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GATE EC Communications Previous Year Questions

60 solved GATE EC questions on Communications, drawn from 9 exam years and grouped by year. Every question shows the official answer and a step-by-step solution.

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Revision companion

Communications: separate the signal model from the channel

Define the message signal, modulation scheme, and channel model before computing bandwidth or error probability. These selected foundations connect analog and digital modulation, sampling, and information theory. The original exercises use ideal mathematical models.

Our study notes and original examples support the PYQs below; they are not official exam questions or a replacement for the current syllabus.

Before you start

  • Fourier transforms, convolution, and the relationship between time and frequency domains.
  • Probability distributions, random variables, and signal-to-noise ratio concepts.

Concepts to revise before solving

Amplitude modulation

Conventional AM with carrier: s(t) = Ac[1 + m(t)]cos(2πfct). The modulation index must satisfy |m(t)| ≤ 1 to avoid envelope distortion. DSB-SC eliminates the carrier, doubling power efficiency but requiring coherent detection. The bandwidth of AM is twice the message bandwidth.

Check yourself: Is the modulation index within [0, 1] for envelope detection to work?

Frequency and phase modulation

FM instantaneous frequency deviates proportionally to the message amplitude. The frequency deviation Δf = kf × max|m(t)|. Carson's rule approximates FM bandwidth as 2(Δf + fm). Narrowband FM has β ≪ 1 and bandwidth ≈ 2fm; wideband FM has β ≫ 1.

Check yourself: Is the modulation index β = Δf/fm narrow-band or wide-band?

Sampling and quantization

The Nyquist rate is twice the maximum signal frequency: fs ≥ 2fmax avoids aliasing for band-limited signals. Quantization with L levels uses ⌈log₂L⌉ bits per sample. Uniform quantization step size Δ = (Vmax − Vmin)/L. Quantization noise power for uniform quantization is Δ²/12.

Check yourself: Is the sampling rate above the Nyquist rate for the actual signal bandwidth?

Digital modulation and error probability

BPSK and QPSK have the same bit error rate: Q(√(2Eb/N0)). QPSK transmits two bits per symbol at the same bandwidth as BPSK. Higher-order QAM increases spectral efficiency but requires higher SNR for the same error rate. Matched filtering maximizes output SNR.

Check yourself: Are you comparing Eb/N0 (per bit) or Es/N0 (per symbol)?

Information theory fundamentals

Shannon's channel capacity C = B log₂(1 + SNR) gives the theoretical maximum error-free bit rate for an AWGN channel with bandwidth B. Entropy H(X) = −Σ p(x)log₂p(x) measures uncertainty. Source coding compresses to the entropy limit; channel coding adds redundancy for error protection.

Check yourself: Is the SNR in linear scale (not dB) when substituting into the capacity formula?

Mistakes to avoid

Using Shannon capacity formula with SNR in dB.
Convert SNR from dB to linear: SNR_linear = 10^(SNR_dB/10) before substituting.
Confusing the Nyquist rate with the Nyquist interval.
The Nyquist rate is 2fmax (samples per second); the Nyquist interval is 1/(2fmax) (seconds between samples).
Applying Carson's rule to AM signals.
Carson's rule is for FM/PM bandwidth estimation. AM bandwidth is simply twice the message bandwidth.

Original teaching example · not a PYQ

Work through the reasoning

Original mini-example: a voice signal with bandwidth 4 kHz is sampled at 8 kHz and quantized to 256 levels using uniform PCM. Find the bit rate and the minimum channel bandwidth for transmission.

  1. Bits per sample: log₂(256) = 8 bits.
  2. Bit rate = sampling rate × bits per sample = 8000 × 8 = 64 kbps.
  3. Minimum Nyquist bandwidth for binary signaling: B = bit rate / 2 = 32 kHz (assuming ideal Nyquist pulse shaping).
  4. Verify: 8 kHz sampling rate ≥ 2 × 4 kHz Nyquist rate, so no aliasing occurs.

Bit rate = 64 kbps; minimum channel bandwidth = 32 kHz.

Try it before reading the answer

An AWGN channel has bandwidth 10 kHz and SNR = 31 (linear). What is the channel capacity?

Show answer and reasoning

C = 50 kbps.

C = B log₂(1 + SNR) = 10000 × log₂(32) = 10000 × 5 = 50000 bps = 50 kbps. Note: 1 + 31 = 32 = 2⁵.

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Supplemental reading, not an official GATE reading list or an endorsement of these notes.

Apply this to the previous-year questions

Previous-year questions by year

This page shows 60 recent questions from the released archive, newest first. For older questions and complete papers, browse all GATE EC papers. Questions can carry more than one subject tag; counts are not marks weightage.

