Quadrature Amplitude Modulation (QAM) Experiments Using the National Instruments PXI-based Vector Signal Analyzer *

OpenStax-CNX module: m14500 1 Quadrature Amplitude Modulation (QAM) Experiments Using the National Instruments PXI-based Vector Signal Analyzer * Robert Kubichek This work is produced by OpenStax-CNX and licensed under the Creative Commons Attribution License 2.0 Abstract This module discusses the use of National Instruments PXI system for understanding QAM signal transmission. The PXI system discussed here has been congured as a software-dened transmitter/receiver system and is used to implement both a spectrum analyzer and a vector signal analyzer under LabView control. It is thus extremely well suited for studying and learning how QAM signals work. 1 Objective The purpose of this module is to study Quadrature Amplitude Modulation ( QAM) through hands-on experiments using a National Instruments (NI) PXI system congured as a software-dened vector signal analyzer (VSA). LabView Virtual Instruments (VI's) provide an extensive set of software application capabilities for studying signals and their spectra using this equipment. In this module, students will gain a basic understanding of using the PXI system, while investigating the properties of M-QAM, constellation graphs and eye diagrams, and the eects of pulse shaping lters on the signal spectrum. QAM systems are used extensively in modern communication systems where maximum throughput is required under limited bandwidth conditions. Examples include V.92 modems included with most personal computer systems, and digital HDTV cable signals that use 64 or 256-QAM. This lab module comprises three sets of experiments. After describing details about the equipment setup, the rst part investigates a provided National Instruments VI to generate a QAM signal using the arbitrary waveform generator. In the second part, the capabilities of the VSA are explored, with application to spectral analysis of QAM signals. Finally, the third part provides experiments with digital QAM receivers and develops better understanding of the QAM waveform. * Version 1.1: May 4, 2007 8:56 pm +0000 http://creativecommons.org/licenses/by/2.0/

OpenStax-CNX module: m14500 2 2 Equipment The National Instruments NI PXI-1042Q is a powerful system that integrates one or more signal analysis and control modules into one system. For example, a fully software-dened transmitter, receiver, and analyzer system such as we study here include the following hardware modules: Arbitrary Waveform Generator (AWG, NI PXI-5421), Upconverter (NI PXI-5610), Downconverter (NI PXI-5600), and Digitizer (NI PXI- 5620). These modules are housed in a single chassis and integrated through an Embedded Controller (NI PXI-8186) and high-speed data bus. A typical conguration for the system is shown below in Figures 1 and 2. Figure 1 Figure 1. Typical set up for PXI system.

OpenStax-CNX module: m14500 3 Figure 2 Figure 2. Front of National Instruments as congured in Figure 1. Connections between hardware units are made using rigid coax. The Up Converter and Down Converter can be directly connected if an RF channel is not desired, or can be bypassed completely. For example, for the particular NI-provided VI's discussed in this module, the AWG is directly connected to the Down Converter and bypasses the Up Converter. The hardware modules are briey described as follows: AWG: Arbitrary Waveform Generator. Capable of generating a wide range of test signals, from simple sine waves to complex M-PSK or M-QAM signals. The AWG output is xed at an intermediate frequency (IF) of 15 MHz. Up Converter: This device modulates the 15 MHz IF signal to any desired output frequency between 250 khz to 2.7 GHz. Down Converter: This device down converts a pass-band signal lying anywhere in the range 9 khz to 2.7 GHz to the digitizer input frequency at 15 MHz. Digitizer: Digitizes the 15 MHz IF signal and makes it available for further real-time digital signal processing by LabView application software. Controller: This is a Windows XP-based system that is tightly integrated with the other PXI modules. It provides device control and real-time analysis of digital signals under LabView Control.

