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OFDM Symbol Extraction

 

In this example, I will show you how to extract only one OFDM Symbol from a complete radio subframe. (Actually it will show you the whole process of creating a subframe and extract a specific symbols from the subframe).

This tutorial shows you how do plot each OFDM symbol directly from the resourceGrid. This is not for extracting OFDM symbol from OFDM modulcated symbol (timedomain data).

 

< SISO - Extracting a OFDM Symbol >

 

    % Since PSS is determined by each eNodeB, you have to define properites of a eNodeB.  

    % NDLRB indicate System Bandwith in the unit of RBs.

    % NDLRB 6 = 1.4 Mhz, NDLRB 15 = 3.0 Mhz, NDLRB 25 = 5.0 Mhz,

    % NDLRB 50 = 10 Mhz, NDLRB 75 = 15 Mhz, NDLRB 100 = 20 Mhz

    % CellRefP indicate number of downlink Antenna. CellRefP = 1 means 1 transmission antenna (SISO)

    % NCellID indicate PCI (Physical Channel Identity) of the Cell

    % NSubframe indicate the subframe number.

    enb.CyclicPrefix = 'Normal';

    enb.PHICHDuration = 'Normal';

    enb.Ng = 'Sixth';

    enb.NDLRB = 6;

    enb.CellRefP = 1;

    enb.DuplexMode = 'FDD';

     

    enb.NCellID = 0;

    enb.NSubframe = 0;

    enb.CFI = 1;

     

    PHICH_Group_Index = 0;

    PHICH_Sequence_Index = 1;

    HARQ_Indicator_Value = 0; % 0 = NACK, 1 = ACK

     

    % Now populate all the information in DCI field as you like. Understanding details of DCI is also pretty huge

    % topics. You would need separate page for DCI for the details.

     

    dci.NDLRB = enb.NDLRB;

    dci.DCIFormat = 'Format1A';

    dci.AllocationType = 0;

    dci.Allocation.RIV = 18;

    dci.ModCoding = 10;

    dci.HARQNo = 0;

    dci.NewData = 0;

    dci.TPCPUCCH = 0;

    dci.DuplexMode = 'FDD';

    dci.NTxAnts = 1;

     

    % once you defined all the detailed fields of DCI, just pass it to lteDCI() function with eNB info as follows,

    % then you will get the bit stream for the DCI.

     

    [dciMessage,dciMessageBits] = lteDCI(enb,dci);

     

    % for this step, you need to set a couple of additional parameters as shown below. C_RNTI will be XORed to CRC bits

    % PDCCHFormat will determined Aggregation Level.

    %          PDCCHFormat 0 indicate Aggregation Level 1

    %          PDCCHFormat 1 indicate Aggregation Level 2

    %          PDCCHFormat 2 indicate Aggregation Level 4

    %          PDCCHFormat 3 indicate Aggregation Level 8

     

    C_RNTI = 100;                         

    pdcchConfig.RNTI = C_RNTI;            

    pdcchConfig.PDCCHFormat = 0;          

     

    % then pass dciMessageBits and pdcchConfig to lteDCIEncode, the you would get the encoded bitstream.

     

    codedDciBits = lteDCIEncode(pdcchConfig, dciMessageBits);

     

    % If you pass the enb into ltePDCCHInfo() function, it will give you the amount of resources that can be allocated

    % for PDCCH allocation. This is not the amount of resource for only one DCI. It will give you the total/maximum

    % amount of the resources that can be allocated for PDCCH.

     

    pdcchDims = ltePDCCHInfo(enb);

     

    % With ltePDCCHSpace, you can get the list of all the possible spaces that can carry PDCCH. In this example,

    % the space were shown in the unit of bits.

     

    pdcchBits = -1*ones(pdcchDims.MTot, 1);

     

    % generate an array with the length that can accommodate all the possible PDCCH bits.

     

    candidates = ltePDCCHSpace(enb, pdcchConfig, {'bits', '1based'});

     

    % select one of the candidate bitSection and assign the codedDcitBits. You can select any candidate bit section,

    % but in this example, I selected the first candidate section.

     

    pdcchBits ( candidates(1, 1) : candidates(1, 2) ) = codedDciBits;

     

    % if pass the encodedBits into ltePDCCH(), it will generate the modulated physical layer symbols.

