Digital Communication Systems · Communications · GATE ECE
Marks 1
Consider a discrete memoryless source with an alphabet of four source symbols. $s(t)$ is a multi-level ( $-1,0,+1,+2$ ) signal representing a long sequence of random symbols from the above source which is generating $10^4$ symbols per second. Which of the following options is the correct value of equivalent Nyquist bandwidth of $s(t)$ ?
A wireless digital transmission scheme is using 16-QAM over an additive white Gaussian noise channel and a maximum-likelihood receiver. Consider the information bit rate from source to be $4 \times 10^6$ bits per second.
The minimum transmission bandwidth (in MHz) of the modulated signal necessary for optimum recovery of information at the receiver is $\_\_\_\_$ .
(rounded off to two decimal places)
A digital communication system transmits through a noiseless bandlimited channel $[-W, W]$. The received signal $z(t)$ at the output of the receiving filter is given by $z(t) = \sum\limits_{n} b[n]x(t-nT)$ where $b[n]$ are the symbols and $x(t)$ is the overall system response to a single symbol. The received signal is sampled at $t = mT$. The Fourier transform of $x(t)$ is $X(f)$. The Nyquist condition that $X(f)$ must satisfy for zero intersymbol interference at the receiver is ______.
Let H(X) denote the entropy of a discrete random variable X taking K possible distinct real values. Which of the following statements is/are necessarily true?
A symbol stream contains alternate QPSK and 16-QAM symbols. If symbols from this stream are transmitted at the rate of 1 mega-symbols per second, the raw (uncoded) data rate is _________ mega-bits per second (rounded off to one decimal place).
A message signal having peak-to-peak value of 2 V , root mean square value of 0.1 V and bandwidth of 5 kHz is sampled and fed to a pulse code modulation (PCM) system that uses a uniform quantizer. The PCM output is transmitted over a channel that can support a maximum transmission rate of 50 kbps . Assuming that the quantization error is uniformly distributed, the maximum signal to quantization
noise ratio that can be obtained by the PCM system (rounded off to two decimal places) is $\_\_\_\_$ .
A 4 kHz sinusoidal message signal having amplitude 4 V is fed to a delta modulator (DM) operating at a sampling rate of 32 kHz . The minimum step size required to avoid slope overload noise in the DM (rounded off to two decimal places) is $\_\_\_\_$ V.
A digital communication system transmits a block of $N$ bits. The probability of error in decoding a bit is $\alpha$. The error event of each bit is independent of the error events of the other bits. The received block is declared erroneous of at least one of its bits is decoded wrongly. The probability that the received block is erroneous, is
Marks 2
The average bit error rate at the input of a $(7,4,1)$ Hamming decoder is 0.10 . The probability that the decoder will fail to decode a received word correctly is $\_\_\_\_$ . (rounded off to two decimal places)
The information bit sequence {1 1 1 0 1 0 1 0 1} is to be transmitted by encoding with Cyclic Redundancy Check 4 (CRC-4) code, for which the generator polynomial is $C(x) = x^4 + x + 1$. The encoded sequence of bits is ____.
Consider a channel over which either symbol xA or symbol xB is transmitted. Let the output of the channel Y be the input to a maximum likelihood (ML) detector at the receiver. The conditional probability density functions for y given xA and xB are :
$${f_{\left. Y \right|{x_A}}}(y) = {e^{ - (y + 1)}}u(y + 1)$$,
$${f_{\left. Y \right|{x_B}}}(y) = {e^{(y - 1)}}(1 - u(y - 1))$$,
where, u( . ) is the standard unit step function. The probability of symbol error for this system is _________ (rounded off to two decimal places).
In a digital communication system, a symbol $S$ randomly chosen from the set $\left\{s_1, s_2, s_3, s_4\right\}$ is transmitted. It is given that $s_1=-3, s_2=-1, s_3=+1$ and $s_4=+2$. The received symbol is $Y=S+W . W$ is a zero mean unit - variance Gaussian random variable and is independent of $S . P_i$ is the conditional probability of symbol error for the maximum likelihood (ML) decoding when the transmitted symbol $S=s_i$. The index $i$ for which the conditional symbol error probability $P_i$ is the highest is $\_\_\_\_$ .
$$\,{u_o}(t) = 5\,\cos \,(20000\,\pi \,t);\,0 \le \,\,t\, \le \,T,$$ and
$${u_o}(t) = 5\,\cos \,(22000\,\pi \,t);\,0 \le \,\,t\, \le \,T,$$
where T is the bit-duration interval and t is in seconds. Both $${u_o}(t)$$ and $${u_1}(t)$$ are zero output the interval $$0 \le \,\,t\, \le \,T$$. With a matched filter (correlator ) based receiver, the smallest positive value of T (in milliseconds) required to have $${u_o}(t)$$ and $${u_1}(t)$$ uncorrelated is
The number of quantitization levels required to reduce the quantization noise by a factor of 4 would be
Assuming the signal to be uniformly distributed between its peak values, the signal to noise ratio at the quantizer output is
If the bits 0 and 1 are transmitted using bipolar pulses, the minimum bandwidth required for distortion free transmission is
x(t) = 125t(u(t) - u (t - 1) + (250 - 125t) (u (t - 1) - u (t - 2 )) so that slope - overload is avoided, would be
Group
1. FM
2. DM
3. PSK
4. PCM
Group 2
P: Slope overload
Q: $${\mu - law}$$
R: Envelope detector
S: Capture effect
T: Hilbert transform
U: Matched filter
The source output is transmitted using two modulation schemes, namely Binary PSK (BPSK) and Quadrature PSK (QPSK).
Let $${B_1}$$ and $${B_2}$$ be the bandwidth requirements of BPSK and QPSK respectively. Assuming that the bandwidth of the above rectangular pulses is 10 kHz, $${B_1}$$ and $${B_2}$$ are
Marks 8
Marks 10
(a) Sketch the impulse response, h(t), of the matched filter.
(b) Sketch the output, y(t), of the matched filter. Fully label your diagram.
(c) If the input to the matched filter consists of the signal, x(t), plus additive white noise of two sided spectral density of $${10^{ - 6}}$$ watts/Hz, find the maximum output SNR of the matched filter.
