(d) (7%) Assume that the channel gain and propagation delay from two base stations to the car are the same. Derive the mathematical expression of the received signal, ignoring the speed of the car.

(a)  (4%) Considering y1(t), y2(t), y3(t), and y4(t), the random processes that are wide-sense stationary are____________

(b) (3%) Considering y1(t), y2(t), y3(t), and y4(t), the random processes that are white are_______________

(c) (2%)Itis _____________(true/false) that the random processes y2(t) and y3(r) are statistically independent.

(d) (6%) The probability that z(t) is greater than 3 at t=20 is____________

(a) (4%) Compute a set of orthonormal basis functionsusing the Gram-Schmidt procedure, whereis proportional to sA(r). The signals sA(X), sB(t), sc(t), and sD(t) can be expressed as a linear combination of these basis functions as__________________________________________________________________________________________________________________ where the basis functions are________________________________________________________________________________________________________________________________________________________

(b) (4%) The TWO candidate signals that would result in minimum average transmitted energy, given that the two messages are equiprobable, are_______________.

(c) (4%) The TWO candidate signals that would provide the lowest average probability of a bit error are____________________________

(d) (6%) To increase data rate, suppose now you want to send THREE messages instead of two, which again occur with equal a priori probability. Suppose SA(t), SB(t), and sc(t) are chosen to represent these messages, and the power spectral density of the noise is . The union bound of the average symbol error probability is_____________________

(a) (3%) Let t0 = 3 and T=4, i.e. h(t) = s(4- t). Determine the mean and variance of the filtered and sampled noise term W.

(b) (6%) Again, let t0 = 3 and T=4. Please find the corresponding bit error rate (BER) of the ML receiver. (Express your answer in Q-function.)

110年 - 110 國立中央大學_碩士班招生考試_通訊工程學系：通訊系統#110494

110年 - 110台灣聯合大學系統_碩士班招生考試_電機類:通訊系統(通訊原理)#105574