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Chapter 3. Noise Modeling in VSS

This chapter describes the noise modeling capabilities of Visual System SimulatorTM (VSS) program.

3.1. Modeling Noise in VSS

The three main forms of noise modeled in the VSS program are thermal circuit noise (which is called circuit noise in the VSS program), channel noise, and phase noise. Circuit noise and channel noise are both based on white Gaussian noise. Circuit noise is primarily specified as a noise temperature, a noise figure, or equivalent noise voltage or current sources. Channel noise is typically specified in noise power spectral density (noise PSD) which are typically in units of dBm/Hz.

RF Budget Analysis simulations primarily work with circuit noise, which is frequency dependent, although they also provide limited support for channel noise. Time Domain simulations are most effective when modeling white channel noise.

Both Time Domain and RF Budget Analysis simulations also support phase noise. VSS phase noise modeling is covered in the Phase Noise section.

Related to noise are the signal to noise and energy to noise ratios used in the VSS program. These are discussed in the SNR, Eb/N0 and Es/N0 section.

A limitation to modeling noise in Time Domain simulations occurs when working with complex envelope signals whose sampling frequency band crosses into negative frequencies. This is discussed in the Noise and Negative Frequency Folding section.

3.2. Circuit Noise

The RF blocks that support thermal noise generation have a NOISE parameter which allows you to control which simulations include noise. The NOISE parameter has four options:

  • RF Budget only

  • RF Budget + Time Domain

  • Noiseless

  • Auto

The default setting is "Auto". With this setting, the noise modeling setting is taken from the RF Noise Modeling setting on the RF Options tab of the Options dialog box for the system diagram. This allows you to change the RF noise modeling settings for all RF blocks in a system diagram at one time. You still have the option of changing settings for individual blocks using the NOISE parameter.

In RF Budget Analysis simulations, noise is modeled by a block when either "RF Budget only" or "RF Budget + Time Domain" is selected. In Time Domain simulations, noise is modeled by a block when "RF Budget + Time Domain" is selected.

The different RF blocks determine how much noise is to be added. Noise is added only to the output signal. Because of this, the noise added represents the noise that is seen by the load. The noise is computed on a frequency dependent basis.

3.2.1. Linear RF Blocks

The linear RF blocks, which include the circuit filter blocks in the Bandpass, Bandstop, Highpass and Lowpass sub-categories of the Filters category, determine the noise to be added using noise correlation matrices. LIN_S obtains a normalized noise correlation matrix Ci directly from the Microwave Office simulation. The other blocks obtain Ci from their Y matrix using the following:

(3.1)

If impedance mismatch modeling is enabled, Ci is adjusted for any voltage divisions on the inputs due to branches.

For a 2-port with port 2 the output port, the noise PSD added at the output, NN, is:

(3.2)
(3.3)
(3.4)

The noise VSD added at the output is computed directly from NN:

(3.5)

ZS is the impedance seen looking into the source's output port.

For the matched load case, ZL is the conjugate of ZS. ROut is obtained from:

(3.6)

ZOUTP is the characteristic impedance of the output port.

For computing noise VSD, ZL is the load impedance and ROut is the real component of ZOUTP.

The temperature T in Equation 3.2 is the temperature parameter T_PHY from the block if the block has a temperature, or is the ambient system temperature setting from the RF Options tab of the Options dialog box for the system diagram.

3.2.2. Amplifiers

There are several ways of specifying noise added by amplifier blocks. These include noise figure NF, equivalent input referred noise voltage, and equivalent input referred noise current. The voltage and current are RMS spectral densities and are normally specified in units of nV/sqrt(Hz) and pA/sqrt(Hz), respectively.

The amplifiers AMP_B, AMP_BV, AMP_F, NL_F and VGA_F support all three methods. AMP_F supports the specification of frequency dependent noise values. NL_S obtains its noise information from the Microwave Office nonlinear noise simulation.

If noise figure is specified, it is converted to an equivalent input referred noise current using the following:

(3.7)

where ZINP is the characteristic impedance of the amplifier's input port.

