Wireless interfaces §

Step 1 — The link budget. A transmitter radiates power $P_{tx}$; the wave spreads over a sphere of radius $d$, so the power density falls as $1/d^2$ (the inverse-square law of wave propagation). Antennas focus the energy: a gain $G_{tx}$ on the transmit side and $G_{rx}$ on the receive side. Collecting the terms in decibels gives the link budget: $P_{rx} = P_{tx} + G_{tx} + G_{rx} - \mathrm{FSPL}$. The Friis equation behind the FSPL formula also carries a $20\log_{10}(f)$ term: at higher frequencies, the same aperture antenna captures less power, which is why mmWave links are short-range.

Step 2 — A worked example. A Wi-Fi access point at 2.4 GHz, 1 m from a laptop: FSPL = 32.44 + 20·log₁₀(0.001) + 20·log₁₀(2400) = 32.44 − 60 + 67.6 ≈ 60 dB. With P_tx = 20 dBm (100 mW) and 0 dB gains, the receiver gets −40 dBm — comfortably above a typical −80 dBm sensitivity. At 100 m the path loss is 80 dB and the received power −60 dBm: still workable, but with much less margin.

Step 3 — Modulation versus range. A receiver needs a minimum signal-to-noise ratio (SNR) per modulation: QPSK carries 2 bits/symbol at ~10 dB SNR; 256-QAM carries 8 bits/symbol but needs ~28 dB; 1024-QAM needs ~35 dB. Since SNR falls with distance, real systems use adaptive modulation: full speed close to the access point, dropping to QPSK at the cell edge. This is the fundamental throughput-versus-range trade-off of every wireless interface below.

Step 4 — Multipath fading. In indoor and urban environments the wave reaches the receiver by many reflected paths of different lengths. The copies add constructively or destructively depending on frequency and position, so the received power fluctuates (fading) rather than following a clean inverse-square curve. Two standard mitigations: OFDM splits the band into many narrow sub-carriers so that each experiences only flat fading, and MIMO uses multiple antennas so that several independent fading paths exist simultaneously.

Step 5 — Explore it interactively. The simulator below computes the link budget and Shannon-limited data rate for five real interfaces. Move the distance slider and watch the achievable modulation fall as the SNR drops.

Step 6 — Sources and limits. The Shannon bound $C = B\log_2(1+\mathrm{SNR})$ is derived in Communication; the wave phenomena (reflection, diffraction, inverse-square spreading) in Wave propagation and Electromagnetism.

Step 1 — Sharing the medium. All devices in a cell share the same frequency band. Classic Wi-Fi coordinates access with CSMA/CA (Carrier Sense Multiple Access with Collision Avoidance): listen before transmitting, back off a random time if busy. Wi-Fi 6 adds OFDMA (Orthogonal Frequency-Division Multiple Access): the access point schedules groups of OFDM sub-carriers to several users simultaneously, which is far more efficient for many small packets.

Step 2 — OFDM sub-carriers. The channel is divided into many narrow sub-carriers (78.125 kHz each in 802.11ax), modulated independently. Because each sub-carrier is narrow compared with the channel’s frequency-selective fading, each experiences only flat fading — this is the multipath defence from Wireless link fundamentals. The diagram shows an OFDMA frame: the AP assigns sub-carrier groups (resource units) to different users.

Step 3 — The bands and channels. 2.4 GHz: three non-overlapping 20 MHz channels (11 channels defined in North America, 13 in Europe). 5 GHz: up to 25 non-overlapping 20 MHz channels depending on region, aggregable into 40/80/160 MHz. 6 GHz (Wi-Fi 6E/7): 7 × 160 MHz channels, or 3 × 320 MHz channels for Wi-Fi 7. Wider channels raise the data rate proportionally but concentrate interference and reduce the number of non-overlapping networks.

Step 4 — MIMO. Multiple antennas at both ends create independent spatial streams: spatial multiplexing multiplies throughput by the stream count, while beamforming focuses energy toward a client and extends range (see the 5G section for the beamforming diagram — the principle is identical).

Step 5 — Worked example (the 9.6 Gb/s peak). The standard’s table value for HE160 MCS11 (1024-QAM, rate 5/6) is 1201 Mb/s per stream at 400 ns guard interval (after pilots, training fields and overhead). Eight spatial streams: 8 × 1201 = 9608 ≈ 9.6 Gb/s. Real throughput is ~60–70% of PHY rate after framing, ACKs and retransmissions.

Step 6 — Sources. IEEE 802.11ax defines the rate tables used above; 802.11be (Wi-Fi 7) adds 320 MHz and 4096-QAM.