     

    pdcch_sym = ltePDCCH(enb, pdcchBits);

    pdcch_sym_ind = ltePDCCHIndices(enb,{'1based','re'});

    pdcch_sym_arrayIndex = 0:length(pdcch_sym)-1;

     

     

    % Now we set various parameters defining PDSCH channel. (In real transmission, you would need to create

    % a dci that is corresponding the configuration here. But in this example, I will go without defining DCI)

     

    pdsch.NTxAnts = 1;

    pdsch.NLayers = 1;

    pdsch.TxScheme = 'Port0';

    pdsch.Modulation = {'16QAM'};

    pdsch.RV = 0;

    pdsch.RNTI = C_RNTI;

     

    % Now I have to create a vector carrying the number of PRB indexes that will be used to carry this PDSCH.

    % for example, pdsch_prbs in following section would create a vector [0 1 2 3]

     

    START_RB = 0;

    N_RB = 4;

     

    pdsch_prbs = (START_RB:(START_RB+N_RB-1)).';

     

    % Now we have to generate a bit sequence which would exactly fit to the number of resource elements that are

    % allocated for PDSCH for this specific subframe. To figure out exact Resource Element information, unlike in other

    % channel processing, I would run ltePDSCHIndices() first. As you see in the following code, ltePDSCHIndices()

    % returns the information that would give you the size of transport block size in the unit of bits.

     

    [pdsch_sym_ind,pdschIndInfo] = ltePDSCHIndices(enb,pdsch,pdsch_prbs,{'1based','re'});

    codedTrBlkSize = pdschIndInfo.G;

     

    % now I would create a bit array that carries the user data. In this example, I generated randomly but in real

    % situation, this would carry your user data (e.g, image, movie, files etc)

     

    dlschTransportBlk = round(rand(1,codedTrBlkSize));

     

    % now if you pass all the information to lteDLSCH), it will generate the encoded codeword data for the transport

    % block you defined.

     

    codeword = lteDLSCH(enb,pdsch,codedTrBlkSize,dlschTransportBlk);

     

    % now if you pass the encoded data (codeword) with eNB and pdsch config to ltePDSCH(), you can generate

    % physical layer symbols for the encoded data.

     

    pdsch_sym = ltePDSCH(enb,pdsch,codeword);

    pdsch_sym_arrayIndex = 0:length(pdsch_sym)-1;

     

    % Following is to create an empty resource grid for one subframe.

     

    resourceGrid = lteDLResourceGrid(enb);

     

    % Following is to create symbols for Cell Specific Reference Signal and make a list of resource index for the

    % reference signal.

     

    rsAnt0 = lteCellRS(enb,0);

    indAnt0 = lteCellRSIndices(enb,0);

    resourceGrid(indAnt0) = rsAnt0;

     

    % Following is to create symbols for PBCH and make a list of resource index for the signal (channel)

     

    mib_bits = lteMIB(enb);

    bch_cw = lteBCH(enb,mib_bits);

     

    % Following is to create symbols for PSS and make a list of resource index for the signal

     

    pss = ltePSS(enb);

    pss_arrayIndex = 0:length(pss)-1;

    pss_sym_ind = ltePSSIndices(enb,0,{'1based','re'});

     

    % Following is to create symbols for SSS and make a list of resource index for the signal

     

    sss = lteSSS(enb);

    sss_arrayIndex = 0:length(sss)-1;

    sss_sym_ind = lteSSSIndices(enb,0,{'1based','re'});

     

    % Following is to create symbols for PCFICH and make a list of resource index for the signal

     

    cfi_cw = lteCFI(enb);

    pcfich_sym = ltePCFICH(enb,cfi_cw);

    pcfich_sym_arrayIndex = 0:length(pcfich_sym)-1;

    pcfich_sym_ind = ltePCFICHIndices(enb,{'1based','re'});

     

    % Following is to create symbols for PHICH and make a list of resource index for the signal

     

    phich_sym = ltePHICH(enb,[PHICH_Group_Index,PHICH_Sequence_Index,HARQ_Indicator_Value]);

    phich_sym_arrayIndex = 0:length(phich_sym)-1;

    phich_sym_ind = ltePHICHIndices(enb,{'1based','re'});

     

    % Following is to create symbols for PBCH and make a list of resource index for the signal (channel)

     

    pbch_sym = ltePBCH(enb,bch_cw);

    pbch_sym_arrayIndex = 0:length(pbch_sym)-1;

    pbch_sym_ind = ltePBCHIndices(enb,{'1based','re'});

     

    % Following part is filling the resource grid with each of the signal.. but if you see carefully I didn't fill this

    % with real symbol number, I just filled it with a constant that I arbitrarily set. This is just for visualization..

    % just to allocate constant/outstanding color for each signal. When you  use this resource grid for real

    % transmission (not for visualization), fill the resourceGrid with real symbol value you generated above.

