Quadrature Amplitude Modulation (QAM)

This tutorial is part of the National Instruments Measurement Fundamentals series. Each tutorial in this series, will teach you a specific topic of common measurement applications, by explaining the theory and giving practical examples. This tutorial covers an introduction to RF, wireless and high-frequency signals and systems.

For the complete list of tutorials, return to the NI Measurement Fundamentals Main page or for more RF tutorials refer to the NI RF Fundamentals main subpage. For more information on National Instruments RF products, visit www.ni.com/rf.

A variety of communication protocols implement quadrature amplitude modulation, or QAM. Current protocols such as 802.11b wireless Ethernet (Wi-Fi) and Digital Video Broadcast (DVB), for example, both utilize 64-QAM modulation. In addition, emerging wireless technologies such as WiMAX, 802.11n, and HSDPA/HSUPA (a new cellular data standard) will implement QAM as well. Thus, understanding the QAM modulation scheme is important because of its widespread use in current and emerging technologies.

QAM modulation involves sending digital information by periodically adjusting the phase and amplitude of a sinusoidal electromagnetic wave. Each combination of phase and amplitude is called a symbol and represents a digital bitstream. First, we will discuss the hardware implementation required to constantly adjust the phase and amplitude of a carrier wave. Second, we will discuss the binary value associated with each symbol.

Hardware Implementation

On a hardware level, quadrature amplitude modulation (QAM), requires changing the phase and amplitude of a carrier sine wave. One of the easiest ways to do this is to generate and mix two sine waves which are 90° out of phase with one another. By adjusting only the amplitude of either signal, we are able to affect the phase and amplitude of the resulting mixed signal.

These two carrier waves represent the I and Q components of our signal. Individually each of these signals can be represented as:

and

Above, the signal I is the “in-phase” component and Q is the “quadrature” component. Note that these are represented as sin and cos because the two signals are 90° out of phase with one another. As a result of the two identities above, we can subtract the two signals to get:



As the equation above illustrates, the resulting identity is a periodic signal whose phase can be adjusted by changing the amplitude of I and Q. Thus, it is possible to perform digital modulation on a carrier signal by adjusting the amplitude of the two mixed signals.
Below, we show a block diagram of the hardware required to generate the IF (intermediate frequency) signal. In the “Quadrature Modulator” block, we can see how the I and Q signals are mixed with LO (local oscillator) before being added together. Again, the two local oscillators are exactly 90° out of phase with one another.



Next, we will discuss exactly how the I and Q components are used to represent actual digital data. To do this, we will discuss the relationship between the QAM symbol map and the actual real-world signal.

QAM Symbol Map

Again, QAM modulation involves sending digital information by periodically adjusting the phase and amplitude of a sinusoidal electromagnetic wave. 4-QAM modulation uses exactly four combinations of phase and amplitude. Moreover, each combination has an assigned 2-bit digital pattern. For example, suppose we wish to generate the bitstream: (1,0,0,1,1,1). Because each symbol has a unique 2-bit digital pattern, these bits are grouped in two’s so that they can be mapped to the corresponding symbols. Here, the original bitstream, (1,0,0,1,1,1), is grouped into the three symbols (10,01,11). Below, we show a modulated waveform (without pulse-shape filtering), such that each symbol is represented by one period of the modulated carrier. Here we can see that digital information is transmitted by changing the phase and amplitude of the carrier signal.


[+] Enlarge Image

One common way to visualize the transitions in phase and amplitude of our carrier wave is with a constellation plot. The constellation plot, shown below, shows each possible phase and amplitude of a carrier signal in polar coordinate form.

At right, we show the symbol map of 4-QAM. As the image also illustrates, each symbol can be represented by a unique phase(Θ) and amplitude(A). Here, 4-QAM consists of four unique combinations of phase and amplitude. The combinations are called “symbols” and are shown as the white dots on the constellation plot. The red lines represent the phase and amplitude transitions from one symbol to another. Note that we have also labeled the digital bit pattern that can be represented by each symbol. Thus, a digital bit pattern can be sent over a carrier signal by generating unique combinations of phase and amplitude.

As we have already mentioned, it is possible to send up to two bits per symbol when using 4-QAM modulation. However, it is also possible to send data at even higher rates by increasing the number of symbols in our symbol map. However, it is also possible to send data at even higher rates by increasing the number of symbols in our symbol map. By convention, the number of symbols in a symbol map is called its “M” and is considered the “M-ary” of the modulation scheme. In other words, 4-QAM has an M-ary of 4 and 256-QAM has an M-ary of 256. Moreover, the number of bits that can be represented by a symbol has a logarithmic relationship to the M-ary. For example, we know that 2 bits can be represented by each symbol in 4-QAM. While this makes sense intuitively, it is actually defined by the equation shown below:

Bits per Symbol = log₂ (M)

Thus, using the equation above, each symbol in 256-QAM can be used to represent an 8-bit digital pattern (log2 (256) = 8). Because the M-ary of a QAM modulation scheme affects the number of bits per symbol, it has a significant affect on the actual data transmission rate.  

Conclusions

QAM is an important modulation scheme because of its widespread adoption in current technologies. Moreover, this scheme can be implemented in LabVIEW with the use of the modulation toolkit. This toolkit, in conjunction with the vector signal generator and vector signal analyzer, is able to implement QAM modulation for signals in the real world.

This tutorial is part of the National Instruments Measurement Fundamentals series. Each tutorial in this series will teach you a specific topic of common measurement applications by explaining the theory and giving practical examples. This tutorial covers an introduction to RF, wireless and high-frequency signals and systems.

For the complete list of tutorials, return to the NI Measurement Fundamentals Main page or for more RF tutorials refer to the NI RF Fundamentals main subpage. For more information on National Instruments RF products, visit www.ni.com/rf.

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