OTFS代码学习记录2（OFDM与OTFS性能比较）
该代码仿真了在无线链路多径衰落的环境下的OFDM与OTFS性能差异，同时加入了LDCP码
Reference
%--------------------------------------------------------------------------
%
% Author: Bradley Bates
% University of Bristol, UK
% email address: [email protected]
% May 2020
%
% Copyright (c) 2020, Bradley Bates
%
%--------------------------------------------------------------------------主函数
主函数main的运行需要用到的function文件：
% The following files are required:
% dataGen.m
% multipathChannel.m
% modOFDM.m
% demodOFDM.m
% ISFFT.m
% SFFT.m
% equaliser.m
% plotGraphs.m接下来开始主函数的研究
首先是各种参数的设置
%--------------------------------------------------------------------------
% Define simulation parameters
%--------------------------------------------------------------------------
M = 16; % Modulation alphabet
k = log2(M); % Bits/symbol
cpSize = 0.07; % OFDM cyclic prefix size
scs = 15e3; % Subcarrier spacing Hz
Bw = 10e6; % System bandwidth Hz
ofdmSym = 14; % No. OFDM symbols / subframe
EbNo = (-3:1:30)'; % Range of energy/bit to noise power ratio
velocity = 120; % Velocity of mobile rx relative tx km/hr
codeRate = 2/4; % FEC code rate used
maxIterations = 25; % Set maximum no. of iterations for LDPC decoder
totalBits = 1e6; % The approx. total no. of bits simulated
repeats = 1; % Number of simulation repetitions 然后是各部分初始化
%--------------------------------------------------------------------------
% Initialise Simulation Components
%--------------------------------------------------------------------------
% Initialise OFDM Mod/Demod variables
numSC = pow2(ceil(log2(Bw/scs))); % 计算载波数为1024
cpLen = floor(cpSize * numSC); % 计算循环前缀编码的长度（注意ceil和floor都是向上取整函数）
numDC = (numSC - 12); % 数据载波数量=载波数-12
% Initialise the AWGN channel
awgnChannel = comm.AWGNChannel('NoiseMethod','Variance', 'VarianceSource','Input port');
errorRate = comm.ErrorRate('ResetInputPort',true);
errorRate1 = comm.ErrorRate('ResetInputPort',true);
% Initialise the LDPC coder/decoder
parityCheck_matrix = dvbs2ldpc(codeRate); % Generate DVB-S.2 paraity check matrix
ldpcEncoder = comm.LDPCEncoder(parityCheck_matrix); % Create encoder system object
ldpcDecoder = comm.LDPCDecoder(parityCheck_matrix); % Create decoder system object
ldpcDecoder.MaximumIterationCount = maxIterations; % Assign decoder's maximum iterations
noCodedbits = size(parityCheck_matrix,2); % Find the Codeword length
% Create Vectors for storing error data
berOFDM = zeros(length(EbNo),3); berCOFDM = zeros(length(EbNo),3); berOTFS = zeros(length(EbNo),3); berCOTFS = zeros(length(EbNo),3);
errorStats_coded = zeros(1,3); errorStats_uncoded = zeros(1,3);
for repetition=1:repeats % Repeat simulation multiple times with a unqique channel for each repeat
% Generate and Encode data
[dataIn, dataBits_in, codedData_in, packetSize, numPackets, numCB] = dataGen(k,numDC,ofdmSym,totalBits,codeRate,ldpcEncoder);
% Generate Rayleigh Fading Channel Impulse Response
txSig_size = zeros((numSC+cpLen),ofdmSym); % Assign the size of the channel
rayChan = multipathChannel(cpSize, scs, txSig_size, velocity); % Create fading channel impulse response
% QAM Modulator
qamTx = qammod(dataIn,M,'InputType','bit','UnitAveragePower',true); % Apply QAM modulation
parallelTx = reshape(qamTx,[numDC,ofdmSym*packetSize]); % Convert to parallel
% Add nulls at index 1
guardbandTx = [zeros(1,ofdmSym*packetSize); parallelTx];
% Add 11 nulls around DC
guardbandTx = [guardbandTx(1:(numDC/2),:); zeros(11,ofdmSym*packetSize); guardbandTx((numDC/2)+1:end,:)];
注意上面使用的comm.AWGNChannel、comm.ErrorRate以及comm.LDPCEncoder均是调用matlab的函数来为信道添加高斯噪声，误码率以及LDCP编码器等，与调用函数类似。参考Add white Gaussian noise to input signal - MATLAB - MathWorks 中国
举个例子：
For example:
awgnchan = comm.AWGNChannel('NoiseMethod','Variance', ...'VarianceSource','Input port');
var = 12; %specifies the variance of the white Gaussian noise
...
