Unformatted text preview: COLUMBIA UNIVERSITY
ELEN E4703 Wireless Communications Prof. Diament Midterm Exam -- 75 minutes March 19, 2007
CLOSED-BOOK EXAM -- No books, no notes, no scratch paper. CALCULATOR ALLOWED. l. [20%] Consider an idealized hexagonal model of a cellular system with base stations at
the centers of the cells. The cluster size is 13 and we measure the interfering signal level from the
nearest co—channel cell to be 28 dB below the weakest in-cell power level. What is the path loss exponent for the environment?
Some possibly relevant formulas: N = i2 + ij + j2 D/R = (3N)"2 S/I = (D/R)“/io 2. [25%] A cell phone used by a truck driver operates at 1.1 GHz and has a short antenna,
2.2 m above the roadway. The base station has an antenna of 16 dB gain installed 13 m above the
ground. The truck is 8.8 km from the base station. By how many dB is the received signal weaker
than it would have been if the ground were perfectly absorbing rather than reﬂective? Some formulas: GlAez/4wd2 G1G2K2/(41td)2 Glozhlzhzz/d4 Glekzo/(41t)3d12d22 3. [20%] A trunked intercom system has 12 channels, of which 8 are currently busy. The
traffic intensity averages 0.6 erlangs per user and the entire system can handle up to 7.5 erlangs.
The GOS is specified to be a 2% probability of blocking. If you had tables of the erlb(C, A) and erlc(C, A) functions, how would you determine
whether the system can meet the speciﬁcation of the GOS? Specify the arguments C, A that you would use in the appropriate function. 4. [15%] A novel type of antenna is claimed to produce a uniform radiation intensity
within a solid angle of 0.45 steradians in a northerly direction but also radiates backward
uniformly within a solid angle of 0.75 steradians in a southerly direction, at half the intensity of
the northward radiation. Assume the antenna is lossless. Find the directivity of this antenna. Recall: D = (41t/P)(dP/dﬂ)m 5. [20%] In a system for which the lognormal path loss model is valid, the noise ﬂoor
kTBF is known to be —80 dBm. The statistical average of the power level at the receiver is
measured as -45 dBm with a standard deviation of 5.5 dB. What is the maximum signal-to-noise
ratio (SNR, in dB) that can be speciﬁed at the receiver to ensure that there be no more than a 2% probability that the received signal will drop below the noise threshold?
From tables: Q(0.02) = 0.492 Q(0.98) = 0.164 Q(2.054) = 0.02 Q(——2.054) = 0.98 ...
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