subplot(7,6,[19 20]);

    plot(abs(DataChunkFFT_RE_Norm));xlim([1, length(DataChunkFFT_RE)]); ylim([0 1.2]);

    set(gca,'xticklabel',[]);set(gca,'yticklabel',[]);

    set(gca,'xtick',[]);set(gca,'ytick',[]);

     

    DataChunkFFT_RE = DataChunkFFT_RE ;

    DataChunkFFT_IFFT = DataChunkFFT_RE;

    DataChunkFFT_IFFT = DataChunkFFT_IFFT/max(abs(DataChunkFFT_IFFT));

    DataChunkFFT_IFFT = DataChunkFFT_IFFT;

    DataChunkFftMag = abs(DataChunkFFT_IFFT);

     

    subplot(7,6,21);

    plot(real(DataChunkFFT_IFFT),imag(DataChunkFFT_IFFT),'ro','MarkerFaceColor',[1 0 0],'MarkerSize',2);

    xlim([-1 1]);ylim([-1 1]);

    set(gca,'xticklabel',[]);set(gca,'yticklabel',[]);

    set(gca,'xtick',[]);set(gca,'ytick',[]);

     

    DataChunkFFT_RE = DataChunkFFT_RE .* EqFactor' ;

    DataChunkFFT_IFFT = DataChunkFFT_RE;

    DataChunkFFT_IFFT = DataChunkFFT_IFFT/max(abs(DataChunkFFT_IFFT));

    DataChunkFFT_IFFT = DataChunkFFT_IFFT;

    DataChunkFftMag = abs(DataChunkFFT_IFFT);

     

    subplot(7,6,[22 23]);

    plot(DataChunkFftMag);xlim([1, length(DataChunkFftMag)]); ylim([0 1.2]);

    set(gca,'xticklabel',[]);set(gca,'yticklabel',[]);

    set(gca,'xtick',[]);set(gca,'ytick',[]);

     

    subplot(7,6,24);

    DataChunkFFT_Comp = DataChunkFFT_IFFT;

    DataChunkFFT_Comp = DataChunkFFT_Comp/max(abs(DataChunkFFT_Comp));

    plot(real(DataChunkFFT_Comp),imag(DataChunkFFT_Comp),'ro','MarkerFaceColor',[1 0 0],'MarkerSize',2);

    xlim([-1 1]);ylim([-1 1]);

    set(gca,'xticklabel',[]);set(gca,'yticklabel',[]);

    set(gca,'xtick',[]);set(gca,'ytick',[]);

     

     

     

    %%%%%%%%%%%%%%%%%%%%%%%%%%%%%% Demodulation of symbol 4 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

    % This is to demodulate the symbol 4 within the slot 0 of Subframe 0. Everything is same

    % as in the symbol 0 analysis except the 'ChunkStart. So I would not explain any further.

     

    ChunkStart = Offset  ...

                + CP_LengthList(1) + Symbol_LengthList(1)  ...

                + CP_LengthList(2) + Symbol_LengthList(2)  ...

                + CP_LengthList(3) + Symbol_LengthList(3)  ...

                + CP_LengthList(4) + Symbol_LengthList(4)  ...

                + CP_LengthList(5);

    ChunkLength = Symbol_LengthList(5);

     

    DataChunk = data((2.* ChunkStart)-1 : (2.*(ChunkStart+ChunkLength)-2));

    DataChunkI = DataChunk(1:2:length(DataChunk));

    DataChunkQ = DataChunk(2:2:length(DataChunk));

    DataChunkComplex = DataChunkI + j*DataChunkQ;

     

    DataChunkFFT = fftshift(fft(DataChunkComplex .* FrequencyShift'));

     

    DataChunkFFT_RE = DataChunkFFT(107:107+(N_RE-1));

    DataChunkFFT_IFFT = ifft(DataChunkFFT_RE);

    DataChunkFFT_IFFT_Norm = DataChunkFFT_IFFT/max(abs(DataChunkFFT_IFFT));

     

    subplot(7,6,[25 26]);

    plot(abs(DataChunkFFT_IFFT_Norm));xlim([1, length(DataChunkFFT_IFFT_Norm)]); ylim([0 1.2]);

    set(gca,'xticklabel',[]);set(gca,'yticklabel',[]);

    set(gca,'xtick',[]);set(gca,'ytick',[]);

     

    DataChunkFFT_RE = DataChunkFFT_RE ;

    DataChunkFFT_IFFT = ifft(DataChunkFFT_RE);

    DataChunkFFT_IFFT = DataChunkFFT_IFFT/max(abs(DataChunkFFT_IFFT));

    DataChunkFFT_IFFT = DataChunkFFT_IFFT;

    DataChunkFftMag = abs(DataChunkFFT_IFFT);

