Field of the Invention

The present invention relates to the field of directional antennas, in particular beam focussing for directional antennas. Background to the Invention

Data rates necessary for modern wireless communications standards (such as the 2G, 3G, 4G and 5G mobile protocols) have led to the requirement for Multiple Input Multiple Output (MIMO) antenna structures. MIMO is enabled through the provision of multiple channels that are sufficiently uncorrelated from one another using diversity schemes such as spatial separation of multiple antennas and/or polarisation diversity. Both polarisation and spatial separation enables multiple channels to be transmitted over the same frequency but it is polarisation diversity that can allow for a more compact antenna solution.

Diversity schemes are often implemented on telecommunications base station antennas. These base station antennas often comprise multiple directional antennas orientated to radiate towards a common area of users. By configuring each directional antenna to operate over a different frequency band, the base station antenna can be afforded a wideband frequency coverage. Multiple antennas are combined into an array to provide high directional gain to minimise beam squint and direct the signal towards the area of users. However, typically, these types of base stations are relatively large which is undesirable when mounting the base station onto a small platform such as a vehicle.

A directional antenna comprising multiple radiating elements in close proximity to one another can be designed to reduce the size of the base station. However, the close proximity of these elements typically results in distortion and spreading of the antenna beam; particularly at higher frequencies. It is therefore an object of the present invention to provide an improved directional antenna for use in base stations that mitigates these issues.

Summary of the Invention

According to a first aspect of the invention there is provided a directional antenna, comprising a planar antenna having a main radiating element for generating radiation of a predetermined wavelength, and a beam focussing module for focussing the radiation along an antenna boresight, the beam focussing module comprising a parasitic beam focussing element configured to resonate at the predetermined wavelength and a means for mounting the parasitic beam focussing element onto the planar antenna, wherein the parasitic beam focussing element comprises a planar disc of electrically conductive material, the means for mounting being arranged to hold the planar disc substantially parallel to and physically separated from the radiating element of the planar antenna, such that the parasitic beam focussing element can electromagnetically couple to the main radiating element at any polarisation.

The electromagnetic coupling between the main radiating element and parasitic beam focussing element helps to focus the beam around the antenna boresight and limit the spread of the radiation pattern. Providing a planar disc has the advantage of coupling to the main radiating element at multiple polarisations such as linear vertical and linear horizontal polarisations. Being able to couple at multiple polarisations is advantageous for systems utilising polarisation diversity in which multiple driven polarisations are required. This is particularly advantageous for base stations providing mobile protocols such as 4G and 5G.

A directional antenna provides a higher gain towards a specific range of azimuth and elevation angles; often referred to as the mainlobe of the antenna. Radiation outside the mainlobe is often referred to as the sidelobes. The angular width of the mainlobe (commonly measured at the minus

3dB point) is often referred to as the half power beamwidth. A directional antenna is particularly useful for base station applications which need to provide higher gain (hence higher Signal-to-Noise Ratio (SNR)) towards a specific area of users.

Typically the antenna's main boresight direction is designed to be perpendicular to the reflector or ground plane. For example, for a planar antenna comprising a flat square ground plane, the boresight is typically perpendicular to the ground plane and in the centre of the square. When an antenna is operating over multiple frequencies in a sufficiently wide frequency band, the mainlobe may become distorted. Distortion may include the main direction of radiation skewing away from the antenna's main boresight direction, it may also include disruption of the beamwidth in azimuth or elevation or both. In addition, distortion may also include the mainlobe becoming less symmetrical about the boresight i.e. wider in some planes within the mainlobe and parallel to the boresight and narrower in other planes. This is undesirable for a base station designed to direct a range of mobile protocols towards a specific area of users as it may lead to deterioration of the SNR for users in given areas.

Planar antennas typically comprise a radiating element located above and connected to a ground plane. The radiating element can be printed onto a dielectric substrates to reduce size and manufacturing costs. Generally, the resonant wavelength of a printed planar antenna is in part a function of the square root of the relative permittivity (the permittivity) of the substrate.

More recently, dual polarised planar antennas comprising multiple radiating elements in the form of three 120° segments printed onto a circuit board have been developed to provide a compact wide band antenna operating over the 2G, 3G, 4G and 5G mobile protocols. Furthermore, multiple directional dual polarised planar antennas can be mounted and excited in such a way as to provide a compact base station which has the capacity to radiate in 360° azimuth directions.