OpenStax-CNX module: m14500 4 3 Part 1: M-QAM Generation and Constellation Graph The Modulation Toolkit provided by NI includes a wide variety of example VI's that implement many dierent communication system functions. The rst exercise will familiarize the user with a VI tool that generates QAM signals, and to look at some of the important QAM parameters. Using the Windows File Explorer, locate the FGEN examples directory, which contains the signal generation VI's. In most installations it can be reached through the Start Menu as follows: 1. Start -> All Programs -> National Instruments -> Modulation -> LabVIEW Support -> Modulation Examples Folder -> FGEN examples. 2. Double click on the MT nifgen QAM Signal Generation.vi, which brings up the front panel for M-QAM generation shown in Figure 3. Figure 3 Figure 3. Front panel of MT nifgen QAM Signal Generation.vi 3.1 Parameter Setup Getting the VI to run properly depends on correct settings of the front-panel parameters. The following explains some of the more important parameter values.

OpenStax-CNX module: m14500 5 NI-FGen Resource Name: the resource name of the device to use. In most installations, it should be set up as AWG, which refers to the NI PXI-5421 Arbitrary Waveform Generator. PN Sequence Order: The VI generates a repeating bit data stream based on a Pseudo-Noise (PN) sequence. The length of the sequence is L = 2 m 1, where m is the PN Sequence Order. For example, when m=5, the length of the repeating bit sequence is 2 m 1 = 31 bits. Symbol Rate, Hz: the number of transmitted symbols per second. Samples Per Symbol: the ratio of the sampling rate employed by system to the transmitter symbol rate. M-QAM: the modulation format. For example, 16-QAM utilizes log 2 16 = 4 bits per symbol. The supported M value ranges from 4 to 256 in increments of powers of two. TX Filter: the type of band-limiting lter employed at the transmitter for pulse-shaping the symbols output by the modulator. Three types are supported, None, Raised Cosine, and Root Raised Cosine. See the theory section. Alpha: the lter parameter for Raised Cosine and Root Raised Cosine. It ranges from 0 to 1. See the theory section. Filter Length: the length of the transmit pulse shaping lter in symbols. IF Frequency, Hz: the center frequency around which the analog passband signal is centered. This should be 15 MHz, which is entered as 15.0M (NOTE: the more detailed description of above parameters can be obtained by right clicking on the panel, then Properties and then Documentation.) 3.2 Theory Review Pulse shaping: Although square pulses can be used to represent the digital data (no lter option), this is not typically done in practice due the excessive bandwidth required. Instead, most systems employ pulse shaping to control bandwidth as well as to minimize Inter-Symbol Interference (ISI). The most common pulse shape has a raised-cosine frequency response, P(f), which can be shown to have zero ISI. The pulse shape, p(t), is derived by inverse Fourier transforming P(f). In many applications, this is implemented by using a pulse shape p r (t) computed from the inverse Fourier transform of the square root of P(f), which is called a root-raised cosine pulse. The receiver front-end lter frequency response is also designed to be the square root of P(f), which means that the overall transmitterreceiver response is P(f), and has zero ISI. Importantly, since the receiver's frequency response matches the pulse response, the result is called a matched lter receiver, which is known to give optimal performance in white noise. Filter length: the raised cosine or root-raised cosine pulses are derived from the P(f) or root P(f) by inverse Fourier transform. Unfortunately, the pulses p(t) and p r (t) are innite in time extent and can only be implemented by truncating them to some convenient nite length. In this VI, pulse length is referred to as the Filter Length, and is specied in terms of the number of symbols. For example, if lter length is set to 8, and there are 16 samples/symbol, then the pulse length is K=8x16=128 samples. Choosing K to be too small causes excessive distortion of the pulse shape and resulting signal spectrum. On the other hand, choosing the length to be too long causes noticeable delays in VI operation due to the increased computational expense of a longer lter. M-QAM: QAM works by using M dierent combinations of voltage magnitude and phase to represent N bits, as described by the relationship M = 2 N. When N is an even integer, the constellation is regular with I and Q each representing 2 N 1 bits. When N is an odd integer, the constellation is not necessarily symmetrical, and nding an optimal distribution of sample points is not straightforward. 3.3 Exercises It is recommended that students go through at least the following exercises. Of course, students are encouraged to play around with the parameters to build a rm understanding of this modulation technique.

