Lab 2 – Pulse Shaping and QAM Constellations

Part 1– QAM and PSK

In this lab you will learn about the constellation and I and Q waveforms of Quadrature Amplitude Modulation (QAM) and Phase Shift Key (PSK). Create the schematic below. The bullet list contains the information about each block. Quick Tip: Mouse scroll wheel moves schematic up/down, Ctrl+mouse wheel moves in and out and Shift+mouse wheel is left/right.

Go to Options->Project Options->Global Units. You can set time to seconds – all time in lab is in seconds. You could also change frequency to MHz, however lab is in GHz.

The blocks that are grey are disabled. Insert them as normal but once the schematic is complete, right-mouse click on them and Toggle Enable. This allows you to turn on/off parts of the schematic.

• RND_D – creates a random string of numbers with M levels, where 2k=M and k is the number of bits. M corresponds to a list of digital bits, e.g. 0110 is level 6, 0111 is level 7. Set M=M where M is a variable that you will create using Ctrl+E. Set M=4. The rate at which the numbers are generated is set by RATE=1e6, this will be our Symbol rate, i.e. the rate at which each point of the constellation is transmitted.
• QAM_MAP – This is a QAM mapper. It does the work that the digital signal processing would do. It takes the M levels of the random sequence and converts them into signals for the I and Q paths for a QAM constellation. Basically recreating the M levels using I and Q signals in QAM format. Set M=M. The output is a complex number that contains both I and Q. You can see the output node is red and the picture shows an I and Q diagram.
• MPSK_MAP – This is a PSK mapper. It does the work that the digital signal processing would do. It takes the M levels of the random sequence and converts them into signals for the I and Q paths for a PSK constellation. Basically recreating the M levels using I and Q signals in PSK format. Set M=M. The output is a complex number that contains both I and Q. You can see the output node is red and the picture shows an I and Q diagram.
• C2RI – converts the complex signal from the mappers to a real signal for the I path and a real signal for the Q path. Basically just splits A-jB into A and B.
• HOLD – takes the input numbers and pads them with zeros after them at a specified time spacing. Set NREP=_SMPSYM. This is setting the padding settings to _SMPSYM, which is a system setting you will now set. Right mouse click on the schematic and select Options. On the Simulator tab, uncheck Use project defaults. Then set Data rate=.001GHz. Note: this is 1e6, which matches our random number generator. Oversampling=8 is already set. Note that in parenthesis, (_SMPSYM) is mentioned. By setting NREP=_SMPSYM, you have connected the HOLD to these system settings. We will explore what HOLD does in this lab. Set HVAL=0; this just makes the extra points it inserts equal to zero.
• PLSSHP – this is a pulse generating and shaping filter. Its input is a set of numbers and it creates a pulse that is shaped by the selected filter. ALPHA=0.35 is set by default, and is used for raised cosine filters. PLSTYP=Rectangular sets the block to only generate a rectangular (ideal) pulse with no filtering. Make sure that is selected. Now click Show Secondary, it is in the lower right of the properties dialog box. It will reveal additional parameters. Set T=1e-6, which is the symbol period.
• LPFB – creates a low pass Butterworth filter with insertion loss LOSS and passband FP. Set FP=.0005 Ghz (0.5 Mhz). Remember the BW is Rp=1/Tp which is 1e6. Setting the pass band below this will put the 3dB point around Rp. We will check this in the lab.
• RI2C – converts the I and Q back to a complex quality, i.e. I+jQ. This is useful for AWR in plotting constellations.
• TP – please label the TP the same names as in the schematic. It will help the graders and also will follow the lab terminology. Quick Trick: Shift+Right Mouse click inverts the TP, Fn+Right Mouse click rotates.

Part 2 – Numbers, bits and signals

Assignment (5pts):