     

    pss_scale = 0.2;

    sss_scale = 0.4;

    phich_scale = 0.7;

    pcfich_scale = 0.5;

    pbch_scale = 0.7;

    pdcch_scale = 0.9;

    pdsch_scale = 0.6;

     

    resourceGrid(pss_sym_ind) = pss_scale .* pss;

    resourceGrid(sss_sym_ind) = sss_scale .* sss;

    resourceGrid(pcfich_sym_ind) = pcfich_scale .* pcfich_sym;

    resourceGrid(phich_sym_ind) = phich_scale .* phich_sym;

    resourceGrid(pbch_sym_ind) = pbch_scale .* pbch_sym(1:length(pbch_sym_ind));

    resourceGrid(pdcch_sym_ind) = pdcch_scale .* pdcch_sym;

    resourceGrid(pdsch_sym_ind) = pdsch_scale .* pdsch_sym;

     

    % Following is for extracting Resource Elements by each symbol. Since there is no specific function to extract REs

    % for each symbol, I would generate RE indices for a specific symbol and extract REs of the indices using

    % lteExtractResources() function.

    % (enb.NDLRB*12) represents the total number of REs within a single OFDM Symbol. enb.NDLRB represents the total

    % number of RBs in a OFDM Symbol and 12 represents the number of REs within a single RB.

     

    symbolNo = 1;

    symbolIdxStart = symbolNo*(enb.NDLRB*12) + 1;

    symbolIdxEnd = symbolIdxStart + enb.NDLRB*12;

    symbolIdxArray = symbolIdxStart:symbolIdxEnd;

    symbolReArray = lteExtractResources(symbolIdxArray,resourceGrid);

     

    % Following is to plot the extracted symbol. Left side plot shows the constellation of all REs in the symbol

    % Right side plot shows the data (IQ data, complex number) along the extracted array index.

    % again the resulting graph here is intentionally distorted a little to give you the distinction among each channels.

    % the signal amplitude in real situation would be much more evenly distributed (less distiction among channels)

    % than the one you see here.

     

    subplot(1,3,1);

    plot(real(symbolReArray ),imag(symbolReArray),'ro','MarkerFaceColor',[1 0 0]);

    axis([-1 1 -1 1]);

     

    subplot(1,3,[2 3]);

    stem(abs(symbolReArray));

    axis([1 length(symbolIdxArray) 0 1]);

     

      enb.NDLRB = 6;

      enb.CellRefP = 1;

      enb.NCellID = 0;

      enb.NSubframe = 0;

      symbolNo = 1;

     

 

< SISO - Plotting All Symbols within a Subframe >

    % Since PSS is determined by each eNodeB, you have to define properites of a eNodeB.  

    % NDLRB indicate System Bandwith in the unit of RBs.

    % NDLRB 6 = 1.4 Mhz, NDLRB 15 = 3.0 Mhz, NDLRB 25 = 5.0 Mhz,

    % NDLRB 50 = 10 Mhz, NDLRB 75 = 15 Mhz, NDLRB 100 = 20 Mhz

    % CellRefP indicate number of downlink Antenna. CellRefP = 1 means 1 transmission antenna (SISO)

    % NCellID indicate PCI (Physical Channel Identity) of the Cell

    % NSubframe indicate the subframe number.

    enb.CyclicPrefix = 'Normal';

    enb.PHICHDuration = 'Normal';

    enb.Ng = 'Sixth';

    enb.NDLRB = 6;

    enb.CellRefP = 1;

    enb.DuplexMode = 'FDD';

     

    enb.NCellID = 0;

    enb.NSubframe = 0;

    enb.CFI = 1;

     

    PHICH_Group_Index = 0;

    PHICH_Sequence_Index = 1;

    HARQ_Indicator_Value = 0; % 0 = NACK, 1 = ACK

     

    % Now populate all the information in DCI field as you like. Understanding details of DCI is also pretty huge

    % topics. You would need separate page for DCI for the details.

     

    dci.NDLRB = enb.NDLRB;

    dci.DCIFormat = 'Format1A';

    dci.AllocationType = 0;

    dci.Allocation.RIV = 18;

    dci.ModCoding = 10;

    dci.HARQNo = 0;

    dci.NewData = 0;

    dci.TPCPUCCH = 0;

    dci.DuplexMode = 'FDD';

    dci.NTxAnts = 1;

     

    % once you defined all the detailed fields of DCI, just pass it to lteDCI() function with eNB info as follows,

    % then you will get the bit stream for the DCI.

