高级通信原理复习题Chapter 22-1 One experiment has four mutually exclusive outcomes ,1,2,3,4i A i =, and a second experiment has three mutually exclusive outcomes ,1,2,3j B j =. The joint probabilities (,)i j P A B are111213212223313233414243(,)0.10,(,)0.08,(,)0.13(,)0.05,(,)0.03,(,)0.09(,)0.05,(,)0.12,(,)0.14(,)0.11,(,)0.04,(,)0.06P A B P A B P A B P A B P A B P A B P A B P A B P A B P A B P A B P A B ============Determine the probabilities (),1,2,3,4i P A i =, and (),1,2,3J P B i =2-19 Determine the mean, the autocorrelation sequence and the power density spectrum of the output of a system with unit sample response1(0)2(1)()1(2)0()n n h n n otherwise = −= = = when the input x(n) is a white-no/se process with variance 2N δ.Chapter 44-11 Consider the four waveforms shown in Fig. P4-11.a Determine the dimensionality of the waveforms and a set of basis functions.b Use the basis functions to represent the four waveforms by vectors 1234,,,s s s s ..,c Determine the minimum distance bclween any pair of vectors.4-12 Determine a set of orthonormal functions for the four signals shown in Fig.P4-12.4-18 Determine the signal space representation of the four signals()ks t, k = 1, 2, 3, 4 shown in Fig. P4-18 byusing as basis functions the orthonormal function1()f t and2()f t. Plot the signal space diagram and show that this signal set is equivalent to that for a four-phase PSK signal.4-20 A PAM partial response signal (PRS) is generated as shown in Fig. P4-20 by exciting an ideal lowpass filter of bandwidth W by the sequence1n n n B I I −=+at a rate 1/2T W =symbols/s. The sequence {}n I consists of binary digits selected independently from the alphabet {1 -1} with equal probability. Hence the filtered signal has the form1()(),2n n v t B g t nT T W∞=−∞=−=∑ a Sketch the signal space diagram for ()v t ) and determine the probability of occurrence of eachsymbol.b Determine the autocorrelation and power density spectrum of the three-levelc The signal points of the sequence {}n B form a Markov chain. Sketch this Markov chain and indicate thetransition probabilities among the state.4-21 The lowpass equivalent representation of a PAM signal is()()n n v t I g t nT ∞=−∞=−∑Suppose g(t) is a rectangular pulse: and 2nn n I a a −=− where {}n a is a sequence of uncorrelated binary-valued (l, -l) random variables that occur with equalprobability. a Determine the autocorrelation function of the sequence {}n Ib Determine the power density spectrum of ()u tc Repeat (b) if he possible values n aare (0,1).Chapter 55-16 Consider the octal signal point constellations in Fig.P5-16.a The nearest-neighbor signal points in the 8-QAM signal constellation are separated in distance by A units.Determine the radii a and b of the inner and outer circles.b The adjacent signal points in the 8-PSK are separated by a distance of A units. Determine the radius r of thecircle.c Determine the average transmitter powers for the two signal constellations and compare the two powers.What is the relative power advantage of one constellation over the other? (Assume that all signal points are equally probable.)5-17 Consider the 8-point QAM signal constellation shown in Fig.P5-16.a Is it possible to assign three data bits to each point of the signal constellation such that nearest (adjacent)points differ in only one bit position?b Determine the symbol rate if the desired bit rate is 90 Mbits/s.5-20Consider the two 8-point QAM signal constellations shown in Fig.P5-20. The minimum distance between adjacent points is 2A. Determine the average transmitted power for each constellation, assuming that the signal points are equally probable. Which constellation is more power-efficient?5-21 For the QAM signal constellation shown in Fig.P5-21, determine the optimum decision boundaries for the detector, assuming that the SNR is sufficiently high so that errors only occur between adjacent points.5-24 Three messages m l , m 2, and m 3 are to be transmitted over an AWGN channel with noise power spectraldensity . The messages area What is the dimensionality of the signal space?b Find an appropriate basis for the signal space. [Hint: You can find the basis without using the Gram-Schmidt procedure.]c Draw the signal constellation for this problem.d Derive and sketch the optimal decision regions R 1, R 2, and R 3.102N ()()(){1010t T otherwise s t ≤≤=()()()()()1212321010t T s t s t T t T otherwise ≤≤ =−=−≤≤e Which of the three messages is more vulnerable to errors and why? In other words, which of, transmittederror mP(),i = 1. 2. 3, is larger?i5-26 Consider a digital communication system chat transmits information via QAM over a voice-band telephone channel at a rate 2400 symbols/s. The additive noise is assumed to be white and Gaussian.a Determine the required to achieve an error probability of at 4800 bits/s.b Repeat (a) for a rate of 9600 bits/s.c Repeat (a) for a rate of 19200 bits(s.d What conclusions do you reach from these results?0b N ζ510−5-47 A radio transmitter has a power output of P r = 1 W at a frequency of l GHz. The transmitting and receiving antennas are parabolic dishes with diameter D = 3 m.a Determine the antenna gains.b Determine the EIRP for the transmitter.c The distance (free space) between the transmitting and receiving antennas is 20km. Determine the signalpower at the output of the receiving antenna in dBm.5-48 A radio communication system transmits at a power level of 0.1W at l GHz. The transmitting and receiving antennas are parabolic, each having a diameter of l m. The receiver is located 30 km from the transmitter.a Determine the gains of the transmitting and receiving antennas.b Determine the EIRP of the transmitted signal.c Determine the signal power from the receiving antenna.5-49 A satellite in synchronous orbit is used to communicate with an earth station at a distance of 40000 km. The satellite has an antenna with a gain of 15 dB and a transmitter power of 3 W. The earth station uses a 10 m parabolic antenna with an efficiency of 0.6. The frequency band is at f = 10 GHz. Determine the received power level at the output of the receiver antenna.5-50 A spacecraft located 100000km from the earth is sending data at a rate of R bits/s. The frequency band is centered at 2 GHz and the transmitted power is 10 W. The earth station uses a parabolic antenna, 50m in diameter, and the spacecraft has an antenna with a gain of 10 dB. The noise temperature of the receiver front end is T 0= 300 K.a Determine the received power level.b If the desired = 10 dB, determine the maximum bit rate that the spacecraft can transmit.0b NζChapter 6Chapter 9。
