Communication Fundamentals¶

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Communication is the transfer of information from a source to an intended destination through a physical channel in a form that the destination can interpret. Its operating principle is source \(\rightarrow\) transducer \(\rightarrow\) transmitter \(\rightarrow\) channel \(\rightarrow\) receiver \(\rightarrow\) destination: the transmitter converts the message into a channel-suitable signal, while the receiver selects, detects and reconstructs it. A carrier may be written as \(c(t)=A_c\cos(2\pi f_ct+\phi_c)\), where \(A_c\) is amplitude, \(f_c\) is frequency in hertz and \(\phi_c\) is phase in radians.

Communication systems are classified as follows:

• By representation: analog communication uses continuously varying waveforms, whereas digital communication uses a finite set of symbols or bits.
• By direction: simplex is one-way, half duplex is two-way but alternate, and full duplex permits simultaneous two-way transfer.
• By medium: guided systems use twisted pair, coaxial cable, waveguide or optical fiber; unguided systems radiate through free space.
• By connection: point-to-point joins one transmitter to one receiver, while point-to-multipoint or broadcast serves several receivers.

Applications include telephone and mobile service, AM/FM and television broadcasting, aviation and emergency radio, satellite/microwave links, industrial telemetry and control, and computer networks. Digital links support regeneration, coding and encryption but need synchronization and may need A/D conversion; analog links are simpler for some sources but accumulate noise. As a scale check, a \(1\,\text{MHz}\) free-space carrier has wavelength \(\lambda=c/f=3\times10^8/10^6=300\,\text{m}\), showing why frequency and medium strongly affect practical implementation.

Practice target: 7-8 minutes; reproduce the four classification axes and at least one application for each major class.

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A communication system transfers a message through a channel while preserving enough information for the destination to recover it. Its complete signal path is shown below.

The information source produces speech, image, data or telemetry. The input transducer, such as a microphone, converts the physical message into an electrical signal \(m(t)\). The transmitter performs source/channel coding, modulation or line coding, multiplexing, frequency conversion, filtering and power amplification so that the signal suits the medium. The channel is copper, fiber, waveguide or free space; it attenuates and distorts the signal and admits noise/interference. A useful channel model is

where \(s(t)\) is transmitted signal, \(h(t)\) is channel impulse response, \(*\) denotes convolution, \(n(t)\) is additive noise and \(r(t)\) is received signal. The receiver selects the wanted channel, amplifies it with low added noise, down-converts, filters, demodulates and decodes it. The output transducer converts the recovered electrical signal back to sound, image or motion, and the destination is the final person or machine.

For example, in radio telephony, voice \(\rightarrow\) microphone \(\rightarrow\) FM transmitter \(\rightarrow\) free-space channel \(\rightarrow\) RF receiver \(\rightarrow\) speaker. If a channel introduces \(20\,\text{dB}\) power loss, \(1\,\text{mW}\) becomes \(1\times10^{-20/10}=0.01\,\text{mW}=10\,\mu\text{W}\) before receiver gain. Practical limitations are attenuation, finite bandwidth, noise, interference, fading and nonlinear distortion; filtering, coding, diversity and adequate link margin reduce their effects.

Practice target: 7-8 minutes; draw the complete labeled chain before explaining one function per block.

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In analog communication, information is represented and processed as a continuously varying voltage/current, and a carrier parameter varies continuously, as in AM or FM. In digital communication, information is mapped to a finite alphabet of symbols or bits. An analog source follows the path sampling \(\rightarrow\) quantization \(\rightarrow\) binary encoding \(\rightarrow\) digital modulation; the receiver makes symbol decisions, decodes and reconstructs the source.

Analog repeaters amplify both signal and accumulated noise, whereas a digital regenerator reshapes, retimes and regenerates decisions, preventing progressive waveform degradation while its error rate remains acceptable. Digital systems support error-control coding, compression, encryption, storage, switching and software/DSP implementation; analog systems can be simpler, have no quantization error and may use less bandwidth for a basic uncoded service. Digital transmission requires bit/symbol/frame synchronization and A/D-D/A conversion for analog sources, and abrupt failure can occur below the receiver decision threshold. Analog quality usually degrades gradually with SNR.

For an ideal \(n\)-bit uniform ADC with full-scale range \(V_{FS}\), quantization step is \(\Delta=V_{FS}/2^n\) volts and full-scale sine quantization SNR is approximately \(6.02n+1.76\,\text{dB}\). Thus an ideal 8-bit conversion gives about \(49.9\,\text{dB}\). Typical analog examples are conventional AM/FM broadcast and legacy analog voice; digital examples are PCM telephony, cellular radio, Wi-Fi and optical data. Hence digital communication offers regeneration and powerful processing at the cost of conversion, synchronization and often greater implementation complexity or bandwidth.

