Quadrature modulation

Quadrature modulation , quadrature amplitude modulation (KAM, KAMn; English Quadrature Amplitude Modulation , QAM ) - a kind of amplitude modulation of the signal, which is the sum of two carrier oscillations of the same frequency , but 90 ° shifted in phase relative to each other ( π / 2 radians , i.e., a quarter of the full angle, therefore “quadrature”), each of which is modulated in amplitude by its modulating signal:

\ S(t)=I(t)\cos(2\pi f_{0}t)+Q(t)\sin(2\pi f_{0}t)

{\ displaystyle \ S (t) = I (t) \ cos (2 \ pi f_ {0} t) + Q (t) \ sin (2 \ pi f_ {0} t)}

\ S (t) = I (t) \ cos (2 \ pi f_ {0} t) + Q (t) \ sin (2 \ pi f_ {0} t)

,

Where $I(t)$ ${\ displaystyle I (t)}$ $I (t)$ and $Q(t)$ ${\ displaystyle Q (t)}$ $Q (t)$ - modulating signals, $f_{0}$ ${\ displaystyle f_ {0}}$ $f_0$ - carrier frequency.

Quadrature Amplitude-Shift Keying ( QASK ) is a manipulation in which both the phase and amplitude of the signal change, which allows you to increase the amount of information transmitted by one state (reference) of the signal.

Content

1 Signal Conditioning
2 Application
3 See also
4 Literature
5 Links

Signal

Signal constellation of the 16-position QAM signal

Assume the number of signals $q$ ${\ displaystyle q}$ equally $2^{m}$ ${\ displaystyle 2 ^ {m}}$ where $m$ ${\ displaystyle m}$ shows the number of bits carried by a single signal. Let for a start $m=2k$ ${\ displaystyle m = 2k}$ , $k$ ${\ displaystyle k}$ - natural. Then ${\sqrt {q}}=2^{k}$ ${\ displaystyle {\ sqrt {q}} = 2 ^ {k}}$ . Then the signal with the number $i$ ${\ displaystyle i}$ two numbers can be matched $i_{1}$ ${\ displaystyle i_ {1}}$ and $i_{2}$ ${\ displaystyle i_ {2}}$ , $i_{1},i_{2}=0,1,...,{\sqrt {q}}-1$ ${\ displaystyle i_ {1}, i_ {2} = 0,1, ..., {\ sqrt {q}} - 1}$ according to the following rule: $i=i_{1}{\sqrt {q}}+i_{2}$ ${\ displaystyle i = i_ {1} {\ sqrt {q}} + i_ {2}}$ . Let be

s_{i_{1}}=A(1-{\frac {2i_{1}}{{\sqrt {q}}-1}})

{\ displaystyle s_ {i_ {1}} = A (1 - {\ frac {2i_ {1}} {{\ sqrt {q}} - 1}})}

and

s_{i_{2}}=A(1-{\frac {2i_{2}}{{\sqrt {q}}-1}})

{\ displaystyle s_ {i_ {2}} = A (1 - {\ frac {2i_ {2}} {{\ sqrt {q}} - 1}})}

.

Then the quantities $s_{i_{1}}$ ${\ displaystyle s_ {i_ {1}}}$ and $s_{i_{2}}$ ${\ displaystyle s_ {i_ {2}}}$ will be evenly spaced $[-A,A]$ ${\ displaystyle [-A, A]}$ . The minimum distance is $\Delta ={\frac {2A}{{\sqrt {q}}-1}}$ ${\ displaystyle \ Delta = {\ frac {2A} {{\ sqrt {q}} - 1}}}$ .

If $m=2k-1$ ${\ displaystyle m = 2k-1}$ , then the signal set is constructed by decimating the signal set for $q=2^{2k}$ ${\ displaystyle q = 2 ^ {2k}}$ . For this case, the minimum distance $\Delta '={\sqrt {2}}\Delta ={\frac {2{\sqrt {2}}A}{{\sqrt {q}}-1}}$ ${\ displaystyle \ Delta '= {\ sqrt {2}} \ Delta = {\ frac {2 {\ sqrt {2}} A} {{\ sqrt {q}} - 1}}}$

Application

Quadrature Modulation: View of the PAL Color Signal on the Vector Analyzer Screen

Quadrature modulation is used to transmit color signals in the television standard PAL and NTSC , in stereo broadcasting , in software-defined radio systems (POR, SDR).

In the simplest POR, a quadrature-modulated signal from the receiver is fed to the input of a sound card , where the ADC is digitized and then processed programmatically; in good systems, the ADC is already built-in, it has more bit depth and speed, and the signal to the computer is digital, usually via USB. POR allows you to receive from the receiver the signal of not one radio station, but immediately a certain frequency range. For its analysis, decoding and display software is used (for example, GQRX , SDR-Radio , etc.)

Literature

Digital signal processing. Sergienko A. B. 2002. p. 458,467-468

Links

Band radio signals. Comprehensive Envelope and Universal Quadrature Modulator