What is a radio link

A radio link moves bits from one place to another through the air. Every link has three parts: a transmitter that turns bits into a radio wave, a channel that carries and damages that wave, and a receiver that turns what arrives back into bits. This lesson walks through each part, then looks at the three numbers that shape every design decision: the carrier frequency, the bandwidth and the received power. It is the starting point of the beginner track and needs no code. The later lessons build each piece in Python.

The vocabulary here is the same whether the link is a Bluetooth earbud, a 5G NR base station or a satellite downlink. The numbers change by orders of magnitude between them. The structure does not.

The signal chain

Start with the transmitter. A stream of bits arrives from the application. The first stage adds structure that the receiver will need. It adds redundancy (channel coding, so the receiver can correct errors), and it groups the coded bits into symbols. Each symbol is a point on a constellation diagram, a complex number with an in-phase part I and a quadrature part Q. Lesson 05 covers how bits map to these points.

The symbols are then shaped into a smooth waveform so that the signal occupies a controlled band of frequencies. A digital-to-analogue converter (DAC) turns the I and Q sample streams into two analogue voltages. A mixer driven by a local oscillator (LO) shifts this low-frequency signal up to the carrier frequency. A power amplifier raises it to the level the link needs, and the antenna converts the electrical signal into a radiated wave.

The receiver runs the chain backwards. The antenna collects a tiny fraction of the transmitted power. A low-noise amplifier (LNA) raises it while adding as little noise of its own as possible. A second mixer shifts it back down to near zero frequency. An analogue-to-digital converter (ADC) samples I and Q, and digital processing synchronises, demodulates and decodes them into bits.

Two features of this chain matter for everything that follows. First, the processing in the left half is digital and works on complex numbers near zero frequency. That representation is called complex baseband, and lesson 02 explains why it works. Second, the right half is analogue and carries real voltages at the carrier frequency. A software-defined radio moves the boundary between the two as far towards the antenna as it can, so that most of the chain becomes code. The software-defined radio hub covers the hardware.

The channel

Everything between the two antennas is the channel. It does four things to the signal.

It attenuates it. A transmitter that radiates 1 W can leave a receiver with less than a picowatt. That is a ratio of 10¹² or more, which is why engineers work in decibels (see below). The attenuation is called path loss. Its simplest model is free-space path loss, which lesson 03 derives.

It delays and smears it. The wave reaches the receiver by several routes: directly, and by reflection off buildings, the ground and vehicles. Each route has its own delay and phase. This is multipath. The copies add, sometimes in phase and sometimes not, so the received power varies over a few centimetres of movement. That variation is fading, the subject of lesson 07.

It adds noise. Every resistor, amplifier and antenna adds random thermal noise, and the sky and the ground add their own. The receiver cannot remove it. It sets the floor below which a signal cannot be recovered. Lesson 04 puts numbers on it.

It adds other people’s signals. Interference from other transmitters in the same or adjacent bands is often the real limit in a busy band. Regulators allocate spectrum to keep it manageable, and the spectrum and regulation hub covers how.

Carrier frequency and what it sets

The carrier frequency is where the signal sits in the radio spectrum. It fixes the wavelength, and the wavelength fixes much of the link’s behaviour. In free space the wavelength is the speed of light divided by the frequency. The speed of light is 299 792 458 m/s exactly, by the definition of the metre. A few values:

Carrier frequency	Wavelength	Half-wavelength (a dipole’s length)
100 MHz	3.00 m	1.50 m
700 MHz	42.8 cm	21.4 cm
2.4 GHz	12.5 cm	6.2 cm
3.5 GHz	8.57 cm	4.28 cm
28 GHz	1.07 cm	5.4 mm

The wavelength sets antenna size. A resonant antenna such as a half-wave dipole is about half a wavelength long. At 100 MHz that is a metre and a half of metal. At 28 GHz it is a few millimetres, so dozens of antenna elements fit in the space of a coin. That is why massive MIMO arrays and beamforming are routine at millimetre-wave frequencies and rare below 1 GHz.

The wavelength also sets how much power an antenna of a given gain collects. An antenna’s effective aperture, the area over which it captures the passing wave, scales with the square of the wavelength for a fixed antenna gain. Between two antennas of fixed gain, the received power therefore falls as the frequency rises. Recommendation ITU-R P.525-5 gives the free-space basic transmission loss between isotropic antennas as 32.4 + 20 log10(f) + 20 log10(d) dB, with f in MHz and d in km. The 20 log10(f) term means that every tenfold increase in frequency costs 20 dB. Moving a link from 700 MHz to 3.5 GHz costs 14.0 dB, and moving it from 3.5 GHz to 28 GHz costs another 18.1 dB, if the antenna gains stay the same.

This is not a law that higher frequencies travel less far. It is a statement about fixed-gain antennas. If the antenna area stays the same instead, the gain rises with frequency at both ends and more than recovers the loss. The catch is that a high-gain antenna has a narrow beamwidth and must be pointed. Millimetre-wave systems spend much of their complexity on that pointing.

Other effects do depend on frequency directly:

• Lower frequencies diffract around obstacles and pass through walls and foliage with less loss. This is why the sub-1 GHz bands carry wide-area coverage.
• Rain attenuates the signal, and the loss per kilometre grows with frequency. Recommendation ITU-R P.838-3 gives a model for this specific attenuation from 1 GHz to 1000 GHz.
• Atmospheric gases absorb at particular frequencies. Recommendation ITU-R P.676-13 shows that near 60 GHz many oxygen absorption lines merge at sea-level pressure into one broad absorption band. A link there loses power to the air itself, which limits range but also limits interference between neighbours.
• Higher bands have more spectrum available. A 100 MHz wide channel is a large share of the spectrum below 1 GHz and a small one at 28 GHz.

