Vector signal analysis in an oscilloscope

& -February 07, 2017

Digital or vector modulation can provide increased spectral efficiency, higher data security, and higher quality communications. This comes at a cost of increased system complexity and a resultant increase in test difficulty.

Adding vector signal analysis (VSA) to an oscilloscope reduces the count of necessary test instruments and simplifies the testing process by consolidating analysis within a single instrument. This article looks at vector signals and the analysis tools needed to effectively measure them.


Vector state measurements

Vector or quadrature signal generation achieves high spectral density by transmitting multiple bits with each symbol sent. Consider quadrature phase shift keying (QPSK) which encodes two digital bits with each transmitted symbol. These two bits can have any of four values, 00, 01, 10, and 11. QPSK uses phase modulation to encode these values, assigning a distinctive phase for each of the two bit digital values. The phase shifts are created by breaking the data stream into two orthogonal components called the in-phase (I) and quadrature (Q) components. These components, having a fixed 90° phase difference, can be added – using different amplitude weights – to create any possible phase. In QPSK, the weighted I and Q components are combined to produce phase shifts of 45°, 135°, 225°, and 315°. This can be visualized by cross-plotting the I and Q components in an X-Y display. An example, using the Teledyne LeCroy VectorLinQ software option is shown in Figure 1.



Figure 1.  Cross plotting the I and Q components of a QPSK signal creates a state transition or trajectory diagram which shows the phase and magnitude of each encoded bi-pair as well as the transition paths between states. Reference (ideal) states as shown as ‘x’ marks and measured states are shown in red.
 

Figure 1 shows the acquired I and Q component waveforms in the two grids to the left, and the state-transition or trajectory for the QPSK signal in the X-Y diagram on the right. The green “×” symbols on the trajectory diagram mark the ideal or reference state locations, and can be customized by the user. The red areas show the measured state locations. The blue traces show the transition paths between states. A related X-Y plot is the constellation diagram. Getting into the subtleties a little more, the difference between a constellation and a state-transition diagram is that the constellation shows specifically the signal position at the recovered symbol clock times (the red points). The state-transition diagram shows these points as well as the trajectories (path the signal takes to get from one symbol to the next). 

Ideally the measured state locations should be under the reference states. The degree to which their location differs from the ideal is measured by the error vector magnitude (EVM) parameter which is also shown to the left above the setup dialog box. The numerical value displayed as EVM is the RMS value of all the digital states’ magnitude errors captured during that acquisition. Also shown is the Phase Error which is the phase difference between the signal vector for each state and the ideal reference vector. The value displayed as Phase Error is the RMS of all the states captured during that acquisition.

 

Modulated carrier

The I and Q components are used to phase modulate a carrier for transmission. Vector Signal Analyzers are capable of acquiring and demodulating such a signal for vector analysis as shown in Figure 2.

Figure 2.  Demodulation and analysis of a QPSK signal on a 100 MHz carrier showing both time and spectral views of the signal as it is processed.

 

Figure 2 is a story board of the processing involved in analyzing the modulated RF carrier. The source, shown as trace M1 in the upper left grid, is a 100 MHz RF carrier that has been phase modulated by a QPSK signal at 1 MSymbol-per-second. The grid to the immediate right of the source is the Fast Fourier Transform (FFT) of the modulated carrier. The FFT provides a frequency domain or spectral view of the signal. It shows a spectral peak, representing the source signal centered at 100 MHz. The dialog box at the bottom of the display shows the VSA software processing flow which is controlled by a template.

There are two default templates: one for baseband I and Q processing, and another for RF processing as shown here. The process starts with a band-limiting Gaussian filter centered at 100 MHz. This is followed by a quadrature mixer where the signal is mixed with a 100 MHz local oscillator and down-converted to baseband. The output of the mixer is lowpass filtered to retain only the baseband signal components.  The filter is actually matched with an identical filter on the transmitter side in order to reduce inter-symbol interference (ISI). Note how the eye diagrams “pinch together” exactly at the clocking point (eye center). This is indicative of matched Nyquist filtering. Of course, having such a filter on the transmitter also helps to reduce occupied channel bandwidth.

The next stage in the process is the Carrier Estimator. This algorithm estimates and compensates for the residual frequency offset in the carrier. This is followed by an equalizer which corrects any frequency-dependent distortion in the signal. Finally a Phase Estimator measures the phase difference between carrier source and the local oscillator. The resultant output consists of the baseband I and Q signals.

The I component is shown in the second grid from the top on the left side. Below it is a zoomed view of the I component. The Q signal component is fourth from the top on the left. A zoomed view of it is in the bottom grid on the left.

Immediately to the right of the I and Q components is the spectral view of those signals. Note that the spectra of these demodulated signals have been shifted in frequency to baseband, beginning at 0 Hz.

The demodulated I and Q components are non-return-to-zero (NRZ) signals which carry the digital information. Immediately to the right of the I and Q zoom traces are eye diagrams of each component. The eye diagrams help to verify the integrity of these signals.

The X-Y display provides the visual analysis of the I and Q components as well as the measured parameters we discussed previously. There are fourteen distinct parameters available.

There are a total of six processing function blocks available for signal operations. These processing tools allow this software to process baseband or RF carriers using PSK, QAM, Circular QAM, ASK, or FSK modulation. There is also a custom MATLAB process which allows users to script their own custom processing functions using MATLAB.

 



 


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