outsignal = awgnchan(insignal,var);%计算输出信号同样是初始化那一副图
parityCheck_matrix = dvbs2ldpc(codeRate)该函数用于生成DVB—S2标准的LDPC码，dvbs2ldpc（r）,r是码率，该函数返回的是该码率下的校验矩阵，输出的该矩阵是稀疏矩阵，r可以是1/4 1/3 2/5 1/2 3/5 2/3 3/4 4/5 5/6 8/9 9/10,码长是64800
初始化完成之后就开始OFDM误码率的计算
%--------------------------------------------------------------------------
% OFDM BER Calculation
%--------------------------------------------------------------------------
% Calculate SNR
snr = EbNo + 10*log10(codeRate*k) + 10*log10(numDC/((numSC)));
% Multicarrier Modulation
frameBuffer = guardbandTx; % Create a 'buffer' so subframes can be individually modulated
txframeBuffer = []; % Initilaise matrix
for w = 1:packetSize
ofdmTx = modOFDM(frameBuffer(:,1:ofdmSym),numSC,cpLen,ofdmSym); % Apply OFDM modulation to a subframe of data
frameBuffer(:, 1:ofdmSym) = []; % Delete modulated data from frameBuffer
txframeBuffer = [txframeBuffer;ofdmTx]; % Add modulated subframe to transmit buffer
end
% Loop through different values of EbNo
for m = 1:length(EbNo)
% Loop through the of packets to be transmitted
for j = 1:numPackets
rxframeBuffer = []; % Initialise matrix
% Transmit each subframe individually
for u = 1:packetSize
% Remove next subframe from the transmit buffer
txSig = txframeBuffer( ((u-1)*numel(ofdmTx)+1) : u*numel(ofdmTx) );
% Apply Channel to input signal
fadedSig = zeros(size(txSig)); % Pre-allocate vector size
for i = 1:size(txSig,1) % Perform elementwise...
for j = 1:size(txSig,2) % ...matrix multiplication
fadedSig(i,j) = txSig(i,j).*rayChan(i,j);
end
end
% AWGN Channel
release(awgnChannel);
powerDB = 10*log10(var(fadedSig)); % Calculate Tx signal power
noiseVar = 10.^(0.1*(powerDB-snr(m))); % Calculate the noise variance
rxSig = awgnChannel(fadedSig,noiseVar); % Pass the signal through a noisy channel
% Equalisation
eqSig = equaliser(rxSig,fadedSig,txSig,ofdmSym);
% Demodulation
rxSubframe = demodOFDM(eqSig,cpLen,ofdmSym); % Apply OFDM demodulation
rxframeBuffer = [rxframeBuffer';rxSubframe']'; % Store demodulated subframe in rx buffer
end
% Remove all null carriers
parallelRx = rxframeBuffer;
parallelRx((numDC/2)+1:(numDC/2)+11, :) = []; % Remove nulls around the DC input
parallelRx(1:1, :) = []; % Remove nulls at index 1
qamRx = reshape(parallelRx,[numel(parallelRx),1]);% Convert to serial
% Uncoded demodulation of entire packet
dataOut = qamdemod(qamRx,M,'OutputType','bit','UnitAveragePower',true);% Apply QAM demodulation
codedData_out = randdeintrlv(dataOut,4831); % De-interleave data
codedData_out(numel(codedData_in)+1:end) = []; % Remove pad bits
errorStats_uncoded = errorRate(codedData_in,codedData_out,0); % Collect error statistics
% Coded demodulation of entire packet
powerDB = 10*log10(var(qamRx)); % Calculate Rx signal power
noiseVar = 10.^(0.1*(powerDB-(EbNo(m) + 10*log10(codeRate*k) - 10*log10(sqrt(numDC))))); % Calculate the noise variance
dataOut = qamdemod(qamRx,M,'OutputType', 'approxllr','UnitAveragePower',true,'NoiseVariance',noiseVar);% Apply QAM demodulation
codedData_out1 = randdeintrlv(dataOut,4831); % De-interleave data
codedData_out1(numel(codedData_in)+1:end) = []; % Remove pad bits
% Decode individual code blocks
dataBits_out = []; % Initialise matrix
dataOut_buffer = codedData_out1;
for q = 1:numCB
dataBits_out = [dataBits_out;ldpcDecoder(dataOut_buffer(1:noCodedbits))]; % Decode data & add it to the data bits out matrix
dataOut_buffer(1:noCodedbits) = []; % Delete decoded data from buffer
end
dataBits_out = double(dataBits_out); % Convert to a double compatible w/ errorStats
errorStats_coded = errorRate1(dataBits_in,dataBits_out,0); % Collect error statistics
end
berOFDM(m,:) = errorStats_uncoded; % Save uncoded BER data
berCOFDM(m,:) = errorStats_coded; % Save coded BER data
