课程名称︰行动通讯 课程性质︰选修 课程教师︰陈光祯 开课学院：电机学院 开课系所︰电信所 考试日期（年月日）︰100/11/10 考试时限（分钟）：2:45~5:00 是否需发放奖励金：是 （如未明确表示，则不予发放） 试题 : Problem 1 [Digital Modulation, Diversity, Coding] Consider the following digital communication: When "1" is transitted, Acos(2πfct) is received. When "0" is transitted, -Acos(2πfct) is received. (a) Under AWGN with zero mean and two-side power spetral density No/2 observed at the receiver input, please find the BER(or error probability) in terms of (Eb/No) with perfection synchronization of timing and phase. (b) Suppose such a signaling suffers from Rayleigh fadding and AWGN, which means the square envelope A has the pdf as 1 f (A) = ---exp(-A/a), a>0 Rayleigh a Please find the average BER. (c) Suppose we use two receivers antenna to implement antenna diversity with antenna separtion more than 10 wave-lengths to resist Rayleigh fadding, Assuming the receiver has a mechanism to determine which antenna has better SNR immediately. Please find the average BER of the diversity with such antenna selection strategy (select the best). Please also explain the performance gain compared with (b). (d) Continuing from (b), we implement an error correcting code to improve the performance, the coding is known as repetition code by repeatly transitting the same symbol for 3 times and decoding is down by majority rule. Please find the average error rate and discuss pros and cons of this machanism. -------------------------------------- Problem 2 [OFDM 20%] In an OFDM system, there are 52 sub-carriers, while 4 of them are pilot sub- carriers. Suppose we use QPSK for modulation and rate 1/2 convolution code. The cyclic prefix occupied 25% of transmission period. (a) What's the purpose of cyclic prefix ? What's the purpose of pilot sub-carriers? (b) If we want to transmit 12M bps information data, what's the symbol duration? (c) Why OFDM is useful to transmit high bandwidth signal in fadding channel? (d) Please explain the cause of PAPR problem in OFDM, What's the most effective solution if the packet error rate must be lower than 2% ? ---------------------- Problem 3 [Multiple Access 15%] In case an infinite number of nodes to contend a channel with totally aggregated traffic following Poisson distribution with λ>0 (a) Please derive the throughtput of pure ALOHA and slotted ALOHA (b) If we add another function to sense before transmission (i.e. carrier sensing) Please explain the Hidden terminal problem and possible solution. -------------------------- Problem 4 [Multiuser Detection 20%] Consider two-user synchronous channel, the equivlent low-pass received signal over one bit/symbol peroid is: r(t) = A1b1s1(t) + A2b2s2(t) + n(t) where bi, i=1,2 denote the bit transmitted by the ith user over the given bit time. (a) Please derive the correlator output in the form of ri=f(b1,b2) +ni i=1,2 (b) Determine the variance and covariance of n1 and n2 (c) Determine the joint pdf p(r1,r2|b1,b2) (d) Assume the bit are equally probable and independent, please derive the optimun detector for b = (b1,b2) based on MAP creterion and show its equvalence to ML. ----------------------------------- Problem 5 [System capacity 15%] Taipei city has 280 km^2 and each base station (BTS) can cover 4 km^2 in avearge. The user density is 1000 per km^2 and each user make 0.3 phone call per hour lasting 1.5 minutes. We design the system to constrain the blocking rate to be 1%. If 4-cell reuse pattern is adopted, please specify the minimun required bandwidth to constuct a GSM cellular operation. Note: Use Erlang B table (next page) ----------------------------------------- --

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