The radiating element is excited by a time varying RF source on transmit which generates a time varying electromagnetic field that is subsequently radiated from the antenna. Typically the length of the radiating element is fixed and therefore is optimised to resonate at intended wavelengths. Depending on the antenna type and ground plane design and configuration, radiating over wide bandwidths can lead to distortion effects in the resultant beam patterns.

Beam focussing may include aligning the antenna main radiating direction towards a particular direction; which may be the antenna's main boresight direction. Beam focussing may also include shaping the mainlobe of the antenna such that it is substantially symmetrical about the main radiating direction. Beam focussing may also include narrowing the beamwidth or spread of the antennas radiation pattern. Beam focussing may also include efforts to increase the directionality of the mainlobe. Furthermore, beam focussing may involve changing characteristics of the mainlobe such that it is substantially similar to the mainlobe at other frequencies thereby ensuring the antenna pattern is stable across multiple frequency bands.

For example, an antenna with a radiating element designed to resonate at the frequency bands utilised by lower frequency bands (for example 2G) may experience beam distortion when operating on higher frequency bands used by some of the 4G and 5G protocols for example. In this instance, beam focussing could be used to adjust the beam pattern at the 4G and 5G frequency bands such that it is similar to the beam pattern across evident at other frequency bands. This is advantageous because a single radiating antenna can provide consistent performance whilst directing the beam towards substantially the same location with a consistent SNR.

A parasitic beam focussing element is designed to mutually couple to a main driven (excited) radiating element in order to focus the beam from the antenna. The electromagnetic fields from the main driven excited element induces surface current on the parasitic beam focussing element which (depending on its electrical size) are subsequently reradiated by the parasitic beam focussing element. Generally, parasitic operation (and sufficient coupling) occurs when the dimensions of the parasitic beam focussing element is a multiple of the predetermined wavelength and appropriately sited such that the electromagnetic fields from the driven main radiating element are sufficient enough to induce surface currents. The antenna may also comprise a parasitic radiator from the prior art to the improve impedance bandwidth of the main radiating elements. Generally, these prior art parasitic radiators are not for beam focussing and will not focus the beam at the predetermined frequency in contrast to our parasitic beam focussing element. Generally, the parasitic radiators may only significantly contribute to the total radiation characteristics when it is electrically large enough to do so. Generally, the parasitic radiator may have some contribution to the radiation characteristics at the predetermined wavelength in addition to the contribution from the ground plane and main radiating elements.

The parasitic beam focussing element comprises a planar disc which has a circular cross section and a narrow thickness. When mounted in proximity to the planar antenna, the circular cross section of the planar disc is substantially parallel to the main radiating element. Having a circular cross section is advantageous because the planar disc is able to couple to the main radiating element when driven at different polarisations. The diameter of the circular cross section influences the resonant wavelength of the parasitic beam focussing element.

Optionally, the diameter of the planar disc is a function of the predetermined wavelength. Optionally, the diameter is a quarter of the predetermined wavelength. This has the advantage that the planar disc resonates at the predetermined wavelength and therefore mutually couples to the main radiating element when electromagnetic fields radiate at the predetermined wavelength.

Optionally, the diameter of the planar disc is between 10mm - 150mm. Optionally between 12mm - 125mm. Optionally, the diameter of the planar disc is between 25mm - 110mm. Optionally, the diameter of the planar disc is 30mm. This has the advantage that the planar disc resonates at a predetermined wavelength utilised by the 2G, 3G, 4G or 5G protocols and therefore a consistent beam pattern may be provided from a single planar antenna when switching between these protocols. The parasitic beam focussing element comprises an electrically conductive material such that the radiation from the main radiating element induces a current within the parasitic beam focussing element.

The parasitic beam focussing element is mounted to the planar antenna such that the planar disc is held substantially parallel to and physically separated from the main radiating element of the planar antenna. For example, where the main radiating element is a quarter wavelength wire which runs parallel to the ground plane, the planar disc is held such that the circular cross section of the planar disc is held parallel to and separated from the quarter wavelength wire (and ground plane).

