Digital Communications - Communications - Electronics & Communication Engineering Previous Year Questions

1

2012 · Electronics & Communication Engineering · Communications · Digital Communications

Electronics & Communication Engineering (EC) 2012

In a baseband communications link, frequencies upto 3500 Hz are used for signaling. Using a raised cosine pulse with 75% excess bandwidth and for no inter-symbol interference, the maximum possible signaling rate in symbols per second is

A

1750

B

2625

C

4000

D

5250

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2

2012 · Electronics & Communication Engineering · Communications · Digital Communications

Electronics & Communication Engineering (EC) 2012

A BPSK scheme operating over an AWGN channel with noise power spectral density of \( N_0/2 \), uses equiprobable signals \( s_1(t) = \sqrt{\frac{2E}{T}} \sin(\omega_c t) \) and \( s_2(t) = -\sqrt{\frac{2E}{T}} \sin(\omega_c t) \) over the symbol interval (0, T). If the local oscillator in a coherent receiver is ahead in phase by 45° with respect to the received signal, the probability of error in the resulting system is

A

\(Q\left( \sqrt{\frac{2E}{N_0}} \right) \)

B

\(Q\left( \sqrt{\frac{E}{N_0}} \right) \)

C

\(Q\left( \sqrt{\frac{E}{2N_0}} \right) \)

D

\(Q\left( \sqrt{\frac{E}{4N_0}} \right) \)

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3

2013 · Electronics & Communication Engineering · Communications · Digital Communications

Electronics & Communication Engineering (EC) 2013 [Session 1]

The bit rate of a digital communication system is \( R \) kbits/s. The modulation used is 32-QAM. The minimum bandwidth required for ISI free transmission is

A

\(R/10 \) Hz

B

\(R/10 \) kHz

C

\(R/5 \) Hz

D

\(R/5 \) kHz

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4

2013 · Electronics & Communication Engineering · Communications · Digital Communications

Electronics & Communication Engineering (EC) 2013 [Session 1]

If the detection threshold is 1, the BER will be

A

\(\frac{1}{2}\)

B

\(\frac{1}{4}\)

C

\(\frac{1}{8}\)

D

\(\frac{1}{16}\)

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5

2013 · Electronics & Communication Engineering · Communications · Digital Communications

Electronics & Communication Engineering (EC) 2013 [Session 1]

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

A

\(\frac{1}{2}\)

B

\(\frac{4}{5}\)

C

1

D

\(\frac{3}{2}\)

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6

2013 · Electronics & Communication Engineering · Communications · Digital Communications

Electronics & Communication Engineering (EC) 2013 [Session 2]

The bit rate of a digital communication system is $R$ kbits/s. The modulation used is 32-QAM. The minimum bandwidth required for ISI free transmission is

A

$R/10$ Hz

B

$R/10$ kHz

C

$R/5$ Hz

D

$R/5$ kHz

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7

2013 · Electronics & Communication Engineering · Communications · Digital Communications

Electronics & Communication Engineering (EC) 2013 [Session 3]

The bit rate of a digital communication system is R kbits/s. The modulation used is 32-QAM. The minimum bandwidth required for ISI free transmission is

A

R/10 Hz

B

R/10 kHz

C

R/5 Hz

D

R/5 kHz

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8

2013 · Electronics & Communication Engineering · Communications · Digital Communications

Electronics & Communication Engineering (EC) 2013 [Session 4]

The bit rate of a digital communication system is \(R\) kbits/s. The modulation used is 32-QAM. The minimum bandwidth required for ISI free transmission is

A

\(R/10\) Hz

B

\(R/10\) kHz

C

\(R/5\) Hz

D

\(R/5\) kHz

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9

2014 · Electronics & Communication Engineering · Communications · Digital Communications

Electronics & Communication Engineering (EC) 2014 [Session 2]

Coherent orthogonal binary FSK modulation is used to transmit two equiprobable signal 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 \(\frac{N_0}{2} = 0.5 \times 10^{-12}\) W/Hz. Using an optimal receiver and the relation \(Q(v) = \frac{1}{\sqrt{2\pi}} \int_{v}^{\infty} e^{-u^2/2} du\), the bit error probability for a data rate of 500 kbps is

A

\(Q(2)\)

B

\(Q(2\sqrt{2})\)

C

\(Q(4)\)

D

\(Q(4\sqrt{2})\)

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10

2014 · Electronics & Communication Engineering · Communications · Digital Communications

Electronics & Communication Engineering (EC) 2014 [Session 4]

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: \[\hat{X} = \begin{cases} +1, & Y > \tau \\ -1, & Y \le \tau \end{cases}\]. To achieve a minimum probability of error \(P\{\hat{X} \neq X\}\), 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 \(\sigma^2\)

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11

2014 · Electronics & Communication Engineering · Communications · Digital Communications

Electronics & Communication Engineering (EC) 2014 [Session 4]

An M-level PSK modulation scheme is used to transmit independent binary digits over a band-pass channel with bandwidth 100 kHz. The bit rate is 200 kbps and the system characteristic is a raised-cosine spectrum with 100% excess bandwidth. The minimum value of M is __________

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12

2014 · Electronics & Communication Engineering · Communications · Digital Communications

Electronics & Communication Engineering (EC) 2014 [Session 4]

Consider a discrete-time channel Y = X + Z, where the additive noise Z is signal-dependent. In particular, given the transmitted symbol X ∈ {−a, +a} at any instant, the noise sample Z is chosen independently from a Gaussian distribution with mean βX and unit variance. Assume a threshold detector with zero threshold at the receiver.

