哈工大2009春季数字通信考试题及答案.docVIP

2009春季数字通信试题及答案 Question One: Determine a set of orthonormal functions for the four signals shown below: (20%) Here give the details of the derivation 1.Answer: Question Two: (20%) Determine the probability error for the signals shown below, then give the bit error probability and symbol error probability of QPSK. 2. Answer: Let us assume that the two signals are equally likely and that signal was transmitted. Then, the received signal from the (matched filter or correlation) demodulator is where represents the additive Gaussian noise component, which has zero mean and variance . If , the decision is made in favor of , and if , the decision is made that was transmitted. Clearly, the two conditional PDFs of are Question Three: (15%) Considering biorthogonal signals shown in below for transmitting information over an AWGN channel. The noise is assumed to have zero-mean and power spectral density . Determine the basis functions for this signal set, the impulse responses of the matched-filter demodulators, and the output waveforms of the matched-filter demodulators when the transmitted signal is . 3. Answer: The impulse responses of the two matched filters are Observe that the for the first matched filter is and . Question Four: (15%) Complex-valued cross-correlation coefficient of any pair of signal waveforms and is defined as Where is the energy of , and is the bandpass representation of the Do you know where the coefficient 1/2 in come from? （2）Can it be defined as ? 4. Answer: (1) Yes Question Five: (20%) Let X be Gaussian distributed with zero mean and variance σ2, consider the random variable Y defined as Determine (the details of the derivation are needed): PDF of Y CDF of Y The characteristic function of Y 5. Answer: so the probability distribution function of Y is and the probability density function of Y is Question Six: (20%) Your own explanation for the figure below, which is the comparison of several modulation methods at 10-5 symbol error