Modulation

Overview

Modulation maps bits onto changes in a carrier that the receiver can detect. A carrier has three properties to change: amplitude, frequency and phase. Every digital scheme in use changes one of them or a combination. The choice decides how many bits each symbol carries, how much SNR the receiver needs, how much bandwidth the signal occupies and how linear the power amplifier must be.

This hub covers the schemes in everyday use, from the on-off keying of a remote control to the 1024QAM of a 5G NR downlink. It is for engineers who need to choose a scheme, read a constellation plot, or understand why a link changed its modulation when the SNR dropped.

Key ideas

Keying a carrier

Amplitude-shift keying (ASK) changes the amplitude. Its simplest form, on-off keying, is cheap to build and still common in low-cost sensors, but it wastes power and is sensitive to fading. Frequency-shift keying (FSK) changes the frequency. With smooth phase transitions it keeps a constant envelope, so the power amplifier can run in saturation at high efficiency. That makes FSK variants popular in battery-powered devices. Phase-shift keying (BPSK, QPSK, 8PSK) changes the phase at constant amplitude. Quadrature amplitude modulation (QAM) changes amplitude and phase together and packs the most bits into each symbol, at the cost of a varying envelope and tighter requirements on noise, linearity and phase noise.

Constellations and mapping

A constellation diagram plots each symbol as a point in the I/Q plane. M points carry log2 M bits per symbol. Gray mapping labels neighbouring points with bit patterns that differ in one bit, so the most likely symbol error, to a neighbour, costs only one bit error. The receiver usually passes soft information to the decoder rather than hard bits: a log-likelihood ratio for each bit, computed from the distance to the nearest points labelled 0 and 1.

3GPP TS 38.211 (Release 19 version) defines π/2-BPSK, QPSK, 16QAM, 64QAM, 256QAM and 1024QAM for NR. Downlink 1024QAM for FR1 was introduced in Release 17. The quality of a real transmitter’s constellation is measured as error vector magnitude (EVM), the RMS distance between measured and ideal points relative to the average power. TS 38.104 sets base station EVM limits that tighten with modulation order, from 17.5 % for QPSK to 3.5 % for 256QAM and 2.5 % for 1024QAM at carriers up to 4.2 GHz. An EVM of 3.5 % corresponds to an error power about 29 dB below the signal.

Bit error rate

On a channel with additive white Gaussian noise, BPSK and Gray-mapped QPSK reach a bit error rate of 10⁻⁵ at an Eb/N0 of about 9.6 dB. Higher orders need more. The standard nearest-neighbour approximation puts the same error rate at about 13.4 dB for 16QAM, 17.8 dB for 64QAM and 22.5 dB for 256QAM. Each step that adds two bits per symbol costs roughly 4 to 5 dB of Eb/N0, and about 6 dB of SNR per symbol at high order.

Fading changes the picture. On a Rayleigh channel without diversity, the error rate falls only in inverse proportion to SNR rather than exponentially, so an uncoded link needs tens of dB more. Coding, interleaving and diversity recover most of that, which is why raw BER curves are a starting point and not a system prediction.

Spectral efficiency and adaptive modulation

Spectral efficiency is bits per second per hertz. A scheme with M points and code rate R carries R log2 M information bits per symbol. Pulse-shaping roll-off, guard bands, reference signals and control overhead reduce the delivered figure further.

Because the SNR of a mobile link changes all the time, modern systems adapt. The receiver reports channel quality, and the transmitter picks the modulation and coding scheme (MCS) that meets a target block error rate, typically on the first transmission, with HARQ catching the remainder. In NR the UE reports a channel quality indicator and the base station selects an MCS index from tables in TS 38.214, including tables that reach 256QAM and 1024QAM. Wi-Fi does the same with its MCS indices. A link that drops from 256QAM to 16QAM when you walk behind a wall is working as designed.

Where to start

Read /learn/beginner/05-digital-modulation/, then /learn/beginner/06-pulse-shaping-and-matched-filters/. The project /projects/qpsk-modem-ber/ builds a QPSK modem and measures its BER curve against theory. Keep /reference/modulation-and-ber/ open. Intermediate lessons on soft demapping and link adaptation are in preparation.

Tools and platforms

Common mistakes

• Comparing schemes at equal SNR per symbol when the question is about energy per bit, or the reverse.
• Forgetting to normalise average constellation energy, which shifts every BER curve.
• Measuring BER with too few errors. Count at least 100 errors per point for a usable estimate.
• Quoting the highest supported order as the typical one. Most of a cell runs at much lower orders.
• Ignoring phase noise and PA compression when choosing a high-order QAM.

Going deeper

• G. Ungerboeck, Channel coding with multilevel/phase signals, IEEE Transactions on Information Theory 28(1), 1982.
• A. J. Goldsmith and S.-G. Chua, Variable-rate variable-power MQAM for fading channels, IEEE Transactions on Communications 45(10), 1997.
• D. Tse and P. Viswanath, Fundamentals of Wireless Communication, Cambridge University Press, 2005, chapter 3 on detection and diversity.
• 3GPP TS 38.211 (NR physical channels and modulation) and TS 38.214 (NR physical layer procedures for data, including MCS and CQI tables).
• 3GPP TS 38.104, the NR base station radio requirements, including EVM limits.