In preferred embodiments, the separation between the planar disc and the main radiating element is between 1 - 10mm, more preferably between 3 - 7mm, most preferably 5mm. The inventor has shown that this leads to improved mutual coupling between the planar disc and the radiating element when radiating at UHF and above. This distance should be optimised in design for desired wavelengths of operation.

The primary function of the means for mounting is to maintain the parasitic beam focussing element a fixed position relative to the main radiating element. In some embodiments, the means for mounting is a hollow, circular, tube with an inner diameter equal to the diameter of the planar discs such that one or more planar discs can be inserted into it and held parallel to the main radiating element. The tube is then attached to the ground plane of the antenna by a suitable bracket and fastenings means such as screws or an adhesive.

Preferably, the means for mounting is arranged to hold the centre of the parasitic beam focussing element substantially along a main direction of radiation of the planar antenna. The centre of the circular cross section of the planar disc is substantially aligned with the antenna's main boresight direction. This has the advantage that when the antenna radiates at the predetermined wavelength, the disc is aligned with the antenna's mainlobe which is influenced to radiate more substantially symmetrical thereby ensuring the beam pattern is more stable across multiple frequencies. Typically, the radiating element radiates at a single fixed polarisation across the operating bandwidth. The polarisation may be linear e.g. vertical, horizontal or slant (+/- 45°); or circular e.g. right hand or left hand polarisations. Generally, the polarisation is dependent on the orientation of the main radiating element. Preferably, the parasitic beam focussing element comprises a plurality of planar discs, more preferably, the parasitic beam focussing element comprises between 2 and 8 planar discs, even more preferably between 3 and 6 planar discs, most preferably 4 planar discs. Multiple planar discs mutually couple with one another when the main radiating element radiates at the predetermined wavelength which has been shown to improve the overall beam focussing effect. The overall number of discs can be optimised to provide a focussing effect for a desired wavelength of operation.

Preferably, the plurality of planar discs all have the same diameter. The inventor has shown that the mutual coupling between multiple planar discs of the same diameter increases the beam focussing effect at substantially a single frequency.

Preferably, the plurality of planar discs have a range of diameters. This has the advantage that each disc mutually couples to the main radiating element at different wavelengths; therefore, beam focussing can be achieved across a plurality of different predetermined wavelengths. In effect this permits a single planar antenna to be operated in a wideband manner and with a consistent beam profile across the band.

Preferably, the plurality of planar discs are separated from each other. Preferably, the separation is between 1-lOmm, more preferably between 3-6mm, most preferably 5mm. By separating the planar discs, the inventor has discovered that the overall level mutual coupling can be optimised and the beam focussing effect can be enhanced.

Optionally, the predetermined wavelength (as a frequency) is UHF band (300MHz - 3GHz) or higher.

This is particularly advantageous for beam focussing on the 2G, 3G, 4G and 5G protocols. Particularly covering the high frequencies used within them where beam pattern from prior art antennas would become distorted with respect to the operating frequency of the main radiating element.

Preferably, the planar antenna is a dual polarised planar antenna configured to radiate at least two orthogonal polarisations. This has the advantage of radiating a focussed beam across the band on both polarisations and is particularly advantageous for configuring multiple channels that operate using different polarisations. A dual polarised planar antenna provides two sufficiently uncorrelated channels operating on different polarisations within the same antenna structure. Generally, there will be a need to provide sufficient isolation between channels to reduce mutual coupling and achieve sufficiently low levels of signal correlation. The antenna may comprise two or more radiating elements orientated at different angles to the vertical. For example, the radiating elements may be orthogonal to each other such as vertical and horizontal or +/-45°. The parasitic beam focussing element of the directional antenna is capable of operating at different polarisations hence can mutually couple to the radiating elements in both of the configured polarisations. This advantageously focusses the beam when either of the radiating elements is operating at the predetermined wavelength.

Preferably, the parasitic beam focussing element comprises a dielectric substrate. This has the advantage of lower manufacturing costs. Optionally, the diameter of the parasitic beam focussing element comprising the dielectric substrate is an integer multiple of half of a transition wavelength in the dielectric. The transition wavelength is the wavelength of the radiation (which in free space is the predetermined wavelength) as it is transitioning through the dielectric which depends on the relative permittivity of the dielectric. The predetermined wavelength in the dielectric A _d is calculated as the predetermined wavelength lo divided by the square root of the relative permittivity Ve _r i.e. A _d

= lo/V r. Optionally, the substrate is has a relative permittivity of between 3 and 10, optionally between 3.5 and 5.5, and optionally the relative permittivity is 4.5 such as Arlon 450 (AR450) which is a commonly available material.

