Communication Fundamentals

Tip

Exam Focus

High-yield items: the general communication chain (source $\to$ transducer $\to$ transmitter $\to$ channel with noise $\to$ receiver $\to$ transducer $\to$ destination); analog vs digital and signal classification; thermal noise $N=kTB$ with the $-174\,dBm/Hz$ floor; noise figure $F=\mathrm{SNR_{in}}/\mathrm{SNR_{out}}$, noise temperature $T_e=(F-1)T_0$ and the Friis cascade; and the two capacity limits—Nyquist $C=2B\log_2 M$ and Shannon $C=B\log_2(1+S/N)$. Remember modulation is needed for practical antennas, channel matching, allocation and multiplexing.

Introduction to Communication

Communication is the transfer of information from a source to a destination through a physical channel in a form the destination can interpret.

Information may be speech/audio, text/data, image/video, telemetry, or navigation, control and signalling messages. Communication lets us exchange information across distance and time, coordinate people and machines, support safety and air-traffic management, enable telephone, broadcasting, Internet and mobile access, permit remote monitoring/control, and share costly transmission media among many users.

Communication classification by signal type, direction, channel and frequency placement.

By signal representation, analog systems carry continuously varying waveforms while digital systems carry discrete symbols/bits. By medium, guided media are twisted pair, coax, waveguide and fiber; unguided media are ground/sky wave, microwave, satellite and free-space optics. By connection, a link is point-to-point or point-to-multipoint/broadcast.

Mode	Direction	Example
Simplex	One direction only	Broadcast radio
Half duplex	Both, not simultaneous	Push-to-talk radio
Full duplex	Both, simultaneous	Telephone call

A message may be sent in its original baseband or translated to a passband around a carrier; the chosen frequency depends on channel response, antenna size, propagation, regulation, bandwidth, noise and hardware.

The Communication System

General communication system: the transmitter conditions the message for the channel, an additive-noise node $\Sigma$ injects $n(t)$, and the receiver recovers the message for the destination.

Block	Function	Example
Information source	Produces the message	Speaker, computer, sensor
Input transducer	Physical quantity $\to$ electrical signal	Microphone, camera
Transmitter	Codes, modulates, up-converts, amplifies	Mod., mixer, PA
Channel	Carries signal; adds loss/distortion	Fiber, copper, air
Noise/interference	Adds unwanted random/deterministic energy	Thermal, adjacent Tx
Receiver	Selects, amplifies, recovers message	Front end, demod.
Output transducer	Electrical $\to$ physical form	Speaker, display
Destination	Final user or machine	Listener, computer

Main blocks of a communication system.

A convenient channel model is $r(t)=s(t)*h(t)+n(t)$, with $s(t)$ transmitted, $h(t)$ the channel impulse response, $n(t)$ additive noise and $r(t)$ received. The transmitter performs source/channel coding, modulation or line coding, multiplexing, frequency conversion, filtering and power amplification. It also provides impedance matching for efficient power transfer with minimal reflection, then couples the conditioned signal to a cable, optical fiber or antenna. Channel impairments are attenuation, amplitude/phase distortion, noise, interference, fading/multipath and dispersion/ISI. The receiver preselects and matches, low-noise amplifies, down-converts and channel-filters, demodulates/detects, recovers timing/carrier, and decodes with error control.

Analog and Digital Communication

In analog communication a carrier parameter varies continuously with the message (AM, FM). In digital communication information is mapped to a finite alphabet; an analog source follows sampling $\to$ quantization $\to$ encoding $\to$ digital modulation.

Feature	Analog	Digital
Representation	Continuous waveform	Discrete symbols/bits
Repeaters	Amplify signal and noise	Regenerate symbol decisions
Error control	Limited	Detection, FEC, ARQ
Processing	Analog filtering/modulation	Compression, encryption, DSP
Multiplexing	FDM common	TDM, statistical, packets
Copy/storage	Degrades per copy	Exact below error threshold
Bandwidth	Often lower	May be higher (coding)
Sync.	Less stringent	Bit/symbol/frame/carrier
Impairment	No quantization	Quantization noise
Examples	AM/FM radio	PCM, mobile, Wi-Fi, optical

Analog versus digital communication.

