OFDM adding repetition coding

Need assistance in correcting an error in my OFDM transmitter and receiver Matlab code shown below. The following error appeared when I tried to run a repetition coding of 3 repetitions.

Error using reshape

Product of known dimensions, 192, not divisible into total number of elements, 64.

Error in ofdm_master (line 392)

rx_equalized_reshaped = reshape(rx_equalized, M, rep, []);

It seems this is an error of dimensions not being divisible by number of elements. Please let me know how I can correct this. I was simply trying to implement repetition coding for 1, 3, and 5 repetitions to the BPSK, QPSK, and 16-QAM modulation.in reference to SNR range -10dB:1:10dB, plotting the probability of error vs the receive SNR.

nsymb = 100;

M = 64; %Number of subcarrier channel

block_size = 64; %Size of each OFDM block to add cyclic prefix

cp_len = round(0.25*block_size); %Length of cyclic prefix

% Initiate SNR range and error count array

SNR_range = -10:1:10;

% BER = zeros(size(SNR_range));

errors = zeros(size(SNR_range));

errors1 = zeros(size(SNR_range));

errors2 = zeros(size(SNR_range));

symbols = 0;

symbols1 = 0;

symbols2 = 0;

% Read the video file

video = VideoReader('test_video.mp4');

% Calculate the total number of bits in the video

total_bits = 0;

% Initialize error count for all frames

error_count = 0;

% Loop through each frame of the video and convert it to a binary data stream

while hasFrame(video)

frame = readFrame(video);

decimal_data = reshape(frame,numel(frame),1);

binary_data = reshape(de2bi(decimal_data,8)',[],1);

% Increment total_bits

% total_bits = total_bits + numel(binary_data);

% Loop over SNR range

for i = 1:length(SNR_range)

snr = SNR_range(i);

disp(snr)

mod = 2;

no_of_data_bits = 64 * log2(mod);

% Loop through each symbol

for j = 1:numel(binary_data)/no_of_data_bits

% Use the binary data as the input source data

data = binary_data((j-1)*no_of_data_bits+1:j*no_of_data_bits);

data_reshaped = reshape(data, log2(mod), no_of_data_bits / log2(mod));

% Perform BPSK modulation on the input source data

modulated_data = qammod(data,mod);

% Repeat the modulated data

rep = 3; % repetitions

modulated_data_rep = repmat(modulated_data, rep, 1);

% Converting the series data stream into parallel data stream to form subcarriers

S2P = reshape(modulated_data,no_of_data_bits/M,M);

% Generate channel

channel_len = 10;

channel = (randn(1, channel_len) + 1i * randn(1, channel_len)) / sqrt(2);

% Zero-padding

channel_padded = [channel, zeros(1, block_size - length(channel))];

% IFFT of subcarriers and add cyclic prefix

number_of_subcarriers = M;

% IFFT does parallel to serial conversion

ifft_Subcarrier = ifft(S2P, block_size);

% Add cyclic prefix

cyclic_prefix = ifft_Subcarrier(:,end-cp_len+1:end);

Append_prefix = [cyclic_prefix ifft_Subcarrier];

% Multipath channel

rcvd_symbol = filter(channel,1,Append_prefix);

% Calculate noise variance for current SNR

noise_var = 1 / (10^(snr/10));

% Generate noisy channel coefficients

noisy_symbol = rcvd_symbol + sqrt(noise_var/2)*(randn(1,80)+1i*randn(1,80));

% Remove cyclic prefix at the receiver

rx_no_cp = noisy_symbol(cp_len+1:end);

% Perform FFT on received data

rx_fft = fft(rx_no_cp, block_size);

% FFT on the channel

channel_fft = fft(channel_padded);

% Equalize channel effect

rx_equalized = rx_fft ./ channel_fft;

% Reshape the received data to apply the repetition decoding

rx_equalized_reshaped = reshape(rx_equalized, M, rep, []);

% Decode the repeated data (majority rule)

rx_equalized_decoded = sum(rx_equalized_reshaped, 2) > rep/2;