     

    subplot(7,6,27);

    plot(real(DataChunkFFT_IFFT),imag(DataChunkFFT_IFFT),'ro','MarkerFaceColor',[1 0 0],'MarkerSize',2);

    xlim([-1 1]);ylim([-1 1]);

    set(gca,'xticklabel',[]);set(gca,'yticklabel',[]);

    set(gca,'xtick',[]);set(gca,'ytick',[]);

     

    DataChunkFFT_RE = DataChunkFFT_RE .* EqFactor' ;

    DataChunkFFT_IFFT = ifft(DataChunkFFT_RE);

    DataChunkFFT_IFFT = DataChunkFFT_IFFT/max(abs(DataChunkFFT_IFFT));

    DataChunkFFT_IFFT = DataChunkFFT_IFFT;

    DataChunkFftMag = abs(DataChunkFFT_IFFT);

     

    subplot(7,6,[28 29]);

    plot(DataChunkFftMag);xlim([1, length(DataChunkFftMag)]); ylim([0 1.2]);

    set(gca,'xticklabel',[]);set(gca,'yticklabel',[]);

    set(gca,'xtick',[]);set(gca,'ytick',[]);

     

    subplot(7,6,30);

    DataChunkFFT_Comp = DataChunkFFT_IFFT;

    DataChunkFFT_Comp = DataChunkFFT_Comp/max(abs(DataChunkFFT_Comp));

    plot(real(DataChunkFFT_Comp),imag(DataChunkFFT_Comp),'ro','MarkerFaceColor',[1 0 0],'MarkerSize',2);

    xlim([-1 1]);ylim([-1 1]);

    set(gca,'xticklabel',[]);set(gca,'yticklabel',[]);

    set(gca,'xtick',[]);set(gca,'ytick',[]);

     

     

    %%%%%%%%%%%%%%%%%%%%%%%%%%%%%% Demodulation of symbol 5 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

    % This is to demodulate the symbol 5 within the slot 0 of Subframe 0. Everything is same

    % as in the symbol 0 analysis except the 'ChunkStart. So I would not explain any further.

     

    ChunkStart = Offset  ...

                + CP_LengthList(1) + Symbol_LengthList(1)  ...

                + CP_LengthList(2) + Symbol_LengthList(2)  ...

                + CP_LengthList(3) + Symbol_LengthList(3)  ...

                + CP_LengthList(4) + Symbol_LengthList(4)  ...

                + CP_LengthList(5) + Symbol_LengthList(5)  ...

                + CP_LengthList(6);

    ChunkLength = Symbol_LengthList(6);

     

    DataChunk = data((2.* ChunkStart)-1 : (2.*(ChunkStart+ChunkLength)-2));

    DataChunkI = DataChunk(1:2:length(DataChunk));

    DataChunkQ = DataChunk(2:2:length(DataChunk));

    DataChunkComplex = DataChunkI + j*DataChunkQ;

     

    DataChunkFFT = fftshift(fft(DataChunkComplex .* FrequencyShift'));

     

    DataChunkFFT_RE = DataChunkFFT(107:107+(N_RE-1));

    DataChunkFFT_IFFT = ifft(DataChunkFFT_RE);

    DataChunkFFT_IFFT_Norm = DataChunkFFT_IFFT/max(abs(DataChunkFFT_IFFT));

     

    subplot(7,6,[31 32]);

    plot(abs(DataChunkFFT_IFFT_Norm));xlim([1, length(DataChunkFFT_IFFT_Norm)]); ylim([0 1.2]);

    set(gca,'xticklabel',[]);set(gca,'yticklabel',[]);

    set(gca,'xtick',[]);set(gca,'ytick',[]);

     

    DataChunkFFT_RE = DataChunkFFT_RE ;

    DataChunkFFT_IFFT = ifft(DataChunkFFT_RE);

    DataChunkFFT_IFFT = DataChunkFFT_IFFT/max(abs(DataChunkFFT_IFFT));

    DataChunkFFT_IFFT = DataChunkFFT_IFFT;

    DataChunkFftMag = abs(DataChunkFFT_IFFT);

     

    subplot(7,6,33);

    plot(real(DataChunkFFT_IFFT),imag(DataChunkFFT_IFFT),'ro','MarkerFaceColor',[1 0 0],'MarkerSize',2);

    xlim([-1 1]);ylim([-1 1]);

    set(gca,'xticklabel',[]);set(gca,'yticklabel',[]);

    set(gca,'xtick',[]);set(gca,'ytick',[]);

     

    DataChunkFFT_RE = DataChunkFFT_RE .* EqFactor' ;

    DataChunkFFT_IFFT = ifft(DataChunkFFT_RE);

    DataChunkFFT_IFFT = DataChunkFFT_IFFT/max(abs(DataChunkFFT_IFFT));

    DataChunkFFT_IFFT = DataChunkFFT_IFFT;

    DataChunkFftMag = abs(DataChunkFFT_IFFT);

