1
GATE ECE 2014 Set 4
+2
-0.6
Consider a discrete-time channel Y = X + Z, where the additive noise Z is signal- dependent. In particular, given the trasmitted symbol $$X\, \in \,\{ \, - \,a,\,\, + \,a\}$$ at any instant, the noise sample Z is chosen independently from a Gaussian distribution with mean $$\beta X$$ and unit variance. Assume a threshold detector with zero threshold at the receiver. When $$\beta$$ = 0 the BER was found to be $$Q\,(a) = 1\, \times \,{10^{ - 8}}$$. $$\left( {Q\,\,(v)\, = {1 \over {\sqrt {2\,\pi } }}\,\int\limits_v^\infty {{e^{ - {u^2}/2}}} } \right.$$ du, and for v > 1,
use $$Q\,(v) \approx \,{e^{ - {v^2}/2}}$$
When $$\beta = - \,0.3,\,$$ the BER is closed to
A
$${10^{ - 7}}$$
B
$${10^{ - 6}}$$
C
$${10^{ - 4}}$$
D
$${10^{ - 2}}$$
2
GATE ECE 2014 Set 4
+2
-0.6
Consider a communication scheme where the binary valued signal X satisfies P{X = + 1} = 0.75 and P {X = - 1} = 0.25. The received signal Y = X + Z, where Z is a Gaussian random variable with zero mean and variance $${\sigma ^2}$$. The received signal Y is fed to the threshold detector. The output of the threshold detector $${\hat X}$$ is: $$\hat X:\left\{ {\matrix{ { + \,1,} & {Y\, > \tau } \cr { - \,1,} & {Y\, \le \,\,\tau .} \cr } } \right.$$\$ To achieve a minimum probability of error $$P\{ \hat X\, \ne \,X\}$$, the threshold $$\tau$$ should be
A
strictly positive
B
zero
C
strictly negative
D
strictly positive, zero, or strictly negative depending on the nonzero value of $${\sigma ^2}$$
3
GATE ECE 2014 Set 2
+2
-0.6
Coherent orthogonal binary FSK modulation is used to transmit two equiprobable symbol waveforms $${s_1}\,(t)\, = \,\alpha \,\,\cos \,\,\,2\,\pi {f_1}\,t\,and\,\,{s_{2\,}}(t)\,\, = \,\alpha \,\,\cos \,\,\,2\,\pi {f_2}\,t$$, where $$\,\alpha = 4\,\,\,mV$$. Assume an AWGN channel with two-sided noise power spectral density $$\,{{{N_0}} \over 2} = 0.5\,\, \times \,{10^{ - 12}}$$ W/Hz. Using an optimal receiver and the relation $$Q(v) = {1 \over {\sqrt {2\,\pi } }}\,\int\limits_v^\infty {e{\,^{ - {u^2}/2}}} \,du$$, the bit error probability for a data rate of 500 kbps is
A
Q (2)
B
$$Q\left( {2\sqrt 2 } \right)$$
C
Q (4)
D
$$Q\left( {4\sqrt 2 } \right)$$
4
GATE ECE 2013
+2
-0.6
Let U and V be two independent zero mean Gaussian random variables of variances $${{1 \over 4}}$$ and $${{1 \over 9}}$$ respectively. The probability $$P(\,3V\, \ge \,\,2U)$$ is
A
4/9
B
1/2
C
2/3
D
5/9
GATE ECE Subjects
Signals and Systems
Network Theory
Control Systems
Digital Circuits
General Aptitude
Electronic Devices and VLSI
Analog Circuits
Engineering Mathematics
Microprocessors
Communications
Electromagnetics
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