USN: .............................................

M.S. Ramaiah Institute of Technology(Autonomous Institute Affiliated to Visvesvaraya Technological University)

Bangalore - 560 054Semester End Examination (January 2009)

Course : 151 Semester M.Tech. (Digital Communications)Subject Code : MDCE13 Subject : Advanced Digital CommunicationsMaximum Marks : 100 Duration: 3 hours

Instruction to Candidates: Answer All Questions

l.a. With the help of a Constellation Diagram (with Gray Coding), describe the principles ofa QPSK System. Also write the Expressions for the Bit Error Rate and Symbol Error Rate ofa QPSK Signal. (10 Marks)1. b. Prove mathematically that a 16-ary QAM (assume Symbol Distance=2a) is moreefficient than a 16-ary PSK System. (10 Marks)

OR2.a. In a BPSK Signal, how are the Signal Components so(t) and s,(t) corresponding to Bits 0and I respectively represented? How do you represent these Signals with the help of BasisFunctions? What is the Bit Error rate of BPSK in the presence of AWGN? (10 Marks)2. b. A Data Sequence 110100010110 is to be transmitted using Binary DPSK Technique(assume the Signal to be NRZI).(i) If s(t)=A cos (2nfft + 8), represent the transmitted Signal in any Signalling Interval ofDuration T, give the Phase of the transmitted Signal for the Data Sequence. Begin with firstBit =0 for the phase of the first Bit to be transmitted. (ii)lf the Data Sequence isuncorrelated, determine and Sketch the Power Density Spectrum of the Signal transmitted byDPSK. (l OMarks)3.a. Derive an Expression to show that the Signal to Noise Ratio decreases as the number ofbits per Symbol increases. Also, define Shannon's Limit. (10 Marks)3.b. Explain with the help of a Block Diagram the OFDM Transmitter. (10 Marks)

OR4.a. A Binary Digital Communication System employs the Signals

So(t) = 0. 0 < t . TS1(t)=A, 0. t < T

for transmitting the information (On-Off Signalling). The Demodulator cross-correlates thereceived signal r(t) with s(t) and samples the Output of the Correlator at t+T. (i) Determinethe Optimum Detector for an AWGN Channel and the Optimum Threshold, assuming that theSignals are equally Probable. (ii) Determine the Probability of Error as a Function of theSNR. How does On-Off Signalling compare with Antipodal Signalling? (10Marks)4.b. What are the Properties of a Matched Filter? Derive the relevant Expressions to provethe Same. (10 Marks)5.a. The Generator Matrix for a Linear Binary Code is

0011101G= 10100111

1001110(i) Express G in Systematic (I 1P1 form. (ii)Determine the Parity Check Matrix H for the

Code. (iii) Construct the Table of Syndromes for the Code. (iv) Determine the MinimumDistance of the Code. (10 Marks)

5.b. In a binary PAM System, the input of the Detector is ym = a,,, + nm + im wherea,,, 1 is the desired Signal, nm is a zero-mean Gaussian random variable with

2variance a,, . and im represents the ISI due to channel distortion. The ISI term is a randomvariable that takes the values -'/2, 0, and '/z with probabilities '/., '/z, and '/4, respectively.Determine the average probability of error as a function of a„''. (10 Marks)

OR6.a. For the (7.4) Cyclic Hamming Code, with Generator Polynomial g(p) = p3 + p2 +l.Construct an (8,4) Extended Hamming Code and list all the Code words. What is dm,n forthe Extended Code? (10 Marks)6.b. What is equalization? Describe the Working of Linear Transversal Filter with thehelp of a neat Block Diagram. (10Marks)7.a. Determine the Tap weight Coefficients of a three-tap zero forcing Equalizer if the ISIspans three Symbols and is characterized by the values x(0) = 1, x(- I) = 0.3, x(1) - 0.2.Also, determine the residual ISI at the output of the Equalizer for the optimum tapcoefficients. (10 Marks)7.b. Describe the Applications of DS Spread Spectrum Signals. (10 Marks)

OR8.a. A rate '/2 convolutional code with dire, = 10 is used to encode a data sequenceoccurring at a rate of 1000bits/s. The modulation is binary PSK. The DS Spread Spectrumsequence has a chip rate of 10MHz. (i) Determine the Coding Gain, (ii) Determine theProcessing Gain, (iii) Determine the Jamming Margin assuming an Cb/Jo = 10. (10 Marks)8.b. Explain the Phenomenon of Rayleigh Fading with relevant Expressions for the ErrorProbability. (I OMarks)9.a. A DS Spread Spectrum system is used to resolve the multipath signal components ina two path radio signal propagation scenario. If the Path Length of the secondary path is300 metres longer than that of the direct path, determine the minimum chip rate necessaryto resolve the multipath components. (10 Marks)9.b. Describe the Frequency hopping concept and describe FHSS system with a neatdiagram. (10 Marks)

OR10.a. A Communication System employs dual Antenna Diversity and Binary OrthogonalFSK Modulation. The received Signals at the two Antennas are ru(t) = aus(t) + nu(t) andr2(t) = a2s(t) + n2(t), where au and a2 are statistically iid Rayleigh random Variables, andnu(t) and n2(t) are statistically independent, zero-mean and white Gaussian randomprocesses with power-spectral density '/2No The two signals are demodulated, squared andcombined (summed) prior to detection. ' Sketch the functional Block Diagram of theentire Receiver, including the Demodulator, the Combiner and the Detector. (10 Marks)10.b. Write Short Notes on: (i) Fading Factors (ii) Multiple Antenna System.

(5x2 Marks)