The 5G NR specifications show the trade in practice. In 3GPP TS 38.101-1 (Release 19), frequency range FR1 runs from 410 MHz to 7125 MHz. Band n78, a widely used mid-band, spans 3300 MHz to 3800 MHz and is operated in time-division duplex. 3GPP TS 38.101-2 (Release 19) splits FR2 into FR2-1, from 24.25 GHz to 52.6 GHz, and FR2-2, from 52.6 GHz to 71 GHz. Band n257, for example, spans 26.5 GHz to 29.5 GHz. Which bands an operator may use is decided country by country by the national regulator.

Bandwidth

Bandwidth is the width of the frequency range the signal occupies. It is set mainly by the symbol rate. A signal that sends 1 million symbols per second needs roughly 1 MHz of spectrum, plus some excess that depends on the pulse shaping covered in lesson 06.

Bandwidth is a resource with two sides. More bandwidth carries more symbols per second, so more bits per second. But the receiver must also accept noise across the whole bandwidth. Thermal noise power is proportional to bandwidth, so doubling the bandwidth doubles the noise power and costs 3 dB of signal-to-noise ratio. Claude Shannon’s capacity formula, which lesson 04 works through, captures both effects in one expression. Its practical message is that data rate grows roughly in proportion to bandwidth but only with the logarithm of signal power.

Bandwidth also interacts with the channel. When the signal’s bandwidth is wider than the channel’s coherence bandwidth, different frequencies in the signal fade differently and the symbols smear into each other. OFDM deals with exactly that problem. It is the multicarrier waveform specified for the LTE downlink in 3GPP TS 36.211 and for 5G NR in 3GPP TS 38.211 (both checked at their Release 19 versions). Lesson 08 builds one.

Decibels, a first look

A decibel expresses a power ratio on a logarithmic scale: 10 times the base-10 logarithm of the ratio. A factor of 10 is 10 dB, a factor of 100 is 20 dB, and a factor of 2 is 3.01 dB, usually rounded to 3 dB. A factor of one half is −3 dB.

Two reasons make decibels the working unit of radio. The first is range. A path loss of 10⁹ is 90 dB, a number you can do arithmetic on in your head. The second is that gains and losses in a chain multiply, and logarithms turn multiplication into addition. A cable that loses half the power (−3 dB) followed by an amplifier with a gain of 100 (+20 dB) gives a net gain of 17 dB.

A decibel on its own is a ratio. To express an absolute power, the reference is named in the unit. dBm is power relative to 1 mW, so 0 dBm is 1 mW, 30 dBm is 1 W and −90 dBm is 1 pW. dBW is power relative to 1 W, so 0 dBW equals 30 dBm. dBi is antenna gain relative to an ideal isotropic antenna that radiates equally in every direction.

The rule that prevents most mistakes: add dB to dBm and get dBm, add dB to dB and get dB, but never add dBm to dBm. A 20 dBm transmitter into a 6 dBi antenna gives 26 dBm of effective isotropic radiated power. Two 0 dBm signals combined give 3 dBm, not 0 dBm plus 0 dBm. Lesson 03 turns this into a full link budget.

Exercise

1. A transmitter puts 23 dBm into a cable with 2 dB of loss, which feeds an antenna with 8 dBi of gain. What is the EIRP in dBm and in watts?
2. A link at 900 MHz is moved to 5.8 GHz with the same antennas and distance. Using the P.525 formula, how many dB of extra path loss does the move cost?
3. A dipole for the 2.4 GHz band is about 6 cm long. How long is a dipole for 433 MHz? Would it fit in a wristwatch?
4. Two receivers are identical except that one uses a 20 MHz bandwidth and the other a 5 MHz bandwidth. By how many dB do their thermal noise powers differ?
5. Redraw the signal chain for a receiver that samples directly at the carrier frequency with no mixer. Which block has to work much harder?

Summary

• A radio link is a transmitter, a channel and a receiver. Both radios convert between digital I and Q samples near zero frequency and an analogue signal at the carrier frequency.
• The channel attenuates, delays, smears and adds noise and interference. Path loss, multipath, fading and noise each get their own lesson later in the track.
• The carrier frequency sets the wavelength, which sets antenna size and, for fixed-gain antennas, adds 20 dB of path loss per tenfold rise in frequency.
• Bandwidth buys symbol rate but admits noise in proportion. Data rate grows with bandwidth and only logarithmically with power.
• Decibels turn chains of gains and losses into sums. dB is a ratio, dBm and dBW are absolute powers, and dBi is antenna gain against an isotropic antenna.

Further reading

• Recommendation ITU-R P.525-5, Calculation of free-space attenuation (11/2024): the free-space loss formulas used in this lesson and the next.
• 3GPP TS 38.101-1, NR user equipment radio transmission and reception, Part 1: Range 1 standalone: the FR1 operating band table, including n78.
• A. Goldsmith, Wireless Communications, Cambridge University Press, 2005: chapter 1 surveys wireless systems and chapter 2 covers path loss and shadowing.
• T. S. Rappaport, Wireless Communications: Principles and Practice, 2nd edition, Cambridge University Press, 2024 reissue: the standard engineering text on cellular radio systems and propagation.