# Berkeley ELENG 121 - Final Exam (7 pages)

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## Final Exam

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## Final Exam

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School:
University of California, Berkeley
Course:
Eleng 121 - Introduction to Digital Communication Systems
##### Introduction to Digital Communication Systems Documents
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EE 121 Introduction to Digital Communication Systems Final Exam Spring 2003 Please put your name on the front page Answer all the questions on the blank pages provided Explain clearly the steps in your answers Yes no answers with no explanations get no marks Waterfall error probability curves are provided at the back for your use throughout the exam Please reference the appropriate plots when you use them You may want to take a look at them now 10 1 6 a Explain briefly what these concepts mean i entropy ii uniquely decodable codes iii Nyquist sampling theorem iv Nyquist criterion v bi orthogonal modulation vi ISI 4 b Is there any relationship between the delay spread and coherence bandwidth in a wireless channel How about between delay spread and coherence time For each case if there is a relationship explain If not give an example of a wireless channel in which the two parameters can be specified separately 2 10 2 Suppose you have calculated the transmit power link budget for a wireless system assuming uncoded binary pulse amplitude modulation binary PAM also known as BPSK an error probability of 10 4 transmission over an AWGN channel 5 a Suppose now there is flat Rayleigh fading and coherent detection is performed How much extra transmit power is needed This is called the fade margin State clearly how you come up with your answer 5 b Suppose now each symbol is repeated twice and interleaved over different coherence time periods Compared to a how much is the fade margin reduced by 3 15 3 A passband communication system uses ideal sinc pulses and signal at Nyquist rate 3 a What is the difference in terms of symbols transmitted in the in phase and quadrature phase between BPSK binary phase shift keying also known as binary PAM and QPSK in such a system Draw a system diagram for each 4 b Compare the spectral efficiency in bits s Hz and Eb N0 performance of BPSK and QPSK over an AWGN channel for the same symbol error probability pe You can assume that pe is small in making any approximations Also you may find the approximation Q x exp x2 2 useful 3 c Suppose the in phase and quadrature phase components of each QPSK symbol carry two independent information bits Repeat the comparison in part a between BPSK and QPSK but now for the same bit error probability 5 d Consider the discrete time baseband equivalent flat Rayleigh fading channel yn hn xn wn where wn CN 0 N0 and hn CN 0 1 In class we have stated that for coherent BPSK the symbol error probability is v u u Eb N0 1 pe 1 t 2 1 Eb N0 Using part c or otherwise compute the probability of bit error for coherent QPSK over the Rayleigh flat fading channel assuming again that the in phase and quadrature phases carry independent information bits Again what is the difference in Eb N0 performance for the same bit error probability 4 10 4 Consider a wireless channel with only one line of sight path which arrives after a delay of Communication is over a passband at carrier frequency fc 1900 MHz and bandwidth W 1 MHz Assume ideal sinc functions are used as transmit pulses 4 a The optimal demodulator matches filter to the transmit waveform and sample at the correct times Since is unknown in practice it has to be estimated so that the sample times can be determined a process known as timing recovery or symbol synchronization In terms of the given system parameters give an order of magnitude approximation of how accurate have to be estimated for proper timing recovery 5 b Since we are communicating on a passband the delay will also cause a phase rotation of the baseband transmitted signal To do coherent detection this phase has to be estimated as well a process known as carrier recovery In terms of the given system paramters give an order of magnitude approximation of how accurate have to be estimated for proper carrier recovery 1 c In practice varies as the mobile moves so have to be continuous tracked for ongoing timing and carrier recovery From your answers in part a and b which do you think it s a more difficult problem timing or carrier recovery Explain 5 27 5 I A sampled complex baseband equivalent channel yn hxn wn where h CN 0 1 and wn is a sequence of independent CN 0 N0 noise 2 a What are the assumptions on the passband physical channel for which this would a reasonable baseband model Why is it reasonable to model the channel gain h as CN 0 1 1 b Suppose h is unknown to the receiver Can you transmit information using BPSK How about QPSK Why 4 c Design a scheme such that the receiver can demodulate without knowing h Give the receiver structure Give an expression for the error probability II Consider now another sampled baseband equivalent channel given by yn ej xn wn where wn CN 0 N0 independent over time and is a random variable uniformly distributed in 0 2 independent of the additive noise 3 a Give an example of a passband physical channel for which this is a reasonable baseband model What is the interpretation of Why is it reasonable to model as uniformly distributed in 0 2 1 b Suppose is unknown to the receiver Can you transmit information using BPSK How about QPSK Why 4 c Design a scheme such that the receiver can demodulate without knowing Give the receiver structure Give an expression for the error probability It s ok if it s not in closed form 4 d Qualitatively compare the performance in part I c and part II c Which channel is harder to communicate over Explain III Let us now consider yet another baseband channel ynA hA xn wnA ynB hB xn wnB where hA hB CN 0 1 are independent and wnA wnB are independent additive CN 0 N0 noise independent of hA and hB 2 a Give an example of a physical scenario for which this is a reasonable channel model In your scenario under what condition is it reasonable to model the channel gains hA hB as independent 5 b Design a scheme that can exploit both the received signals ynA and ynB in detecting the transmitted symbols but without needing to know the gains hA and hB 3 c Qualitatively compare the performance of this scheme with that in part I c Explain the nature of the performance improvement if any 6 28 6 Communication is done over the baseband W W through an M ary orthogonal code in conjunction with binary PAM modulation of each coded symbol The transmit pulse is a raised cosine waveform with a roll off factor of 10 The orthogonal code is implemented through the Hadamard matrix HM defined recursively as H1 1 HM HM 2 HM 2 HM 2 HM 2 M 2 The questions below refer to a system for general M unless

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