## Problem

When simulating phase noise in VSS, the simulated phase noise does not match the phase noise mask. Another issue is that the simulation time for a phase noise measurement is unreasonably long.

## Solution

This article addresses simulation of phase noise in the time domain. Some common issues associated with time domain phase noise measurements are:

- Simulated phase noise does not match the phase noise mask
- Excessive simulation times
- Incorrect phase noise results when total integrated noise power is too high
- Measurement not automatically recognizing correct carrier frequency
- Phase noise in the presence of broadband thermal noise
- Digital modulation EVM results do not match theoretical inclusion of phase noise in the system

Detailed information on the VSS time domain phase noise measurement can be found in the following places in the AWRDE help file:

- VSS Modelling Guide, Noise Modelling in VSS
- PHASENS block
- PHS NOISE measurement

This article summarizes the principles of VSS time domain phase noise measurements and applies these principles to examples. Please refer to installed example **Phase_Noise.emp** for sample system diagrams and associated phase noise measurements.

**Theory**

The VSS blocks that generate phase noise are:

- TONE
- PHSNOISE_CH
- PHASENS
- OSC_S
- FMULT_B
- FMULT_B2

VSS time domain phase noise modelling starts by approximating the phase noise mask using a windowed FIR filter whose frequency response is designed to match the phase noise mask single-sideband phase noise versus frequency response. White noise is then passed through the FIR filter which yields the actual phase noise response.

The number of required FIR filter taps to faithfully reproduce correct phase noise results is dependent on both the sampling frequency and the minimum phase noise offset frequency. The minimum sampling frequency is dependent on the type of signal, CW vs. multitone vs. digitally modulated, and will be discussed with each specific case below.

The number of FIR filter taps is not automatically calculated and must be set using the secondary parameter PNNFLT for the blocks that support phase noise generation. Equation (1) shows the PNNFLT parameter calculation.

By default, PNNFLT is set to a value of 10,000 which may or may not be optimum for a particular simulation. Below is a plot showing PNNFLT value as a function of both sampling frequency and minimum offset frequency. Increasing either the sampling frequency or decreasing the minimum offset frequency increases the number of FIR filter taps and consequently increases the simulation time.

Setting the resolution bandwidth is also a very important consideration for both spectrum and integrated phase noise measurements. The number of FFT bins required for either spectrum or integrated phase noise measurement impacts the ability to successfully model low offset frequency, or close-in, phase noise. The lower the minimum offset frequency, the higher the number of FFT bins needed. But, as the number of FFT bins increase, so does the simulation time. Equation (2) describes the relationship between sampling frequency, minimum offset frequency and number of FFT bins required:

Note that this equation has a scaling factor of 0.3 in the denominator that is not found in the other resources mentioned above. This scaling factor accounts for the fact that the resolution bandwidth of the phase noise measurement should be narrower than the minimum offset frequency for best correlation between simulation data an the phase noise mask at the lowest offset frequencies. This scaling factor may need to be adjusted on a case by case basis depending on the characteristics of the phase noise mask. A value of 0.3 is a good place to start in most cases.

Below is a graph of required minimum number of FFT bins as functions of both sampling frequency and minimum phase noise offset frequency using equation (2):

High phase noise power also impacts the ability to successfully match simulated phase noise to the desired phase noise mask. Phase noise is added to the phase of each time sample in the VSS simulation and as the average phase noise power increases, the phase of each sample can randomly exceed +/- 2*PI . Once this occurs, the resulting phase of the time sample is indistinguishable from whether the phase noise was generated by high average phase noise level or significantly lower average phase noise level. The result is that the simulated phase noise is lower than the target phase noise mask in the frequency regions where the phase noise is the highest.

How to determine minimum and maximum offset frequencies, sampling frequency, PNNFLT value and number of FFT bins required is dependent on whether the source is a CW signal or a modulated signal. Each topic will be addressed below.

**CW Source**

For the example of generating phase noise for a CW signal, the TONE source will be used as shown:

The number of FIR filter taps for the filter used to generate the phase noise pedestal is controlled with the PNNFLT parameter. By default, this is a hidden parameter that can be found by exposing the secondary parameters of the TONE block and unchecking the associated box in the Hide column

As described in the help file for the TONE block, the phase noise mask is contained in a data file with format as shown:

The phase noise mask can be plotted using the Data > PlotCol measurement as shown:

In this example the desire is to simulate phase noise over a frequency offset range from 100 Hz to 100 MHz.

