Stochatic Model

Question 10 (3.5 Marks) Consider the RF front-end of a communication system consisting of two cascaded amplifiers (A, and A.). Suppose G and G, denote power gains (in dB) of the amplifiers A, and A, respectively and F and F, represent the associated noise factors. There are three receivers (X, Y, Z) that use in their RF stages, the aforesaid type of cascaded amplifiers (A, and A.). Due to varying ambient temperature, the noise 7 performance of the amplifiers is observed to change. As such, the three receivers (X, Y. Z) are used only on prorated basis in time-scale as, 30 %, 20 % and 50 % respectively so as to avoid noise-related performance degradation, (denoted as the state, R). Further, the compiled statistics on receiver operation yield data on probabilities: p(R/X), pR/Y) and p/R/Z), Given that (A, and A.) are characterized by: G; = 15 dB. G = 25 dB. F. - 1.33 and F; - 1,5; further, as regard to (X, Y, Z) and the state, R. the following data is availed: p(R/X) = 0.01,p(R/Y) = 0.03 and p[RUZ)=0.02. Hence, determine the items listed below and choose correct set of answers in the multiple-choices shown as regard to the items evaluated: (i) Overall noise figure (NF) of the cascade set of amplifiers (A. and A.) in dB (ii) Prior probability of the state, p(R) (iii) Conditional probability, p{X/R) (iv) Conditional probability, p(Y/R) Conditional probability, p(Y/R) Multiple-choices on the answer-set Choices 0 (1) NF in dB) PR) 1 2.288 0.119 2 0.280 0.010 3 3.287 0.079 4 2.299 0.069 1.289 0.019 p(X/R) 0.1777 0.1070 0.1779 0.3578 0.1579 PYR 0.4154 0.3057 0.3758 0.3258 0.3158 (9) PIZR) 0.6266 0.7267 0.7273 0.3263 0.5263