OpenStax-CNX module: m14500 6 Exercise 1: Choose M=4 (i.e., 4-QAM), with no pulse shaping. Note that this case corresponds to QPSK since amplitude values are equal for all symbols and four dierent phases are used to encode the binary data. Study carefully the constellation diagram. It shows In-phase (I) voltage on the horizontal axis and Quadrature (Q) voltage on the vertical axis. Signal values at the center of each symbol interval are marked with a dot, and lines are used to show transitions between symbols. An example constellation diagram is shown in Figure 4, and displays in-phase and quadrature voltages on the horizontal and vertical axes, respectively. Note that the two voltage levels on the in-phase axis represent one bit, while the two quadrature voltage levels represent the second bit, for a total of two bits per pulse. Figure 4 Figure 4. Constellation graph of 4-QAM with no pulse shaping.

OpenStax-CNX module: m14500 7 Exercise 2: Choose M=4 and pulse shaping with Raised Cosine. In Figure 5, note that transition paths are now arcs, corresponding to the more gradual voltage change between pulses. This reduces the required bandwidth for the signal. Figure 5 Figure 5. Constellation graph of 4-QAM with Raised Cosine pulse shaping. Exercise 3: Choose M=4 and pulse shaping with Root-Raised Cosine. As shown in Figure 6, the sample points (dots) are spread out and depend on the value of previous bits. This indicates that the current symbol is being interfered with by previous symbols, in other words we see inter-symbol interference. This is because the root-raised cosine pulse does not have the zero ISI property. Fortunately, the receivers root P(f) lter will restore zero-isi and this will not be a problem.

OpenStax-CNX module: m14500 8 Figure 6 Figure 6. Constellation graph of 4-QAM with Root Raised Cosine pulse shaping. Exercise 4: Choose M=16. Now there are 4 in-phase voltage levels and 4 quadrature voltage levels at each sample point. This means that 2 bits can be represented by the I component and 2 bits by the Q component giving 4 bits per symbol. Since sample points are closer together than for M=4, the 16-QAM system is inherently more susceptible to noise. On the other hand, 16-QAM represents 4 bits/symbol compared to 2 bits/symbol for 4-QAM, providing double the throughput for the same transmission bandwidth. Example diagrams are shown in Figures 7-9.

OpenStax-CNX module: m14500 9 Figure 7 Figure 7. Constellation graph of 16-QAM without pulse shaping.

OpenStax-CNX module: m14500 10 Figure 8 Figure 8. Constellation graph of 16-QAM with Raised Cosine pulse shaping.

OpenStax-CNX module: m14500 11 Figure 9 Figure 9. Constellation graph of 16-QAM with Root Raised Cosine pulse shaping. 4 Part 2: Spectrum Analysis The RFSA Demo VI provides a powerful spectrum analysis tool. When the Down Converter is connected to an appropriate antenna (and optionally a preamplier), the VI provides an eective way to look at many types of external RF signals and their spectra. When the Down Converter is attached directly to the AWG as in this set of exercises, the VI allows us to analyze the spectrum of a wide variety of signals that are generated using VI's in the Modulation Toolkit.

