Binary Amplitude Shift Keying (BASK) is a technique of sending binary information by sending one of two signals levels, with one level assigned to be a binary 1 and one level assigned to be a binary 0. One common mapping is to send a level of when the binary information is a 1 and to send at when the binary information is a 0. For this project we will assume a BASK system with the input being a binary random variable and The random variable is a simple mapping and the random variable corresponds to the symbol bit in a string of symbols, generated by the mapping of the input bit . For the various values for different values are independent and identically distributed, with . (1.1) As in Project 2, this sequence of i.i.d. random values is corrupted by additive white Gaussian noise, where the pdf of the noise is . (1.2) Our model for our received signal is , (1.3) −A +A B ∈{0,1} Pr⎡B = 0 ⎣ ⎤ ⎦ = p0 , Pr⎡B = 1 ⎣ ⎤ ⎦ = 1− p0. M b = 0 ! m = −A, b = 1! m = A Mk k-th Bk Bk and Mk k fB (b) = p0 b = 0 1− p0 b = 1 ⎧ ⎨ ⎪ ⎩ ⎪ f M (m) = p0 m = +A 1− p0 m = −A ⎧ ⎨ ⎪ ⎩ ⎪ fN (n) ~ N(0,σ2 ) = 1 2πσ2 e−n2 /(2σ2 ) , − ∞ < n < ∞ R = M + N 2 and we can assume that the random variables are independent. Hint: This is the same model used in Project 3, except we will be varying the noise variance. Hint: Notice that we are NOT using M and N as the number of rows and number of columns in your R matrix, as we have done before! Please be careful and don’t confuse them! We are tasked to design a Maximum A Priori (MAP) detection method that will examine the value received random variable, at the time instant , and estimate the value of the corresponding input binary digit, where the is the binary digit used to create the BASK value , and is the estimate at the output of the MAP detector. For this simple model, the Signal to Noise ratio, , is defined as , (1.4) and is often expressed in decibels, . Throughout your implementation of this Project, please assume that the value of , so that and Figure 1 shows the bits, messages, noise, received value, estimates and errors. The pmf for the input bits is not changed for any particular set of experiments. The entire process is repeated for various values of , which specify the variance by means of (1.