GATE EC 20266 questions

  1. Set 1 Q22Consider a discrete memoryless source with an alphabet of four source symbols. s(t)s(t) is a multi-level (-1, 0, +1, +2) signal representing a long sequence of…MCQ · +1 marks · Medium
  2. Set 1 Q32A wireless digital transmission scheme is using 1616-QAM over an additive white Gaussian noise channel and a maximum-likelihood receiver. Consider the…NAT · +1 marks · Medium
  3. Set 1 Q44A QPSK modulated signal from an additive white Gaussian noise (AWGN) channel is received with an Eb/No=8.4E_b/N_o = 8.4 dB at the input of a coherent QPSK…MCQ · +2 marks · Medium
  4. Set 1 Q55Let the relevant bandwidth (BB) of a digital communication system be 1 MHz1\text{ MHz} and kT=−174 dBm/HzkT = -174\text{ dBm/Hz}, where kk is Boltzmann’s constant and ‘TT’…MSQ · +2 marks · Medium
  5. Set 1 Q57Consider a real, narrowband signal x(t)=A(t)cos⁡[2πfct+θ(t)]x(t) = A(t)\cos[2\pi f_c t + \theta(t)] where the maximum frequency components of A(t)A(t) and θ(t)\theta(t) are fMf_M and…MSQ · +2 marks · Hard
  6. Set 1 Q63The average bit error rate at the input of a (7,4,1)(7, 4, 1) Hamming decoder is 0.100.10. The probability that the decoder will fail to decode a received word…NAT · +2 marks · Hard

GATE EC 20259 questions

  1. Set 1 Q14Consider a frequency-modulated (FM) signal f(t)=Accos⁡(2πfct+3sin⁡(2πf1t)+4sin⁡(6πf1t))f(t) = A_c \cos(2\pi f_c t + 3 \sin(2\pi f_1 t) + 4 \sin(6\pi f_1 t)), where AcA_c and fcf_c are, respectively,…MCQ · +1 marks · Medium
  2. Set 1 Q15Consider an additive white Gaussian noise (AWGN) channel with bandwidth WW and noise power spectral density N02\frac{N_0}{2}. Let PavP_{av} denote the average…MCQ · +1 marks · Medium
  3. Set 1 Q28Consider a message signal m(t)m(t) which is bandlimited to [−W,W][-W, W], where WW is in Hz. Consider the following two modulation schemes for the message signal: *…MSQ · +1 marks · Medium
  4. Set 1 Q33The generator matrix of a (6,3) binary linear block code is given by…NAT · +1 marks · Medium
  5. Set 1 Q41A source transmits symbol SS that takes values uniformly at random from the set {−2,0,2}\{-2,0,2\}. The receiver obtains Y=S+NY = S + N, where NN is a zero-mean…MCQ · +2 marks · Medium
  6. Set 1 Q42Consider a real-valued random process f(t)=∑n=1Nanp(t−nT),f(t) = \sum_{n=1}^{N} a_n p(t - nT), where T>0T > 0 and NN is a positive integer. Here, p(t)=1p(t) = 1 for…MCQ · +2 marks · Hard
  7. Set 1 Q44A 10-bit analog-to-digital converter (ADC) has a sampling frequency of 1 MHz and a full scale voltage of 3.3 V. For an input sinusoidal signal with frequency…MCQ · +2 marks · Medium
  8. Set 1 Q54The random variable XX takes values in {−1,0,1}\{-1,0,1\} with probabilities P(X=−1)=P(X=1)=αP(X = -1) = P(X = 1) = \alpha and P(X=0)=1−2αP(X = 0) = 1 - 2\alpha, where 0<α<1/20 < \alpha < 1/2.…MSQ · +2 marks · Medium
  9. Set 1 Q60XX and YY are Bernoulli random variables taking values in {0,1}\{0,1\}. The joint probability mass function of the random variables is given by:…NAT · +2 marks · Medium

GATE EC 20247 questions

  1. Set 1 Q14A digital communication system transmits through a noiseless bandlimited channel [−W,W][-W, W]. The received signal z(t)z(t) at the output of the receiving filter is…MCQ · +1 marks · Medium
  2. Set 1 Q20A white Gaussian noise w(t)w(t) with zero mean and power spectral density N02\frac{N_0}{2}, when applied to a first-order RC low pass filter produces an output…MCQ · +1 marks · Easy
  3. Set 1 Q28An amplitude modulator has output (in Volts) s(t)=Acos⁡(400πt)+Bcos⁡(360πt)+Bcos⁡(440πt).s(t) = A \cos(400\pi t) + B \cos(360\pi t) + B \cos(440\pi t). The carrier power normalized to 1Ω1\Omega…NAT · +1 marks · Medium
  4. Set 1 Q34A source transmits symbols from an alphabet of size 16. The value of maximum achievable entropy (in bits) is ________.NAT · +1 marks · Easy
  5. Set 1 Q45A source transmits a symbol ss, taken from {−4,0,4}\{-4, 0, 4\} with equal probability, over an additive white Gaussian noise channel. The received noisy symbol rr…MCQ · +2 marks · Medium
  6. Set 1 Q47The information bit sequence {1 1 1 0 1 0 1 0 1}\{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…MCQ · +2 marks · Medium
  7. Set 1 Q57Let X(t)=Acos⁡(2πf0t+θ)X(t) = A \cos(2\pi f_0 t + \theta) be a random process, where amplitude AA and phase θ\theta are independent of each other, and are uniformly…NAT · +2 marks · Hard

