Qam

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QAM redirects here; for other uses of that abbreviation, see QAM (disambiguation) .

Quadrature amplitude modulation (QAM) is a Modulation scheme which conveys Data by changing (''modulating'') the Amplitude of two Carrier Wave s. These two waves, usually Sinusoid s, are Out Of Phase with each other by 90 ° and are thus called Quadrature carriers — hence the name of the scheme.

OVERVIEW

As with all Modulation schemes, QAM conveys Data by changing some aspect of a base signal, the Carrier Wave , (usually a Sinusoid ) in response to a data signal. In the case of QAM, the amplitude of two quadrature waves is changed (''modulated'' or ''keyed'') to represent the data signal.

Phase Modulation (analogue PM) and Phase-shift Keying (digital PSK) can be regarded as a special case of QAM, where the amplitude of the modulating signal is constant, with only the phase varying. This can also be extended to Frequency Modulation (FM) and Frequency-shift Keying (FSK), as this can be regarded as a special case of phase modulation.

Although analogue QAM is possible, this article focuses on digital QAM. Analogue QAM is used in NTSC and PAL television systems, where the I- and Q-signals carry the components of chroma (colour) information. "Compatible QAM" or C-QUAM is used in AM Stereo Radio to carry the Stereo Difference information.

As for many digital modulation schemes, the Constellation Diagram is a useful representation and is relied upon in this article.

In QAM, the constellation points are usually arranged in a square grid with equal vertical and horizontal spacing, although other configurations are possible (see e.g. Cross-QAM ). Since in digital Telecommunications the data are usually Binary , the number of points in the grid is usually a power of 2 (2,4,8...). Since QAM is usually square, some of these are rare — the most common forms are 16-QAM, 64-QAM, 128-QAM and 256-QAM. By moving to a higher-order constellation, it is possible to transmit more Bit s per symbol. However, if the mean energy of the constellation is to remain the same (by way of making a fair comparison), the points must be closer together and are thus more susceptible to Noise and other corruption; this results in a higher Bit Error Rate and so higher-order QAM can deliver more data less reliably than lower-order QAM.

If data-rates beyond those offered by 8- PSK are required, it is more usual to move to QAM since it achieves a greater distance between adjacent points in the I-Q plane by distributing the points more evenly. The complicating factor is that the points are no longer all the same amplitude and so the Demodulator must now correctly detect both Phase and Amplitude , rather than just phase.

64-QAM and 256-QAM are often used in , 16-QAM and 64-QAM are currently used for Digital Terrestrial Television ( Freeview and Top Up TV ).

IDEAL STRUCTURE

Transmitter

The following picture shows the ideal structure of a QAM transmitter:

First the flow of bits to be transmitted is split into two equal parts: this process generates two independent signals to be transmitted. They are encoded separately just like they were in an ASK modulator. Then one channel (the one "in phase") is multiplied by a cosine, while the other channel ("in quadrature") is multiplied by a sine. This way there is a phase of 90° between them. They are simply added one to the other and sent through the real channel.

The sent signal can be expressed in the form:

:

s(t) = \sum_{n=-\infty}^{\infty} v_c

{Link without Title} \cdot h_t (t - n T_s) \cos 2 \pi f_0 t - v_s {Link without Title} \cdot h_t (t - n T_s) \sin 2 \pi f_0 t

Receiver

The receiver simply performs the inverse process of the transmitter. Its ideal structure is shown in the picture below:

Multiplying by a cosine (or a sine) and by a low-pass filter it is possible to extract the component in phase (or in quadrature). Then there is only an ASK demodulator and the two flows of data are merged back. Differently from the ASK, the frequency the A/D converter is working to is not twice the maximum frequency of the transmitted signal, but twice the maximum frequency of the signal itself. For example, if a 1 MHz-wide signal is transmitted at a central frequency of 100 MHz, the A/D converter has to work at 2 MHz (not at 202 MHz, like in ASK).

In any application, the low-pass filter will be within ''h_r (t)'': here it was shown just to be clearer.

Performance

The diagrams that were shown represent the so called ''rectangular QAM'', and it can be seen like two different ASK-modulated channels. The performance for the QAM modulation can be easily deduced by the known results for the ASK modulation (see the Related Article ). Let us introduce the following notation:

''L'' is the number of possible levels of voltage to be used

''h_{r_{(t)'' is the impulse response of the filter that is used at the receiver}}

''G'' is the total gain introduced by the transmitter, the receiver and by the effect of the channel

''A'' is the maximum value of the voltage that can be transmitted

Q(x)

is related to the Complementary Gaussian Error Function by:

Q(x) = rac{1}{2}\operatorname{erfc}\left(rac{x}{\sqrt{2}}
ight)

, which is the probability that ''x'' will be under the tail of the Gaussian PDF towards positive Infinity .

The error-rates quoted here are those in Additive White Gaussian Noise ( AWGN ).

Where Coordinate s for constellation points are given in this article, note that they represent a ''non-normalised'' constellation. That is, if a particular mean average energy were required (e.g. unit average energy), the constellation would need to be linearly scaled.

RECTANGULAR QAM

so
:

\,P_s = 1 - \left(1 - P_{sc}
ight)^2

.

The bit-error rate will depend on the exact assignment of bits to symbols, but for a Gray-coded assignment with equal bits per carrier:
:

P_{bc} = rac{4}{k}\left(1 - rac{1}{\sqrt M}
ight)Q\left(\sqrt{rac{3k}{M-1}rac{E_b}{N_0}}
ight)

,
so
:

\,P_b = 1 - \left(1 - P_{bc}
ight)^2

	valign	top for rectangular 8-QAM]]
	valign	"top" rowspan=2For odd <math>k</math>, such as 8-QAM (<math>k=3</math>) it is harder to obtain symbol-error rates, but a tight upper bound is:

Two rectangular 8-QAM constellations are shown, without bit-assignments. These two both have the same minimum distance between symbol points and thus the same symbol-error rate.

The exact bit-error rate,

P_b

will depend on the bit-assignment.

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