First consideration is the minimum and maximum offset frequencies. These must be within the range of the phase noise mask in the data file. However, for successful low offset frequency correspondence between phase noise mask and simulation data, the phase noise mask must have a data points <= 0.3*Minimum Offset Frequency (consistent with equation (2)). Shown below is the phase noise simulation when the phase noise mask minimum frequency only ranges to the minimum offset frequency used for the simulation. The results are poor correspondence at low offset frequencies:

So for this example where the desired minimum offset frequency is 100 Hz, the phase noise mask data must range down to at least 30 Hz. Either extrapolate the phase noise mask data to a lower frequency or simulate with a higher minimum offset frequency if phase noise mask frequency range is insufficient.

Next consideration is the sampling frequency, Fs. For CW simulation, Fs must be >= 2 * Maximum Offset Frequency. Next are the calculations of PNNFLT and Number of FFT bins for the Resolution Bandwidth used for the power spectrum measurement. PNNFLT calculation is described in equation (1) and Number of RBW FFT bins is described in equation (2).

Creating output equations for these calculations as shown here offers some convenience:

Fs and PNNFLT_val can be applied to the TONE source parameters SMPFRQ and PNNFLT respectively. The measurement for phase noise is PHS_NOISE under System > Noise under the graph measurement tree. Leave most settings at default except for the highlighted items below:

Note, if RBW/#Bins is not set to #FFT Bins, then the maximum number of FFT bins is capped at 1.048e6. The equivalent bandwidth can be found by hovering over the phase noise measurement in the graph with the mouse, left click and hold to bring up details on the FFT measurement. To override the FFT bin cap, the RBW/#Bins Type must be set to # FFT Bins.

By following all the guidelines given above, the simulated phase noise should match the phase noise mask as shown.

Depending on the characteristics of the phase noise mask frequency response especially in the region at the minimum frequency offset, there still may be deviations between the mask and low frequency offset simulation results. Try experimenting with increasing the number of FFT bins for the PHS_NOISE measurement. For instance instead of using 0.3*Min Offset Frequency in the denominator of equation (2), try using 0.1*Min Offset Frequency and ensure that there is phase noise mask data down to at least 0.1*Min Offset Frequency.

Regarding excessive simulation time, there are two phases to the simulation. First the phase noise FIR filter is constructed. Once activating the **Run/Stop System Simulators** with large PNNFLT values, there is a period of time where the graph measurement do not appear to be updating. This is the FIR phase noise filter calculation and is signified by **Configuring system simulation** message in the status bar.

After this stage, the measurement may or may not update depending on system diagram configuration. If this occurs, reactivating **Run/Stop System Simulators** will update the measurement. Reducing PNNFLT value is the only remedy to speeding up this phase of the measurement. Without sacrificing the accuracy of the simulation measurement results versus the phase noise mask data, sampling frequency must be reduced and/or minimum offset frequency must be increased.

During the simulation phase of the simulation, the number of FFT bins in the PHS_NOISE measurement settings dictates simulation time. Again the same tradeoff for PNNFLT must be made: reducing sampling frequency and/or increasing minimum offset frequency.

__CW Measurement With High Average Phase Noise Level__

As discussed above, time domain phase simulation accuracy suffers when the integrated phase noise level is too high. Here is one example where the simulated phase noise measurement does not correlate very well.

Empirically it is found that once rms integrated phase noise exceeds -25 dBc, or 4.5 degrees, or 0.08 radians, then simulated time domain phase noise begins to lose accuracy.

Since time domain integrated phase noise measurement, INTG_PHS_NOISE, also suffers in accuracy under the conditions of high phase noise, the RF Budget integrated phase noise measurement, C_IPHS_NOISE, is the best way to determine the integrated phase noise level when suspected accuracy is in question.

__CW Phase Noise Plus Broadband Thermal Noise__

When broadband thermal noise is included in the system diagram, the phase noise measurement will be the summation of phase noise and thermal noise. Shown below are phase noise measurement results with (green trace) and without (red trace) thermal noise added to the system.

Thermal noise generates equal amounts of AM noise and phase noise and it is the phase noise portion of thermal noise that is measured by the VSS phase noise simulation. Be aware that once thermal noise dominates over the phase noise, then the phase noise floor will be that of the thermal noise. This is fairly obvious with the PHS_NOISE measurement plotted on a graph, however the integrated phase noise measurement (INTG_PHS_NOISE) where the results are a single value that the effects of thermal noise will not be so obvious.

**Integrated Phase Noise**

Time domain integrated phase noise is found under System > Noise > INTG_PHS_NOISE. All the considerations for making a CW spectrum measurement in the above section must be applied to integrated phase noise measurement. The dialog box below for the time domain integrated phase noise measurement shows entries for offset frequencies as well as the number of FFT bins.