Step 1 — Design goals. Bluetooth targets personal-area networking: headphones, keyboards, mice, wearables. The driving constraints are power (µW in sleep, mW transmitting) and cost, not peak throughput — a sensor that must run a year on a coin cell accepts 100 ms of latency to save radio-on time.

Step 2 — Frequency hopping. The 2.4 GHz band is crowded (Wi-Fi, microwave ovens, Zigbee). Bluetooth defends itself with FHSS: 79 × 1 MHz channels (BR/EDR) or 40 × 2 MHz channels (LE), hopping pseudo-randomly. A narrowband interferer only corrupts the occasional hop; the link retransmits and adapts the channel map. The animation below shows a BLE connection hopping across its 37 data channels (37–39 are reserved for advertising); the red channels are corrupted by a fixed Wi-Fi network.

Step 3 — Connection events and power. A BLE connection exchanges data only during short connection events, separated by the connection interval (7.5 ms – 4 s, negotiated). One frequency hop occurs per connection event. A longer interval means fewer hops, less radio-on time, lower power, more latency — the central trade-off of BLE scheduling.

Step 4 — Worked example. A BLE mouse with a 100 ms connection interval wakes for ~2 ms per event: a duty cycle of ~2%, averaging tens of µW. A BR/EDR audio link instead streams continuously at 1600 hops/s, accepting ~1 mW for constant throughput.

Step 5 — Sources. The Bluetooth Core Specification defines the hopping sequences, channel map and connection intervals.

Step 1 — Near field versus far field. Every antenna has two regions. In the far field, energy radiates away as waves and power falls as $1/r^2$. In the near field (within roughly one wavelength: 22 m at 13.56 MHz), the dominant interaction is magnetic coupling between loop antennas, and the coupled energy falls as $1/r^3$. That extra power of $r$ is what confines NFC to centimetres — a security feature as much as a limitation: eavesdropping or relay attacks require proximity.

Step 2 — Load modulation. The tag is passive: it has no battery. The reader’s 13.56 MHz field induces a current in the tag’s loop antenna, which powers the tag’s chip. The tag then answers by loading its antenna slightly, which the reader senses as a tiny change in the reader’s own field current — speaking by modulating the reader’s power, not by transmitting.

Step 3 — Worked example. A contactless payment: the phone is held within 4 cm of the terminal. The reader polls at 13.56 MHz; the card responds with its UID and payment data (EMV). The whole transaction takes under a second; the RF exchange itself is a few milliseconds.

Step 4 — Relation to RFID. NFC is a subset of RFID (Radio-Frequency Identification). The distinction: NFC supports peer-to-peer mode (two powered devices take turns as reader and tag), while classic RFID is strictly reader→tag.

Step 5 — Sources. ISO/IEC 14443 defines the A/B modulation and framing; the NFC Forum defines the higher-level modes (P2P, card emulation, NDEF data exchange).

Step 1 — Niche. Zigbee sits between Bluetooth (higher rate, fewer devices, star topology) and LoRa (kilometre range, bits per second). Its niche: hundreds of battery-powered sensors (lights, locks, thermostats) forming a self-healing mesh in a home or building, each message a few dozen bytes.

Step 2 — The mesh. Three node types: a coordinator (one per network), routers (mains-powered, forward packets), and end devices (battery-powered, sleep almost always, talk only to their parent router). Routing over multiple hops extends coverage far beyond a single 10–100 m radio hop; if a router dies, packets reroute — the dashed link below.

Step 3 — Power discipline. End devices sleep > 99% of the time and wake on a beacon or a schedule. A sensor sending 20 bytes every 60 s at 250 kb/s is on the air for 20×8/250000 = 0.64 ms per minute — a duty cycle of ~0.001%, which is how a coin cell lasts years.

Step 4 — Coexistence. Zigbee shares 2.4 GHz with Wi-Fi and Bluetooth. Its 5 MHz DSSS channels are narrow and low-power; deployments place the network on a 2.4 GHz channel between the Wi-Fi channels (e.g. Zigbee channels 15, 20 or 25 sit between the popular Wi-Fi 1, 6 and 11).

Step 5 — Related low-power and wide-area interfaces. UWB (802.15.4z, ~500 MHz bandwidth at 6–8 GHz) trades range (~10 m) for centimetre-precision ranging — used for digital car keys and asset trackers. LoRa uses sub-GHz ISM bands with chirp spread spectrum to trade rate (kb/s) for kilometres of range in IoT telemetry. GNSS (GPS, Galileo: L-band 1.1–1.6 GHz) is a receive-only wireless interface: one-way satellite broadcasts, position computed from the time-of-arrival of four or more satellites.

