Radio fundamentals

How radio carries data, from first principles: electromagnetic waves and the spectrum, decibels, antennas, modulation and OFDM, how signals travel, bend and fade, noise and the Shannon limit, link budgets, duplexing, who regulates the airwaves, and how to listen with a software-defined radio. The background for Wi-Fi, Cellular, Bluetooth, Satellite and Mesh & IoT; signals and packets in general are in Networking from scratch.

What a radio wave is

A radio wave is an electromagnetic (EM) wave: an electric field and a magnetic field oscillating together, at right angles to each other and to the direction of travel. It needs no medium and moves at the speed of light, c = 299,792,458 m/s in a vacuum (about 300,000 km/s, a little slower in air). An alternating current in a wire pushes charges back and forth; accelerating charges launch the wave. Radio, infrared, visible light and X-rays are the same thing at different frequencies.

Think of ripples spreading from a stone dropped in a pond: how many crests pass a point each second is the frequency, and the distance between crests is the wavelength.

Shortcut: λ in meters ≈ 300 ÷ f in MHz.

The radio spectrum

The ITU divides radio into bands that are each 10 times higher in frequency than the one before. Low frequencies travel far and pass through things but offer little room for data and need large antennas; high frequencies offer wide channels but short range. One 20 MHz Wi-Fi channel is as wide as the entire FM broadcast band.

"Microwave" loosely means 300 MHz to 300 GHz.

Decibels

Radio powers span enormous ranges: a 100 W transmitter and a 1 pW received signal differ by 10¹⁴. The decibel (dB) expresses a power ratio on a log scale, so multiplying becomes adding:

Add and subtract dB freely along a link (+20 dBm, +8 dBi, −100 dB = −72 dBm). Two equal powers combined are +3 dB, not double the dBm. For voltages and field strengths the factor is 20, not 10.

Antennas

An antenna turns a current into a radio wave and back again. The simplest is a half-wave dipole: two rods, each about a quarter wavelength, fed in the middle. The alternating current sloshes charge from end to end, and at that length the antenna resonates, so most of the power leaves as a wave instead of reflecting back into the transmitter. Receiving is the same process in reverse: an antenna has the same pattern and gain for both (reciprocity).

• Gain is how much stronger an antenna's signal is in its best direction than an isotropic antenna's, in dBi. A dipole has 2.15 dBi. Higher gain always means a narrower beam.
• A dish's gain is about η(πD/λ)², where D is its diameter and η its efficiency (≈ 0.5–0.7).
• Polarization must match: a vertical antenna hears a horizontal one 20 dB or more weaker. GPS and many satellite links use circular polarization so orientation doesn't matter.

60 cm satellite dish at 12 GHz, efficiency 0.6
  λ = 0.3 / 12 = 0.025 m
  gain = 0.6 × (π × 0.6 / 0.025)² = 0.6 × 75.4² ≈ 3400
       = 10 × log10(3400) ≈ 35 dBi

An array feeds many small antennas with controlled phase delays so their waves add up in one direction and cancel in others; changing the delays steers the beam with no moving parts. MIMO (multiple input, multiple output) puts several antennas at both ends: in a room full of reflections each antenna pair sees a different mix, so several independent spatial streams share one channel and capacity grows with the number of antennas (2×2 and 4×4 in Wi-Fi, 64 elements on many 5G base stations). Beamforming sets each antenna's phase and amplitude so the signal peaks at the receiver; MU-MIMO aims different beams at different users at the same time.

Modulation

A carrier is a steady sine wave at the channel's frequency; on its own it says only "I'm here". Modulation changes one of its three properties in step with the data, and the receiver (demodulator) reads the changes back out.