% Perform BPSK demodulation

rx_demod = qamdemod(rx_equalized(:), mod); % (:) used to create vectors

% Calculate bit error rate

rx_demod_bits = dec2bin(rx_demod, log2(mod)) - '0';

% Calculate bit error rate

errors(i) = errors(i) + sum(rx_demod_bits(:) ~= data(:));

symbols = symbols + numel(data);

if j > nsymb

break

end

end

mod = 4;

no_of_data_bits = 64 * log2(mod);

% Loop through each symbol

for j = 1:numel(binary_data)/no_of_data_bits

% Use the binary data as the input source data

data = binary_data((j-1)*no_of_data_bits+1:j*no_of_data_bits);

% data_reshaped2 = reshape(data, no_of_data_bits / log2(mod), log2(mod));

data_reshaped = reshape(data, length(data) / log2(mod), log2(mod));

data_char = char(data_reshaped + '0');

data_dec = bin2dec(data_char);

% Perform BPSK modulation on the input source data

modulated_data = qammod(data_dec,mod);

% Converting the series data stream into parallel data stream to form subcarriers

% S2P = reshape(modulated_data,no_of_data_bits/M,M);

S2P = transpose(modulated_data);

% Generate channel

channel_len = 10;

channel = (randn(1, channel_len) + 1i * randn(1, channel_len)) / sqrt(2);

% Zero-padding

channel_padded = [channel, zeros(1, block_size - length(channel))];

% IFFT of subcarriers and add cyclic prefix

number_of_subcarriers = M;

% IFFT does parallel to serial conversion

ifft_Subcarrier = ifft(S2P, block_size);

% Add cyclic prefix

cyclic_prefix = ifft_Subcarrier(:,end-cp_len+1:end);

Append_prefix = [cyclic_prefix ifft_Subcarrier];

% Multipath channel

rcvd_symbol = filter(channel,1,Append_prefix);

% Calculate noise variance for current SNR

noise_var = sqrt(2) / (10^(snr/10));

% Generate noisy channel coefficients

noisy_symbol = rcvd_symbol + sqrt(noise_var/2)*(randn(1,80)+1i*randn(1,80));

% Remove cyclic prefix at the receiver

rx_no_cp = noisy_symbol(cp_len+1:end);

% Perform FFT on received data

rx_fft = fft(rx_no_cp, block_size);

% FFT on the channel

channel_fft = fft(channel_padded);

% Equalize channel effect

rx_equalized = rx_fft ./ channel_fft;

% Perform BPSK demodulation

rx_demod = qamdemod(rx_equalized(:), mod); % (:) used to create vectors

rx_demod_bits = dec2bin(rx_demod, log2(mod)) - '0';

% Calculate bit error rate

errors1(i) = errors1(i) + sum(rx_demod_bits(:) ~= data(:));

symbols1 = symbols1 + numel(data);

if j > nsymb

break

end

end

mod = 16;

%%%%%%%%%%

no_of_data_bits = M * log2(mod);

% Loop through each symbol

for j = 1:numel(binary_data)/no_of_data_bits

% Use the binary data as the input source data

data = binary_data((j-1)*no_of_data_bits+1:j*no_of_data_bits);

% data_reshaped2 = reshape(data, no_of_data_bits / log2(mod), log2(mod));

data_reshaped = reshape(data, length(data) / log2(mod), log2(mod));

data_char = char(data_reshaped + '0');

data_dec = bin2dec(data_char);

% Perform BPSK modulation on the input source data

modulated_data = qammod(data_dec,mod);

% Converting the series data stream into parallel data stream to form subcarriers

% S2P = reshape(modulated_data,no_of_data_bits/M,M);

S2P = transpose(modulated_data);

% Generate channel

channel_len = 10;

channel = (randn(1, channel_len) + 1i * randn(1, channel_len)) / sqrt(2);

% Zero-padding

channel_padded = [channel, zeros(1, block_size - length(channel))];

% IFFT of subcarriers and add cyclic prefix

number_of_subcarriers = M;

