Quadrature amplitude modulation
A family of modulation methods conveying two signals on orthogonal carriers.
Quadrature amplitude modulation, or QAM, refers to a group of signal modulation techniques common in modern telecommunications for sending data. The basic idea is to transmit two separate analog signals by adjusting the amplitudes of two different versions of the same carrier wave. These two analog channels can be used directly or combined to carry digital bit streams through a joint form of amplitude-shift keying that works across the synchronized channels. The two carrier waves share the same frequency but are offset by 90° from each other—a relationship called orthogonality or quadrature. The transmitted signal is simply the sum of these two waves. Because they are orthogonal, a receiver can cleanly separate and demodulate them. A key assumption is that the modulating signals are low-frequency, narrowband waveforms compared to the carrier frequency. In M-ary amplitude-shift keying, the phase stays constant while the amplitude varies; in phase-shift keying (PSK), the amplitude stays constant while the phase varies. QAM combines both ideas: it modulates both amplitude and phase, or equivalently, it merges two binary PSK signals on orthogonal carriers. QAM is widely used in digital communications, for example in 802.11 Wi-Fi standards. By choosing a larger constellation size, very high spectral efficiencies are possible, limited only by channel noise and linearity. In optical fiber systems, as bit rates increase, QAM16 and QAM64 can be created optically using a three-path interferometer. In a QAM signal, one carrier lags the other by 90°. Its amplitude modulation is called the in-phase component, I(t), and the other is the quadrature component, Q(t). The overall waveform can be written as: s(t) = sin(2π f_c t) I(t) + cos(2π f_c t) Q(t) where f_c is the carrier frequency. At the receiver, a coherent demodulator multiplies the incoming signal separately by a cosine and a sine wave to recover estimates of I(t) and Q(t). For example: r(t) = s_c(t) cos(2π f_c t) = I(t) cos²(2π f_c t) – Q(t) sin(2π f_c t) cos(2π f_c t) Using trigonometric identities, this becomes: r(t) = ½ I(t) [1 + cos(4π f_c t)] – ½ Q(t) sin(4π f_c t)
- Carrier phase offset
- 90°
- Orthogonality condition
- quadrature
- Carrier waves
- two
- Carrier frequency
- fc
- Demodulation method
- coherent demodulator multiplying received signal with cosine and sine signals
Lore & Background
The two carrier waves in QAM are of the same frequency and are out of phase with each other by 90°, a condition known as orthogonality or quadrature. The transmitted signal is created by adding the two carrier waves together. At the receiver, the two waves can be coherently separated (demodulated) because of their orthogonality. Another key property is that the modulations are low-frequency/low-bandwidth waveforms compared to the carrier frequency, which is known as the narrowband assumption.
In M-ary transmission amplitude-shift keying the phase is the same but with different amplitudes, while phase-shift keying (PSK) has the same amplitude but different phases. Combining these concepts leads to QAM, where both amplitude and phase are modulated, or two binary PSK signals are combined with orthogonal carriers.
QAM is used extensively as a modulation scheme for digital communications systems, such as in 802.11 Wi-Fi standards. Arbitrarily high spectral efficiencies can be achieved with QAM by setting a suitable constellation size, limited only by the noise level and linearity of the communications channel. QAM is being used in optical fiber systems as bit rates increase; QAM16 and QAM64 can be optically emulated with a three-path interferometer.
Reader's Guide
QAM's significance lies in its ability to double information capacity by exploiting the spectral redundancy of double-sideband (DSB) modulation, at the expense of increased demodulation complexity. In a QAM signal, one carrier lags the other by 90°, and its amplitude modulation is referred to as the in-phase component, I(t), while the other is the quadrature component, Q(t). At the receiver, a coherent demodulator multiplies the received signal separately with both a cosine and sine signal to produce the received estimates of I(t) and Q(t). Low-pass filtering removes high-frequency terms, allowing each component to be received independently. The addition of two sinusoids is a linear operation that creates no new frequency components, so the bandwidth of the composite signal is comparable to that of the DSB components. A DSB signal has zero-crossings at a regular frequency, which makes it easy to recover the phase of the carrier sinusoid. QAM is used extensively in digital communications systems, including 802.11 Wi-Fi standards, and in optical fiber systems as bit rates increase, with QAM16 and QAM64 being optically emulated with a three-path interferometer.
Did You Know?
- The two carrier waves in QAM are out of phase by 90°, a condition called orthogonality or quadrature.
- QAM can achieve arbitrarily high spectral efficiencies by setting a suitable constellation size, limited only by noise and channel linearity.
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