Solutions for Exercises (Wireless Communications)

Solutions for Exercises (Wireless Communications)

Q1.

If a total of 33MHz of bandwidth is allocated to a particular FDD cellular telephone system which uses two 25kHz simplex channels to provide full duplex voice and control channels, computer the number of channels available per cell if a system uses: (a) 4-cell reuses, (b) 7-cell reuses, (c) 12 cell reuse. If 1 MHz of the allocated spectrum is dedicated to control channels, determine an equitable distribution of control channels and voice channels is each cell for each of the three systems.

Solution

Given:

Total bandwidth=33MHz

Channel bandwidth=25 kHz2 simplex channels=50 kHz/duplex channel

Total available channels = 33000/50 = 660 channels.

A 1 MHz spectrum for control channels implies that there are 1000/50 = 20 control channels out of the 660 channels available.

In practice, only the 640 voice channels would be allocated since the control channels are allocated separately as 1 per cell.

Here, the 640 voice channels must be equitable distributed to each cell within the cluster.

(a) For N = 4 , we can have 5 control channels and 160 voice channels per cell. In practice, however, each cell only needs a single control channel (the controls have a greater reuse distance than the voice channels). Thus, one control channel and 160 voice channels would be assigned to each cell.

(b) For N=7, each cell have one control channel, four cells would have 91 voice channels, and three cells would have 92 voice channels. (491+392=640)

(c) For N=12, each cell would have one control channel, 8 cells would have 53 voice channels, and, 4 cells would have 54 voice channels. (853+454=640)

Q2

If a signal to interference ratio of 15 dB is required for satisfactory forward channel performance of a cellular system, what is the frequency reuse factor and cluster size that should be used for maximum capacity if the path loss exponent is (a) n = 4, (b) n = 3 ? Assume that there are 6 co-channels cells in the first tier, and all of them are at the same distance from the mobile. Use suitable approximations.

Solution

(a) n = 4

First, let us consider a 7-cell reuse pattern.

the co-channel reuse ratio Q=D/R = 4.583.

the signal-to-noise interference ratio is given by

S/1 = (1/6)  (4.583)4 = 75.3 = 18.66dB.

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