1.a) If a mobile radio link operates with a 9 dB SNR and uses a 200 KHz channel, find the theoretic maximum data capacity based on noise/bandwidth (Shannon formula).

  SNR=0.9

Max data rate =   ? 185Kbps

b) If the same channel uses GMSK modulation (a binary scheme), what is the maximum data capacity based on number of symbols/bandwidth (Nyquist formula)?

GMSK n = 1 bits/symbol= m=2

Max data rate = 2 2 * 200,000 Hz = 400 Kbps

c) How do these numbers compare to the GSM (DCS-1900) standard which uses a 200 KHz channel, GMSK, and offers a data rate of 270.8 Kbps? Explain why there is a difference.

Max data rate = = 270.8 *1000 bps =

S/N= 0.407

We can see from the above calculation, GSM(DCS-1900)s' SNR is lower than

Max data rate = 2bps = 270.8*1000 bps= 2* 400,000 bps

M= symbols = 0.204

2. A certain area is covered by a cellular radio system with 84 cells and a cluster size of N. 300 voice channels are available in the system. Users are uniformly distributed over the area covered by the cellular system, and the offered traffic per user is 0.06 Erlang. Assume that blocked calls are cleared and the designated blocking probability is 1%.

1. Determine the maximum carried traffic per cell if cluster size N = 4 is used. Repeat for cluster sizes of 7 and 12.

Maximum carried traffic per cell = 300 / 84?4 channels

1. Determine the maximum number of users that can be served by the system for a blocking probability of 1% and cluster size of N = 4. Repeat for cluster sizes of 7 and 12.

   If cluster size if N=4

   There are 84/4=21 clusters in system

   Maximum carried traffic per clusters= 4*4= 16 channels A=U=1%*16=U0.06 => U?3

   Maximum number of users= 3*21=63 users

   If cluster size if N=7

   There are 84/7=12 clusters in system

   Maximum carried traffic per cluster= 4*7 = 28 channels A=U=1%*28=U0.06=> U?5

   Maximum number of users=5*12=60 users

   If cluster size if N=12

   There are 84/12=7 clusters in system

   Maximum carried traffic per cluster= 4*12 = 48 channels A=U=1%*48=U0.06=> U=8

   Maximum carried traffic per cluster=8*7=56 users

3. Think of a phase diagram and the points representing valid symbols for a PSK scheme (see figure 2.29).

a) How can a receiver decide which symbol was originally sent when a received "point" lies somewhere in between other points in the diagram?

b) In regards to error detection/correction, why is it difficult to code more and more bits per phase shift?

4.

a) Explain how handoffs are initiated in first generation cellular systems.

b) Explain how handoffs are initiated in second generation (and later) cellular systems.

c) Why is MAHO possible for second-generation cell phones but not for first generation phones?

5. Assume we have a single branch of a Rayleigh fading signal and that the average Signal to Noise Ratio (SNR) is 25 dB.

a) Calculate the probability that the instantaneous SNR drops below 10 dB.

b) Repeat the calculation for a number of branches M = 2, 3, and 4.

c) Do increases in branches of diversity follow the law of diminishing returns? Explain why or why not.

(The law of diminishing returns says that you get a smaller and smaller return (benefit) as you invest more and more. An example would be: if you spend $100 on insulating your home, you might save $100 on heating costs. Then if you spend another $100, you might only save $50 (because all the major leaks were sealed using the first $100). If you spend yet another $100, you might get no return or benefit from your investment. So the returns gets smaller and smaller ($100, $50, $0) with each addition of resources. Sometimes the law of diminishing returns holds and sometimes it does not.)