Introduction

A key. feature of IMT-2020 systems are beamforming array antennas which use phase shifting to an array of individually fed antenna elements to dynamically steer a beam towards a specific user in order to maximise throughput.

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The beamforming element antenna is specified as a standard equation based antenna plugin in SEAMCAT.

Figure: Beamforming element antenna parameters

The input parameters and the corresponding notation as used in the following equations are:

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The total gain AEθ,φ is calculated as follows:

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AEθ,φ=GE,max-min-AE,Hθ+AE,Vφ,Am

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AE,Vφ=-min12φ-90φ3dB2,SLAv

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Note that the notation for azimuth and elevation planes in these sections is the opposite of that used in M.2101 – this is for consistency with the wider SEAMCAT conventions, where φ=elevation and θ=azimuth.

This implementation is equivalent to the 3GPP TR 36.814 antenna pattern ( Anchor_Ref99889735_Ref99889735Table A.2.1.1-2) which is also available in SEAMCAT as a separate antenna.

Note that it is possible to use the element antenna in isolation (i.e. not as part of a beamforming array), however in this case any tilt settings will not be handled correctly. For this case it is recommended to instead use the 3GPP TR 36.814 antenna plugin directly.

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Once the element antenna has been specified, it can be applied to the composite array plugin which specifies the dimensions of the array:

The element antenna can be modified by selecting Edit next to Element antenna. The other input parameters and the corresponding notation as used in the following equations are as follows

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1. "use element antenna pattern": in this case no beamforming is applied outside of the system link's own channel. This is in line with the M.2101 specifications
2. "use composite antenna pattern": in this case beamforming is applied outside of the system link's own channel. This option provides additional flexibility to the user, recognising that in practice some degree of beamforming will occur in nearby channels (see section 10.6.4 below for additional options).

For example:

• If VLR uses Beamforming antenna and is selected "use element antenna pattern" then for Unwanted interference SEAMCAT will use composite antenna gain for VLR and for Blocking interference it will use element antenna gain for VLR (outside channel).
• If ILT uses Beamforming antenna and is selected "use element antenna pattern" then for Unwanted interference SEAMCAT will use element antenna gain for ILT (outside channel) and for Blocking interference it will use composite antenna gain for ILT.

 
The antenna peak gain is pre-calculated and shown for the input parameters (e.g. 23.1 dBi in Figure 4 Figure above). This is provided for validation purposes.

Tilting of antennas is handled as for other antennas (see section x.y.z).

The beamforming gain Gθ,φ is calculated as follows:Gθ,φ=AEθ,φ+10log10m=1NHn=1NVcosZn,m2+m=1NHn=1NVsinZn,m2NHNV
Zn,m=2πn-1dVλcosφ+sinφi,etilt+m-1dHλsinθsinφ-cosφi,etiltsinθi,escan
where

where:

• AEθ,φis the element gain as calculated in equation (2)above
• φi,etilt is the elevation beamsteering direction
• θi,escanis the azimuth beamsteeting direction

(Note that the equations differ from those in M.2101 to remove the dependency on complex numbers, but are mathematically equivalent).

The beamsteering angles represent the pointing of the beam from BS to UE for downlink (or UE to BS for uplink) on the system link, and the same values are used for the interference link, e.g. for IMT-2020 as the interfering system:

φi,etilt=-φILT→ILR NB this angle is specified with respect to the mechanical boresight (normal to the array) with positive values indicating downtilt.

θi,escan=θILT→ILR

The system link gain is calculated for θILT→ILR and φILT→ILR as:
GILT→ILR=GφZ_ILT→ILR,θILT→ILR=AEφZ_ILT→ILR,θILT→ILR+10log10m=1NHn=1NVcosZn,m2+m=1NHn=1NVsinZn,m2NHNV
where
Zn,m=2πn-1dVλcosθZ_ILT→ILR+sinφi,etilt+m-1dHλsinφZ_ILT→ILRsinθILT→ILR-cosφi,etiltsinθi,escan

G_{ILT\rightarrow I L R}=G\left(\varphi_{Z_ILT\rightarrow I L R},\theta_{ILT\rightarrow I L R}\right)=A_E\left(\varphi_{Z_ILT\rightarrow I L R},\theta_{ILT\rightarrow I L R}\right)+10\log_{10}{\left(\frac{\left|\sum_{m=1}^{N_H}\sum_{n=1}^{N_V}\cos{Z_{n,m}}\right|^2+\left|\sum_{m=1}^{N_H}\sum_{n=1}^{N_V}\sin{Z_{n,m}}\right|^2}{N_HN_V}\right)}

where:

Z_{n,m}=2\pi\left(\left(n-1\right)\left(\frac{d_V}{\lambda}\right)\left(\cos{\theta_{Z_ILT\rightarrow I L R}}+\sin{\varphi_{i,etilt}}\right)+\left(m-1\right)\left(\frac{d_H}{\lambda}\right)\left(\sin{\varphi_{Z_ILT\rightarrow I L R}}\sin{\theta_{ILT\rightarrow I L R}}-\cos{\varphi_{i,etilt}}\sin{\theta_{i,escan}}\right)\right)

Note that the subscript Z in φZ_ILT→ILR indicates the transformed angle with respect to the Z axis (axis of rotation of the downtilt of the array – see section x.y.z).