**Multi-Tone CW Source**

Multi-Tone CW source can be created using the TONE source with multiple frequencies surrounded by curly brackets {} as the FRQ parameter:

One issue that the user may encounter using default settings for the phase noise (PHS_NOISE) or integrated phase noise (INT_PHS_NOISE) is that the phase noise measurement results are flat with frequency as shown below:

The issue is that by default, the phase noise measurement is made at the simulation center frequency which can be determined by adding the CTRFRQ annotation to the system diagram. In the above example the simulation center frequency is 1100 MHz whereas the tone frequencies are 1000 and 1200 MHz. To explicitly set the phase noise measurement frequency to one of the tone frequencies, use the Carrier Freq. parameter in the measurement properties as shown:

The other consideration is the sampling frequency. For the single CW, the sampling frequency must be at least twice the maximum offset frequency. For the multi-tone signal, the tone frequency spacing must be factored in as well. In the case of the multi-tone signal, determine the frequency range as being the lowest tone frequency minus the maximum frequency offset to the highest tone frequency plus the maximum frequency offset. For the example with two tones spaced 200 MHz apart and with maximum frequency offset of 100 MHz, the entire frequency range is 400 MHz as shown below:

Sampling frequency must be at least twice the frequency range, which in this case is 800 MHz. The equations for calculating number of Tone source FFT bins as well as the number of FFT bins for the phase noise measurement follow those of the single CW signal. Adding equation to the system diagram helps with the calculations:

**Digitally Modulated Signals**

Adding phase noise to a modulated signal affects both EVM and BER measurement results. Phase noise can either be added using an LO with a TONE source that has phase noise enabled or by using the phase noise channel block, PHSNOISE_CH. For both cases, the same considerations apply for generating phase noise and configuring the system diagram.

Phase noise tends to rotate the constellation points as shown with this 16 QAM example:

There is an obvious impact on EVM performance due to the added phase noise. Additionally, Bit Error Rate, BER, results at higher SNR levels shows more degradation that the same system without phase noise:

Setting the sampling frequency for a digitally modulated signal is based more on the bandwidth of the digitally modulated signal than the characteristics of the phase noise mask. Show below is an EVM measurement system with a 16 QAM source:

The complex IQ data at the output of the receiver in the measurement path was extracted and processed to compute phase. The results are shown here:

The first observation is that the phase noise falls off abruptly at one-half the bandwidth of the modulated signal. This applies to other digital modulation formats including PSK and OFDM. The second observation is the roll-off effect on phase noise at lower offset frequencies. The phase noise falls off at lower offset frequencies, an effect very similar to carrier tracking in a digital receiver. The low offset frequency roll-off is that of 2^{nd} order high-pass filter. The placement of the ALIGN block in the system diagram changes the effective corner frequency of the low offset phase noise roll-off as shown here:

There is a corresponding effect on measured EVM:

The placement of the ALIGN block has the same roll-off effect for QAM and PSK based modulation formats. For OFDM systems, the ALIGN block cannot be placed in front of the receivers and for OFDM systems there is the same low offset frequency phase noise roll-off seen with the other modulation formats.

Setting simulation parameters for digitally modulated signals is quite different than the considerations for a CW signal. First, the maximum offset frequency is dependent on the modulation bandwidth, not the phase noise mask. The maximum offset frequency can be set to one-half the modulation bandwidth. Next, the sampling frequency should be set to at least 4 times the maximum offset frequency (not 2 times as for the CW case). Next, the minimum offset frequency can be set somewhat higher than the minimum mask offset frequency due to the roll-off affect from the ALIGN blocks. Note: for BER systems the ALIGN block is often not used in which case the roll-off effect does not take place and the minimum offset frequency should be set lower.

Using Output Equations can help with calculations of sampling frequency and number of FIR filter taps for the phase noise generation parameter PNNFLT:

**Excessive Simulation Time**

Finally, the issue of long simulation times will be addressed. Sampling frequency, number of phase noise FIR filter taps (PNNFLT parameter) and number of FFT bins for the PHS_NOISE and INTG_PHS_NOISE measurements all contribute to the simulation time. Reducing these parameter values decreases the simulation time. The primary driver for these parameters is the phase noise frequency offset range. Trying to simultaneously measure with a very low minimum offset frequency and a very high maximum offset frequency is going to lead to a long simulation time. Justification for examining the entire frequency range of the available phase noise mask should be thought through.

Worth mentioning again is the two parts of the simulation. The first part consists of configuring the FIR filters that generate the phase noise. During this phase graph data is not being updated, nor is the simulation window actively showing a simulation taking place. This first part is entirely dependent on the PNNFLT value – the higher this value, the longer the configuration phase of the simulation. The second part of the simulation is where the graph measurement data is being updated and the simulation window is showing simulation status. Sampling frequency and number of FFT bins dictate the length of simulation time.

Another consideration in the PHS_NOISE and INTG_PHS_NOISE measurements is the number of averages set with the VBW/#Avg. measurement parameter. Simulations can appear to be stalled while waiting for the requested number of averages (VBW also drives the number of averages). Reducing the number of averages (or increasing the VBW value) will speed up the measurement.