errorStats_uncoded = errorRate(codedData_in,codedData_out,1); % Reset the error rate calculator
errorStats_coded = errorRate1(dataBits_in,dataBits_out,1); % Reset the error rate calculator
end接着是OTFS的误码率计算
%--------------------------------------------------------------------------
% OTFS BER Calculation
%--------------------------------------------------------------------------
% Calculate SNR
snr = EbNo + 10*log10(codeRate*k) + 10*log10(numDC/((numSC))) + 10*log10(sqrt(ofdmSym));
% Multicarrier Modulation
frameBuffer = guardbandTx; % Create a 'buffer' so subframes can be individually modulated
txframeBuffer = []; % Initilaise matrix
for w = 1:packetSize
otfsTx = ISFFT(frameBuffer(:,1:ofdmSym)); % Apply OTFS modulation to a subframe of data
ofdmTx = modOFDM(otfsTx,numSC,cpLen,ofdmSym); % Apply OFDM modulation
frameBuffer(:, 1:ofdmSym) = []; % Delete modulated data from frameBuffer
txframeBuffer = [txframeBuffer;ofdmTx]; % Add modulated subframe to transmit buffer
end
% Loop through different values of EbNo
for m = 1:length(EbNo)
% Loop through the of packets to be transmitted
for j = 1:numPackets
rxframeBuffer = []; % Initialise matrix
% Transmit each subframe individually
for u = 1:packetSize
% Remove next subframe from the transmit buffer
txSig = txframeBuffer( ((u-1)*numel(ofdmTx)+1) : u*numel(ofdmTx) );
% Apply Channel to input signal
fadedSig = zeros(size(txSig)); % Pre-allocate vector size
for i = 1:size(txSig,1) % Perform elementwise...
for j = 1:size(txSig,2) % ...matrix multiplication
fadedSig(i,j) = txSig(i,j).*rayChan(i,j);
end
end
% AWGN Channel
release(awgnChannel);
powerDB = 10*log10(var(fadedSig)); % Calculate Tx signal power
noiseVar = 10.^(0.1*(powerDB-snr(m))); % Calculate the noise variance
rxSig = awgnChannel(fadedSig,noiseVar); % Pass the signal through a noisy channel
% Equalisation
eqSig = equaliser(rxSig,fadedSig,txSig,ofdmSym);
% Demodulation
otfsRx = demodOFDM(eqSig,cpLen,ofdmSym); % Apply OFDM demodulation
rxSubframe = SFFT(otfsRx); % Apply OTFS demodulation
rxframeBuffer = [rxframeBuffer';rxSubframe']'; % Store demodulated subframe in rx buffer
end
% Remove all null carriers
parallelRx = rxframeBuffer;
parallelRx((numDC/2)+1:(numDC/2)+11, :) = []; % Remove nulls around the DC input
parallelRx(1:1, :) = []; % Remove nulls at index 1
qamRx = reshape(parallelRx,[numel(parallelRx),1]); % Convert to serial
% Uncoded demodulation of entire packet
dataOut = qamdemod(qamRx,M,'OutputType','bit','UnitAveragePower',true);% Apply QAM demodulation
codedData_out = randdeintrlv(dataOut,4831); % De-interleave data
codedData_out(numel(codedData_in)+1:end) = []; % Remove pad bits
errorStats_uncoded = errorRate(codedData_in,codedData_out,0); % Collect error statistics
% Coded demodulation of entire packet
powerDB = 10*log10(var(qamRx)); % Calculate Rx signal power
noiseVar = 10.^(0.1*(powerDB-(EbNo(m) + 10*log10(codeRate*k) - 10*log10(sqrt(numDC))))); % Calculate the noise variance
dataOut = qamdemod(qamRx,M,'OutputType', 'approxllr','UnitAveragePower',true,'NoiseVariance',noiseVar);% Apply QAM demodulation
codedData_out1 = randdeintrlv(dataOut,4831); % De-interleave data
codedData_out1(numel(codedData_in)+1:end) = []; % Remove pad bits
% Decode individual code blocks
dataBits_out = []; % Initialise matrix
dataOut_buffer = codedData_out1;
for q = 1:numCB
dataBits_out = [dataBits_out;ldpcDecoder(dataOut_buffer(1:noCodedbits))]; % Decode data & add it to the data bits out matrix
dataOut_buffer(1:noCodedbits) = []; % Delete decoded data from buffer
end
dataBits_out = double(dataBits_out); % Convert to a double compatible w/ errorStats
errorStats_coded = errorRate1(dataBits_in,dataBits_out,0); % Collect error statistics
end
berOTFS(m,:) = errorStats_uncoded; % Save uncoded BER data
