Telecommunications

Why every link decomposes into source coder, channel coder, modulator, channel, and their inverses: the source coder strips redundancy the source happened to have, the channel coder puts back redundancy shaped to the noise, and Shannon's separation theorem says doing them separately costs nothing — asymptotically. A GSM voice call carries the argument end to end, and shows where the theorem stops applying.

How a radio signal weakens between two antennas: the Friis equation derived from spreading plus receive aperture, why free-space loss rises with frequency even though a vacuum absorbs nothing, and the mechanisms that take over once the ground, terrain, the atmosphere, rain or the ionosphere get involved.

Where the noise floor of a radio link actually comes from: kTB and the −174 dBm/Hz constant at 290 K, noise figure and noise temperature as two spellings of the same quantity, the Friis cascade formula that makes the first stage own the answer, and the external noise — lightning, the galaxy, and human electrical activity — that at HF sits 40 dB above anything the receiver contributes.

An antenna is a reciprocal spatial transducer: its current distribution shapes radiation on transmit and weights arriving fields on receive. This entry separates directivity, gain, realized gain, effective aperture and polarization; connects them to Friis; and shows how impedance, arrays, field zones and measurement geometry decide whether a datasheet number exists in the real link.

One equation in dB from the transmitter's power amplifier to the demodulator's decision: EIRP minus every loss plus every gain, divided by the noise the receiver makes for itself, compared against the Es/N0 a given modulation and code rate demands. Two budgets worked end to end — a Ku-band GEO satellite hop and a 5G NR uplink — show that closing on paper and closing in the field are different claims.

Four media, four different things that stop you. Twisted pair dies of crosstalk long before it dies of loss; coax trades minimum attenuation against power handling to land on 50 and 75 ohms; waveguide has a hard low-frequency cutoff and exists because metal loss above 10 GHz is otherwise ruinous; fibre is loss-limited at 0.2 dB/km once coherent DSP takes dispersion off the table. The bandwidth-distance product spans seven orders of magnitude across them.

The decibel is not a unit — it is a level, the logarithm of a ratio to a stated reference, and every confusion around it comes from an unstated reference or from mixing the 10 lg and 20 lg forms. This covers where the factor of two comes from, the absolute references (dBm, dBu, dBFS, dBi, dBc), the relative-level machinery telephony built on top (dBr, dBm0, TLP), and why you can add gains in dB but never powers.

Why a baseband signal has to be carried by something else at all, and the two ways to do it: amplitude modulation, whose carrier burns at least two-thirds of the transmitter power and caps sideband efficiency at 33%, and angle modulation, which buys noise immunity by spending bandwidth — quadratically, per Carson's rule, with a hard threshold underneath it.

Line coding turns bits into a constrained baseband waveform whose spectrum, transition density, DC balance, and error visibility fit the physical channel. This entry derives those tradeoffs, compares common mappings on one bit sequence, and connects block coding and scrambling to clock recovery and link diagnostics.

Every digital modulation is a set of points in the I/Q plane, and one number — the minimum Euclidean distance between them — fixes the error probability. How BPSK through 256-QAM trade bits per symbol against required Eb/N0, why Gray coding is what makes BER ≈ SER/k, what pulse shaping costs in bandwidth, and why peak-to-average power ratio, not noise, is often the binding constraint.

Digital detection reduces a noisy waveform to sufficient statistics and chooses among hypotheses. This entry derives the AWGN matched filter, turns Euclidean distance into BER, works a BPSK decision numerically, and shows how priors, soft metrics, synchronization, and model mismatch change a real detector.

Direct-sequence spread spectrum multiplies data by a faster chip sequence and recovers it by aligned correlation. This entry derives processing gain, works desired and interfering codes chip by chip, explains PN and OVSF correlation, and connects acquisition, multipath, RAKE combining, and near–far power control.

A receiver architecture decides where frequency translation, selectivity, gain, and digitization occur: superheterodyne, zero-IF, low-IF, and direct-RF-sampling receivers move the same signal through different impairment and dynamic-range bottlenecks.

Distortion is any deterministic change that prevents a signal from emerging as a scaled, delayed copy of itself. This entry separates amplitude and group-delay distortion from nonlinear compression and intermodulation, then connects each mechanism to the measurement and correction that can actually reveal or repair it.

