11.1 GPS L1 C/A from satellite to fix
A GPS satellite transmits 50 bps of navigation data, BPSK-modulated, spread by a 1.023 Mcps PRN code unique to that satellite, on the L1 carrier at 1575.42 MHz. By the time the signal reaches the surface of the Earth, it is at about dBm, well below the thermal noise floor in any 2 MHz front-end. Each receiver tracks (typically) at least four satellites simultaneously. Each tracking channel multiplies the received band by a locally-generated copy of that satellite's PRN, integrates for a millisecond (one full PRN period), and despreads. The 43 dB of processing gain plus a few seconds of coherent integration lifts the signal out of the noise. Once locked, the navigation message is read at 50 bps, ephemeris and almanac are decoded over 30 seconds (a full subframe set takes longer), pseudorange to each satellite is measured from the code phase, and a four-equation, four-unknown system (three coordinates and clock bias) solves for receiver position. This was in everyone's car by 2010 and in everyone's phone by 2015.
11.2 Voyager 1 telemetry from beyond the heliopause
Distance: 24 billion kilometers as of 2024. Two-way light time: 45 hours. Received signal power: about W, twenty orders of magnitude below your phone's receive sensitivity. It works because of three things: 70-meter Deep Space Network dishes with cryogenic LNAs (system noise temperature about 30 K), a long coherent integration time of seconds per symbol, and concatenated channel coding (rate-1/2 K=7 convolutional inner code with Viterbi decoding, plus an outer Reed-Solomon RS(255, 223) code, with a depth-4 interleaver between them). Net data rate from Voyager 1 today: 160 bps. The system operates within 1.6 dB of Shannon, an engineering marvel from 1977.
11.3 The cellular voice revolution and A5/1
GSM, the dominant 2G cellular standard, encrypts the air interface with a stream cipher called A5/1. It uses three short LFSRs whose state is XORed into the bits as they go on air. The cipher was developed in the 1980s under export restrictions and weakened deliberately. By 2009, time-memory tradeoff attacks had reduced A5/1 to a few seconds of cracking on commodity hardware. Hundreds of millions of GSM voice calls are still made daily on 2G networks where it survives, and they are vulnerable. The lessons cross over to digital comms generally: a good modulation and channel code do not save you from a weak cipher, and export-grade cryptography is rarely safe.
11.4 Wi-Fi 6 mixed-mode in your home
A Wi-Fi 6 access point talks to a 2018 laptop using 256-QAM and to a 2024 phone using 1024-QAM, on different MU-MIMO streams within the same OFDMA frame. The frame carries some packets through LDPC at rate 5/6 and others through rate 1/2 LDPC for higher robustness. Between bursts, the radio falls back to QPSK to manage retries and beacons. All of this is happening across an 80 MHz channel that may have notches from microwaves, baby monitors, and your neighbour's APs. The receiver runs adaptive equalization plus per-subcarrier compensation, and the MAC layer uses CRC-32 to confirm each frame. Every operation we discussed in this chapter, every chapter, is happening on the air right now in your own house.