Gain patterns

• ITU and ETSI Gain Patterns
• Additional Gain Patterns
• Archived Gain Patterns

ITU and ETSI Gain Patterns

• Note on the IMT-MODEL Gain Patterns
• Note on the IMT-MODEL Non-Co-Frequency Gain Pattern

The gain patterns in Visualyse Interplanetary come from a number of sources including:

Table 1: References for ITU-R and ETSI Visualyse Interplanetary Gain Patterns

These documents can be accessed from:

http://www.itu.int

http://www.etsi.org

Registration and/or payment might be required for some documents.

Some patterns are not defined for the full range of offaxis angles. For example ITU-R Rec.S.465 does not define the pattern for offaxis angles less than 1°: in this case it is assumed to be parabolic until reaching the first side-lobe, i.e.

$$G=\max \left[\begin{array}{l}{G}_{\max }-12\left(\frac{\varphi }{{\varphi }_0}\right),\\ 52-10{\log }_{10}(D/\lambda )-25{\log }_{10}{\varphi }_{\min }\end{array}\right]$$

Variations for Recommendation S.465 and S.580 gain patterns extend the pattern using the methodology in the ITU’s Antenna Pattern Library (APL).

Note on the IMT-MODEL Gain Patterns

In order to activate the beamforming of these gain patterns, the antenna type, station and link options should be:

• Antenna type: ensure “Electronically steerable” is checked
• Station antenna pointing:
  • For the BS: set fixed pointing angles
  • For the UEs: point at another station (the BS) using random offsets of azimuth = {-60, +60}, elevation = {-90, +90}
• Link: either a Fixed or Dynamic link from the BS to the UE (or vice versa) to activate the antenna pointing. Note that a transmit or receive link cannot be used

The BS antenna azimuth could also be defined via the Monte Carlo service area Define Variable.

The parameters used to configure this gain pattern take account of the frequency, typically defined in the link.

Note on the IMT-MODEL Non-Co-Frequency Gain Pattern

For antenna types defined by the IMT-MODEL patterns, there are options to select how the gain pattern changes for non-co-frequency interference paths.

The following options are available from the Advanced Beam Options dialog:

• Use co-frequency pattern: the M.2101 pattern is used with D/lambda = 0.5 for both co-frequency and non-co-frequency scenarios
• Single element pattern: the M.2101 single element pattern is used if the victim centre frequency is non-co-frequency
• Assume D/lambda = 0.46: in the M.2101 gain pattern a D/lambda of 0.46 is used rather than 0.5
• Variable D/lambda: it is assumed that at the centre frequency supplied the D/lambda = 0.5, and so for other frequencies the D is derived and fixed but the lambda varies depending upon the victim frequency

The definition of what constitutes “co-frequency” and what “non-co-frequency” for the IMT-MODEL gain pattern is set via:

• Centre Frequency: this is the centre frequency that the IMT-MODEL antenna has been tuned to
• Co-Frequency Bandwidth: this is the total bandwidth that is defined as being co-frequency in range:
  • Minimum = CentreFrequency – CoFrequencyBandwidth./2
  • Maximum = CentreFrequency + CoFrequencyBandwidth./2

Outside this frequency range the interference path is assumed to be non-co-frequency.

To activate these non-co-frequency gain patterns it is necessary to set the Interference Path option:

• Calculate Interfering Signal using Victim Frequency = true

This will use the victim centre frequency when calculating the interfering signal and hence allow the antenna type to identify if the path is co-frequency (to the IMT-MODEL antenna) or non-co-frequency. It will not affect other calculations, in particular the mask integration adjustment or NFD.

Additional Gain Patterns

Other useful gain patterns are:

• Bessel
• Capped Bessel
• GPS L1
• GPS L2
• GPS User
• Linear with angle
• Omni directional
• Parabolic rolloff
• Sine(x)/x

These are specified in the sections below.

Bessel

This is the theoretical model for antenna performance, and is given below.

If:

$$D/\lambda =\frac{1.61374}{\pi \times \sin \left(\frac{{\phi }_0}{2}\right)}$$

Then:

$$G_{REL}=20{\log }_{10}\left(\frac{2\times |j1(\pi (D/\lambda )\phi )|}{\pi D/\lambda |\sin \phi |}\right)$$

Capped Bessel

The capped Bessel follows the Bessel for the main beam, and then for the side-lobes it connects the peaks.

