b Add zero mean Gaussian noise with variance \u03c3 2to the signal generated in Part

# B add zero mean gaussian noise with variance σ 2to

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b) Add zero-mean Gaussian noise with variance σ 2 to the signal generated in Part a) and generate the received signal. Then, perform correlations of the received signal with the basis functions and obtain the correlator outputs, r 1 and r 2 , for all the symbols. In addition, for σ = 8 , plot the first 100 [ r 1 r 2 ] pairs (i.e., [ r 1 r 2 ] pairs for the first 100 symbols) on a figure (also mark the signal constellation points on the same figure) and comment on the results. How does this figure change with σ ? c) Apply the ML rule on the correlator outputs in Part b) and estimate the transmitted symbols. Calculate both the probability of symbol error and the probability of bit error for σ = 8 . Compare the probability of symbol error with the theoretical expression for the probability of symbol error. Provide two different mappings of the bits to signals so that the probabilities of bit error are different. What type of mapping would minimize the probability of bit error? Please specify. d) Based on the algorithm in Parts b) and c), plot the probability of symbol error versus the SNR such that the error probability ranges from about 0.5 to about 10 - 3 . Also plot the theoretical probability of symbol error on the same figure. Comment on the results. Reporting Requirements: Note that you are not allowed to use the built-in functions from Matlab (or, other resources) to complete the project. You must write your own code, and conduct your simulations using that code. Both the Matlab

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