GATE EC 20234 questions

  1. Set 1 Q30For a real signal, which of the following is/are valid power spectral density/densities?MSQ · +1 marks · Medium
  2. Set 1 Q45Let a frequency modulated (FM) signal x(t)=Acos⁡(ωct+kf∫−∞tm(λ)dλ)x(t) = A \cos\left(\omega_c t + k_f \int_{-\infty}^{t} m(\lambda) d\lambda\right), where m(t)m(t) is a message signal of…MCQ · +2 marks · Hard
  3. Set 1 Q59Let X(t)X(t) be a white Gaussian noise with power spectral density 12\frac{1}{2} W/Hz. If X(t)X(t) is input to an LTI system with impulse response e−tu(t)e^{-t}u(t).…NAT · +2 marks · Medium
  4. Set 1 Q65The frequency of occurrence of 8 symbols (a-h) is shown in the table below. A symbol is chosen and it is determined by asking a series of “yes/no” questions…NAT · +2 marks · Medium

GATE EC 20228 questions

  1. Set 1 Q23The frequency response H(f)H(f) of a linear time-invariant system has magnitude as shown in the figure. [figure] Statement I: The system is necessarily a…MCQ · +1 marks · Medium
  2. Set 1 Q29Let H(X) denote the entropy of a discrete random variable XX taking KK possible distinct real values. Which of the following statements is/are necessarily…MSQ · +1 marks · Hard
  3. Set 1 Q35A 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…NAT · +1 marks · Medium
  4. Set 1 Q51Consider an FM broadcast that employs the pre-emphasis filter with frequency response Hpe(ω)=1+jωω0,H_{pe}(\omega) = 1 + \frac{j\omega}{\omega_0}, where…MSQ · +2 marks · Medium
  5. Set 1 Q61The transition diagram of a discrete memoryless channel with three input symbols and three output symbols is shown in the figure. The transition probabilities…NAT · +2 marks · Hard
  6. Set 1 Q62Consider communication over a memoryless binary symmetric channel using a (7,4)(7, 4) Hamming code. Each transmitted bit is received correctly with probability…NAT · +2 marks · Medium
  7. Set 1 Q63Consider a channel over which either symbol xAx_A or symbol xBx_B is transmitted. Let the output of the channel YY be the input to a maximum likelihood (ML)…NAT · +2 marks · Hard
  8. Set 1 Q64Consider a real valued source whose samples are independent and identically distributed random variables with the probability density function, f(x)f(x), as…NAT · +2 marks · Hard

GATE EC 202110 questions

  1. Set 1 Q31The autocorrelation function RX(τ)R_X(\tau) of a wide-sense stationary random process X(t)X(t) is shown in the figure. [figure] The average power of X(t)X(t) is…NAT · +1 marks · Easy
  2. Set 1 Q32Consider a carrier signal which is amplitude modulated by a single-tone sinusoidal message signal with a modulation index of 50%. If the carrier and one of the…NAT · +1 marks · Medium
  3. Set 1 Q33A speech signal, band limited to 4 kHz4\text{ kHz}, is sampled at 1.251.25 times the Nyquist rate. The speech samples, assumed to be statistically independent and…NAT · +1 marks · Hard
  4. Set 1 Q34A 4 kHz4\text{ kHz} sinusoidal message signal having amplitude 4 V4\text{ V} is fed to a delta modulator (DM) operating at a sampling rate of 32 kHz32\text{ kHz}. The…NAT · +1 marks · Medium
  5. Set 1 Q44A digital transmission system uses a (7,4)(7,4) systematic linear Hamming code for transmitting data over a noisy channel. If three of the message-codeword pairs…MCQ · +2 marks · Medium
  6. Set 1 Q59A sinusoidal message signal having root mean square value of 4 V4\text{ V} and frequency of 1 kHz1\text{ kHz} is fed to a phase modulator with phase deviation…NAT · +2 marks · Medium
  7. Set 1 Q60Consider a superheterodyne receiver tuned to 600 kHz600\text{ kHz}. If the local oscillator feeds a 1000 kHz1000\text{ kHz} signal to the mixer, the image frequency (in…NAT · +2 marks · Easy
  8. Set 1 Q61In a high school having equal number of boy students and girl students, 75%75\% of the students study Science and the remaining 25%25\% students study Commerce.…NAT · +2 marks · Hard
  9. Set 1 Q62A 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)…NAT · +2 marks · Medium
  10. Set 1 Q63Consider a polar non-return to zero (NRZ) waveform, using +2 V and -2 V for representing binary '1' and '0' respectively, is transmitted in the presence of…NAT · +2 marks · Medium