The amplifiers interpret input referred noise voltage and current using the following model:

Interpretation of Vn and In in VSS amplifiers

Figure 3.1. Interpretation of Vn and In in VSS amplifiers


Note that the voltage and current sources are correlated.

Noise PSD and noise VSD are computed using noise correlation matrices as for the linear RF filters. A normalized noise correlation matrix Ci is first computed as:

(3.8)
(3.9)
(3.10)

The Y matrix is obtained from the linear voltage gain, S11 and S22 parameters of the amplifier.

By default the actual noise correlation matrix used is generated from a single output referred voltage source whose voltage is equivalent to the output noise voltage generated by the initial noise correlation matrix. Using an output referred noise voltage source prevents the noise generated by the amplifier from dropping when the amplifier is in compression (the gain applied to the noise seen at the amplifier's input does still drop with compression).

For RF Budget Analysis simulations, input referred noise sources can be forced by setting the NOISEPORT parameter to "Input Port". The original noise correlation matrix will then be used for the simulation.

Input referred noise sources will also be used if for some reason the impedance seen looking out either the input or output port cannot be determined.

3.2.3. Mixers

The VSS behavioral mixers MIXER_B and MIXER_F use single sided noise figure to specify noise. The noise figure is converted to an equivalent input referred noise current similar to the amplifiers. However, because the noise figure is single sided the conversion is:

(3.11)

3.2.4. Additional Notes

The following are additional items to note when working with circuit noise.

In Time Domain simulations the VSS program adds noise directly to the samples as the noise is generated. While simplifying the simulation, it presents several problems. One problem occurs when the sampling frequency band crosses DC - noise folding occurs. This problem is discussed in detail in the Noise and Negative Frequency Folding section.

The second problem occurs when combining signals whose noise levels represent the ambient noise temperature.

Both these problems do not apply to RF Budget Analysis simulations.

Combining Signals with Ambient Noise

Because noise is directly added to the signal samples as the samples are generated, the noise cannot later be separated from the signal. In most cases this is not an issue.

However, in the case of a passive lossy combiner this becomes a problem when the signals being combined have noise near the ambient noise temperature. In a physical passive combiner, if the input signals all have noise levels at the ambient noise temperature, the noise level at the output of the combiner is also at the ambient noise temperature.

Unfortunately in VSS Time Domain simulations, because the noise is incorporated directly into the signal samples, the noise at the output of the combiner is effectively the sum of the noise at all the inputs. For a two-input combiner with both inputs having a noise temperature of 290 K the output noise is at 580 K, or 3.01 dB too high.

The workaround is to only generate noise on one of the inputs to the combiner, preferably the primary input.

3.3. Channel Noise

Channel noise is primarily used when performing BER measurements on a system design. The additive white Gaussian noise channel block AWGN models white Gaussian channel noise.

Note that when circuit noise samples are being generated in a Time Domain simulation, the circuit noise is automatically included in the channel noise.

3.4. Phase Noise

The following blocks support the generation of phase noise:

Block Description
Channels > Phase Noise > PHSNOISE_CH Phase Noise Channel
RF Blocks > Freq. Multipliers > FMULT_B Behavioral Frequency Multiplier
RF Blocks > Freq. Multipliers > FMULT_B2 Behavioral Frequency Multiplier, 2nd Generation
RF Blocks > Sources > TONE Tone(s) Source
RF Blocks > Sources > Simulation Based > OSC_S Oscillator with Optional Phase Noise Effects
Sources > Noise > PHASENS Phase Noise Source

With the exception of OSC_S, phase noise is specified as a phase noise mask in dBc/Hz at specific frequency values. The mask can be entered either in a text data file or as a vector of frequency-dBc/Hz pairs of values. OSC_S obtains its phase noise mask directly from the Microwave Office phase noise simulation.