Optionally, the substrate has a thickness of between 0.5 and 10mm, optionally between 1 and 5mm, optionally between 1 and 2mm, and optionally 1.6mm which is a widely available and standard thickness of substrate.

According to a second aspect of the invention there is provided a base station antenna array comprising a plurality of directional antennas of the first aspect of the invention.

Preferably, the directional antennas each cover a separate azimuth and/or elevation sector. This may be achieved by mounting the antennas together into an array where each directional antenna is substantially equi-spaced with their ground planes are back-to-back and mainlobes are pointing away from one another. This has the advantage of providing 360° of azimuth coverage.

Preferably, there are 3 directional antennas each covering distinct 120° sectors of azimuth.

Preferably, the plurality of directional antennas are operated independently. This has the advantage of providing a different directional beam pattern towards a specific sector.

Preferably, the plurality of directional antennas are operated in phase with each other across all segments. This advantageously provides improved combined omnidirectional beam pattern. The combined directional beam patterns can result in a high gain omnidirectional beam pattern. Advantageously, by ensuring the directional beam patterns are consistent across different frequency bands, the parasitic beam focussing element also ensures the combined omnidirectional beam pattern is consistent across its operating frequency range.

Preferably, the plurality of directional antennas are operated to only receive signal data for data processing. This has the advantage of providing a direction finding and/or direction of arrival / line of bearing deduction capability. This is particularly advantageous for applications which require a receive only mode.

According to a third aspect of the invention there is provided the use of a planar disc of electrically conductive material as a parasitic beam focussing element for a directional antenna. According to a fourth aspect of the invention there is provided a method of manufacturing a directional antenna, comprising the steps of:

- Providing a planar antenna having a main radiating element for generating radiation of a predetermined wavelength;

- Providing a beam focussing module for focussing the radiation along an antenna boresight, the beam focussing module comprising a parasitic beam focussing element configured to resonate at the predetermined wavelength, the parasitic beam focussing element comprises a planar disc of electrically conductive material;

- Providing a means for mounting the parasitic beam focussing element onto the planar antenna; - Arranging the means for mounting to hold the planar disc substantially parallel to and physically separated from the main radiating element of the planar antenna, such that the parasitic beam focussing element can electromagnetically couple to the main radiating element at multiple polarisations.

Brief Descriptions of the Drawings Embodiments of the invention will now be described by way of example only and with reference to the accompanying drawings, in which:

Figure 1 illustrates in perspective view a directional antenna without a beam focussing module;

Figure 2 illustrates the 3D directional beam pattern from the antenna of Figure 1 at several frequencies; Figure 3 illustrates in perspective view the directional antenna of Figure 1 with a beam focussing module comprising a parasitic beam focussing element;

Figure 4 illustrates in cutaway side view a parasitic beam focussing element with four planar discs;

Figure 5 illustrates the 3D directional beam pattern from the directional antenna of Figure 3 at several frequencies;

Figure 6 illustrates in perspective view a base station comprising three directional antennas each with a beam focussing module comprising a parasitic beam focussing element;

Figure 7 illustrates the 2D omnidirectional beam pattern of the base station of Figure 6 at several frequencies. Detailed Description

Figure 1 illustrates an embodiment of a dual polarised directional antenna 100 without a beam focussing module capable of operating on the 2G, 3G, 4G and 5G protocols. The directional antenna 100 comprises two driven dipoles 101 printed in the centre (around the antenna's main boresight direction z) and opposite sides of a square flat plate substrate 102. The dipole 101a at the front of the substrate 102 is polarised at linear +45° slant (shown in Figure 1). The opposite dipole 101b, polarised at -45° slant is on the back of the substrate 102 (not shown in Figure 1). The dipoles 101 are 116mm in length, measured linearly between the outer periphery of the radiating arms. The dipoles 101 are driven from a centre feed connected to an external RF source. In addition, four linear parasitic radiators 103 are also printed onto the substrate 102 orientated in vertical and horizontal polarisations. The antenna's main boresight direction z for the planar antenna 100 is shown as a dashed line which is perpendicular to the substrate 102 and extending from the centre of the directional antenna 100. Behind the substrate 102 is a winged ground plane 104 which comprises a middle plate in between two angled winged plates. The substrate 102 is mounted in front of, separated from and substantially parallel to the middle plate of the winged ground plane 104. The outer plates are angled at 60° to the middle plate of the winged ground plane 104 creating the wing shape around the substrate 102. In use, the ground plane reflects the signal radiated from the dipoles 101 and the linear parasitic radiators 103 back towards the substrate and away from the ground plane to provide a dual polarised directional planar antenna 100. Figure 2 illustrates the mainlobe of the radiation pattern generated through EM modelling the directional antenna 100 in figure 1 at 3 different frequencies within the 2G, 3G, 4G and 5G protocols. The z axis being the main boresight direction of the directional antenna 100.