berCOTFS(m,:) = errorStats_coded; % Save coded BER data
errorStats_uncoded = errorRate(codedData_in,codedData_out,1); % Reset the error rate calculator
errorStats_coded = errorRate1(dataBits_in,dataBits_out,1); % Reset the error rate calculator
end
endok最后就是plot
%--------------------------------------------------------------------------
% Figures
%--------------------------------------------------------------------------
% Plot BER / EbNo curves
plotGraphs(berOFDM, berCOFDM, berOTFS, berCOTFS, M, numSC, EbNo);二者误码率图像：
dataGen.m
%--------------------------------------------------------------------------
%
% Generates and encodes random binary data
%
%--------------------------------------------------------------------------
% Input arguments:
%
% k Bits/Symbol
% numDC Number of data subcarriers
% ofdmSym Totol ofdm symbols per subframe
% totalBits The approximate total bits to be simulated by the system
% codeRate LDPC code rate
% ldpcEncoder LDPC encode system object
%
%--------------------------------------------------------------------------
% Function returns:
%
% dataIn The input encoded data to the modulator
% dataBits_in The binary generated initial data before coding
% codedData_in The binary codewords
% packetSize No. of subframes / "packet"
% numPackets Number of packets required to satisfy totalBits
% numCB No. of code blocks / "subframe"
%
%--------------------------------------------------------------------------
% Calculate subframe size
% Initialise information about frames to be transmitted
packetSize = 1; % No. of subframes / "packet"
numCB = 1; % No. of code blocks / "subframe"
noCodedbits = 64800; % Codeword length
% Calculate exact no. of frames and bits required for simulation
subframeSize = [k*numDC*ofdmSym 1]; % Calculate size of a subframe
maxSubframes = ceil(totalBits./subframeSize(1)); % Total no. of subframes to be transmitted
% Determine number of code block and number of subframes/packet
if subframeSize(1) == noCodedbits % If same size do nothing
numCB = 1;
packetSize = 1;
elseif subframeSize(1) > noCodedbits % Match for when subframe > codeword
[numCB, packetSize] = rat(subframeSize(1)./ noCodedbits,1e-1);
elseif subframeSize(1) < noCodedbits % Match for when subframe < codeword
[packetSize, numCB] = rat(noCodedbits./ subframeSize(1),1e-1);
end
% Ensure theres always enough data bit capacity
while numCB*noCodedbits >= subframeSize(1)*packetSize
packetSize = packetSize + 1;
% Divide both by 2 if possible
if (rem(numCB,2) == 0) && (rem(packetSize,2) == 0) && numCB*noCodedbits <= subframeSize(1)*packetSize
packetSize = packetSize./2;
numCB = numCB./2;
end
end
% Calculate the pad bits required to round up to the nearest whole subframe
padBits = zeros((subframeSize(1)*packetSize - numCB*noCodedbits),1);% Calculate the number of pad bits
numPackets = round(maxSubframes./packetSize); % Total no. of "packets" to be transmitted
numPackets(~numPackets)=1; % If 0 packets set to 1
% Generate Random Input Data
%range shuffle; % Shuffle random no. generator
codedData_in = []; % Initialse arrays
dataBits_in = [];
for q = 1:numCB
dataBits = randi([0,1],[noCodedbits*codeRate,1]); % Generate binary datafor each frame of the burst
dataBits_in = [dataBits_in;dataBits]; % Concatenate binary data
codedData_in = [codedData_in; ldpcEncoder(dataBits)]; % Generate LDPC codeblocks
end
paddedData_in = [codedData_in; padBits]; % Append pad bits to coded bits
dataIn = randintrlv(paddedData_in,4831); % Interleave paddedData randdeintrlv
% Print info about data output
% fprintf(['\n',num2str(numCB),' code block(s)\n', num2str(packetSize), ' subframes/packet \n'])