Step 6 — Sources. IEEE 802.15.4 defines PHY and MAC; the Connectivity Standards Alliance defines the Zigbee routing and application layers on top.

Step 1 — Flexible OFDM numerology. 5G NR uses OFDM (downlink) and DFT-s-OFDM (uplink, lower peak-to-average power for handsets) with scalable sub-carrier spacing: 15, 30, 60, 120 or 240 kHz. The spacing sets the slot length: a slot is 14 OFDM symbols, so at 15 kHz a slot is 1 ms, at 30 kHz 0.5 ms, at 120 kHz 0.125 ms — finer spacing for wide coverage, coarser for low latency and mmWave.

Step 2 — Massive MIMO and beamforming. Base stations use 64–256 antenna elements. Driving each element with a controlled phase shift makes the wavefronts add constructively in one direction and cancel elsewhere: a steerable beam with ~10·log₁₀(N) dB of array gain (18 dB for 64 elements) aimed at each user. This is what lets the same spectrum serve many users simultaneously without interfering.

Step 3 — mmWave and slicing. FR2 (24–71 GHz) offers up to 400 MHz per carrier but suffers the frequency term of the path-loss formula plus atmospheric absorption: ~100–200 m cells, suited to stadiums and dense urban hotspots. Network slicing lets one physical network carry multiple virtual networks with different QoS (IoT, URLLC, eMBB).

Step 4 — Worked example. A mid-band deployment: 3.5 GHz, 100 MHz, 4-layer MIMO. Per stream, 100 MHz at 30 kHz spacing gives 273 resource blocks × 12 = 3276 sub-carriers; at 256-QAM (8 bits/symbol) with 14 symbols per 0.5 ms slot, that is 3276 × 8 × 14 / 0.0005 ≈ 734 Mb/s per stream, ≈ 2.9 Gb/s for 4 streams before overhead — consistent with real-world mid-band 5G measurements of 1–2 Gb/s.

Step 5 — Sources. 3GPP TS 38.211 defines the OFDM numerology and resource grid; ITU-R M.2150 (IMT-2020) sets the 20 Gb/s peak-rate requirement.

Step 1 — The geometry sets the latency. One-way propagation delay is slant range / c. The diagram shows the three regimes and the slant range from a ground terminal to a satellite (longer than the altitude, except directly overhead).

Step 2 — Path loss and Doppler. At 12 GHz over a 1200 km LEO slant range, FSPL = 32.44 + 20·log₁₀(1200) + 20·log₁₀(12000) ≈ 169.6 dB; at 20 GHz over 550 km it is ≈ 173 dB. Both ends answer with high-gain antennas: the Starlink user terminal is a phased array (~1280 elements) that steers its beam electronically as satellites cross the sky. A LEO satellite moves at ~7.5 km/s, so the Doppler shift is Δf = v·f/c = 7500 × 20×10⁹ / 3×10⁸ ≈ 500 kHz at 20 GHz — three orders of magnitude beyond a terrestrial mobile cell’s Doppler, and the terminal must track and compensate it continuously.

Step 3 — Latency and TCP. LEO one-way is ~4–6 ms of pure propagation per hop (20–60 ms end-to-end with multiple hops and processing); GEO is ~119 ms one-way, so a single-hop echo (terminal → satellite → gateway) round-trips in ~238 ms, and a user-to-user connection across two GEO hops sees ~480–600 ms RTT. Long RTT inflates the bandwidth-delay product, so TCP needs large windows (or satellite-specific proxies) to keep the pipe full — see Networks.

Step 4 — Worked example. A Starlink user terminal links to a LEO satellite in Ku-band: downlink 10.7–12.7 GHz, uplink 14.0–14.5 GHz (the Ka-band 20/30 GHz links connect satellites to the gateways). The phased array (~1280 elements) hands the beam from satellite to satellite every few minutes as LEO satellites pass overhead; per-user downlink rates are ~50–250 Mbps.

Step 5 — Sources. ITU-R regulates the Ku/Ka spectrum allocations; the CCSDS defines the space-link protocols used above them.

A Wi-Fi 6 router (4×4 MIMO, 160 MHz, 256-QAM, rate 5/6) and a 5G NR cell (4-layer MIMO, 100 MHz, 256-QAM, 30 kHz sub-carrier spacing) both serve a single user. Which provides the higher peak PHY rate, and by what factor?