OpenStax-CNX module: m14500 12 4.1 Theory Review The bandwidth of a QAM signal depends directly on the symbol rate, i.e., the number of symbols per second. The relationship of bandwidth to the data rate depends on the number of bits per symbol. For example, a 1 Mbps signal using 4-QAM has the same bandwidth as a 2 Mbps signal using 16-QAM since 16-QAM has twice as many bits per symbol. When rectangular pulse shapes are used (i.e., TX lter is none), the spectrum displays large side lobes compared to the main lobe, resulting in signicant band spread. The rst null is always the reciprocal of the pulse width τ, and the main lobe width is 1/2τ Hz wide. For example, using the default pulse rate of R=100,000 symbols/sec, the pulse width is τ =1/100000=.01ms, and the main lobe bandwidth is 2/.01ms = 200 khz. When raised-cosine or root raised-cosine pulses are used, the bandwidth is approximately B=(1+alpha) R, where alpha is the roll-o parameter set in the nifgen VI discussed in Part I. As discussed above, these pulses not only reduce inter-symbol interference, but do so with signicantly reduced bandwidth resulting from rounded pulse shape. Bandwidth ranges from R (alpha=0) to 2R (alpha=1) Hz. The trade o is that pulses for alpha close to 0 are very spread out, which increases susceptibility to ISI. Furthermore, the pulse is truncated when implemented in software, and this causes other unwanted artifacts. 4.2 Setup Go through the following steps to analyze the spectrum of the signal generated in Part 1. 1. Make sure the nifgen VI described in Part 1 is still running, and set the IF Frequency to be 15 MHz, set M-QAM to be 16, set TX Filter to be none, and keep all other parameters to the default. 2. Run the RFSA Demo Panel using the Windows Start button: Start - > All Programs -> National Instruments -> NI-RFSA -> RFSA Demo Panel. 3. Set up the Demo Panel parameters as follows: Center Frequency: the center frequency of displayed spectrum. It should be the same as the AWG IF of 15 MHz. Span: frequency span of the displayed spectrum. Initially set this to 2 MHz by entering 2.0 M into the parameter box. Alternatively, try checking the Start/Stop box. This changes the parameter boxes to be Starting Frequency and Stopping Frequency. The following diagram shows the front panel of the spectrum analyzer.

OpenStax-CNX module: m14500 13 Figure 10 Figure 10. Spectrum of 16-QAM without pulse shaping. 4.3 Exercises and Questions: 1. Once you have a spectrum display, determine the frequencies of the rst and second zero crossings (nulls). Conrm that the main lobe bandwidth matches that given in the Theory Review. Are the nulls spaced by 1/2τ as discussed earlier? What is the amplitude of the second lobe relative to the highest lobe? 2. In the nifgen VI, change the type of TX Filter to raised cosine, and examine the corresponding spectrum. Try dierent values of Alpha and explain the changes. Recall that bandwidth is approximately B = (1+alpha) R. 3. Try dierent values of Filter Length in nifgen. As discussed in the Theory section in Part 1, this determines how much the pulse shape is truncated. What changes are seen in the spectrum when this parameter is made smaller? 4. Try dierent values of M in nifgen to change the number of bits per symbol, and repeat the above procedure. Explain the changes in bandwidth.

OpenStax-CNX module: m14500 14 5 Part 3: 3-D Eye Diagram In this nal section, we investigate some of the digital receiver VI's that are available. Since the focus here is QAM, two VI's are of most interest: MT RFSA QAM Eye Diagram.vi and MT RFSA QAM 3D Eye Diagram.vi. We'll focus on the 3D Eye VI since it can produce all types of eye diagrams and constellation diagrams. Eye diagrams are useful in analysis and understanding digital communication waveforms. When eye diagrams and constellation diagrams are used together, they provide a nearly complete picture of the signal. One of the NI VI's, 3D Eye, combines these into a powerful 3-dimensional display that shows the tight link between these two types of diagrams. Eye diagrams can be thought of as an oscilloscope display where old traces are not erased but persist over time. Two eye diagrams are necessary for viewing the complete QAM signal, one to show the in-phase voltage waveform as a function of time, and one to show the quadrature waveform. In contrast, the constellation diagram shows the quadrature waveform on the vertical axis plotted against the in-phase waveform on the horizontal axis, without explicit dependence on time. The QAM signal is thus seen to be a three-dimensional I vs. Q vs. Time signal. Accordingly, the 3DEye Vi allows users to select I vs. Time, Q vs. Time, or I vs. Q. Most interestingly, users can click and drag the screen display to view the 3-D signal from any aspect. Although only a few exercises are suggested here, the main goal is to get users to play with dierent viewing angles in order to gain a more complete understanding of QAM and its properties. In particular note that when pulse shaping is used, the trajectories between sample points are smoothly curving across all dimensions. (Remember, a smooth waveform leads to reduced bandwidth). 1. To begin these exercises keep the coax cables hooked up the same as before. Exit the spectrum analysis VI, but make sure that the nifgen VI from Part 1 is still running. As described in Part 1, set up this VI with IF Frequency to be 15M Hz, set M-QAM to be 16, set TX Filter to be none, and keep all other parameters to the default. Run the module. 2. Go to the RFSA examples folder by using the Windows Start button: Start -> All Programs -> National Instruments -> Modulation -> LabVIEW Support -> Modulation Examples Folder -> RFSA examples. 3. Start the MT RFSA QAM 3DEye.vi, which brings up the front panel for 3-D Eye Diagram. To stop the module, click the STOP button. It takes a little while before the module stops, so just wait. 4. In the front panel, the Down Converter Device Number should be 2, and Digitizer Resource name is DAQ::5. These two parameters should already be set as the default. If not, change these two parameters properly and right click it. Go to Data Operations and then Make Current Value Default, this will make these values default. 5.1 Examples and Exercises The following examples illustrate some of the wide variety of analysis plots that are available in the 3D eye VI. To explore various waveforms, it is easy to adjust the QAM parameters in nifgen.vi in real time and observe the resulting eye diagram. The following diagram shows the 3D Eye front panel. Be sure to set up the receiver parameters (samples per symbol, M-QAM, etc.) to match those in the transmitter VI. To see the types of displays available, on the right side of the panel under Views click Constellation to get a constellation diagram. Then choose I-Eye or Q-Eye.

