exorcise

1. HW#1 Cellular Communication
1. Use the cosine law and hexagonal geometry to show that for the co-channel reuse ratio (𝑄)
this equation 𝑄 =
𝐷
𝑅
= √3𝑁 holds where 𝑁 = 𝑖2
+ 𝑗2
+ 𝑖𝑗.
2. When a user changes its position between cells, it should be transferred to a new BS which is
called “handoff”. The handoff should happen quickly from the time at which received power is
equal to threshold 𝑃𝑟,ℎ𝑎𝑛𝑑 𝑜𝑓𝑓 to the time that the minimum power for keeping the call is
received, 𝑃𝑟,𝑚𝑖𝑛𝑖𝑚𝑢𝑛. For the AMPS handoff happens within 10 seconds and for GSM within 2
seconds. What is the appropriate handoff margin, Δ = 𝑃𝑟,ℎ𝑎𝑛𝑑 𝑜𝑓𝑓 − 𝑃𝑟,𝑚𝑖𝑛𝑖𝑚𝑢𝑛, for a cell with
500 meters radius with a) AMPS b)GSM? Let the maximum speed of users be 35 m/s, and consider
just free space path loss 𝑃 = 𝑃0 (
𝑑0
𝑑
)
𝑛
where path loss exponent n=4.
3. Let N = 7, each cell has C = 100 channels, and users who make calls with λ = 0.01 per minute
with average holding time 3 minutes. For blocked-calls-cleared and a GOS of 2%, what is the
number of users which can be supported in this cell? Next, using 120 degree sectoring, and
otherwise identical system parameters, what is the number of users which can be supported in
this cell? What percentage reduction in capacity does sectoring with constant N cause?

2. 4. For the same system of previous problem, now
assume that with 120 degree sectoring, that N can be
reduced from 7 to 4. What number of users can be
supported? Why we can reduce the number of cells?
Compared to Omni directional, how much does SIR
improve with 60 and 120 degree sectoring?
5. In a cellular network, for increasing the number of users, the
number of cells in clusters is reduced to 7 providing more
channel reuse. However, the 10 dB SIR is not enough. What is
your idea for increasing SIR? Downtilt of directional antennas
can help for more SIR. The figure (a) shows the vertical pattern
of three transmitting antennas. If the radius of cell is 500m and
the downtilt is 10 degree from horizon and the height of
antennas is 10m, what position in the cell is in the main lobe of
antenna? Which of those antennas can improve SIR by 5 dB?
Hint: consider the figure (b).
 Due date is 8th Farvardin 99
 Please upload your answers as Name_StdNum.zip in CECM
(a)
(b)