• Plot the following on the same graph (20us time axis), but on different Left axis, grouped as follows:
• Input_M
• Cplx_Cstln – real and imaginary; R_Cplx_Cstln (real part); I_Cplx_Cstln (real part)
• Set Traces in the Plot Properties box to show a symbols, but no lines. This helps visualize that these are a sequence of numbers, not a signal. On the right side of the Traces tab, unselect “Auto Interval” under Symbol and set interval to 1. This will put a symbol for each number or data point.
• I_# and I (real parts of both).
• Set Traces in the Plot Properties box to show a symbol, but no line, for I_#, as it is a series of numbers, not a signal. The PLSSHP block creates the signal. On the right side of the Traces tab, unselect “Auto Interval” under Symbol and set interval to 1. This will put a symbol for each number or data point.
• Describe each signal, what does it represent. Is it a number sequence or a signal that we might measure on the oscilloscope? If a number sequence, what do the numbers represent?
• Input_M
• Cplx_Cstln
• R_Cplx_Cstln
• I_Cplx_Cstln
• I_#
• I
• Plot the constellation of Out. Project-> Add Graph-> Constellation. Then add new measurement IQ time span of 1000 Symbols.
• What is the intersymbol spacing (min distance between two points). You can use Graph->Marker-> Add Marker to add a marker to get quantitative data.
• What is the maximum signal amplitude (the max. deviation from the origin)

Now set M=16.

Assignment (8pts):

• Plot the same graph as above.
• What has changed in M
• What has changed in the R_Cplx_Cstln
• What has changed in I
• Plot the constellation
• What is the intersymbol spacing (min distance between two points). You can use Graph->Marker-> Add Marker to add a marker to get quantitative data.
• What is the maximum signal amplitude (the max. deviation from the origin)
• Comment on the power and noise immunity between this 4 QAM and 16 QAM example. NOTE: the QAM_MAP keeps the max I and Q numbers to 1, so as we increase the modulation, it puts it inside the same limits, i.e. 1x1.

Set M=64

Assignment (1pt):

• Plot the constellation.

Now toggle the enable on the QAM_MAP to disable it and then enable the MPSK_MAP. Set M=4.

Assignment (2 pts):

• Plot the waveforms you did for the 4 QAM and comment on any differences/similarities.
• Plot the constellation. Comment on and differences/similarities with the 4 QAM

Set M=16.

Assignment (5 pts):

• Plot the waveforms you did for the 16 QAM and comment on any differences/similarities.
• Plot the constellation. Comment on any difference/similarities with 16 QAM.
• What is the minimum intersymbol spacing?
• What is the max. signal amplitude?
• Comment on the power and noise immunity between this 16 PSK and 16 QAM example.

Part 3 – Pulse filtering and eye diagrams.

Toggle the QAM_MOD so that you are in 4 QAM mode. To change the filtering in this section you can click on the PLSSHP filters and change Rectangular to Raised Cosine, etc. Or you can toggle the LPFB on and the PLSSHP off. Make sure to do it to both the I and Q paths.

Assignment (5pts):

• Plot the spectrum of I for a Rectangular spectrum (use dBm for all spectrum plots)
• Plot the spectrum of I for a Raised Cosine spectrum
• Plot the spectrum of I for a LPF spectrum (Fp=.0005 Ghz)
• Comment on the spectrum of each with respect to bandwidth.
• Change M=16. Do the spectrums change? If they do, how and why? If not, why not?

Assignment (7pts):

• Plot the I waveform for a Rectangular Filter. Comment on shape.
• Plot the I waveform for a Raised Cosine Filter. Comment on the shape.
• Plot the I waveform for a LPF. Comment on the shape.
• Plot the eye diagram of M=4 with a rectangular pulse. Project->Add Graph->Rectangular. Then Add Measurement and under System you will find Eye Diagram. Select Eye. Set Time span to 3 us which will show 3 complete symbol periods (don’t set to 3 symbols, it doesn’t work for some reason. Use 3 us). Set Max Number of Traces to 1600. It will now overlay 1600*3 symbols on top of each other, 3 symbols at a time.
• Plot the eye diagram with a Raised Cosine Filter. Comment on differences. Is there a point where you could sample and get a clean signal?
• Plot the constellation with a Raised Cosine filter. Plot with the trace being markers only (default) and then with lines only (have to set in properties box). Markers only is called the IQ constellation. Lines only is called the Trajectory plot. Comment on differences between it and a Rectangular filter.
• Plot the eye diagram with a Low Pass Filter. Comment on differences. Is there a point where you could sample and get a clean signal?

Change M=16.

Assignment (7 pts):

• Plot the I waveform, Constellation and eye diagram for a Rectangular Filter. Comment on differences between 4 QAM.
• Plot the I waveform, Constellation and eye diagram for a Raised Cosine Filter. Comment on differences between 4 QAM.
• Plot the I waveform, Constellation and eye diagram for a Low Pass Filter. Comment on differences between 4 QAM.