     

    [dciMessage,dciMessageBits] = lteDCI(enb,dci);

     

    % for this step, you need to set a couple of additional parameters as shown below. C_RNTI will be XORed to CRC bits

    % PDCCHFormat will determined Aggregation Level.

    %          PDCCHFormat 0 indicate Aggregation Level 1

    %          PDCCHFormat 1 indicate Aggregation Level 2

    %          PDCCHFormat 2 indicate Aggregation Level 4

    %          PDCCHFormat 3 indicate Aggregation Level 8

     

    C_RNTI = 100;                         

    pdcchConfig.RNTI = C_RNTI;            

    pdcchConfig.PDCCHFormat = 0;          

     

    % then pass dciMessageBits and pdcchConfig to lteDCIEncode, the you would get the encoded bitstream.

     

    codedDciBits = lteDCIEncode(pdcchConfig, dciMessageBits);

     

    % If you pass the enb into ltePDCCHInfo() function, it will give you the amount of resources that can be allocated

    % for PDCCH allocation. This is not the amount of resource for only one DCI. It will give you the total/maximum

    % amount of the resources that can be allocated for PDCCH.

     

    pdcchDims = ltePDCCHInfo(enb);

     

    % With ltePDCCHSpace, you can get the list of all the possible spaces that can carry PDCCH. In this example,

    % the space were shown in the unit of bits.

     

    pdcchBits = -1*ones(pdcchDims.MTot, 1);

     

    % generate an array with the length that can accommodate all the possible PDCCH bits.

     

    candidates = ltePDCCHSpace(enb, pdcchConfig, {'bits', '1based'});

     

    % select one of the candidate bitSection and assign the codedDcitBits. You can select any candidate bit section,

    % but in this example, I selected the first candidate section.

     

    pdcchBits ( candidates(1, 1) : candidates(1, 2) ) = codedDciBits;

     

    % if pass the encodedBits into ltePDCCH(), it will generate the modulated physical layer symbols.

     

    pdcch_sym = ltePDCCH(enb, pdcchBits);

    pdcch_sym_ind = ltePDCCHIndices(enb,{'1based','re'});

    pdcch_sym_arrayIndex = 0:length(pdcch_sym)-1;

     

     

    % Now we set various parameters defining PDSCH channel. (In real transmission, you would need to create

    % a dci that is corresponding the configuration here. But in this example, I will go without defining DCI)

     

    pdsch.NTxAnts = 1;

    pdsch.NLayers = 1;

    pdsch.TxScheme = 'Port0';

    pdsch.Modulation = {'16QAM'};

    pdsch.RV = 0;

    pdsch.RNTI = C_RNTI;

     

    % Now I have to create a vector carrying the number of PRB indexes that will be used to carry this PDSCH.

    % for example, pdsch_prbs in following section would create a vector [0 1 2 3]

     

    START_RB = 0;

    N_RB = 4;

     

    pdsch_prbs = (START_RB:(START_RB+N_RB-1)).';

     

    % Now we have to generate a bit sequence which would exactly fit to the number of resource elements that are

    % allocated for PDSCH for this specific subframe. To figure out exact Resource Element information, unlike in other

    % channel processing, I would run ltePDSCHIndices() first. As you see in the following code, ltePDSCHIndices()

    % returns the information that would give you the size of transport block size in the unit of bits.

     

    [pdsch_sym_ind,pdschIndInfo] = ltePDSCHIndices(enb,pdsch,pdsch_prbs,{'1based','re'});

    codedTrBlkSize = pdschIndInfo.G;

     

    % now I would create a bit array that carries the user data. In this example, I generated randomly but in real

    % situation, this would carry your user data (e.g, image, movie, files etc)

     

    dlschTransportBlk = round(rand(1,codedTrBlkSize));

     

    % now if you pass all the information to lteDLSCH), it will generate the encoded codeword data for the transport

    % block you defined.

     

    codeword = lteDLSCH(enb,pdsch,codedTrBlkSize,dlschTransportBlk);

     

    % now if you pass the encoded data (codeword) with eNB and pdsch config to ltePDSCH(), you can generate

    % physical layer symbols for the encoded data.

     

    pdsch_sym = ltePDSCH(enb,pdsch,codeword);

    pdsch_sym_arrayIndex = 0:length(pdsch_sym)-1;

     

    % Following is to create an empty resource grid for one subframe.

     

    resourceGrid = lteDLResourceGrid(enb);

     

    % Following is to create symbols for Cell Specific Reference Signal and make a list of resource index for the

    % reference signal.

