Qam

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 Like all Modulation schemes, QAM conveys Data by changing some aspect of a carrier signal, or the Carrier Wave , (usually a Sinusoid ) in response to a data signal. In the case of QAM, the amplitude of two waves, 90 degrees out-of-phase with each other (in quadrature) are changed (''modulated'' or ''keyed'') to represent the data signal. Phase Modulation (analog 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), for these can be regarded a special case of phase modulation. ANALOG QAM When transmitting two signals by modulating them with QAM, the transmitted signal will be of the form: : $\ s(t) = I (t) \cos (2 \pi f_0 t) + Q (t) \sin (2 \pi f_0 t)$ , where $I(t)$ and $Q(t)$ are the modulating signals and $f_0$ is the carrier frequency. At the receiver, these two modulating signals can be Demodulated using a Coherent Demodulator . Such a receiver multiplies the received signal separately with both a Cosine and Sine signal to produce the received estimates of $I(t)$ and $Q(t)$ respectively. Because of the Orthogonality property of the carrier signals, it is possible to detect the modulating signals independently. In the ideal case $I(t)$ is demodulated by multiplying the transmitted signal with a cosine signal: : $\begin{align} r_i(t) = & s(t) \cos (2 \pi f_0 t) \ = & I(t) \cos (2 \pi f_0 t)\cos (2 \pi f_0 t) + Q(t) \sin (2 \pi f_0 t)\cos (2 \pi f_0 t) \end{align}$ Using standard Trigonometric Identities , we can write it as: : $\end{align}$ Low-pass Filter ing $r_i(t)$ removes the high frequency terms (containing $(4\pi f_0 t)$ ), leaving only the $I(t)$ term, unaffected by $Q(t)$ . Similarly, we may multiply $s(t)$ by a sine wave and then low-pass filter to extract $Q(t)$ . It should be noted that here we assumed that the phase of the received signal is known at the receiver. If the demodulating phase is even a little off, it results in Crosstalk between the modulated signals. This issue of Carrier Synchronization at the receiver must be handled somehow in QAM systems. The coherent demodulator needs to be exactly in phase with the received signal, or otherwise the modulated signals cannot be independently received. For example Analog Television systems transmit a burst of the transmitting colour subcarrier after each horizontal synchronization pulse for reference. Analog 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. DIGITAL QAM Like for many digital modulation schemes, the Constellation Diagram is a useful representation which 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 (e.g. Cross-QAM). Since in digital Telecommunications the data is 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, with a Carrier Frequency $f_0$ and $H_t$ the frequency response of the transmitter's filter: 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 Amplitude-shift Keying (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: : $s(t) = \sum_{n=-\infty}^{\infty} \left v_c [n \cdot h_t (t - n T_s) \cos (2 \pi f_0 t) - v_s \cdot h_t (t - n T_s) \sin (2 \pi f_0 t) ight,$ where $v_c and v_s[n$ are the voltages applied in response to the $n$ ^th symbol to the cosine and sine waves respectively. Receiver The receiver simply performs the inverse process of the transmitter. Its ideal structure is shown in the picture below with $H_r$ the receive filter's frequency response: 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. In any application, the low-pass filter will be within ''h_r (t)'': here it was shown just to be clearer. DIGITAL QAM PERFORMANCE The following definitions are needed in determining error rates: $M$ = Number of symbols in modulation constellation $E_b$ = Energy-per- Bit $E_s$ = Energy-per-symbol = $kE_b$ with ''k'' bits per symbol $N_0$ = Noise Power Spectral Density ( W / Hz ) $P_b$ = Probability of bit-error $P_{bc}$ = Probability of bit-error per carrier $P_s$ = Probability of symbol-error $P_{sc}$ = Probability of symbol-error per carrier $Q(x) = rac{1}{\sqrt{2\pi}}\int_{x}^{\infty}e^{-t^{2}/2}dt,\ x\geq{}0$ . $Q(x)$ 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 for rectangular 16-QAM.]] Rectangular QAM constellations are, in general, sub-optimal in the sense that they do not maximally space the constellation points for a given energy. However, they have the considerable advantage that they may be easily transmitted as two Pulse Amplitude Modulation (PAM) signals on quadrature carriers, and can be easily demodulated. The non-square constellations, dealt with below, achieve marginally better bit-error rate (BER) but are harder to modulate and demodulate. The first rectangular QAM constellation usually encountered is 16-QAM, the constellation diagram for which is shown here. A Gray Code d bit-assignment is also given. The reason that 16-QAM is usually the first is that a brief consideration reveals that 2-QAM and 4-QAM are in fact Binary Phase-shift Keying (BPSK) and Quadrature Phase-shift Keying (QPSK), respectively. Also, the error-rate performance of 8-QAM is close to that of 16-QAM (only about 0.5dB better), but its data rate is only three-quarters that of 16-QAM. Expressions for the symbol error-rate of rectangular QAM are not hard to derive but yield rather unpleasant expressions. For an even number of bits per symbol, $k$ , exact expressions are available. They are most easily expressed in a ''per carrier'' sense: : $P_{sc} = 2\left(1 - rac{1}{\sqrt M} ight)Q\left(\sqrt{rac{3}{M-1}rac{E_s}{N_0}} ight)$ , 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 : $\,P_b = 1 - \left(1 - P_{bc} ight)^2$ . Odd- $k$ QAM For odd $k$ , such as 8-QAM ( $k=3$ ) it is harder to obtain symbol-error rates, but a tight upper bound is: : $P_s \leq{} 4Q\left(\sqrt{rac{3kE_b}{(M-1)N_0}} ight)$ . Two rectangular 8-QAM constellations are shown below without bit assignments. These both have the same minimum distance between symbol points, and thus the same symbol-error rate (to a first approximation). The exact bit-error rate, $P_b$ will depend on the bit-assignment. Note that neither of these constellations are used in practice, as the non-rectangular version of 8-QAM is optimal.
	Image:Rectangular 8QAM V2pngAlternative	"http://wwwinformationdelightinfo/information/entry/constellation_diagram" class="copylinks">Constellation Diagram for rectangular 8-QAM

	APPAREL
	BABY
	BEAUTY
	BOOKS
	CAR TOYS
	CELL PHONES
	DVD'S
	ELECTRONICS
	GOURMET FOOD
	GROCERIES
	HEALTH & PERSONAL
	HOME & GARDEN
	JEWELRY
	MUSIC
	MUSIC INSTRUMENTS
	OFFICE PRODUCTS
	SOFTWARE
	SPORTING GOODS
	TOOLS & HARDWARE
	TOYS
	VIDEO GAMES
	SHOPPING HOME

	MORE SHOPPING...

	CATEGORIES ABOUT QUADRATURE AMPLITUDE MODULATION

	radio modulation modes

	data transmission

Information About

Qam