Digital communication gains regeneration, error control, encryption, computer compatibility and flexible software-defined processing, at the cost of A/D–D/A conversion, quantization error, synchronization, often greater bandwidth, and a threshold (abrupt) failure when the bit-error rate becomes excessive; analog quality instead degrades gradually with SNR.

Signal Classification

A signal is a function conveying information about a physical phenomenon, written $x(t)$ in continuous time or $x[n]$ in discrete time.

Signal classification by amplitude/time, repetition, predictability and energy measure.

An analog signal has continuous amplitude; a digital signal takes values from a finite set. Discrete time does not imply digital amplitude: sampled-but-unquantized data is discrete-time yet analog-valued. A signal is periodic if a least $T_0>0$ (integer $N_0>0$) satisfies $x(t+T_0)=x(t)$ ($x[n+N_0]=x[n]$), with $f_0=1/T_0$; otherwise it is aperiodic. Deterministic signals follow a known formula; random signals (thermal noise, message data) need statistical descriptions.

Caution

Key Formula — Energy and average power

$$E=\int_{-\infty}^{\infty}\left\lvert x(t)\right\rvert^2\,dt,\qquad P=\lim_{T\to\infty}\frac{1}{2T}\int_{-T}^{T}\left\lvert x(t)\right\rvert^2\,dt.$$

Class	Condition	Example
Energy signal	$0<E<\infty$, $P=0$	Finite-duration pulse
Power signal	$0<P<\infty$, $E=\infty$	Nonzero periodic sinusoid

A nonzero signal cannot be both an energy and a power signal, and some are neither. A baseband signal spans from/near DC to a maximum message frequency (speech, NRZ data); a passband signal occupies a band about a nonzero carrier (AM, FM, PSK, QAM). Modulation translates baseband to passband without ideally altering the information. The carrier is $c(t)=A_c\cos(2\pi f_c t+\phi_c)$; amplitude, frequency or phase may be varied, giving AM/ASK, FM/FSK, PM/PSK and (amplitude$+$phase) QAM.

Spectrum and Bandwidth

The spectrum gives amplitude and phase versus frequency; for an aperiodic signal $X(f)=\mathcal{F}\!\left\{x(t)\right\}=\int_{-\infty}^{\infty}x(t)\mathrm{e}^{-\mathrm{j}2\pi f t}\,dt$. Bandwidth conventions include absolute, null-to-null, $3\,dB$ (half-power), occupied (e.g. $99\%$ of power) and channel bandwidth—always state which is meant when comparing modulations.

Caution

Key Formula — Frequency and wavelength

$$c=f\lambda,\qquad c\approx3e8\,m/s.$$

Band	Frequency	Typical use
LF	30–300 kHz	Long-wave, navigation
MF	0.3 –3 MHz	AM broadcast
HF	3–30 MHz	Shortwave/ionospheric
VHF	30–300 MHz	FM, aviation radio
UHF	0.3 –3 GHz	Mobile, TV, GNSS, Wi-Fi
SHF	3–30 GHz	Microwave, radar, satellite
EHF	30–300 GHz	Millimeter-wave

Note

Key Point — Range myth

Higher frequency does not automatically mean longer range. Range depends on path loss, propagation mode, atmospheric absorption, terrain, antennas, power, receiver sensitivity and regulation.

Noise in Communication Systems

Noise is unwanted random electrical energy that obscures or alters the desired signal; structured unwanted energy from another system is interference.

Noise classification into internal (device) and external (environmental) sources.

Their spectra distinguish frequency-independent thermal noise from the low-frequency rise of flicker noise.

One-sided noise PSD: flat thermal (white) noise, low-frequency $1/f$ flicker noise, and a band-limited white spectrum of bandwidth $B$.