% fprintf([ num2str(numel(padBits)),' pad bits out of ', num2str((subframeSize(1)*packetSize)),' data bits = ', num2str(100*(numel(padBits)/(subframeSize(1)*packetSize))),' percent pad bits!\n'])
% fprintf(['Total packets: ', num2str(numPackets),'\n'])
% fprintf(['Total bits: ', num2str(numPackets*packetSize*(subframeSize(1))),'\n'])
endSFFT.m
%--------------------------------------------------------------------------
% Input arguments:
% inSig Input N x M matrix to be transformed
%--------------------------------------------------------------------------
% Function returns:
% outSig Output N x M matrix
%--------------------------------------------------------------------------
[N, M] = size(inSig); % Calculate N and M
outSig = sqrt(M/N) * ifft( fft(inSig, [], 1), [], 2); % Apply transform注意fft和ifft如果未指定任何值[]，则输出的大小与输入相同，1、2表示维度
举个例子
a =
1 2 3
4 5 6
>> [N, M] = size(a);
>> outSig = sqrt(M/N) * ifft( fft(a, [], 1), [], 2);
>> outSig
outSig =
8.5732 + 0.0000i -1.2247 - 0.7071i -1.2247 + 0.7071i
-3.6742 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i
返回的是与a大小一样的ISFFT.m
%--------------------------------------------------------------------------
% Input arguments:
% inSig Input N x M matrix to be transformed
%--------------------------------------------------------------------------
% Function returns:
% outSig Output N x M matrix of doppler-Delay domain symbols
%--------------------------------------------------------------------------
[N, M] = size(inSig); % Calculate N and M
outSig = sqrt(N/M) * fft( ifft(inSig, [], 1), [], 2); % Apply inverse transformmodOFDM.m（实现OFDM编码）
%--------------------------------------------------------------------------
%
% Modulates random input data into OFDM symbols
%
%--------------------------------------------------------------------------
% Input Arguments:
% dataIn Input data vector
% numSC The number of subcarriers used
% cpLen Length of the cyclic prefix
% ofdmSym No. of ofdm symbols per subframe
%--------------------------------------------------------------------------
% Function returns:
% dataOut Output OFDM symbols
%--------------------------------------------------------------------------
% Calculate variables
cyclicPrefix_start = numSC - cpLen;
% Perform IFFT
ifftSubcarrier = ifft(dataIn,[],2);
%Finding cyclic prefix for each subcarrier
for i=1:cpLen
for j=1:ofdmSym
cyclicPrefix_data(i,j) = ifftSubcarrier(i+cyclicPrefix_start,j);
end
end
% Add cyclic prefix to the data
appendedCP = vertcat(cyclicPrefix_data, ifftSubcarrier);
% Convert to serial
dataOut = reshape(appendedCP,[numel(appendedCP),1]);multipathChannel.m
%--------------------------------------------------------------------------
%
% Generates and encodes random binary data
%
%--------------------------------------------------------------------------
% Input arguments:
%
% cpSize Size of the cyclic prefix
% delta_f OFDM subcarrier spacing (Hz)
% inSig Input signal dimensions used to generate channel dimensions
% totalBits The approximate total bits to be simulated by the system
% velocity Channel mobility in km/hr
%
%--------------------------------------------------------------------------
% Function returns:
%
% outSig Channel impulse response (serial vector)
%
%--------------------------------------------------------------------------
% Create N x M channel matrix
[N, M]= size(inSig'); % Size of inSig is used to create channel model
n = zeros(1,N); % delay_Doppler rows (doppler)
m = zeros(1,M); % delay_Doppler cols (delay)
H = transpose(n).*m; % Create matrix
% Generate Channel Parameter
maxDelayspread = 0.5*((cpSize)/delta_f); % Calculate max delay spread with 1/2 rule pf thumb
L = round(2*maxDelayspread * M*delta_f); % Calculate necesary paths from bandwidth
step = maxDelayspread/L; % calculate difference between delays
