563489578934

Sec. 8–13 Study-Aid Examples 661
caused by multiple reflections. For this example, choose d 0 = 50 feet, n = 3, and X dB = 7 dB.
(The exponent, n, would be 2 for the free-space case and 4 for a 2-ray ground-reflection case.)
For a distance of 200 feet between the device and the base station, calculate the CNR at the
detector input of the base station receiver and the BER for the detected data at the receiver output.
Solution. See SA8_3.m. The CNR is obtained by using Eq. (8–67) to replace (L FS ) dB in
Eq. (8–43). Using the values just given, we get (P EIRP ) dBw =-30.86 dBw. T system = 1,540 K, and
L dB (200) = 88.18 dB. From Eq. (8–43) with the device located 200 feet from the base station, the
CNR is
a C N b dB
= 13.22 dB, 200 feet spacing
Also, using Eq. (8–44), we get (E b N 0 ) dB = 16.23 dB. For this case of OOK with (noncoherent)
envelope detection, the BER is obtained by using Eq. (7–58). The bit rate is R = 1T = 2 Mbs,
and the IF bandwidth is B P = 4 MHz. For a spacing of 200 feet between the device and the base
station, the BER of the base station output data stream is
P e = 1.36 * 10 -5 ,
200 feet spacing
Using other values for d in these equations, MATLAB can compute the CNR and BER over
a whole range of spacing from 50 feet to 500 feet. The MATLAB plots are shown in
Figures 8–40 and 8–41.
10 0
BER for data at receiver output
10 1
10 2
10 3
10 4
BER
10 5
10 6
10 7
10 8
10 9
50 100 150 200 250
10 10 d (feet)
300 350 400 450 500
Figure 8–41
BER for a wireless link. (Plot from SA8_3.m)