Quadrature Amplitude Modulation (QAM)

Principle of QAM: two signal components

Quadrature Amplitude Modulation (QAM) is a digital linear modulation in which a block of bits selects a pair of I and Q component values. The signal can therefore change both amplitude and phase. QAM combines amplitude-level selection with phase determined by the relationship between the components, so it includes aspects of Amplitude-Shift Keying (ASK) and Phase-Shift Keying (PSK), while the implementation uses two orthogonal carrier components.

For each symbol, the modulator selects an I level and a Q level. The pair gives a point in the complex plane and therefore determines the signal amplitude and phase. For a binary-labelled constellation with $M=2^k$ points, one symbol carries $k$ bits. At the same symbol rate, this raises the gross bit rate, while occupied bandwidth depends mainly on symbol rate and pulse shaping. Maintaining point spacing may require more power or SNR.

How QAM works: the two quadrature carriers

QAM uses two carrier components with the same frequency and a 90-degree phase separation, which is one quarter of a cycle. They are called quadrature carriers.

In-phase carrier (I): Represented by the cosine wave $\cos(2\pi f_c t)$ .
Quadrature carrier (Q): Represented by the sine wave $\sin(2\pi f_c t)$ , equivalent to a cosine shifted by 90° in phase.

The binary input stream is split into substreams that select I and Q levels. Since the two carriers are , a receiver can separate the I and Q branches. Under one sign convention, the passband signal is $s(t)=I(t)\cos(2\pi f_c t)-Q(t)\sin(2\pi f_c t)$ . The final waveform is the sum of both components.

The constellation diagram: visualizing QAM

QAM states are shown on a 2D plot called a constellation diagram. The horizontal axis gives I-component values and the vertical axis gives Q-component values. Each point represents one symbol and its assigned bit sequence. With orthonormal basis functions, symbol energy increases with $I^2+Q^2$ .

Hierarchy of QAM

In common square constellations, the number in "n-QAM" gives the number of points, where $n = 2^k$ and $k$ is the number of bits per symbol.

4-QAM (QPSK): Has 4 points and encodes $k=2$ bits per symbol (e.g., '00', '01', '10', '11'). With suitable scaling and rotation, it is functionally equivalent to quadrature phase-shift keying.
16-QAM: Has 16 points, often in a 4x4 grid, and encodes $k=4$ bits per symbol. At the same symbol rate, its raw bit rate is twice that of 4-QAM.
64-QAM, 256-QAM, and beyond: Higher-order schemes carry more bits per symbol ( $k=6$ , $k=8$ , and so on) and increase potential spectral efficiency. DOCSIS 3.1 can use 4096-QAM ( $k=12$ ).

The speed and reliability trade-off

Higher-order QAM provides a greater bit rate at a given symbol rate. At a fixed average symbol energy, adding points reduces the distance between neighbors and increases the effect of noise, interference, and nonlinear distortion.

Noise that keeps a QPSK point inside its decision region can move a 256-QAM point into a neighboring region. For coherent detection over AWGN with Gray mapping, an often-used approximation for square $M$ -QAM is $P_b \approx \frac{4}{\log_2 M}\left(1-\frac{1}{\sqrt{M}}\right)Q\left(\sqrt{\frac{3\log_2 M}{M-1}\frac{E_b}{N_0}}\right)$ . The expression assumes uncoded transmission. $Q$ is the normal-tail function, and $E_b/N_0$ is the dimensionless ratio of bit energy to noise power spectral density. Higher-order modulation requires a higher to meet a target error rate. Selecting the QAM order balances throughput, range, and the link-quality margin.

QAM modulator block diagram

A QAM modulator splits the input stream into I and Q values and uses them to control two orthogonal carrier components.

Serial-to-parallel converter: The serial bit stream is grouped into blocks of $k$ bits, where $k$ is the number of bits per symbol. For square QAM with even $k$ , the mapper divides each block into I and Q substreams.
Digital-to-analog converters (DAC): Each parallel stream is sent to a DAC that generates an analog level corresponding to the symbol value. This produces the I(t) and Q(t) signals.
Multiplication with carriers: The I(t) signal is multiplied by the cosine carrier, and Q(t) is multiplied by the sine carrier shifted by 90°.
Summation: The two modulated components are added to create the QAM signal, whose amplitude and phase depend on the I, Q pair. The signal is then sent to the transmission channel.

Practical applications

QAM spectral efficiency makes it common in many communication systems:

Wi-Fi: Wi-Fi 5 (802.11ac) and Wi-Fi 6 (802.11ax) use formats including 256-QAM and 1024-QAM to increase throughput.
Cable internet: DOCSIS uses high-order QAM, up to 4096-QAM in DOCSIS 3.1, for transmission over coaxial cable networks.
Digital television: DVB-T/T2 and ATSC 3.0 use QAM variants for terrestrial transmission. ATSC 1.0 uses 8-VSB, while DVB-S2 uses APSK. These standards belong to other modulation families.
Cellular networks: LTE and 5G NR use QAM, including QPSK, 16-QAM, 64-QAM, and 256-QAM, for data transmission between devices and base stations.
Optical communication: High-capacity optical links use coherent QAM with dual polarization and other techniques to transmit hundreds of gigabits or terabits per second over a single fiber.