The phase noise channel block PHSNOISE_CH is useful for modeling phase noise from an LO that would be added to a narrowband signal by an ideal mixer (a mixer that only generates the 1,1 spurs) without incorporating a mixer in the design. For example, a QAM signal generated by QAM_SRC with center frequency set to 1 GHz passing through a PHSNOISE_CH block produces similar results to a QAM signal at baseband passing through an ideal mixer with a 1 GHz LO with a similar phase noise mask:

Use of PHSNOISE_CH with a modulated signal to model baseband upconversion

Figure 3.2. Use of PHSNOISE_CH with a modulated signal to model baseband upconversion


Note the adjustment to the OUTLVL parameter of the baseband QAM_SRC. This is to reflect the fact that OUTLVL for QAM_SRC at baseband represents the average power of each channel, which are then combined by the upconversion mixer.

3.4.1. Phase Noise in RF Budget Analysis

RF Budget Analysis simulations model phase noise at the frequency offsets specified in the phase noise sources. Phase noise is modeled as dBc values at each frequency offset for each simulation frequency. The phase noise values for a simulation frequency remain fixed until they reach a block that performs a frequency translation on the simulation frequency, such as mixers or frequency multipliers, or they encounter another source of phase noise.

The simulator interpolates phase noise values between frequency offsets using linear interpolation with log-frequency and dBc values. This interpolation is used when computing integrated phase noise, or when phase noise is to be added to a signal already containing phase noise. Such a case occurs when both the input and LO to a mixer contain phase noise.

The Cascaded Phase Noise measurement C_PHS_NOISE and the Cascaded Integrated Phase Noise measurement C_IPHS_NOISE are used for RF Budget Analysis phase noise measurements.

3.4.2. Phase Noise in Time Domain Simulations

Modeling phase noise in Time Domain simulations can be tricky. One of the biggest problems is trying to model close-in phase noise, that is, phase noise very close to the carrier. How well the phase noise is modeled depends on both how the phase noise is generated and how the phase noise is measured.

Generating Phase Noise

The VSS program generates time domain phase noise by applying an FIR filter to a white Gaussian noise source. The FIR filter is used to shape the noise to match the phase noise mask.

The phase noise generating blocks PHSNOISE_CH, PHASENS, TONE and OSC_S then add the phase noise samples to the phase of a complex signal to apply the phase noise to the signal.

The number of taps used for the FIR filter ultimately determines the minimum frequency offset of the modeled phase noise. The number of taps is specified by the PNNFLT parameter of the block. Note that minimum offset modeled is larger than the sampling frequency divided by PNNFLT due to the windowing used to design the FIR filter.

Generally, the number of taps to use for the FIR filter is:

(3.12)

The factor of 2 is to account for any windowing effects and may depend upon the close-in phase noise shape. The best approach is to configure a TONE block with the desired sampling frequency and to adjust the PNNFLT until you obtain the desired minimum frequency offset. Note that you may need to adjust the PHS_NOISE measurement to display the desired minimum frequency offset.

A windowed FIR frequency sampling design algorithm is used to design the FIR filter in order to reduce the sidelobes inherent in the FIR frequency sampling design technique. The Windowed FIR Filters section of the RF Modeling in VSS chapter further discusses windowed FIR frequency sampling design.

The amount of phase noise that can be successfully modeled is inversely proportional to the sampling frequency. This is due to the random phase samples wrapping around ±π. As the amount of phase noise to be generated increases, more of the noise wraps around ±π, effectively aliasing the noise.

In general, as the average phase noise of the FIR filter bins approaches the inverse of the sampling frequency, the ability to generate phase noise near the desired dBc/Hz level diminishes. The average phase noise of the FIR filter bins can be computed from:

(3.13)
(3.14)

where freq[n] is the frequency of the n'th bin, and FLower, FUpper, PNdBc, Lower and PNdBc, Upper are the points from the phase noise mask bounding freq[n]. freq[n] is computed from:

(3.15)

The average phase noise level to be generated also affects how well the phase noise can be modeled. If the level is too high, the modeling is poor. To see why, look at phase noise for what it is in a time domain simulation: noise added to the phase of a sample. The noise added to each sample is a function of the average phase noise level and the sampling frequency  At some average phase noise level, the noise added to the sample exceeds +/- 2 PI. At this point the phase of the sample plus the noise is indistinguishable from the phase of the original sample plus noise that is -/+ 2 PI from the original noise added, and this wrapped around noise level is one that would be generated by a much lower phase noise level.