     

    rsAnt0 = lteCellRS(enb,0);

    indAnt0 = lteCellRSIndices(enb,0);

    resourceGrid(indAnt0) = rsAnt0;

     

    % Following is to create symbols for PBCH and make a list of resource index for the signal (channel)

     

    mib_bits = lteMIB(enb);

    bch_cw = lteBCH(enb,mib_bits);

     

    % Following is to create symbols for PSS and make a list of resource index for the signal

     

    pss = ltePSS(enb);

    pss_arrayIndex = 0:length(pss)-1;

    pss_sym_ind = ltePSSIndices(enb,0,{'1based','re'});

     

    % Following is to create symbols for SSS and make a list of resource index for the signal

     

    sss = lteSSS(enb);

    sss_arrayIndex = 0:length(sss)-1;

    sss_sym_ind = lteSSSIndices(enb,0,{'1based','re'});

     

    % Following is to create symbols for PCFICH and make a list of resource index for the signal

     

    cfi_cw = lteCFI(enb);

    pcfich_sym = ltePCFICH(enb,cfi_cw);

    pcfich_sym_arrayIndex = 0:length(pcfich_sym)-1;

    pcfich_sym_ind = ltePCFICHIndices(enb,{'1based','re'});

     

    % Following is to create symbols for PHICH and make a list of resource index for the signal

     

    phich_sym = ltePHICH(enb,[PHICH_Group_Index,PHICH_Sequence_Index,HARQ_Indicator_Value]);

    phich_sym_arrayIndex = 0:length(phich_sym)-1;

    phich_sym_ind = ltePHICHIndices(enb,{'1based','re'});

     

    % Following is to create symbols for PBCH and make a list of resource index for the signal (channel)

     

    pbch_sym = ltePBCH(enb,bch_cw);

    pbch_sym_arrayIndex = 0:length(pbch_sym)-1;

    pbch_sym_ind = ltePBCHIndices(enb,{'1based','re'});

     

    % Following part is filling the resource grid with each of the signal.. but if you see carefully I didn't fill this

    % with real symbol number, I just filled it with a constant that I arbitrarily set. This is just for visualization..

    % just to allocate constant/outstanding color for each signal. When you  use this resource grid for real

    % transmission (not for visualization), fill the resourceGrid with real symbol value you generated above.

     

    pss_scale = 0.2;

    sss_scale = 0.4;

    phich_scale = 0.7;

    pcfich_scale = 0.5;

    pbch_scale = 0.7;

    pdcch_scale = 0.9;

    pdsch_scale = 0.6;

     

    resourceGrid(pss_sym_ind) = pss_scale .* pss;

    resourceGrid(sss_sym_ind) = sss_scale .* sss;

    resourceGrid(pcfich_sym_ind) = pcfich_scale .* pcfich_sym;

    resourceGrid(phich_sym_ind) = phich_scale .* phich_sym;

    resourceGrid(pbch_sym_ind) = pbch_scale .* pbch_sym(1:length(pbch_sym_ind));

    resourceGrid(pdcch_sym_ind) = pdcch_scale .* pdcch_sym;

    resourceGrid(pdsch_sym_ind) = pdsch_scale .* pdsch_sym;

     

    % Following is to plot the all 14 symbols within a subframe separately. If you see the code, this is exactly same as

    % the previous example. The only difference is the for loop around the plot routine.

    for symbolNo = 0:13

      symbolIdxStart = symbolNo*(enb.NDLRB*12) + 1;

      symbolIdxEnd = symbolIdxStart + enb.NDLRB*12;

      symbolIdxArray = symbolIdxStart:symbolIdxEnd;

      symbolReArray = lteExtractResources(symbolIdxArray,resourceGrid);

       

      subplot(14,10,(symbolNo*10)+ 1);

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

      axis([-1 1 -1 1]);

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

       

      subplot(14,10,[((symbolNo*10)+2):((symbolNo*10)+10)]);

      stem(abs(symbolReArray));

      axis([1 length(symbolIdxArray) 0 1]);

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

    end;

     

      enb.NDLRB = 6;

      enb.CellRefP = 1;

      enb.NCellID = 0;

      enb.NSubframe = 0;

     

 

 

Disclaimer ! :

 

This page is only to show you the overall logics and visualization for various LTE physical layer channels. I haven't investigated much about verifying about the accuracy.

If you think the code is not so efficient, it is 100% my fault. I haven't made any effort for effiecient code. I just tried to create code as simple as possible for the readers. As you know, easy-to-read code is not always efficient for a specific chipset.

If you find any mistake in terms of accuracy, it is also very highly likely be my fault. Not the problem of Matlab tool box itself.

Any comment and corrections if you find any mistake will be welcome and appreciated.