QUESTION BANK SUBJECT: DIGITAL COMMUNICATION (15EC61) Module 1 1. Explain Digital communication system with a neat block diagram. 2. What are the differences between digital and analog communication systems? 3. Differentiate between baseband and passband transmission. 4. State the sampling theorem. Show that the spectrum of the sampled signal is given by G s(f ) F s G(f nf s). n 1. Explain Line coding. What is the necessity for line coding? 2. Explain the various Line coding techniques, their advantages and disadvantages. 3. The bit sequence 1 0 1 1 1 0 1 0 1 1 is to be transmitted using the following formats: (i) Uni-polar RZ and NRZ; (ii) Bipolar RZ and NRZ; (iii) Split-phase Manchester; (iv) Polar quaternary NRZ; Draw all the waveforms. 4. Find the power spectral density (PSD) and draw the normalized PSD for the line codes in Q.21. 5. The binary data 1 0 1 1 0 0 1 1 0 1 0 1 is transmitted over a base band channel. Draw the waveforms for the transmitted data using following formats: (i) Unipolar RZ; (ii) Unipolar NRZ; (iii) Bipolar RZ; (iv) Split-phase Manchester; Compare above schemes for their bandwidth requirements. Module 2 1. With a neat block diagram explain the conceptualized model of a digital communication system. 2. Explain the concept of AWGN channel. 1
3. Explain the concept of optimum receiver. 4. Explain the concept and the various stages involved in Gram- Schmidt orthogonalization procedure. 5. Explain the geometric interpretation (or representation) of signals. 6. Explain the role of detection and estimation theory in digital communication. 7. Explain the concepts of estimation with its 3 criteria used. 8. Show that the outputs of bank of correlators with noisy input are statistically independent and determine the variance of each output if the power spectral density of the input noise is N / 2. 9. Give the steps used for finding basis functions using orthogonalization procedure, for N = 2. 10. With reference to the parameter a (estimate), given the noise corrupted signal x(t) and observation vector X(t), define the following terms with related equations: (i) Minimum mean square estimate; (ii) Maximum A Posteriori (MAP estimate). 11. List the functions of correlation receiver. 12. Refer to the waveforms s1(t), s2(t), s3(t) as shown in the figures below. o (i) Show that, s1(t), s2(t), s3(t) do not form an orthogonal set. (ii) Find the orthonormal basis set for the above three signal waveforms. (iii) Show that the non-orthogonal set in part (i) can be expressed as a linear combination of the orthonormal basis set of part (ii). 2
13. Determine the response of a bank of correlators to noisy input. Module -3 1. What is Modulation? 2. Differentiate between band pass channel and low pass channel. 3. Explain the two types of digital modulation techniques. 4. Explain coherent binary Amplitude Shift Keying (ASK) or On-Off Keying. Give the signal-space diagram of ASK. 5. With neat block diagram explain the coherent generation and detection of ASK. 6. Explain coherent Binary Phase Shift Keying (BPSK). With neat block diagrams explain the coherent generation and detection of BPSK signal. 7. Give the geometrical representation of BPSK signals. 8. Plot the power spectral density of BPSK with relevant mathematical equations and hence, find the bandwidth of BPSK. 9. Explain coherent Binary Frequency Shift Keying (BFSK). With neat block diagrams explain the coherent generation and detection of BFSK. 10. Plot the power spectral density of BFSK and hence, find its bandwidth. 11. Give the geometrical representation of orthogonal BFSK and nonorthogonal BFSK. 12. Explain the non-coherent detection of ASK and FSK. 13. Explain the generation and detection of non-coherent PSK (DPSK). What is the bandwidth required for DPSK? 14. Explain the concept of Quadrature Phase Shift Keying (QPSK). Explain the generation and detection of QPSK with neat block diagrams and waveforms. 3
15. With a neat block diagram explain the PLL system used for carrier synchronization in QPSK. 16. Give the signal space representation of QPSK. 17. Plot the power spectral density of QPSK with relevant mathematical equations hence, find the bandwidth of QPSK. 18. With neat block diagrams of transmitters and receivers explain M- ary FSK system. 19. Determine the bandwidth required for M-ary FSK system. Give the geometrical representation of M-ary FSK and find out the distance between signal points. 20. With neat block diagram of M-ary PSK transmitter and receiver. 21. From the basic principles of probability prove that, E b P e =erfc QPSK N. o 22. For a given input binary sequence 0 1 1 0 1 0 0 0, sketch the inphase and quadrature phase components of QPSK. Then by adding these two waveforms, draw the final QPSK waveform. 23. What is the meaning of shift keying in digital modulation technique? List any 4 goals of modulation / detection techniques. 24. The bit stream 1011100011 is to be transmitted using DPSK technique. Determine the encoded sequence and transmitted sequence. Also write the block diagram of the modulator and demodulator for the same and explain. 25. Obtain the expression for probability of error for PSK with coherent receiver. 26. A binary signal transmitted using PSK has a bit rate of 100 Kbps. Sketch the PSK waveform for binary data 110 if carrier frequency used 1 is f= c, where 3 t t c = T b. c 27. For the binary sequence 01101000, explain the signal space diagram for coherent QPSK system. Draw the respective waveforms. 4