OpenStax-CNX module: m14500 15 Figure 11 Figure 11. 3D Eye VI front panel Exercise 1: 4-QAM (no pulse shaping). While generating 4-QAM without pulse shaping, select a Constellation diagram. The result should resemble that in Figure 12. Then select I-Eye and Q-Eye diagrams. An example is shown in Figure 13. Since a square pulse is being used, the diagrams display the output of the lossy integrator implemented in the receiver. This results in ramp waveforms at symbol transitions.

OpenStax-CNX module: m14500 16 Figure 12 Figure 12. Constellation graph of 4-QAM without pulse shaping.

OpenStax-CNX module: m14500 17 Figure 13 Figure 13. In-phase eye diagram of 4-QAM without pulse shaping. Exercise 2: 4-QAM (with pulse shaping). While generating 4-QAM, change the nifgen to use pulse shaping with a raised cosine pulse. Select a constellation diagram, and verify that the result resembles that in Figure 14 Then view the I-Eye and Q-Eye diagrams. In this case, there is no receiver lter or integrator, so the constellation and eye diagrams directly reect the raised-cosine pulse waveform. An example eye diagram is shown in Figure 15. Now change the transmitter to use root raised-cosine pulses. Do you see any dierence in the receiver diagrams? Note that in this case the receiver applies a matched lter to produce the displayed output. The result should resemble the raised cosine pulse result seen in Figures 14 and 15.

OpenStax-CNX module: m14500 18 Figure 14 Figure 14. Constellation diagram of 4-QAM with Raised Cosine pulse shaping.

OpenStax-CNX module: m14500 19 Figure 15 Figure 15. In-phase eye diagram of 4-QAM with Raised Cosine pulse shaping. Exercise 3: 3D Eye diagram (16-QAM with no pulse shaping). Finally, we experiment with the 3D Eye capability of this VI. Begin by selecting 16-QAM and no pulse shaping in the transmitter VI. Select I-Eye as shown in Figure 16, and then Q-Eye and Constellation (not shown).

OpenStax-CNX module: m14500 20 Figure 16 Figure 16. In-phase eye diagram for 16-QAM and no pulse shaping. To create a 3D eye diagram, simply use the mouse to hover the curser over the display. Click the left mouse button and drag the cursor around and a 3 dimensional view emerges. By moving the display around, one can generate in-phase vs. time, quadrature vs. time, in-phase vs. quadrature, and any combination of these views. An example is shown in Figure 17.

OpenStax-CNX module: m14500 21 Figure 17 Figure 17. 3D Eye Diagram showing all 3 dimensions of the I/Q signal. Exercise 4: Playing around with the 3D Eye diagram. Take some time to play around with the 3D display. It is not only fascinating, but it provides valuable insight into how QAM really works. Try generating M-QAM signals for dierent values of M and check out the 3D Eye diagram from dierent observation angles. Next, use pulse shaping and try to understand how the constellation plots are consistent with the dierent eye diagram views.