GPS L1

The following pattern is used:

$$\begin{array}{ll}{G}_{abs}=11.77+\frac{3.4}{1+\exp \left[-\left(\frac{\theta -4.944}{1.537}\right)\right]}& \text{ if }0\le \theta \le 11\\ G_{abs}=-33.61+\frac{49.03}{1+\exp \left[-\left(\frac{\theta -21.83}{-2.440}\right)\right]}& \text{ if }11<\theta \le 22\\ G_{abs}=-10.86+\frac{10.02}{1+\exp \left[-\left(\frac{\theta -24.13}{1.194}\right)\right]}& \text{ if }22<\theta \le 29\\ G_{abs}=-7.749+\frac{6.753}{1+\exp \left[-\left(\frac{\theta -40.32}{-3.216}\right)\right]}& \text{ if }29<\theta \le 45\\ G_{abs}=-7.319+\frac{4.783}{1+\exp \left[-\left(\frac{\theta -46.49}{1.122}\right)\right]}& \text{ if }45<\theta \le 52\end{array}$$

$$\begin{array}{ll}{G}_{abs}=-27.12+\frac{27.05}{1+\exp \left[-\left(\frac{\theta -73.79}{-10.12}\right)\right]}& \text{ if }52<\theta \le 82\\ G_{abs}=37.65-1.266\theta +0.0111\theta -3.19e^{-5}{\theta }^3& \text{ if }82<\theta \le 174\\ G_{abs}=323.1-2.05\theta & \text{ if }174<\theta \le 176\\ G_{abs}=-38.27+\frac{6.199}{1+\exp \left[-\left(\frac{\theta -177.4}{0.6702}\right)\right]}& \text{ otherwise }\end{array}$$

Then:

$$G_{rel}=G_{abs}-11.90104866$$

Note this assumes that the peak gain is set to $11.90104866\mathrm{dB}$.

GPS L2

The following pattern is used:

$$\begin{array}{ll}{G}_{abs}=-67.31+\frac{80.51}{1+\exp \left[-\left(\frac{\theta -33.91}{-4.677}\right)\right]}& \text{ if }0\le \theta \le 30\\ G_{abs}=-19.79+\frac{17.58}{1+\exp \left[-\left(\frac{\theta -30.416}{4.51}\right)\right]}& \text{ if }30<\theta \le 47\\ G_{abs}=-27.62+\frac{28.58}{1+\exp \left[-\left(\frac{\theta -88.75}{-21.57}\right)\right]}& \text{ if }47<\theta \le 97\\ G_{abs}=-97.44-2.081\theta +-0.0167\theta -4.05e^{-5}{\theta }^3& \text{ if }97<\theta \le 174\\ G_{abs}=-30.23+\frac{9.609}{1+\exp \left[-\left(\frac{\theta -176.1}{0.9522}\right)\right]}& \text{ otherwise }\end{array}$$

Then:

$$G_{rel}=G_{abs}-13.13461172$$

Note this assumes that the peak gain is set to $13.13461172\mathrm{dB}$.

GPS User

The following pattern is used from ITU-R document 8D/142 from $13^{\text{th }}$ October 1998:

$$G_{abs}=7-1.957e^{-3}{\theta }^{2.01}\text{ if }\theta \le 80$$

$$G_{abs}=21.59-0.3882\theta +5.455e^{-4}{\theta }^2\text{ otherwise }$$

Then:

$$G_{rel}=G_{abs}-7$$

Note this assumes that the peak gain is set to $7\mathrm{dB}$.

Linear

This algorithm is used so that the offaxis angle can be determined from the offaxis gain. The equation is:

$${\mathrm{G}}_{\mathrm{rel}}=-\theta$$

Omni Directional

This gives the same value in all directions and is hence essentially isotropic. The peak gain is set by default to 0 dB, but can be any user entered value.

Parabolic

This pattern is parabolic with floor defined. The equation is:

$$G_{\text{rel }}=\max \left[G_{\text{floor }},-12{\left(\frac{\theta }{{\theta }_{3\mathrm{dB}}}\right)}^2\right]$$

The ${\mathrm{G}}_{\text{floor }}$ is input by the user. A typical value is $-30\mathrm{dB}$.

Sin(x)/x

The calculation is the same as the Bessel Function, but replacing the call to Bessel by sin.

Archived Gain Patterns

The following gain patterns are included in Visualyse Interplanetary for reasons of backward compatibility:

• Appendix 29 Earth Station
• Analytic ES
• Analytic NGSO
• Cosine
• FSATMULTI_1A Earth Station
• FSATMULTI_1A Type A
• NGSO FSS RX
• NGSO FSS TX
• SMATV
• Sine
• SkyBridge RX Type A
• SkyBridge TX Type A
• TVRO
• Teledesic 2 - RX
• Teledesic 2 - RX fixed BW
• Teledesic 2 - TX
• Teledesic 2 - TX fixed BW
• Teledesic Type A
• Teledesic Type B
• Teledesic Type C

More information is available on request.