For example, suppose an average phase noise level of -80 dB generated noise to be added to the phase of a sample that is around +/- 2.1 PI. For the time domain simulation, this is equivalent to adding noise to the phase that is +/- 0.1 PI (from 2.1 PI - 2 PI). This noise of +/- 0.1 PI could be generated with an average phase noise level of -100 dB (this value is an example to demonstrate that there is an average phase noise level that would also generate this same amount of noise). In effect this is an aliasing of phase noise, and is similar to how a signal outside of the sampling frequency band aliases back into the sampling frequency band.

Measuring Phase Noise

There are two VSS measurements for working with phase noise in Time Domain simulations: Swept Integrated Phase Noise INTG_PHS_NOISE and Phase Noise (dBc/Hz, log frequency) PHS_NOISE. Both measurements are found in the System > Noise measurement category.

INTG_PHS_NOISE measures phase noise within a frequency band. It can present the phase noise as phase jitter, time jitter, or dBc. The frequency band is specified relative to a carrier frequency.

PHS_NOISE displays phase noise in dBc/Hz versus frequency. The frequency axis should normally be set to a log scale.

Both measurements operate by performing a power spectrum measurement, converting the measured spectrum to dBc/Hz. By default they utilize a large number of FFT bins along with windowing and cumulative averaging.

Measuring phase noise can be tricky, particularly when measuring close to the carrier. There are two main reasons for this. First is the issue of resolution bandwidth. The closer to the carrier the frequency of interest, the smaller the resolution bandwidth must be, and the larger the number of FFT bins required to perform the spectrum measurement. The order of the filter used to shape the phase noise must also be taken into account, as a larger filter order may be needed.

The second problem is due to the phase noise making the signal non-periodic. When an FFT is performed to obtain the power spectrum, the signal is truncated. This effectively spreads the power of the signal over the bins of the FFT. The solution to this is to apply a window function to the signal prior to the FFT. The window essentially smooths the edges of the time domain signal, reducing the effects of truncation and thereby reducing the spreading of the power. The drawback is that the application of the window function spreads the carrier due to the wide main lobe. The net result is a more accurate spectrum in the majority of the sampling frequency band, but a less accurate spectrum near the carrier.

Figure 3.3 compares a PHS_NOISE measurement with windowing set to the default Blackman-Harris 4 term window function, a PHS_NOISE measurement with no windowing applied, and the phase noise mask used to generate the signal. With windowing, the carrier has been spread to about 3.6 kHz as can be seen by the wide bump ending at 3.6 kHz. Beyond 3.6 kHz, however, the windowed curve follows the phase noise mask closely.

Without windowing, the carrier has been spread to about 1 kHz, allowing a measurement of the phase noise starting from that point. However, the curve does deviate from the phase noise mask until approximately 200 kHz.

Comparison of phase noise measurements with and without windowing

Figure 3.3. Comparison of phase noise measurements with and without windowing


In the PHS_NOISE measurement, the range of frequencies measured is limited by default to ignore the main lobe spectral spreading due to the windowing and to ignore the frequencies near the edges of the sampling frequency band. The frequencies near the edges of the sampling frequency band are generally not meaningful when performing RF simulations, as they contain artifacts such as resampling filter transition bands used by nonlinear and circuit filter models, or the wrap-around nature of digital filters.

The online help for PHS_NOISE and INTG_PHS_NOISE contains more information on using these measurements.

3.5. SNR, Eb/N0 and Es/N0

The VSS program supports the three noise ratios SNR (signal-to-noise ratio), Eb/N0 (bit energy to noise PSD ratio) and Es/N0 (symbol energy to noise PSD ratio) in several different ways.

All three ratios base the signal power component on the static signal power property. This is a signal property that represents the average signal power as the signal progresses through the link. The property is static because it is determined at the start of each simulation sweep and does not vary during the sweep.

The signal source blocks are generally blocks that have a power level parameter. These include the RF tone source block TONE and the various transmitters such as QAM_TX or QAM_SRC. The signal power property is updated by blocks along the signal path that change the signal power level, such as amplifiers, filters and mixers.

