Binary Hypothesis Testing

Generate a sequence of bits:

% Number of bits being transmitted
B = 1000*100;
transmittedBits = randi(2, B , 1)  - 1;

Modulation:

% Number of samples per detection test.
N = 10;
% The signal shape
signal = ones(N, 1);
transmittedSequence = SPX_Modulator.modulate_bits_with_signals(transmittedBits, signal);

Adding noise:

sigma = 1;
noise = sigma * randn(size(transmittedSequence));
% We add noise to transmitted data to create received sequence
receivedSequence = transmittedSequence + noise;

Matched filtering:

matchedFilterOutput = SPX_MatchedFilter.filter(receivedSequence, signal);

Generating sufficient statistics:

signalNormSquared = signal' * signal;
sufficientStatistics = matchedFilterOutput / signalNormSquared;

Thresholding:

% We define optimal detection threshold
eta = 0.5;
% We create the received bits
receivedBits = sufficientStatistics >= eta;

Detection results:

result = SPX_BinaryHypothesisTest.performance(...
    transmittedBits, receivedBits)

% Number of False sent, False received
result.FF
% Number of False sent, True received
result.FT
% Number of True sent, False received
result.TF
% Number of True sent, True received
result.TT
% Number of times hypothesis 0 was sent.
result.H0
% Number of times hypothesis 1 was sent.
result.H1
% Number of times 0 was detected.
result.D0
% Number of times 1 was detected.
result.D1
% A priori probability of 0
result.P0
% A priori probability of 1
result.P1
% Detection probability
result.PD
% False alarm probability
result.PF
% Miss probability
result.PM
% Accuracy (probability of correct decisions)
result.Accuracy
% Probability of error
result.Pe
% Precision : Truth sent given that truth was detected
result.Precision
% Recall : Truth detected given that truth was sent.
result.Recall
% F1 score
result.F1