GATE EC 20206 questions

  1. Set 1 Q22A digital communication system transmits a block of NN bits. The probability of error in decoding a bit is α\alpha. The error event of each bit is…MCQ · +1 marks · Easy
  2. Set 1 Q32A binary random variable XX takes the value +2+2 or −2-2. The probability P(X=+2)=αP(X = +2) = \alpha. The value of α\alpha (rounded off to one decimal place),…NAT · +1 marks · Easy
  3. Set 1 Q34The random variable…NAT · +1 marks · Medium
  4. Set 1 Q52For the modulated signal x(t)=m(t)cos⁡(2πfct)x(t) = m(t) \cos(2\pi f_c t), the message signal m(t)=4cos⁡(1000πt)m(t) = 4 \cos(1000\pi t) and the carrier frequency fcf_c is 11 MHz. The signal…MCQ · +2 marks · Medium
  5. Set 1 Q57SPM(t)S_{PM}(t) and SFM(t)S_{FM}(t) as defined below, are the phase modulated and the frequency modulated waveforms, respectively, corresponding to the message signal…NAT · +2 marks · Hard
  6. Set 1 Q58In a digital communication system, a symbol SS randomly chosen from the set {s1,s2,s3,s4}\{s_1, s_2, s_3, s_4\} is transmitted. It is given that…NAT · +2 marks · Hard

GATE EC 20196 questions

  1. Set 1 Q17A linear Hamming code is used to map 4-bit messages to 7-bit codewords. The encoder mapping is linear. If the message 0001 is mapped to the codeword 0000111,…MCQ · +1 marks · Medium
  2. Set 1 Q32The baseband signal m(t)m(t) shown in the figure is phase-modulated to generate the PM signal ϕ(t)=cos⁡(2πfct+km(t))\phi(t) = \cos(2\pi f_c t + k m(t)). The time tt on the x-axis…NAT · +1 marks · Medium
  3. Set 1 Q44A 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 N0/2N_0/2. Binary…MCQ · +2 marks · Medium
  4. Set 1 Q55Let a random process Y(t)Y(t) be described as Y(t)=h(t)∗X(t)+Z(t)Y(t) = h(t) * X(t) + Z(t), where X(t)X(t) is a white noise process with power spectral density SX(f)=5S_X(f) = 5 W/Hz.…NAT · +2 marks · Medium
  5. Set 1 Q56A voice signal m(t)m(t) is in the frequency range 5 kHz to 15 kHz. The signal is amplitude-modulated to generate an AM signal…NAT · +2 marks · Medium
  6. Set 1 Q57A random variable XX takes values −1-1 and +1+1 with probabilities 0.2 and 0.8, respectively. It is transmitted across a channel which adds noise NN, so that…NAT · +2 marks · Hard

GATE EC 20184 questions

  1. Set 1 Q25Consider the following amplitude modulated signal: s(t)=cos⁡(2000πt)+4cos⁡(2400πt)+cos⁡(2800πt).s(t) = \cos(2000 \pi t) + 4 \cos(2400 \pi t) + \cos(2800 \pi t). The ratio (accurate to three decimal…NAT · +1 marks · Medium
  2. Set 1 Q26Consider a binary channel code in which each codeword has a fixed length of 5 bits. The Hamming distance between any pair of distinct codewords in this code is…NAT · +1 marks · Medium
  3. Set 1 Q27A binary source generates symbols X∈{−1,1}X \in \{-1,1\} which are transmitted over a noisy channel. The probability of transmitting X=1X = 1 is 0.5. Input to the…NAT · +1 marks · Medium
  4. Set 1 Q37Let c(t)=Accos⁡(2πfct)c(t) = A_c \cos(2\pi f_c t) and m(t)=cos⁡(2πfmt)m(t) = \cos(2\pi f_m t). It is given that fc≫5fmf_c \gg 5 f_m. The signal c(t)+m(t)c(t) + m(t) is applied to the input of a…MCQ · +2 marks · Medium

Other GATE EC topics

Engineering Mathematics(226)General Aptitude(209)Electronic Devices(149)Digital Circuits(140)Signals & Systems(135)Analog Circuits(122)Network Theory(112)Control Systems(110)Electromagnetics(104)

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