Practice target: 7-8 minutes; write paired definitions, then compare at least six technical features and examples.

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A signal is a measurable function that carries information, written \(x(t)\) in continuous time or \(x[n]\) in discrete time. Classification indicates how a signal is represented, predicted, repeated, measured energetically and placed in frequency.

1. Analog and digital: an analog signal has continuous amplitude, usually continuous time, such as microphone voltage. A digital signal represents a finite symbol set by physical pulse levels. A sampled but unquantized waveform is discrete-time but not digital in amplitude; therefore these terms must not be treated as synonyms.
2. Periodic and aperiodic: continuous-time \(x(t)\) is periodic if a least \(T_0>0\) satisfies \(x(t+T_0)=x(t)\); \(f_0=1/T_0\) hertz. Discrete-time periodicity requires an integer \(N_0>0\) with \(x[n+N_0]=x[n]\). A carrier sinusoid is periodic; a speech utterance or isolated pulse is aperiodic.
3. Deterministic and random: a deterministic signal is specified exactly by a formula or sequence. A random signal, such as thermal noise or unpredictable data, is described by probability density, mean, autocorrelation and power spectral density.
4. Energy and power: for continuous time,

With a voltage across \(1\,\Omega\), these correspond numerically to joules and watts. An energy signal has \(0<E<\infty\) and \(P=0\), e.g. a finite pulse. A power signal has \(0<P<\infty\) and \(E=\infty\), e.g. a nonzero periodic sinusoid. A nonzero signal cannot belong to both classes, and some signals belong to neither. 5. Baseband and passband: baseband spectrum lies at or near \(0\,\text{Hz}\) up to message bandwidth \(B_m\), as for speech or NRZ data. Passband spectrum is translated around a nonzero carrier \(f_c\), as in AM, FM, PSK or QAM. Modulation moves the spectrum while ideally preserving its information.

For \(x(t)=2\cos(2\pi1000t)\) volts across \(1\,\Omega\), \(T_0=1\,\text{ms}\), so it is analog, periodic, deterministic, and a power signal with \(P=A^2/2=2\,\text{W}\) and infinite total energy. A finite \(2\,\text{V}\) rectangular pulse of duration \(1\,\text{ms}\) instead has \(E=V^2T/R=0.004\,\text{J}\) and zero long-term average power. These checks show why classification depends on mathematical behavior, not merely on waveform appearance.

Practice target: 15-17 minutes; define every pair, write the periodicity and energy/power tests, and attach one correct example to each.

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Noise is unwanted random electrical energy that masks or changes a desired communication signal; structured unwanted energy from another system is more precisely called interference. Noise is classified as internal device noise, external environmental noise and system-generated impairment.

Thermal or Johnson noise results from random carrier motion in every resistive element above absolute zero. Its available power in bandwidth \(B\) is

where \(k=1.38\times10^{-23}\,\text{J/K}\), \(T\) is kelvin and \(B\) is hertz. Its approximately flat PSD is \(N_0=kT\,\text{W/Hz}\); at \(290\,\text{K}\) the density is about \(-174\,\text{dBm/Hz}\). Shot noise is due to discrete random charge crossing a junction; its mean-square current is \(i_n^2=2qIB\,\text{A}^2\), where \(q\) is electron charge and \(I\) is DC current. Flicker noise has PSD roughly proportional to \(1/f^\alpha\) and dominates semiconductor circuits at low frequency. Transit-time noise becomes important when carrier transit time approaches an RF period.

External noise includes atmospheric noise from lightning and natural discharges, strongest mainly at lower radio frequencies; extraterrestrial noise from the sun and galaxy; and industrial/man-made noise from motors, ignition, switching converters, power lines and digital equipment. System-generated terms include crosstalk, impulse noise, oscillator phase noise, nonlinear intermodulation \(mf_1\pm nf_2\), and ADC quantization noise.

Noise lowers received SNR, produces analog hiss/speckle and increases digital bit-error probability. It is controlled by limiting bandwidth, cooling or selecting low-noise devices, placing a high-gain LNA first, shielding/grounding, balanced transmission, filtering, impedance matching, coding, interleaving and diversity. Numerically, at \(290\,\text{K}\) in \(10\,\text{kHz}\), \(N=kTB\approx4.0\times10^{-17}\,\text{W}=-134\,\text{dBm}\). Doubling bandwidth doubles noise power, a \(3\,\text{dB}\) increase, which explains why a receiver should pass no more spectrum than necessary.

Practice target: 16-18 minutes; draw the classification, state both thermal and shot-noise equations, then finish with effects and remedies.

