1
GATE ECE 2014 Set 1
+2
-0.6
Consider a random process $$X\left( t \right) = \sqrt 2 \sin \left( {2\pi t + \varphi } \right),$$ where the random phase $$\varphi$$ is uniformly distributed in the interval $$\left[ {0,\,\,2\pi } \right].$$ The auto - correlation $$E\left[ {X\left( {{t_1}} \right)X\left( {{t_2}} \right)} \right]$$ is
A
$$\cos \left( {2\pi \left( {{t_1} + {t_2}} \right)} \right)$$
B
$$\sin \left( {2\pi \left( {{t_1} - {t_2}} \right)} \right)$$
C
$$\sin \left( {2\pi \left( {{t_1} + {t_2}} \right)} \right)$$
D
$$\cos \left( {2\pi \left( {{t_1} - {t_2}} \right)} \right)$$
2
GATE ECE 2014 Set 1
Numerical
+2
-0
Let $$Q\left( {\sqrt y } \right)$$ be the BER of a BPSK system over an AWGN channel with two - sided noise power spectral density N0/2. The parameter 𝛾 is a function of bit energy and noise power spectral density. A system with two independent and identical AWGN channels with noise power spectral density N0/2 is shown in the figure. The BPSK demodulator receives the sum of outputs of both the channels

If the BER of this system is $$Q\left( {b\sqrt y } \right),$$ then the value of b is -----------.

3
GATE ECE 2013
+2
-0.6
Bits 1 and 0 are transmitted with equal probability. At the receiver, the pdf of the respective received signals for both bits are as shown below.

If the detection threshold is 1, the BER will be

A
$${1 \over 2}$$
B
$${1 \over 4}$$
C
$${1 \over 8}$$
D
$${1 \over 16}$$
4
GATE ECE 2013
+2
-0.6
Bits 1 and 0 are transmitted with equal probability. At the receiver, the pdf of the respective received signals for both bits are as shown below.

The optimum threshold to achieve minimum bit error rate (BER) is

A
$${1 \over 2}$$
B
$${4 \over 5}$$
C
1
D
$${3 \over 2}$$
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