Objective The purpose of this module is to study Quadrature Amplitude Modulation (QAM) through hands-on experiments using a National Instruments (NI) PXI system configured as a software-defined 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 effects of pulse shaping filters 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 first 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.

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-defined 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 configuration for the system is shown below in Figures 1 and 2.

Figure 1. Typical set up for PXI system.

Figure 2. Front of National Instruments as configured 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 briefly 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 fixed 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.

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 different communication system functions. The first 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: “Start” -> “All Programs” -> “National Instruments” -> “Modulation” -> “LabVIEW Support” -> “Modulation Examples Folder” -> “FGEN examples”. 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. Front panel of “MT niFGen QAM Signal Generation.vi”

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. “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=2m−1 size 12{L=2 rSup { size 8{m} } - 1} {}, where m is the PN Sequence Order. For example, when m=5, the length of the repeating bit sequence is 2m−1=31 size 12{2 rSup { size 8{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 log216=4 size 12{"log" rSub { size 8{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 filter 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 filter 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 filter 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.”)

Theory Review Pulse shaping: Although square pulses can be used to represent the digital data (“no filter” 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 pr(t) size 12{p rSub { size 8{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 filter frequency response is also designed to be the square root of P(f), which means that the overall transmitter-receiver 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 filter” 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 pr(t) size 12{p rSub { size 8{r} } \( t \) } {} are infinite in time extent and can only be implemented by truncating them to some convenient finite length. In this VI, pulse length is referred to as the “Filter Length,” and is specified in terms of the number of symbols. For example, if filter 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 filter. M-QAM: QAM works by using M different combinations of voltage magnitude and phase to represent N bits, as described by the relationship M=2N size 12{M=2 rSup { size 8{N} } } {}. When N is an even integer, the constellation is regular with I and Q each representing 2N−1 size 12{2 rSup { size 8{N - 1} } } {} bits. When N is an odd integer, the constellation is not necessarily symmetrical, and finding an optimal distribution of sample points is not straightforward.

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 firm understanding of this modulation technique. 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 different 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. Constellation graph of 4-QAM with no pulse shaping. 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. 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) filter will restore zero-ISI and this will not be a problem.

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.

Figure 7. Constellation graph of 16-QAM without pulse shaping.

Figure 8. Constellation graph of 16-QAM with Raised Cosine pulse shaping.

Figure 9. Constellation graph of 16-QAM with Root Raised Cosine pulse shaping.

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 preamplifier), the VI provides an effective 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.

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 filter” is “none”), the spectrum displays large side lobes compared to the main lobe, resulting in significant band spread. The first null is always the reciprocal of the pulse width τ size 12{τ} {}, and the main lobe width is 1/2τ size 12{1/2τ} {} Hz wide. For example, using the default pulse rate of R=100,000 symbols/sec, the pulse width is τ size 12{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-off 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 significantly reduced bandwidth resulting from rounded pulse shape. Bandwidth ranges from R (alpha=0) to 2R (alpha=1) Hz. The trade off 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.

Setup Go through the following steps to analyze the spectrum of the signal generated in Part 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. Run the “RFSA Demo Panel” using the Windows Start button: “Start” -> “All Programs” -> “National Instruments” -> “NI-RFSA” -> “RFSA Demo Panel”. 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.

Figure 10. Spectrum of 16-QAM without pulse shaping.

Exercises and Questions: Once you have a spectrum display, determine the frequencies of the first and second zero crossings (nulls). Confirm that the main lobe bandwidth matches that given in the Theory Review. Are the nulls spaced by 1/2τ size 12{1/2τ} {} as discussed earlier? What is the amplitude of the second lobe relative to the highest lobe? In the niFGEN VI, change the type of “TX Filter” to raised cosine, and examine the corresponding spectrum. Try different values of Alpha and explain the changes. Recall that bandwidth is approximately B = (1+alpha) R. Try different 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? Try different values of M in niFGEN to change the number of bits per symbol, and repeat the above procedure. Explain the changes in bandwidth.

Part 3: 3-D Eye Diagram In this final 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 different 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). 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. 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”. 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. 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.

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.”

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.

Figure 12. Constellation graph of 4-QAM without pulse shaping.

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 filter or integrator, so the constellation and eye diagrams directly reflect 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 difference in the receiver diagrams? Note that in this case the receiver applies a matched filter to produce the displayed output. The result should resemble the “raised cosine” pulse result seen in Figures 14 and 15.

Figure 14. Constellation diagram of 4-QAM with Raised Cosine pulse shaping.

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).

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.

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 different values of M and check out the 3D Eye diagram from different observation angles. Next, use pulse shaping and try to understand how the constellation plots are consistent with the different eye diagram views.