Module 4 1. With a neat block diagram explain base band binary data transmission system. 2. What is Inter Symbol Interference (ISI) problem? What is the ideal solution to ISI? 3. What is Nyquist s criterion for distortionless base band binary transmission? 4. Explain the concept of correlative coding. 5. Explain the concept of adaptive equalizer with a block diagram. 6. With a neat block diagram explain the concept of duobinary encoder without pre-coding. 7. Explain the concept of pre-coded duo-binary scheme, with a block diagram taking an example of a binary sequence 0 1 1 0 1 0 0. Specify the related outputs of each block in the scheme. 8. Explain the modified duo-binary technique, with a block diagram along with frequency and impulse response sketches. 9. Explain the concept of eye pattern in data transmission system. 10. A binary PAM wave is required to be transmitted via a channel having a bandwidth of 75 KHz. The bit duration is 10 µsec. Find a raised cosine pulse spectrum that satisfies these requirements. 11. The binary data 0 1 1 1 0 0 1 0 1 are applied to the input of a modified duo-binary system. (i) Construct the modified duo-binary coder output and corresponding receiver output without a pre-coder; (ii) Suppose that, due to error in transmission the level produced by the third digit is reduced to zero, construct the new receiver output. 12. The information in an analog waveform with maximum frequency f = 3 KHz is to be transmitted over an M-ary PAM system, where the m number of pulse levels is M = 16. The quantization distortion is specified not to exceed 1% of the peak to peak amplitude of the analog signal. (i) What is the minimum number of bits/sample or bits per PCM word that should be used in digitizing the analog waveform; 5
(ii) What is the minimum required sampling rate and what is the resulting bit transmission rate; (iii) What is the PAM pulse or symbol transmission rate. 13. Explain raised cosine spectrum with related equations and diagram with respect to base band data transmission. 14. Discuss the base band transmission of M-ary data. 15. 1. Under what conditions an optimum filter is known as a matched filter? 2. A polar NRZ waveform has to be received with the help of a matched filter. Here, binary 1 is represented by a rectangular positive pulse. Also, binary 0 is represented by a negative pulse. Determine and sketch the impulse response of the matched filter. 3. Compute the probability of error ( P e ) for the matched filter. 4. Prove that the maximum signal to noise ratio for the matched filter S 2E is found to be. N N omax o 5. Prove that for a matched filter, the maximum signal component occurs at t = T (i.e., sampling instant) and has magnitude E, i.e., energy of the signal x(t). 6. Prove that the output signal of a matched filter is proportional to the shifted version of the autocorrelation function of the input signal to which the filter is matched. 7. List the properties of matched filter. 8. Compute the probability of error for the detection of PCM signal using a matched filter receiver. The binary coded PCM signal is represented by pulse of amplitude A of duration T for binary 1 and binary 0 is represented by zero pulse of duration T. 9. Compute the probability of error using matched filter receiver for the following modulated signals: (i) ASK; (ii) PSK; (iii) FSK; 10. In a FSK system, Transmitted binary data rate = 2.5 Mbps; PSD of 20 zero mean AWGN = 10 Watts / Hz; Amplitude of received signal = 1 6
µv signal in the absence of noise. Determine the average probability of symbol error assuming coherent detection. 11. Mathematically show that the matched filter is matched in amplitude and phase of the input signal. 12. Explain the detection of known signals in noise. 13. A binary data is transmitted using ASK over an AWGN channel at a rate of 2.4 Mbps. The carrier amplitude at the receiver is 1 µv. The 15 noise PSD N / 2 is 10 Watt/Hz. Find the average probability of error if o the detection is coherent. Take erfc(5) 6 3x10. 14. Explain the concept of Detection of signals with unknown phase in noise using quadrature receiver with correlators. Specify the related equations and block diagram. 15. The finite energy signal s(t) is as shown in the figure. (i) Sketch the impulse response h opt (t) of optimum filter matched to signal s(t). (ii) Determine the value of the output signal at t = T assuming noise is zero and the input is s(t). 16. A signal s(t) of duration T sec. is as follows: a T ;0 t s(t)= 2 2 ; a T - ; t T 2 2 (i) Determine the impulse response of a filter matched to this signal and sketch it as a function of time. (ii) Plot the matched filter output as a function of time. (iii) What is the peak value of the output? 7
17. In a bipolar binary system, if priori probabilities are p(s1) = p(s2) 9 = 1/2, η/2 = 10 W/Hz, A = 10 mv and transmission rate of data is 10-4 Kbps, given Q 10 7.8x10 ; (i) Find the probability of error P e. (ii) If the bit rate is increased to 100 Kbps, what value of A is needed to attain the same P e as in part (i) above? Module 5 1. Explain the concept of spread spectrum 2. What is a random binary sequence? List all the properties of Maximum length sequences and explain each property. 3. With a neat block diagram explain Direct Sequence (DS) spread spectrum. 4. Write short notes on applications of spread spectrum. 5. What are pseudo-noise sequences? Why they are used in spread spectrum modulation? 6. What is processing gain and jamming margin? 7. Give the advantages and disadvantages of direct sequence and frequency hop spread spectrum techniques. 8. Explain the frequency hop spread spectrum system. 9. A slow FH / MFSK system has the following parameters: The number of bits / MFSK symbol = 4, The number of MFSK symbol / hop = 5. Calculate the processing gain of the system in decibels. 10. Explain the terms Multi path suppression and Range determination with respect to Spread Spectrum. 11. In a direct sequence SS modulation, it is required to have a jamming margin greater than 26 db. The E b/n o is set at 10. Determine 8
the minimum processing gain and minimum number of stages required to generate maximum length sequence. 12. In a direct sequence spread spectrum modulation scheme, a 14 stage linear feedback shift register is used to generate PN code sequence. Find: (i) The period of code sequence; (ii) Processing gain. 13. With a neat diagram, explain transmitter and receiver of slow frequency hop spread M-ary frequency shift keying system. 14. Explain the application of spread spectrum technique to CDMA. 15. In a direct sequence spread spectrum system, a 20 stage feedback shift register is used to generate maximum length PN sequence. What is the processing gain? 9