With digital data the same knobs are switched between a few fixed states, called keying: ASK (amplitude-shift keying; OOK, on-off keying, in car key fobs and fiber), FSK (frequency-shift; GFSK in Bluetooth), PSK (phase-shift; BPSK in GPS, QPSK on satellite links) and QAM (quadrature amplitude modulation), which changes amplitude and phase together. Each distinct state is a symbol; a constellation diagram plots every allowed symbol as a point, with distance from the center as amplitude and angle as phase. The two axes are called I (in-phase) and Q (quadrature).

Each step up (4× the points, 2 more bits per symbol) needs roughly 6 dB more SNR, so radios use adaptive modulation and coding: dense QAM near the access point or tower, QPSK or BPSK far away, switching many times a second. The coding rate (3/4, 5/6) says how much of each symbol is FEC.

OFDM

OFDM (orthogonal frequency-division multiplexing) sends data on many narrow subcarriers side by side instead of one fast carrier, each carrying its own QAM symbol. The spacing is chosen so each subcarrier's peak falls on every other subcarrier's zero (orthogonal), so they overlap without interfering. Two things make it the default for modern radio:

• Each subcarrier's symbols are long, and a short copy of the end of each symbol (the cyclic prefix) is sent first, so echoes arriving a little late don't smear one symbol into the next.
• A fade that wipes out a few subcarriers loses only a few symbols, which FEC repairs.

Transmitters build OFDM with an inverse FFT and receivers take it apart with an FFT. OFDMA gives different groups of subcarriers to different users at the same time.

Free-space path loss

Even in empty space a signal weakens with distance because its power spreads over an ever larger sphere: power per square meter falls with 1/d² (the inverse-square law). For two isotropic antennas the loss is

2.4 GHz at 100 m:  20·log10(0.1) + 20·log10(2400) + 32.44
                 = −20 + 67.6 + 32.44 = 80.0 dB
2.4 GHz at 1 km:   100.0 dB  (10× the distance = +20 dB)
5.8 GHz at 1 km:   107.7 dB  (2.4× the frequency ≈ +7.7 dB)

• Doubling the distance costs 6 dB; ten times the distance costs 20 dB.
• The frequency term comes from the receiving antenna's size, which shrinks with wavelength. With same-size dishes at both ends, higher frequencies win it back, since dish gain grows with f².
• Indoors and in cities, loss grows faster than in free space (as d³ or d⁴ is common) because of walls, bodies and clutter.

Line of sight and the Fresnel zone

Above about 30 MHz, radio travels mostly in straight lines: the two ends need line of sight (LOS), and hills, buildings and the curve of the Earth block it. The atmosphere bends signals slightly downward, so the radio horizon is a little beyond the visible one:

horizon (km) ≈ 4.12 × √(antenna height in m)
30 m mast:                 4.12 × 5.48 ≈ 23 km
30 m mast to a 2 m phone:  4.12 × (5.48 + 1.41) ≈ 28 km

Clear sight isn't enough. Most of the energy travels in a football-shaped region around the straight line, the first Fresnel zone. An obstacle inside it causes reflection and diffraction losses even when the two antennas can see each other.

radius at the middle of the link: r = ½ × √(λ × d)
1 km at 2.4 GHz:   ½ × √(0.125 × 1000)  ≈ 5.6 m
10 km at 5.8 GHz:  ½ × √(0.0517 × 10000) ≈ 11.4 m

Ground wave, skywave and the ionosphere

How far a signal goes depends heavily on frequency, because the ground and the upper atmosphere treat different frequencies differently.

• Ground wave: LF and MF waves, vertically polarized, follow the Earth's curve, best over seawater. AM stations reach a few hundred kilometers this way by day.
• Skywave: the ionosphere is a set of layers of gas ionized by the Sun's ultraviolet and X-rays, from about 60 to over 500 km up. The D layer (≈ 60–90 km) absorbs MF and low HF by day and vanishes at night, which is why AM radio carries much farther after dark. The E (≈ 90–150 km) and F (≈ 150–500 km) layers bend HF back down; one hop covers up to about 4,000 km, and several hops can circle the globe.
• The skip zone lies beyond the ground wave and short of the first skywave landing: no signal.
• The highest frequency that still comes back (the MUF, maximum usable frequency) changes with time of day, season and the 11-year solar cycle. Above it, waves escape into space, which is why satellites use VHF and higher. The ionosphere still delays GPS signals slightly; dual-frequency receivers measure and remove that error.