Thermal (Johnson–Nyquist) noise from random carrier motion exists in every resistor above absolute zero and is approximately white over ordinary bands. Shot noise arises from discrete carrier crossing of a junction. Flicker noise ($1/f^\alpha$, $\alpha\approx1$) dominates at low frequency. Transit-time noise appears when carrier transit approaches an RF period.

Caution

Key Formula — Thermal and shot noise

$$N=kTB,\quad N_0=kT,\quad kT_0\approx-174\,dBm/Hz\ (T_0=290\,K); \qquad \overline{i_n^2}=2qIB.$$

Here $k=1.38e-23\,J/K$, $q$ is electron charge and $I$ the DC current. External noise: atmospheric (lightning, strongest at low radio frequencies), extraterrestrial (solar/galactic) and industrial/man-made (motors, ignition, switching supplies, power lines, digital electronics). Important system-generated terms are:

• Intermodulation: nonlinear mixing creates unwanted $mf_1\pm nf_2$ products, which can fall inside the wanted channel.

• Crosstalk: capacitive, inductive or radiative coupling leaks another channel into the wanted one, so speech, tones or data patterns from that channel become observable at the receiver.

• Impulse noise: short, high-amplitude, broad-spectrum disturbances produce clicks or spikes in analog output and bursts of digital bit errors.

• Quantization noise: finite-level approximation in an ADC produces granular error and raises the conversion noise floor; unlike propagation noise, it is not a physical channel-noise source.

• Oscillator phase noise: random phase fluctuations spread carrier energy into spectral skirts, degrading close-channel selection and coherent detection.

Together, noise and interference appear as audio hiss/clicks, video speckle, false analog readings, threshold errors and increased BER. Mitigation includes limiting receiver bandwidth, using a low-noise high-gain first stage, shielding/grounding/filtering and separating sources, using balanced transmission and suitable matching, raising power or antenna gain within constraints, and applying coding, interleaving, diversity and robust modulation.

SNR, Noise Figure and Cascaded Receivers

Caution

Key Formula — SNR, noise factor and noise temperature

$$\mathrm{SNR}=\frac{S}{N},\quad \mathrm{SNR_{dB}}=10\log_{10}\!\frac{S}{N};\qquad F=\frac{\mathrm{SNR_{in}}}{\mathrm{SNR_{out}}}\ge 1,\quad \mathrm{NF}=10\log_{10}F.$$$$T_e=(F-1)T_0,\qquad T_0=290\,K.$$

Use $20\log_{10}$ for a voltage ratio only across equal impedance. An ideal noiseless device has $F=1$, $\mathrm{NF}=0\,dB$; noise temperature is convenient for antennas and very-low-noise front ends.

Note

Law — Friis cascade formula

For stages with linear power gains $G_i$ and linear noise factors $F_i$,

$$F_{\text{total}}=F_1+\frac{F_2-1}{G_1}+\frac{F_3-1}{G_1 G_2}+\cdots$$

Stage 1 contributes directly; later noise is divided by preceding gain, so a low-noise amplifier with adequate gain should come first. Never substitute dB values—convert gains and noise figures to linear ratios first.

[!NOTE]

Example — Friis two-stage receiver ([10] marks)

An LNA has $G_1=10\,dB$, $\mathrm{NF_1}=2\,dB$; a following mixer has $\mathrm{NF_2}=8\,dB$. Convert to linear:

$$G_1=10,\qquad F_1=10^{0.2}=1.585,\qquad F_2=10^{0.8}=6.310.$$$$F_T=1.585+\frac{6.310-1}{10}=2.116,\qquad \mathrm{NF_T}=10\log_{10}(2.116)=3.26\,dB.$$

Equivalent cascade temperature $T_e=(2.116-1)\times290\approx324\,K$. Without the LNA’s preceding gain the mixer would dominate receiver noise.
Tip: always convert dB to linear before applying Friis.