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Signal-to-noise ratio (SNR) measures wanted signal power relative to noise power at the same reference point and bandwidth:

The \(20\log_{10}\) form is used for voltage only when the compared impedances are equal. Larger SNR gives more faithful analog recovery and generally lower digital error probability.

The noise factor of a two-port is its degradation of SNR:

An ideal noiseless stage has \(F=1\) and \(NF=0\,\text{dB}\). The same added input-referred noise can be represented by equivalent noise temperature

where the standard reference is \(T_0=290\,\text{K}\). Temperature representation is especially useful for antennas, satellite links and very-low-noise RF front ends.

For cascaded stages having linear power gains \(G_i\) and linear noise factors \(F_i\), Friis formula is

Stage 1 contributes directly, whereas each later added-noise term is divided by all preceding gain. This follows by referring each stage's output noise back to the cascade input. Hence a receiver places a low-noise amplifier with adequate gain before a lossy cable or mixer: the first stage largely sets system sensitivity. Excessive gain is still limited by overload, compression and strong interferers. All \(F_i\) and \(G_i\) must be converted from dB to linear values before substitution.

For an LNA with \(G_1=10\,\text{dB}=10\) and \(NF_1=2\,\text{dB}\) followed by a mixer with \(NF_2=8\,\text{dB}\),

The equivalent cascade temperature is \((2.116-1)290\approx324\,\text{K}\). Without the LNA's preceding gain, the mixer contribution would be much larger. Friis assumes matched, stable stages under the stated gain/noise definitions; practical mismatch, image noise and bandwidth must also be considered.

Practice target: 16-18 minutes; define the four quantities, state Friis in linear form, and complete one two-stage calculation.

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Channel capacity is the highest information rate that can be transmitted with arbitrarily small error probability under the stated channel model. For an ideal noiseless low-pass channel of bandwidth \(B\) hertz using \(M\) distinguishable signal levels, the Nyquist result is

The factor \(2B\) is the maximum zero-ISI symbol rate in baud under ideal pulse shaping, and each symbol carries \(\log_2M\) bits. Increasing \(M\) raises rate but, in a real noisy channel, reduces spacing between levels and therefore increases decision errors.

For an additive white Gaussian-noise channel, Shannon-Hartley gives

where \(S/N\) is the received linear signal-to-noise power ratio over \(B\). Nyquist describes the bandwidth/level or ISI limit for a noiseless model; Shannon gives the fundamental noisy-channel information limit and does not prescribe a particular modulation or code. Rates below Shannon capacity can approach arbitrarily low error only with sufficiently long, suitable coding; finite systems still have error and delay. A practical design must respect both waveform bandwidth and noise constraints.

For \(B=3\,\text{kHz}\) and \(SNR=30\,\text{dB}\), \(S/N=10^{30/10}=1000\), so \(C_S=3000\log_2(1001)\approx29.9\,\text{kbit/s}\). With binary Nyquist signaling, \(C_N=2(3000)\log_2 2=6\,\text{kbit/s}\); more levels increase this ideal Nyquist value but require enough SNR. Capacity rises linearly with \(B\) only when the numerical SNR is held fixed and logarithmically with SNR.

Practice target: 7-8 minutes; write both boxed equations, define every symbol, state the assumptions, and include the dB-to-linear conversion.

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Modulation is the controlled variation of a high-frequency carrier's amplitude, frequency or phase by a baseband message. It translates the message spectrum to a chosen passband without ideally changing the information.

The main reasons are: (1) practical antennas, because wavelength is \(\lambda=c/f\) and resonant antenna dimensions are fractions of \(\lambda\); (2) channel matching, since antennas, microwave links and AC-coupled media pass allocated nonzero frequency bands; (3) frequency allocation and selective reception, allowing a tuned receiver to separate stations; (4) multiplexing, by placing different messages on different carriers; (5) efficient radiation and useful propagation, by selecting a suitable regulated band; and (6) noise/interference management, because frequency placement and modulation determine available filtering and immunity.

For a \(3\,\text{kHz}\) audio signal radiated directly, \(\lambda=3\times10^8/(3\times10^3)=100\,\text{km}\) and a quarter-wave antenna would be about \(25\,\text{km}\). Translation to \(100\,\text{MHz}\) gives \(\lambda=3\,\text{m}\) and a quarter-wave near \(0.75\,\text{m}\). In FDM, each modulated message occupies a separate channel around its carrier and guard bands prevent overlap.

Modulation and multiplexing are related but different: modulation maps one message onto a waveform; multiplexing combines several users. Modulation does not automatically increase range or eliminate noise, and it costs bandwidth, power or circuit complexity depending on the scheme. The chosen carrier must satisfy propagation, spectrum regulation, antenna, hardware and link-budget requirements.

Practice target: 7-8 minutes; define modulation, calculate one antenna-size example, and explain at least five distinct needs.