A] Description of the transmission scheme
Assume a baseband transmission scheme that sends a stream of binary rectangular pulses of height A = ±1 V (assume that the positive pulse represents a binary 1 and the negative pulse represents a binary 0). This is the polar or antipodal signaling. The transmitted signal is contaminated by additive noise (the noise is added to the signal). For the detection scheme, we will assume that the noise has zero mean. The noise process you will generate will have a nonzero mean. However, you will use the mean and variance estimators to determine an estimate of the mean and the variance using the generated noise with no signal transmitted (see the D section of module 8). You will then subtract the estimated mean from the noise process rendering it zero-mean (approximately). You will then use a detector to decide whether a 0 or a 1 was transmitted over a string of bits whose length will be specified the same for everybody. You will compare the received string and the transmitted string to determine the number of errors thereby allowing you to determine an estimate of the average probability of error. The transmitted string will be made of as many 0s as 1s if we assume that the a-priori probability of a 1 or a 0 is 1/2. If the a-priori probability of a 0 is 0.3, then out of 10 bits, 3 of them will be 0s. These numbers may make sense only if the string is very long but we will work with these given parameters.
B] Description of the simulation
Learn to generate a Gaussian random variable, and a Laplacian random variable. For the Laplace density function, use information wherever you can find it (example, the Matlab Central website gives an example for the Laplace RV, [login to view URL]
where the download button is on the top right location. I would like you to run a histogram to show that it has a valid Laplacian density function. Choose a = 0 (zero mean) so that it corresponds to our requirement, and also makes it easier to plot (easy symmetry).
Transmit the sequence using the following cases:
Gaussian noise (variance 0.1 and 1) and use two comparators: the first one will compare one single sample to 0, and the second one where you will compare the average of 100 samples (assumed to have been taken within the bit interval) and compare to 0 again. If greater than 0, the bit should have been 1 and 0 otherwise. The comparison will be repeated for the case of unequal probability and the same threshold 0 (which may not be optimum). Compile your results and comment.
Laplacian noise (variance 0.1 and 1) is to be the underlying contamination. Repeat the process. Note that the detector will not be optimum in this case regardless of equal or unequal probabilities.
The sequences you will be working with are
Equal probabilities: 10001100010111101001
Unequal probabilities: 10001000011000001001
User-Friendliness is of the utmost importance and proper documentation is very important
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