While used to convey the signal power portion of the noise ratios, the signal power property's primary use is for automatic gain control in receivers. The receiver blocks use the signal power property to determine an appropriate scaling for demodulation and detection of the received signal.

The static signal power property at each output port can be displayed using the SIGPWR annotation as well as the static signal power properties measurement PWR_PROP, found under the System > Tools category.

Eb/N0, Es/N0 and one form of SNR also use the static channel noise PSD property to determine their noise component. The channel noise PSD is an estimate of the power spectral density of channel noise generated as it passes through the link. The channel noise PSD property can be displayed using the NOISEPSD annotation with output type set to "Generated Noise PSD". It can also be displayed using the NOISE_PROP measurement in the System > Tools category.

The channel noise PSD property is adjusted differently depending on the block it passes through. For filters, the property is adjusted by applying the average voltage gain over the signal bandwidth, centered at the center frequency. The signal bandwidth is the sampling frequency divided by the oversampling rate or samples per symbol associated with the signal.

For nonlinear blocks such as the RF amplifiers and mixers, the property is adjusted by creating a set of samples with average power equal to the noise power over the sampling frequency, passing those samples through the nonlinearity, then converting the average power of the modified samples back to noise PSD over the sampling frequency.

3.5.1. SNR

The VSS program supports two forms of signal-to-noise ratio measurements. The first form normally represents the frequency dependent circuit SNR and is available only in RF Budget Analysis through the cascaded signal to noise ratio measurement C_SNR found in the System > RF Budget Analysis category. This SNR uses for its noise component the frequency dependent node noise temperature property. It can also optionally include channel noise.

The second form of SNR is similar to Eb/N0 and Es/N0. It is normally used when performing BER measurements in Time Domain simulations and is only available in Time Domain simulations. This form of SNR is frequency independent and uses the static channel noise PSD property for its noise component. The noise power is computed over the signal bandwidth, which is the sampling frequency divided by the signal's oversampling rate. Equation 3.16 illustrates this computation:

(3.16)

The second form of SNR can be displayed using the EsN0_PROP measurement found in the System > Tools category.

3.5.2. Eb/N0 and Es/N0

Eb/N0 and Es/N0 are normally used when working with modulated signals, particularly when performing bit error rate measurements in the time domain. They are only available in Time Domain simulations. Eb/N0 and Es/N0 can be displayed using the EsN0 annotation or the EsN0_PROP measurement found in the System > Tools category.

One of the features of the VSS program is the ability to automatically determine Eb/N0 and Es/N0 at a BER meter based on the signal and noise characteristics of the received signal. This can, of course, be overridden at the BER meter by specifying explicit values for the SWPVAR parameter.

Note that when you use a transmitter and AWGN channel, Eb/N0 or Es/N0 at the BER meter includes the effects of all the blocks between the transmitter and receiver. Therefore, the Eb/N0 and Es/N0 values displayed in a BER may not match the ratio of the transmitter's power to the AWGN's channel, particularly if the signal encounters compression.

Eb/N0 and Es/N0 use the static channel noise PSD property for their noise component.Equation 3.17 and Equation 3.18 illustrate the computations.

(3.17)
(3.18)

3.6. Noise and Negative Frequency Folding

Negative frequency folding occurs when working with complex envelope signals whose center frequency is less than 1/2 the sampling frequency. When that occurs, part of the sampling frequency band contains negative frequencies. Conceptually, negative frequency content is equivalent to the complex conjugate of the corresponding positive frequency content. When the center frequency is greater than 0, the default behavior of VSS spectrum measurements is to automatically convert negative frequency content to the equivalent positive frequency content, or to "fold" the negative frequency content into the positive frequencies.

Noise and negative frequency folding

Figure 3.4. Noise and negative frequency folding


However, when working with noise, frequency folding results in a doubling of noise PSD where the frequencies have been folded. The noise is no longer white but has a 3 dB step. To avoid this scenario when modeling noise, the center frequency should either be 0 or greater than 1/2 the sampling frequency to avoid negative frequency folding.

The Negative Complex Envelope Frequencies section of the Simulation Basics chapter explores negative frequencies in detail.

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