1
GATE ECE 2011
+2
-0.6
A four phase and an eight-phase signal constellation are shown in the figure below.

For the constraint that the minimum distance between pairs of signal points be d for both constellations, the radii r1, and r2 of the circles are

A
r1 = 0.707d, r2 = 2.782d
B
r1 = 0.707d, r2 = 1.932d
C
r1 = 0.707d, r2 = 1.545d
D
r1 = 0.707d, r2 = 1.307d
2
GATE ECE 2011
+2
-0.6
A four phase and an eight-phase signal constellation are shown in the figure below.

Assuming high SNR and that all signals are equally probable, the additional average transmitted signal energy required by the 8-PSK signal to achieve the same error probability as the 4-PSK signal is

A
11.90 dB
B
8.73 dB
C
6.79 dB
D
5.33 dB
3
GATE ECE 2010
+2
-0.6
Consider a base band binary PAM receiver shown below. The additive channel noise $$n(t)$$ is white with power spectral density $${S_N}\left( f \right) = {N_0}/2 = {10^{ - 20}}$$ $$W/Hz$$. The low-pass filter is ideal with unity gain and cut -off frequency $$1MHz$$. Let $${Y_k}$$ represent the random variable $$y\left( {{t_k}} \right)$$.
$${Y_k} = {N_k}$$ if transmitted bit $${b_k} = 0$$
$${Y_k} = a + {N_k}$$ if transmitted bit $${b_k} = 1$$
Where $${b_k} = 0$$ represents the noise sample value. The noise sample has a probability density function, $${P_{{N_k}}}\left( n \right)\,\,\,\,\,\,\, = 0.5\alpha {e^{ - \alpha \left| n \right|}}$$ (This has mean zero and variance $$2/{\alpha ^2}$$). Assume transmitted bits to be equiprobable and threshold $$z$$ is set to $$a/2 = {10^{ - 6}}V$$.

The value of the parameter $$\alpha$$( in V-1 ) is

A
$${10^{10}}$$
B
$${10^{7}}$$
C
$$1.414 \times {10^{ - 10}}$$
D
$$2 \times {10^{ - 20}}$$
4
GATE ECE 2010
+2
-0.6
Consider a base band binary PAM receiver shown below. The additive channel noise $$n(t)$$ is white with power spectral density $${S_N}\left( f \right) = {N_0}/2 = {10^{ - 20}}$$ $$W/Hz$$. The low-pass filter is ideal with unity gain and cut -off frequency $$1MHz$$. Let $${Y_k}$$ represent the random variable $$y\left( {{t_k}} \right)$$.
$${Y_k} = {N_k}$$ if transmitted bit $${b_k} = 0$$
$${Y_k} = a + {N_k}$$ if transmitted bit $${b_k} = 1$$
Where $${b_k} = 0$$ represents the noise sample value. The noise sample has a probability density function, $${P_{{N_k}}}\left( n \right)\,\,\,\,\,\,\, = 0.5\alpha {e^{ - \alpha \left| n \right|}}$$ (This has mean zero and variance $$2/{\alpha ^2}$$). Assume transmitted bits to be equiprobable and threshold $$z$$ is set to $$a/2 = {10^{ - 6}}V$$.

The probability of bit error is

A
$$0.5 \times {e^{ - 3.5}}$$
B
$$0.5 \times {e^{ - 5}}$$
C
$$0.5 \times {e^{ - 7}}$$
D
$$0.5 \times {e^{ - 10}}$$
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