Interference becomes tractable when it is traced as a complete path: a source generates energy, a conducted or radiated mechanism couples it, and a susceptible victim turns it into failure. This entry classifies the paths and signal modes, derives SINR and C/I accounting, explains shielding and boundary filtering, and gives a measurement-led workflow for reducing emissions, breaking coupling, or hardening the victim.

Fading is not one impairment: shadowing moves the local mean, multipath reshapes the signal across time and frequency, and diversity works only when its observations are sufficiently independent.

A coherent receiver must acquire and track sample time, carrier frequency and phase, gain, and frame position while controlling channel memory. This entry connects Nyquist pulse shaping, timing and carrier loops, frame correlation, equalization, eye diagrams, and acquisition diagnostics into one receiver workflow.

RF measurement converts a received waveform into traceable frequency, power, bandwidth, field-strength, occupancy, modulation and direction evidence. This entry explains the calibrated antenna-to-detector chain, spectrum-analyzer RBW/VBW/detector tradeoffs, overload and noise traps, uncertainty budgets, monitoring sampling, and a reproducible measurement workflow.

Redundancy buys error control by spacing codewords apart in Hamming distance - detect d-1 errors, correct half that - at the price of code rate. How the trade sits under the Shannon capacity bound, why capacity-approaching codes abandoned distance maximisation, and how the ARQ/FEC/hybrid choice is really decided by the feedback channel and the latency budget.

Binary linear block codes turn parity equations into a decoder: generator matrices create legal words, parity-check matrices identify error cosets, and minimum distance states exactly what can be detected or corrected. This entry builds and decodes a complete Hamming (7,4) example, extends it to SECDED, and uses classical bounds to judge proposed code parameters.

Cyclic codes turn shifts into polynomial algebra: a CRC uses the remainder to detect corruption, while BCH and Reed–Solomon codes use structured roots and syndromes to locate and correct errors. This entry derives the common machinery, works a CRC exactly, and makes every field, polynomial, shortening, and byte-order convention explicit.

Convolutional encoders turn a bit stream into a finite-state trellis; Viterbi decoding finds the maximum-likelihood sequence by retaining one survivor per state. This entry fixes generator conventions, works a complete noisy trellis, derives hard and soft metrics, and covers termination, puncturing, distance, complexity, and interoperability.

Entropy coding assigns short representations to probable symbols without losing information. This entry derives the entropy limit and Kraft condition, builds a canonical Huffman code, narrows an arithmetic-coding interval by hand, and explains the exact model, precision, termination, and corruption contracts required by real formats.

Multiplexing lets independent flows share one physical medium by assigning separable regions of time, frequency, wavelength, code, or space. This entry derives the separation and guard costs, connects fixed FDM/TDM to statistical multiplexing, WDM, OFDM/OFDMA and MIMO, and shows how synchronization and scheduling determine whether the channels remain separable.

Radar and radio ranging estimate delay, Doppler, angle and sometimes target structure from a deliberately transmitted waveform. This overview derives the range and velocity observables, explains why bandwidth and coherent time set resolution, exposes pulse/FMCW ambiguities and false alarms, and separates one-way synchronization from two-way propagation measurement.

A cellular network is a moving, interference-limited packet system: it reuses spectrum across cells, keeps a subscriber reachable while radio context appears and disappears, and coordinates radio scheduling with core-network sessions. GSM, GPRS, UMTS, LTE, and 5G are traced as successive answers to switching, mobility, and capacity—not as a list of generation labels.

A satellite link couples an RF/optical budget to moving orbital geometry: range sets spreading loss and delay, velocity sets Doppler and handover, elevation sets atmospheric exposure, and topology decides which gateway or inter-satellite path actually carries the traffic. This entry derives those couplings and turns them into an availability and acquisition workflow.

Broadcasting spends one high-power transmission to serve an unknown number of passive receivers. This overview follows content into an RF multiplex, explains why one-way delivery requires strong framing/FEC and field-strength planning, shows when a single-frequency network helps or self-interferes, and separates international spectrum allocation from national channel assignment.

How a trunked land-mobile-radio system shares a channel pool among talkgroups, grants calls through a control channel, and behaves under congestion, roaming, and partial failure.