課程名稱︰通信原理 課程性質︰選修 課程教師︰陳光禎 開課學院：電機資訊學院 開課系所︰電機工程學系 考試日期（年月日）︰104.1.15 考試時限（分鐘）：120分鐘 是否需發放獎勵金：是 試題 : 1.[Match Filter,20%] Given pulse waveform g(t), 0<t<T and AWGN w(t), we intend to derive the matched filter that optimizes SNR at filter output as the fol- lowing figure. Please derive the optimal h(t) wih proper definitions by you. --------------- x(t) | Linear Filter | y(t) \ g(t) → + → | h(t) | → \___ ↑ --------------- Sample period T w(t) 2.[Optimal Receiver,20%] We use the following waveforms to represent binary signaling and then transmit over the AWGN channel, with zero mean and 2-side P.S.D. N_0/2. Assuming perfect synchronization, please design the optimal receiver and the BER in terms of E_b/N_0. H_0: (2A)√2 cos2πf_1t - A√2 cos2πf_2t H_1: -A√2 cos2πf_1t + (2A)√2 cos2πf_2t where |f_2-f_1|>>1 (symbol period). Please comment with your reasons whether this modulation is good or not. Is this minimum energy signaling method？ 3.[General Digital Modulation,20%] The general received waveform at the recei- ver can be represented by r(t) = K*A*cos(2πf_c*t+θ) + L*A*sin(2πf_c*t+θ) + n(t), where n(t) is AWGN with zero mean and 2-side P.S.D. N_0/2, and K,L are determined by the modulation (A>0). The following table represents to transmit 3 bits in an equally probable symbol. Please derive the receiver and approximate its symbol error rate performance as precise as possible. K L 000 -1 1 001 1 5 010 -2 3 011 2 -4 100 -3 4 101 3 -3 110 -4 -2 111 5 -1 4.[MPSK,20%] The M-ary phase shifted keying (M-PSK) can be used as a higher- dimensional modulation method. (a)(5%)For 8-PSK, how many bits can be carried by a symbol？ (b)(5%)For 1MHz bandwidth, considering roll-off factor 25%, what is the max- imal transmitted bits per second by using 8-PSK？ (c)(5%)Please write down the mathematical representation and plot the signal constellation on I-Q plane. (d)(5%)Under AWGN with zero mean and 2-side P.S.D. N_0/2, please approximate BER in terms of E_b/N_0 as precise as you can. 5.[ISI and Equalizer,20%] Please do the following questions with your reasons. (a)(5%)Once we have nonlinear distortion in the channel, inter-symbol inter- ference (ISI) is a challenge other than noise. Please draw the block dia- gram for a linear optimum receiver facing ISI. (b)(5%)Please explain the Nyquist criterion and thus zero-forcing equalizer. (c)(5%)We can also design equalizer based on MMSE criterion. Please explain how it works. (d)(5%)Please show the structure of decision feedback equalizer and explain how it works. --

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