Multipath, fading and penetration

• Reflection: signals bounce off the ground, walls, water and metal.
• Diffraction: they bend around edges such as hilltops and roofs, more at lower frequencies.
• Scattering: rough surfaces, foliage and rain spray energy in many directions.
• Multipath: the receiver gets several copies with slightly different delays, which add up or cancel. Moving half a wavelength (6 cm at 2.4 GHz) can change the signal by 20–30 dB. Long delays smear symbols together (intersymbol interference), which OFDM's cyclic prefix absorbs.
• Fading is fast (small-scale, from multipath and motion) or slow (shadowing by buildings and hills). Motion also shifts frequency slightly (Doppler).

Penetration falls as frequency rises. Low bands (600–900 MHz) reach deep indoors and cover wide areas, which is why mobile operators prize them. 5 and 6 GHz Wi-Fi loses more through walls than 2.4 GHz. Millimeter waves (24 GHz and up) are stopped by walls, bodies, leaves and coated glass. Rain attenuates signals above about 10 GHz (satellite rain fade), and oxygen absorbs about 15 dB per km near 60 GHz, which keeps 60 GHz links short and private. Metal reflects almost everything; concrete, brick and water absorb a lot.

Noise, SNR and Shannon capacity

Noise is the random signal that is always present: thermal noise from electrons jiggling in the receiver itself, natural noise from the sky, electrical noise from machines, and interference from other transmitters. Thermal noise is −174 dBm per hertz of bandwidth at room temperature, and a real receiver adds its noise figure, typically 3–8 dB:

noise floor, 20 MHz channel
  −174 dBm/Hz + 10 × log10(20,000,000) = −174 + 73 = −101 dBm
  + a 6 dB noise figure                            = −95 dBm

SNR (signal-to-noise ratio) is the received signal minus the noise floor, in dB; SINR also counts interference. Claude Shannon showed in 1948 that a channel of bandwidth B can carry at most

bits per second without errors, with S/N as a plain ratio, not dB.

20 MHz channel, signal −68 dBm, noise −95 dBm
  SNR = 27 dB = 10^(27/10) ≈ 500
  C = 20 MHz × log2(501) ≈ 20 MHz × 8.97 ≈ 179 Mb/s
+3 dB of power (SNR 1000): ≈ 199 Mb/s, only +1 bit/s per Hz
2× the bandwidth at the same SNR: ≈ 358 Mb/s

Capacity grows in proportion to bandwidth but only with the logarithm of power, which is why operators pay for spectrum and add MIMO streams rather than shouting louder. Real systems stay below the limit: one Wi-Fi 6 stream in 20 MHz tops out at 143 Mb/s (1024-QAM, which needs an SNR in the mid-30s dB).

Link budget

A link budget adds up every gain and loss between transmitter and receiver to predict the received power and check it against what the receiver needs.

received (dBm) = TX power − TX cable loss + TX antenna gain
               − path loss
               + RX antenna gain − RX cable loss
margin (dB)    = received − receiver sensitivity

• The −82 dBm figure is the 802.11 minimum sensitivity for 6 Mb/s OFDM; for 54 Mb/s it is −65 dBm, so this link would not hold the fastest legacy rate. Real chips do a few dB better than the minimums.
• Keep a fade margin of 10–20 dB for fixed links, more for moving ones, plus a rain margin above 10 GHz.
• EIRP is capped by regulators: in the EU, 2.4 GHz Wi-Fi may radiate at most 20 dBm EIRP (100 mW); in the US, 1 W into an antenna of up to 6 dBi (36 dBm EIRP), with more allowed for fixed point-to-point links.
• A link must close in both directions; the weaker end (often a phone or sensor) usually decides.

