高级通信原理习题(含解答).pdf

高级通信原理复习题高级通信原理复习题 Chapter 2 2 1 One experiment has four mutually exclusive outcomes 1 2 3 4 i A i and a second experiment has three mutually exclusive outcomes 1 2 3 j Bj The joint probabilities ij P A Bare 111213 212223 313233 414243 0 10 0 08 0 13 0 05 0 03 0 09 0 05 0 12 0 14 0 11 0 04 0 06 P A BP A BP A B P A BP A BP A B P A BP A BP A B P A BP A BP A B Determine the probabilities 1 2 3 4 i P Ai and 1 2 3 J P Bi 2 19 Determine the mean the autocorrelation sequence and the power density spectrum of the output of a system with unit sample response 1 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 2 N Chapter 4 4 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 k s t k 1 2 3 4 shown in Fig P4 18 by using as basis functions the orthonormal function 1 f tand 2 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 sequence 1nnn BII at a rate 1 2TW 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 form 1 2 n n v tB g tnT T W a Sketch the signal space diagram for v t and determine the probability of occurrence of each symbol b Determine the autocorrelation and power density spectrum of the three level c The signal points of the sequence n B form a Markov chain Sketch this Markov chain and indicate the transition probabilities among the state 4 21 The lowpass equivalent representation of a PAM signal is n n v tI g tnT Suppose g t is a rectangular pulse and 2nnn Iaa where n a is a sequence of uncorrelated binary valued l l random variables that occur with equal probability a Determine the autocorrelation function of the sequence n I b Determine the power density spectrum of u t c Repeat b if he possible values n a are 0 1 Chapter 5 5 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 the circle 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 20 Consider 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 ml m2 and m3 are to be transmitted over an AWGN channel with noise power spectral density The messages are a 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 R1 R2 and R3 1 02N 1 0 10 t T otherwise s t 1 2 1 232 1 0 1 0 tT ststTtT otherwise e Which of the three messages is more vulnerable to errors and why In other words which of P i 1 2 3 is larger i error m transmitted 5 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 therequired 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 5 10 5 47 A radio transmitter has a power output of Pr 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 signal power 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