[試題] 103-1 陳光禎 通信原理 期末考
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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02/13 23:47, , 1F
02/13 23:47, 1F