(SEM VI) THEORY EXAMINATION 2024-25 DIGITAL COMMUNICATION

BEC601 – DIGITAL COMMUNICATION

Time: 3 Hours | Max Marks: 70

SECTION A – Short Answer Questions

(2 × 7 = 14 marks | Attempt ALL)
Write definition / formula + 1–2 crisp points

a. Random Variable & Probability in Communication

A random variable assigns numerical values to outcomes of a random experiment.
In communication systems, noise and signals are modeled as random variables to analyze probability of error and performance.

b. Mean and Variance of a Random Variable             Mean (μ): Average value (expected value)

Variance (σ²): Measure of spread around the mean
They describe signal power and noise fluctuations.

c. Comparison of PSK and FSK

d. Digital Communication System & Advantages

A system that transmits information using discrete symbols (bits).

Advantages over analog:                                      Better noise immunity

Easier encryption and error control

e. BER of BPSK in AWGN Channel

Pb=Q(2EbN0)P_b = Q\left(\sqrt{\frac{2E_b}{N_0}}\right)Pb​=Q(N0​2Eb​​​)

BPSK has minimum BER among binary schemes.

f. Applications of DS-SS Systems

GPS

Military communication (anti-jamming)

g. Signal Space Representation

It represents signals as vectors in orthogonal basis functions, simplifying detection and error probability analysis.

SECTION B – Medium Answer Questions

(7 × 3 = 21 marks | Attempt ANY THREE)
Write definition → explanation → diagram/example

a. Statistical Averages & Properties

Statistical averages describe long-term behavior of random processes.

Properties:

Linearity                                          Time average = ensemble average (ergodic process)

Used in noise and signal analysis.

b. Scrambler and Unscrambler

A scrambler randomizes data to avoid long runs of 0s or 1s.
An unscrambler recovers original data.

Draw block diagram (LFSR based).

c. ASK, FSK, PSK – Working & Constellation

ASK: Amplitude varies             FSK: Frequency varies                         PSK: Phase varies

Draw constellation diagrams and compare bandwidth & noise performance.

d. Spread Spectrum Communication

Spreads signal over wide bandwidth → low power density.

Types:             Direct Sequence (DS-SS): PN code multiplication

Frequency Hopping (FH-SS): Rapid carrier frequency changes

Characteristics: Anti-jamming, security, interference resistance.

e. Systematic (7,4) Cyclic Code (Numerical)

Given generator polynomial:

g(x)=x3+x2+1g(x)=x^3+x^2+1g(x)=x3+x2+1

Construct all codewords using message bits + parity bits.

SECTION C – Attempt ANY ONE

(7 marks)

a. Power Spectral Density (PSD)

PSD describes power distribution over frequency.

Relation with autocorrelation:

S(f)=∫−∞∞R(τ)e−j2πfτdτS(f) = \int_{-\infty}^{\infty} R(\tau)e^{-j2\pi f\tau} d\tauS(f)=∫−∞∞​R(τ)e−j2πfτdτ 

b. Random Process in Communication

A random process is a collection of random variables indexed by time.
Used to model noise, fading, and information signals.