biterr
Compute number of bit errors and bit error rate (BER)
Syntax
Description
[
compares the unsigned binary representation of elements in number,ratio] = biterr(x,y)x to those
in y. The function returns number, the number of
bits that differ in the comparison, and ratio, the ratio of
number to the total number of bits. The function determines the order
in which it compares x and y based on their sizes.
For more information, see the Algorithms section.
[
returns the binary comparison result of number,ratio,individual] = biterr(___)x and y as
matrix individual. You can specify any of the input argument
combination from the previous syntaxes.
Examples
Create two binary matrices.
x = [0 0; 0 0; 0 0; 0 0]
x = 4×2
0 0
0 0
0 0
0 0
y = [0 0; 0 0; 0 0; 1 1]
y = 4×2
0 0
0 0
0 0
1 1
Determine the number of bit errors.
numerrs = biterr(x,y)
numerrs = 2
Compute the number of column-wise errors.
numerrs = biterr(x,y,[],'column-wise')numerrs = 1×2
1 1
Compute the number of row-wise errors.
numerrs = biterr(x,y,[],'row-wise')numerrs = 4×1
0
0
0
2
Compute the number of overall errors. Behavior is the same as the default behavior.
numerrs = biterr(x,y,[],'overall')numerrs = 2
Demodulate a noisy 64-QAM signal and estimate the bit error rate (BER) for a range of Eb/No values. Compare the BER estimate to theoretical values.
Set the simulation parameters.
M = 64; % Modulation order k = log2(M); % Bits per symbol EbNoVec = (5:15); % Eb/No values (dB) numSymPerFrame = 100; % Number of QAM symbols per frame
Convert the EbN0 values to SNR.
snrdB =convertSNR(EbNoVec,"ebno","snr",BitsPerSymbol=k);
Initialize the results vector.
berEst = zeros(size(EbNoVec));
The main processing loop executes these steps.
Generate binary data and convert to 64-ary symbols.
QAM-modulate the data symbols.
Pass the modulated signal through an AWGN channel.
Demodulate the received signal.
Convert the demodulated symbols into binary data.
Calculate the number of bit errors.
The while loop continues to process data until either 200 errors are encountered or 1e7 bits are transmitted.
for n = 1:length(snrdB) % Reset the error and bit counters numErrs = 0; numBits = 0; while numErrs < 200 && numBits < 1e7 % Generate binary data and convert to symbols dataIn = randi([0 1],numSymPerFrame*k,1); dataSym = bit2int(dataIn,k); % QAM modulate using 'Gray' symbol mapping txSig = qammod(dataSym,M); % Pass through AWGN channel rxSig = awgn(txSig,snrdB(n),'measured'); % Demodulate the noisy signal rxSym = qamdemod(rxSig,M); % Convert received symbols to bits dataOut = int2bit(rxSym,k); % Calculate the number of bit errors nErrors = biterr(dataIn,dataOut); % Increment the error and bit counters numErrs = numErrs + nErrors; numBits = numBits + numSymPerFrame*k; end % Estimate the BER berEst(n) = numErrs/numBits; end
Determine the theoretical BER curve by using the berawgn function.
berTheory = berawgn(EbNoVec,'qam',M);Plot the estimated and theoretical BER data. The estimated BER data points are well aligned with the theoretical curve.
semilogy(EbNoVec,berEst,'*') hold on semilogy(EbNoVec,berTheory) grid legend('Estimated BER','Theoretical BER') xlabel('Eb/No (dB)') ylabel('Bit Error Rate')
Input Arguments
Output Arguments
Algorithms
The function uses the sizes of x and y to
determine the order in which it compares their elements.
If inputs are matrices of the same dimensions, then the function compares the inputs element by element.
numberis a nonnegative integer in this case. For example, see case (a) in the figure.If one input is a matrix and the other input is a column vector, then the function compares each column of the matrix element by element with the column vector. The number of rows in the matrix must be equal to the length of the column vector. In other words, if the matrix has dimensions m-by-n, then the column vector must have dimensions m-by-1. For example, see case (b) in the figure.
If one input is a matrix and the other input is a row vector, then the function compares each row of the matrix element by element with the row vector. The number of columns in the matrix must be equal to the length of the row vector. In other words, if the matrix has dimensions m-by-n, then the row vector must have dimensions 1-by-n. For example, see case (c) in the figure.
