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We have a spectrum of 20MHz that we will use on a wireless cellular system, which requires 50kHz per channel. The system is using cluster size K = 4 and the radius of every cell is R = 1 km.

a) Find the distance between two cells that use the same kind of channels.

My ans: We can use the formula: \$D = R\sqrt{3K} = 3.4 km\$

b) Calculate the max number of calls that could be served simultaneously from the system per km2.

My ans: From given, \$\dfrac{20000 kHz}{50 kHz} = 400\$ channels, we have though K = 4, so we have 100 channel per cell. So I believe that 100 is the max calls per km2, because from given it says that cell radius is 1 km.

c) If the system becomes duplex, the users of the system during the peak hour, they do on average 1.5 calls/hour with average duration 120sec. We have Erlang-B and the GoS is 1%. Calculate the average number of calls per hour for every cell and the spectral efficiency.

My ans: Duplex: \$\dfrac{20000 kHz}{100 kHz} = 200\$ channels per cluster, so we have 50 channels per cell. Gos = 1% and cell got 50c, so from Erlang-b table we find that A = 37.90 or just 37.

Though \$A = \lambda H\$, so \$\lambda\$ = 37 calls / 1.5 calls per hour = 26 calls/hour.

Now this is what I tried so far but I am not sure if any of this is correct, so I just want a second opinion.

The last part, wants to find the spectral efficiency. But I really can't find how to do this. I searched a bit, and found this formula:

$$SE = \frac{A_c}{B_T\;C\;M\;S_u}$$

Though I am not sure how to use it exactly.

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Check WCY Lee's book these are old AMPS calculation methods for spectral efficiency, there are some graphical methods to estimate efficiency using hexagonal geometries.

Page 186 - Mobile Communications Design Fundamentals (By William C. Y. Lee)

Also to calculate offerred traffic you have to convert call attempts/hr to attempts/second, thus

\$ \LARGE A_o= \frac{\frac{1.5 calls}{hr}}{\frac{3600s}{hr}} \times 120s \$

\$ \Large A_o= 0.050 \text{ erlangs or 50 } \frac{mErlangs}{sub}\$

Here is the link for the book:

Mobile Communications Design Fundamentals W CY Lee

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