Channel Capacity

Caution

Key Formula — Nyquist and Shannon capacity

$$C_N=2B\log_2 M\ bit/s\quad(\text{noiseless, }M\text{ levels}),$$$$C_S=B\log_2\!\Big(1+\frac{S}{N}\Big)\ bit/s\quad(\text{AWGN channel}).$$

The Nyquist limit gives the maximum zero-ISI symbol rate ($2B$ baud) with each symbol carrying $\log_2 M$ bits; more levels raise the rate but shrink level spacing and increase errors in noise. Shannon–Hartley gives the fundamental noisy-channel limit: rates below $C_S$ allow arbitrarily small error with sufficiently long coding, but it prescribes no particular code and $S/N$ must be the received linear ratio.

Nyquist	Shannon
Ideal noiseless pulse channel	Noisy AWGN channel
Depends on levels $M$	Depends on received SNR
ISI-free signalling rate	Fundamental info-rate limit
$2B\log_2 M$	$B\log_2(1+S/N)$

Note

Example — Shannon and Nyquist capacity ([5] marks)

For $B=3\,kHz$ and $\mathrm{SNR}=30\,dB$, first convert: $S/N=10^{30/10}=1000$. Then

$$C_S=3000\log_2(1001)\approx29.9\,kbit/s.$$

With binary Nyquist signalling ($M=2$), $C_N=2(3000)\log_2 2=6\,kbit/s$; more levels raise this ideal value but require enough SNR.
Tip: convert SNR from dB to a linear ratio before using Shannon.

Modulation and Multiplexing Overview

Modulation varies a carrier’s amplitude, frequency or phase according to a message, translating information to a suitable frequency band without ideally changing the information.

Modulation is needed for (1) practical antennas, since $\lambda=c/f$ and resonant dimensions are fractions of $\lambda$; (2) channel matching to bandpass/AC-coupled media; (3) frequency allocation and selective tuning; (4) multiplexing; (5) efficient radiation/propagation in a regulated band; and (6) noise/interference strategy, though modulation does not by itself universally reduce noise. For a $3\,kHz$ audio tone radiated directly, $\lambda=100\,km$ and a quarter-wave antenna would be $\approx25\,km$; at $100\,MHz$, $\lambda=3\,m$ and quarter-wave $\approx0.75\,m$.

Method	Divides	Example
FDM	Frequency bands	Broadcast, cable TV
TDM	Time slots	PCM telephony
WDM	Optical wavelengths	Fiber backbone
CDM	Spreading codes	CDMA, GNSS

FDM spectrum: baseband channels placed in adjacent frequency bands separated by guard bands.

TDM performs the corresponding separation in time by assigning each source a repeating slot.

TDM frame: user time slots TS0 – TS$n$ repeating within each frame.

Multiplexing combines users onto a medium while modulation maps a message onto a waveform; the two often work together but are not synonymous.

Note

Key Point — Revision — Communication Fundamentals

• Chain: source $\to$ transducer $\to$ transmitter $\to$ channel/noise $\to$ receiver $\to$ transducer $\to$ destination; $r=s*h+n$.

• Analog is continuous; digital uses discrete symbols and regenerative decisions (coding, encryption) at the cost of sync and A/D conversion.

• Signals: analog/digital, periodic/aperiodic, deterministic/random, energy ($0<E<\infty$) vs power ($0<P<\infty$), baseband/passband.

• Thermal noise $N=kTB$; density $\approx-174\,dBm/Hz$ at 290 K; shot noise $\overline{i_n^2}=2qIB$.

• $F=\mathrm{SNR_{in}}/\mathrm{SNR_{out}}$, $T_e=(F-1)T_0$; Friis $F_T=F_1+(F_2-1)/G_1+\cdots$ (linear units only).

• Nyquist $C=2B\log_2 M$; Shannon $C=B\log_2(1+S/N)$.

• Modulation enables practical antennas, channel matching, allocation and multiplexing (FDM/TDM/WDM/CDM).