The same equations are applicable for IMT as the interfering link receiver, with ILT→ILR replaced by ILR →ILT.

The interference link gain is calculated for θILT→VLR and φILT→VLR as:GILT→VLR=GφZ_ILT→VLR,θILT→VLR=AEφZ_ILT→VLR,θILT→VLR+10log10m=1NHn=1NVcosZn,m2+m=1NHn=1NVsinZn,m2NHNV
Zn,m=2πn-1dVλcosφZ_ILT→VLR+sinφi,etilt+m-1dHλsinφZ_ILT→VLRsinθILT→VLR-cosφi,etiltsinθi,escan

G_{ILT\rightarrow V L R}=G\left(\varphi_{Z_ILT\rightarrow V L R},\theta_{ILT\rightarrow V L R}\right)=A_E\left(\varphi_{Z_ILT\rightarrow V L R},\theta_{ILT\rightarrow V L R}\right)+10\log_{10}{\left(\frac{\left|\sum_{m=1}^{N_H}\sum_{n=1}^{N_V}\cos{Z_{n,m}}\right|^2+\left|\sum_{m=1}^{N_H}\sum_{n=1}^{N_V}\sin{Z_{n,m}}\right|^2}{N_HN_V}\right)}

Z_{n,m}=2\pi\left(\left(n-1\right)\left(\frac{d_V}{\lambda}\right)\left(\cos{\varphi_{Z_ILT\rightarrow V L R}}+\sin{\varphi_{i,etilt}}\right)+\left(m-1\right)\left(\frac{d_H}{\lambda}\right)\left(\sin{\varphi_{Z_ILT\rightarrow V L R}}\sin{\theta_{ILT\rightarrow V L R}}-\cos{\varphi_{i,etilt}}\sin{\theta_{i,escan}}\right)\right)

where φi,etilt and θi,escan are the same as calculated for the system link.

Similar cases apply for IMT-2020 as the victim system with:
φi,etilt=-φVLT→VLR
θi,escan=θVLT→VLR
and ILT→VLR replaced by VLR→ILT in the remaining terms.

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Beamforming arrays are applicable for both base stations and UEs.

For the case of base stations (downlink transmitter or uplink receiver) the array pointing reference is fixed according to the cellular layout, where the azimuth reference is towards East, and the elevation reference is towards the horizon. The user may specify an offset from this direction in the azimuth plane (Azimuth additional offset), and a mechanical downtilt (Elevation additional offset) where negative values indicate downtilt.

For the case of mobile stations (UEs), it is possible to set the pointing reference with respect to the base station (BS). The default settings in SEAMCAT are as follows:

Azimuth:

• Pointing reference: towards the BS
• Additional offset: Uniform distribution from -60° to +60°

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• Pointing reference: towards the horizon
• Additional offset: Uniform distribution from -90° to +90°

Figure 5: Mobile station pointing settings

This is intended to reflect random user behaviour with the implementation of a UE with 2 antenna arrays pointing in opposite directions, where only the array which points towards the serving base station is active.

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A separate implementation of the beamforming antenna in 3GPP TR 37.840 section 5.4.4 is available in the library. This antenna is equivalent to the M.2101 antenna as outlined above, with the exception that there is an additional correlation parameter ρ which allows the user to specify the degree of beamforming correlation (between 0 and 1) according to:
Gθ,φ=AEθ,φ+10log101+ρm=1NHn=1NVcosZn,m2+m=1NHn=1NVsinZn,m2NHNV-1

Beamforming antenna plotting

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Both of these options are illustrated below:

Figure 6: Beamforming antenna plot using "Gain envelope" mode

Figure 7: Beamforming antenna plot using "Full pattern" mode, with azimuth beamsteering angle set to 40 degrees

It is also possible to see the beamforming pattern on the individual event results – this can be useful to verify the gain values in a specific direction, as illustrated below:

Figure 8: Example of beamforming plots for interference between 2 IMT-2020 networks - ILT BS (red) to VLR UE (blue) - on the Event Results layout