Polytechnic University, Dept. of Electrical and Computer Engineering
EE 3414, Multimedia Communication Systems-Part I
Spring 2003
Homework 5
Reading Assignment: (All are provided as handouts) 1. N. Chandran and M. C. Valenti, “Three generations of cellular wireless systems.” IEEE Potentials , Volume: 20, Issue: 1, pp. 32 -35, Feb/Mar 2001. 2. M. Frodigh, S. Parkvall, C. Roobol, P. Johansson and P. Larsson, “Future- generation wireless networks.” IEEE Personal Communications, Volume: 8, Issue: 5, pp. 10-17, Oct 2001. 3. “Wi-Fi hotspot networks sprout like mushrooms.” IEEE Spectrum , Volume: 39, Issue: 9, pp. 18-20, Sep 2002. 4. R. Schneiderman, “Bluetooth's slow dawn.” IEEE Spectrum , Volume: 37, Issue: 11, pp. 61-65, Nov 2000.
Written Assignment:
1. Consider the following vector representation for the 8-PSK modulation scheme
x x x x xA x x x
The radius of the circle is A. The 8 points (corresponding to modulating signals) are uniformly distributed around the circle. Find a. The minimum distance dmin b. Find the average energy Eav c. How many number of bits/symbol can this modulation scheme transmit?
2. What is fading? Is it advantageous to have fading in a wireless channel? Explain quantitavely using lecture notes for Lecture 8. You may find Figure 1 helpful. 3. Suppose we have an application that requires error probability (bit error rate, denoted by BER) of 10-3. What is the signal to noise ratio (SNR) per bit in dB required for a fading channel with no diversity (or equivalently diversity level 1)? Let this SNR be (SNR1)dB. What is SNR required if we have 2 level diversity? Denote this by (SNR2)dB. What about 3 level diversity (denoted by (SNR3)dB)? Find the ratios SNR1/ SNR2 and SNR2/ SNR3. Note that these ratios are not in dB. Comment on why diversity is useful. You may find lecture notes of Lecture 8 and Figure 1 helpful.
Figure 1: Bit error rate versus SNR for fading channels
4. Consider a CDMA system that uses the spreading codes (in vector form) s1= (1,1,1,1), s2= (1,-1,1,-1), s3= (1,1,-1,-1) and s4= (1,-1,-1,1). Show that these sequences form an orthogonal set, that is