Faculty of Engineering Sciences
Electronics and Communications Department
Fall 2012
ELE 353
Data Communication Systems
Sheet(7)
Performance Analysis of General Binary systems
Dr. Amr Abouel Magd Ahmed
Eng : Ahmed Al Wakeel
2012 – 2013
Sheet ( 7 )
(1)
In coherent schemes, a small pilot is added for synchronization. Because the pilot does
not carry information, it causes degradation in Pb. Consider coherent PSK using the
following two pulses of duration Tb each:
𝑝(𝑡) = 𝐴 √1 − 𝑚2 cos 𝑤𝑐 𝑡 + 𝐴𝑚 sin 𝑤𝑐 𝑡
𝑞(𝑡) = −𝐴 √1 − 𝑚2 cos 𝑤𝑐 𝑡 + 𝐴𝑚 sin 𝑤𝑐 𝑡
Where 𝐴𝑚 sin 𝑤𝑐 𝑡 is the pilot. Show that when the channel noise is white gaussian,
𝟐𝑬𝒃 (𝟏 − 𝒎𝟐 )
√
𝑷𝒃 = 𝑸 [
]
𝓝
(2)
Binary data is transmitted by using a pulse p(t) for 0 and a pulse 3p(t) for 1. Determine
the error probability Pb of this receiver as a function of Eb/N if 0 and 1 are equiprobable.
(3)
It is required to transmit 2.08 * 106 binary digits per second with Pb ≤ 10-6. There
possible schemes are considered:
(a) Binary.
(b) 16-ary ASK.
(c) 16-ary PSK.
The channel noise PSD is Sn(ω) = 10-8. Determine the transmission bandwidth and the
signal power required at the receiver input in each case.
(4)
A binary source emits data at a rate of 256,000 bits/s. Multi amplitude-shift keying
(MASK) with M = 2, 16 and 32 is considered. In each case, determine the signal power
required at the receiver input and the minimum transmission bandwidth required if Sn(ω)
= 10-8 and the bit error rate Pb is required to be less than 10-7.
(5)
Repeat Problem 4 for M-ary PSK.
(6)
A binary PCM system using polar NRZ signaling operates just above the error threshold
with an average probability of error equal to 10-6. Suppose that the signaling rate is
doubled. Find the new value of the average probability of error.
(7)
A continuous time signal is sampled and then transmitted as a PCM signal. The random
variable at the input of the decision device in the receiver has a variance of 0.01 volts2.
(a) Assuming the use of polar NRZ signaling, determine the pulse amplitude that must
be transmitted for the average error rate not to exceed 1 bit in 108 bits.
(b) If the added presence of interference causes the error rate to increase to 1 bit in 106
bits, what is the variance of the interference?
(8)
A slow FH/MFSK system has the following parameters:
Number of bits per MFSK symbol = 4
Number of MFSK symbols per hop = 5
Calculate the processing gain of the system.
(9)
A fast FH/MFSK system has the following parameters:
Number of bits per MFSK symbol = 4
Number of MFSK symbols per hop = 4
Calculate the processing gain of the system.