pathDelays = (0:step:maxDelayspread); % Discrete even delays of L-path channel
%range shuffle; % Shuffle random no. generator
avgPathGains_dB = -(randi([3,7],[L,1])); % Generate random path gains in dB
avgPathGains = 10.^(0.1*avgPathGains_dB); % Convert to linear
% Calculate Max Doppler Shift
v = velocity*1e3/3600; % Mobile speed (m/s)
fc = 3.5e9; % Carrier frequency
fd = round(v*fc/physconst('lightspeed'));% Maximum Doppler shift to nearest Hz
% Generate doppler spreads w/ Jake's model
for l=0:L-1
Vi(l+1) = fd* cos( (2*pi*l)/(L-1) );
end
% Initialize channel variables
T = 1/delta_f; % unextended OFDM symbol period
Ts = (1+cpSize)/delta_f; % OFDM symbol period)
Ti = pathDelays; % Path delays
hi = avgPathGains; % Path gains
% Create matrix representation of channel
for m=1:M % Loop along the rows
for n=1:N % Loop down the cols
for x=1:L % Loop to sum terms in the channel memory
% Define terms of model
expTerm = (-2*1i*(pi)) * ((m+M/2).*delta_f.*Ti(x) - Vi(x).*(n).*Ts);
hiPrime = hi(x)*(1 + 1i*(pi).*Vi(x).*T);
% Produce channel impulse response model
H(n, m) = H(n, m) + exp(expTerm) * hiPrime;
end
end
end
% Convert to serial
outSig = reshape(H',[n*m,1]);
endequaliser
%--------------------------------------------------------------------------
%
% Equalises a faded signal
%
%--------------------------------------------------------------------------
% Input arguments:
%
% rxSig The received faded signal w/ noise applied
% fadedSig The received faded signal, NO noise
% txSig Transmitted signal prior to channel
% ofdmSym Totol ofdm symbols per subframe
%
%--------------------------------------------------------------------------
% Function returns:
%
% eqSig The equalised output signal (serial vector)
%
%--------------------------------------------------------------------------
% Input parameters
pilotSpacing = 4; % Subcarrier sampling period (4 is best)
noSamples = numel(rxSig)/ofdmSym; % No. of times the channel is sampled
numSC = pow2(floor(log2(noSamples))); % Calc. no. of OFDM subcarrier
% Reformat input data into a matrix to make sampling easier
fadedSig_matrix = reshape(fadedSig, [noSamples,ofdmSym]);
txSig_matrix = reshape(txSig, [noSamples,ofdmSym]);
% Remove cyclic prefix as do no need to equalise it
fadedSig_matrix(1:(noSamples-numSC),:) = []; % Remove cp
txSig_matrix(1:(noSamples-numSC),:) = []; % Remove cp
% Sample signal
h = zeros(size(txSig_matrix)); % Pre allocate matrix
for i = 1:size(txSig_matrix,1) % Loop rows
for j = 1:size(txSig_matrix,2) % Loop Columns
% Sample every pilotSpacing subcarrier (incuding first and last subcarriers)
if i==1
sample(i,j) = fadedSig_matrix(i,j)./txSig_matrix(i,j);
elseif 0 == mod(i,pilotSpacing)
sample(i/pilotSpacing+1,j) = fadedSig_matrix(i,j)./txSig_matrix(i,j);
end
end
end
% Linearly Interpolate samples between subcarriers
interpPoints = ( (1+(1/pilotSpacing)) : (1/pilotSpacing) : size(sample,1) );% Calc. points to interpolate
for j = 1:size(txSig_matrix,2)
h(:,j) = interp1(sample(:,j),interpPoints);
end
% Keep only 1st, 7th and 14th samples per carrier
h1 = [h(:,1)';h(:,7)';h(:,14)']';
% Linearly Interpolate samples between symbols
interpPoints1 = ( 1 : (1/6) : 2 ); % Calc. points to interpolate
interpPoints2 = ( (2+(1/7)) : (1/7) : 3 );
for i = 1:size(txSig_matrix,1)
h17(i,:) = interp1(h1(i,:),interpPoints1); % Interpolate 1-7
h714(i,:) = interp1(h1(i,:),interpPoints2); % interpolate 7-14
end
% Concatenate matracies
h = [h17';h714']';
% Set eq of CP carriers to same as 1st carrier
for k = 1:(noSamples-numSC)
h = [h(1,:);h];
end
% Convert back into serial
H = reshape(h,[numel(h),1]);
H(isnan(H)) = 1; % Set all NaN's to 1
% Equalise the signal
eqSig = rxSig ./ H;
eqSig(isnan(eqSig))=0; % Set all NaN's to 0