When β = 0, the BER was found to be Q(a) = 1 × 10⁻⁸ (Q(v) = 1/√(2π) ∫_v^∞ e^−u2/2 du, and for v > 1, use Q(v) ≈ e^−v2/2).

When β = −0.3, the BER is closest to

A

10⁻⁷

B

10⁻⁶

C

10⁻⁴

D

10⁻²

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13

2016 · Electronics & Communication Engineering · Communications · Digital Communications

Electronics & Communication Engineering (EC) 2016 [Session 1]

Consider binary data transmission at a rate of 56 kbps using baseband binary pulse amplitude modulation (PAM) that is designed to have a raised-cosine spectrum. The transmission bandwidth (in kHz) required for a roll-off factor of 0.25 is ______

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14

2016 · Electronics & Communication Engineering · Communications · Digital Communications

Electronics & Communication Engineering (EC) 2016 [Session 1]

A digital communication system uses a repetition code for channel encoding/decoding. During transmission, each bit is repeated three times (0 is transmitted as 000, and 1 is transmitted as 111). It is assumed that the source puts out symbols independently and with equal probability. The decoder operates as follows: In a block of three received bits, if the number of zeros exceeds the number of ones, the decoder decides in favor of a 0, and if the number of ones exceeds the number of zeros, the decoder decides in favor of a 1. Assuming a binary symmetric channel with crossover probability p = 0.1, the average probability of error is __________

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15

2016 · Electronics & Communication Engineering · Communications · Digital Communications

Electronics & Communication Engineering (EC) 2016 [Session 2]

A speech signal is sampled at 8 kHz and encoded into PCM format using 8 bits/sample. The PCM data is transmitted through a baseband channel via 4-level PAM. The minimum bandwidth (in kHz) required for transmission is ______

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16

2016 · Electronics & Communication Engineering · Communications · Digital Communications

Electronics & Communication Engineering (EC) 2016 [Session 2]

An information source generates a binary sequence \(\{a_n\}\). \(a_n\) can take one of the two possible values \(-1\) and \(+1\) with equal probability and are statistically independent and identically distributed. This sequence is precoded to obtain another sequence \(\{b_n\}\), as \(b_n = a_n + k a_{n-3}\) . The sequence \(\{b_n\}\) is used to modulate a pulse \(g(t)\) to generate the baseband signal \(X(t) = \sum_{n=-\infty}^{\infty} b_n g(t - nT)\), where \(g(t) = \begin{cases} 1, & 0 \leq t \leq T \\ 0, & \text{otherwise}. \end{cases}\) If there is a null at \(f = \frac{1}{3T}\) in the power spectral density of \(X(t)\), then \(k\) is ______

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17

2016 · Electronics & Communication Engineering · Communications · Digital Communications

Electronics & Communication Engineering (EC) 2016 [Session 2]

An ideal band-pass channel 500 Hz - 2000 Hz is deployed for communication. A modem is designed to transmit bits at the rate of 4800 bits/s using 16-QAM. The roll-off factor of a pulse with a raised cosine spectrum that utilizes the entire frequency band is ________

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18

2016 · Electronics & Communication Engineering · Communications · Digital Communications

Electronics & Communication Engineering (EC) 2016 [Session 3]

A binary baseband digital communication system employs the signal \( p(t) = \begin{cases} \frac{1}{\sqrt{T_s}} & 0 \le t \le T_s \\ 0 & \text{otherwise} \end{cases} \) for transmission of bits. The graphical representation of the matched filter output y(t) for this signal will be

A

A graph showing y(t) as a constant value from t=0 to t=2T_s, dropping to zero at t=2T_s.

B

A graph showing y(t) rising linearly from 0 at t=0 to 0.5 at t=T_s, constant until t=2T_s.

C

A graph showing y(t) rising linearly from 0 at t=0 to 1 at t=T_s, then falling linearly to 0 at t=2T_s.

D

A graph showing y(t) rising linearly from 0 at t=0 to 1 at t=T_s/2, then falling linearly to 0 at t=T_s.

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19

2017 · Electronics & Communication Engineering · Communications · Digital Communications

Electronics & Communication Engineering (EC) 2017

A sinusoidal message signal is converted to a PCM signal using a uniform quantizer. The required signal-to-quantization noise ratio (SQNR) at the output of the quantizer is 40 dB. The minimum number of bits per sample needed to achieve the desired SQNR is ________

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20

2019 · Electronics & Communication Engineering · Communications · Digital Communications

Electronics & Communication Engineering (EC) 2019

A single bit, equally likely to be 0 and 1, is to be sent across an additive white Gaussian noise (AWGN) channel with power spectral density \(N_0/2\). Binary signaling, with \(0 \to p(t)\) and \(1 \to q(t)\), is used for the transmission, along with an optimal receiver that minimizes the bit-error probability. Let \(\varphi_1(t), \varphi_2(t)\) form an orthonormal signal set. If we choose \(p(t) = \varphi_1(t)\) and \(q(t) = -\varphi_1(t)\), we would obtain a certain bit-error probability \(P_b\). If we keep \(p(t) = \varphi_1(t)\), but take \(q(t) = \sqrt{E} \varphi_2(t)\), for what value of \(E\) would we obtain the same bit-error probability \(P_b\)?

A

0

B

1

C

2

D

3

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