% IFFT does parallel to serial conversion

ifft_Subcarrier = ifft(S2P, block_size);

% Add cyclic prefix

cyclic_prefix = ifft_Subcarrier(:,end-cp_len+1:end);

Append_prefix = [cyclic_prefix ifft_Subcarrier];

% Multipath channel

rcvd_symbol = filter(channel,1,Append_prefix);

% Calculate noise variance for current SNR

noise_var = sqrt(10) / (10^(snr/10));

% Generate noisy channel coefficients

noisy_symbol = rcvd_symbol + sqrt(noise_var/2)*(randn(1,80)+1i*randn(1,80));

% Remove cyclic prefix at the receiver

rx_no_cp = noisy_symbol(cp_len+1:end);

% Perform FFT on received data

rx_fft = fft(rx_no_cp, block_size);

% FFT on the channel

channel_fft = fft(channel_padded);

% Equalize channel effect

rx_equalized = rx_fft ./ channel_fft;

% Perform BPSK demodulation

rx_demod = qamdemod(rx_equalized(:), mod); % (:) used to create vectors

rx_demod_bits = dec2bin(rx_demod, log2(mod)) - '0';

% Calculate bit error rate

errors2(i) = errors2(i) + sum(rx_demod_bits(:) ~= data(:));

symbols2 = symbols2 + numel(data);

if j > nsymb

break

end

end

% rx_demod_bits, data = ofdm_loop(2, binary_data, M, nsymb, ...)

% errors(i) = errors(i) + sum(rx_demod_bits(:) ~= data(:));

% symbols = symbols + numel(data);

% rx_demod_bits, data = ofdm_loop(4, binary_data, M, nsymb, ...)

% errors1(i) = errors1(i) + sum(rx_demod_bits(:) ~= data(:));

% symbols1 = symbols1 + numel(data);

% rx_demod_bits, data = ofdm_loop(16, binary_data, M, nsymb, ...)

% errors2(i) = errors2(i) + sum(rx_demod_bits(:) ~= data(:));

% symbols2 = symbols2 + numel(data);

end

break

end

% Divide the accumulated BER by the total number of symbols to get the average BER for this SNR

% BER = BER / (total_bits/no_of_data_bits);

% Calculate BER for each SNR

BER_2 = errors ./ symbols;

BER_4 = errors1 ./ symbols1;

BER_16 = errors2 ./ symbols2;

% Plot BER vs SNR

figure(8);

semilogy(SNR_range, BER_16, 'b-o', SNR_range, BER_4, 'r-s',SNR_range, BER_2, 'g-*');

% semilogy(SNR_range, BER_2, 'g-*');

% legend( '16QAM','QPSK','BPSK');

xlabel('SNR (dB)');

ylabel('BER');

grid on;

% xlabel('SNR (dB)');

% ylabel('Bit Error Rate');

% >>>>>>> Stashed changes

title('Probability of Error vs SNR');

Answer 1

[Santosh Fatale]

Hi Jose,

I investigated the code shared by you and below are my findings/observation:

• The variable modulated_data_rep is initialised but never used anywhere in the code.
• I would recommend referring to the documentation on the repmat function. The repmat function repeats the input vector/matrix copy as per the specification. For example: repmat([1; 2; 3],3,1) creates a 9-by-1 column vector using 3-by-1 input vector. The output vector would be [1; 2; 3;1; 2; 3;1; 2; 3]. Kindly ensure that the repetition coding you are implementing is the same as the one in the communication standards.
• The error message you are encountering is since input constraints to reshape functions are not satisfying. You could reshape the m-by-n matrix to p-by-q only if . The conditions assures that the number of elements in the original matrix and the reshaped matrix are same.

In the code, the original matrix is of size 64-by-1() and reshaped matrix would be 64-by-3 ().

Refer to the following documentation link to learn more about reshape and repmat functions.

• reshape
• repmat

I would request you to share all essential files while posting a query on the forum to understand it precisely. It is also recommended to utilize code option available while posting a query.

[Jose Iglesias]

Thank you so much for your assistance!