     

    subplot(7,6,[34 35]);

    plot(DataChunkFftMag);xlim([1, length(DataChunkFftMag)]); ylim([0 1.2]);

    set(gca,'xticklabel',[]);set(gca,'yticklabel',[]);

    set(gca,'xtick',[]);set(gca,'ytick',[]);

     

    subplot(7,6,36);

    DataChunkFFT_Comp = DataChunkFFT_IFFT;

    DataChunkFFT_Comp = DataChunkFFT_Comp/max(abs(DataChunkFFT_Comp));

    plot(real(DataChunkFFT_Comp),imag(DataChunkFFT_Comp),'ro','MarkerFaceColor',[1 0 0],'MarkerSize',2);

    xlim([-1 1]);ylim([-1 1]);

    set(gca,'xticklabel',[]);set(gca,'yticklabel',[]);

    set(gca,'xtick',[]);set(gca,'ytick',[]);

     

    %%%%%%%%%%%%%%%%%%%%%%%%%%%%%% Demodulation of symbol 6 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

    % This is to demodulate the symbol 6 within the slot 0 of Subframe 0. Everything is same

    % as in the symbol 0 analysis except the 'ChunkStart. So I would not explain any further.

    ChunkStart = Offset  ...

                + CP_LengthList(1) + Symbol_LengthList(1)  ...

                + CP_LengthList(2) + Symbol_LengthList(2)  ...

                + CP_LengthList(3) + Symbol_LengthList(3)  ...

                + CP_LengthList(4) + Symbol_LengthList(4)  ...

                + CP_LengthList(5) + Symbol_LengthList(5)  ...

                + CP_LengthList(6) + Symbol_LengthList(6)  ...

                + CP_LengthList(7);

    ChunkLength = Symbol_LengthList(7);

     

    DataChunk = data((2.* ChunkStart)-1 : (2.*(ChunkStart+ChunkLength)-2));

    DataChunkI = DataChunk(1:2:length(DataChunk));

    DataChunkQ = DataChunk(2:2:length(DataChunk));

    DataChunkComplex = DataChunkI + j*DataChunkQ;

     

    DataChunkFFT = fftshift(fft(DataChunkComplex .* FrequencyShift'));

     

    DataChunkFFT_RE = DataChunkFFT(107:107+(N_RE-1));

    DataChunkFFT_IFFT = ifft(DataChunkFFT_RE);

    DataChunkFFT_IFFT_Norm = DataChunkFFT_IFFT/max(abs(DataChunkFFT_IFFT));

     

    subplot(7,6,[37 38]);

    plot(abs(DataChunkFFT_IFFT_Norm));xlim([1, length(DataChunkFFT_IFFT_Norm)]); ylim([0 1.2]);

    set(gca,'xticklabel',[]);set(gca,'yticklabel',[]);

    set(gca,'xtick',[]);set(gca,'ytick',[]);

     

    DataChunkFFT_RE = DataChunkFFT_RE ;

    DataChunkFFT_IFFT = ifft(DataChunkFFT_RE);

    DataChunkFFT_IFFT = DataChunkFFT_IFFT/max(abs(DataChunkFFT_IFFT));

    DataChunkFFT_IFFT = DataChunkFFT_IFFT;

    DataChunkFftMag = abs(DataChunkFFT_IFFT);

     

    subplot(7,6,39);

    plot(real(DataChunkFFT_IFFT),imag(DataChunkFFT_IFFT),'ro','MarkerFaceColor',[1 0 0],'MarkerSize',2);

    xlim([-1 1]);ylim([-1 1]);

    set(gca,'xticklabel',[]);set(gca,'yticklabel',[]);

    set(gca,'xtick',[]);set(gca,'ytick',[]);

     

    DataChunkFFT_RE = DataChunkFFT_RE .* EqFactor' ;

    DataChunkFFT_IFFT = ifft(DataChunkFFT_RE);

    DataChunkFFT_IFFT = DataChunkFFT_IFFT/max(abs(DataChunkFFT_IFFT));

    DataChunkFFT_IFFT = DataChunkFFT_IFFT;

    DataChunkFftMag = abs(DataChunkFFT_IFFT);

     

    subplot(7,6,[40 41]);

    plot(DataChunkFftMag);xlim([1, length(DataChunkFftMag)]); ylim([0 1.2]);

    set(gca,'xticklabel',[]);set(gca,'yticklabel',[]);

    set(gca,'xtick',[]);set(gca,'ytick',[]);

     

    subplot(7,6,42);

    DataChunkFFT_Comp = DataChunkFFT_IFFT;

    DataChunkFFT_Comp = DataChunkFFT_Comp/max(abs(DataChunkFFT_Comp));

    plot(real(DataChunkFFT_Comp),imag(DataChunkFFT_Comp),'ro','MarkerFaceColor',[1 0 0],'MarkerSize',2);

    xlim([-1 1]);ylim([-1 1]);

    set(gca,'xticklabel',[]);set(gca,'yticklabel',[]);

    set(gca,'xtick',[]);set(gca,'ytick',[]);