Duplexing and multiple access

A radio generally can't hear on a frequency while it transmits on it: its own signal is many orders of magnitude stronger than anything arriving. Two-way radio uses one of two duplexing schemes:

Sharing a channel among many users works as described in Networking from scratch, with some radio-specific twists:

Regulation

Spectrum is finite and shared by everyone in range, so governments decide who may transmit where, at what power, and for what.

• The ITU (International Telecommunication Union, a UN agency) keeps the Radio Regulations, a treaty that allocates bands to services (broadcast, mobile, satellite, radar, amateur). They are revised at a World Radiocommunication Conference (WRC) every 3–4 years; WRC-23 met in Dubai and the next is WRC-27.
• The world is split into three ITU regions with partly different allocations, which is why some devices are sold in regional versions.
• National regulators apply the rules, license users and certify equipment (an FCC ID in the US, CE marking in the EU).

ISM bands (industrial, scientific and medical) were set aside for equipment such as microwave ovens and RF heaters; unlicensed radios share them and must tolerate the interference.

Most of Wi-Fi's 5 GHz and 6 GHz spectrum is not ISM but separate unlicensed allocations (U-NII in the US).

Software-defined radio

A software-defined radio (SDR) does in software what radios once did with dedicated circuits. The hardware only filters and amplifies the antenna signal, shifts a chosen slice of spectrum down to a low frequency (the tuner and mixer) and digitizes it with an ADC into a stream of I/Q samples: pairs of numbers that are exactly the I and Q coordinates of the constellation diagram. Demodulation and decoding then run on a computer. Phones and base stations work the same way inside.

Software: SDR++, GQRX or SDR# for a live spectrum waterfall; GNU Radio to build signal chains; dump1090 for aircraft ADS-B; rtl_433 for sensors. Things to listen to: FM broadcast, airband voice (AM, 118–137 MHz), aircraft positions at 1090 MHz, weather stations and doorbells at 433.92 MHz, and ships' AIS at 161.975 and 162.025 MHz near coasts. An RTL-SDR can't reach 2.4 GHz Wi-Fi.

rtl_test                      # find the dongle; Ctrl-C
rtl_fm -f 96.3e6 -M wbfm -s 200000 -r 48000 - \
  | aplay -r 48000 -f S16_LE -t raw -c 1   # an FM station
rtl_power -f 88M:108M:10k -i 10 -e 5m fm.csv  # band scan
rtl_433                       # decode 433.92 MHz sensors
dump1090 --interactive        # aircraft at 1090 MHz

Your Wi-Fi card is a receiver too:

iw dev wlan0 link             # signal in dBm, rate, channel
sudo iw dev wlan0 scan | grep -E 'SSID|signal|freq'

On macOS, Option-click the Wi-Fi menu to see RSSI (received power in dBm) and noise.

References

• ITU Radio Regulations (opens in a new tab): the international treaty allocating the spectrum
• ITU-R V.431 (opens in a new tab): names and limits of the frequency bands (VLF to EHF)
• ITU-R P.525 (opens in a new tab): calculating free-space attenuation
• ITU World Radiocommunication Conferences (opens in a new tab): how allocations change
• NTIA United States Frequency Allocation Chart (opens in a new tab): who uses every US band
• 47 CFR Part 15 (opens in a new tab): US rules for unlicensed radio devices
• NOAA Space Weather Prediction Center: Ionosphere (opens in a new tab): layers and how the Sun changes them
• Shannon, "A Mathematical Theory of Communication" (1948) (opens in a new tab): the channel capacity paper
• PySDR (opens in a new tab): a free, hands-on guide to SDR, I/Q samples, modulation and OFDM
• RTL-SDR quick start guide (opens in a new tab): setting up a dongle and first things to receive