When the dipoles 101 are driven at a low frequency band, they radiate an antenna pattern 200 in which the main direction of radiation is substantially parallel to the antenna's main boresight direction z and the mainlobe is substantially symmetrical. This antenna pattern 200 is primarily generated by the dipoles 101; the linear parasitic radiators 103 have minimal effect.

When driven at a medium frequency band, the main direction of radiation of the antenna pattern 201 is also substantially parallel to the antenna's main boresight direction z and the mainlobe is substantially symmetrical. The antenna pattern 201 is slightly narrower than that of 200; which is likely caused by the increase in frequency.

At a high frequency band, the antenna pattern 202 is noticeably distorted when compared to the antenna patterns at the low 200 and medium 201 frequency bands. The main radiating direction in antenna pattern 203 is not parallel to the antenna's main boresight direction z. The mainlobe is not symmetrical about the boresight; the beam width along a plane approximately 45° to the xy plane is significantly wider than the beam width within any plane within the mainlobe and parallel to the xz plane.

In use, the directional antenna 100 will not provide a consistent service when switching from low and/or medium frequency bands to higher frequency bands utilised by mobile protocols. At a higher frequency band, the antenna pattern 202 becomes misaligned and distorted and will therefore provide a lower SNR towards the intended direction.

Turning to Figure 3, there is an embodiment of a dual polarised directional antenna 300 comprising two driven dipoles 301, one at -45° polarisation 301a (shown) the other at +45° polarisation behind the substrate 301b (not shown) and four linear parasitic radiators 303 (at horizontal and vertical polarisations) printed in the centre (around the antenna's main boresight direction z) of a square flat plate substrate 302. The substrate 302 is mounted in front of and separated from a metal winged ground plane 304 such that it is substantially parallel to a flat plate in the middle section. In addition, the directional antenna 300 has a parasitic beam focussing element 305 mounted onto and in the centre of the substrate 302. The parasitic beam focussing element 305 comprises four planar discs 307 comprising AR450 substrate held within a mounting means in the form of a tubular mount 306 which is secured to the substrate 302.

Figure 4 illustrates an embodiment of the parasitic beam focussing element 305 in a cutaway side view. The tubular mount 306 is transparent for illustrative purposes only. The tubular mount 306 holds 4 planar discs 307 stacked together such that when mounted, the face of each planar disc 307 is substantially parallel to and separated from each other and the substrate 302 and aligned along the antenna's main boresight direction z. Each planar disc 307 is separated from adjacent planar discs 307 by a distance 412 of 5mm (measured from the front face of one disc to the front face of the adjacent disc). Each planar disc 307 comprises a substrate having a relative permittivity of 4.5 and a thickness c of 1.6mm. The total axial length 414 of the stacked planar discs 307 is 16.6mm. The inner diameter b of the tubular mount 306 is 30mm matching the diameter of the planar discs 307.

Figure 5 illustrates the antenna beam patterns generated by EM modelling the planar antenna 300 at various frequencies used by the 2G, 3G, 4G and 5G protocols. The z axis being the antenna's main boresight direction of the planar antenna 300. At a low frequency band, the antenna pattern 500 from planar antenna 300 is substantially parallel to the z axis and the mainlobe is substantially symmetrical. Similarly, at a medium frequency band the antenna pattern 501 is similar to that of the low frequency band 500; albeit with a slightly narrower and more symmetrical mainlobe. Furthermore, at a high frequency band, the antenna pattern 502 from planar antenna 300 is substantially parallel to the z axis and the mainlobe is substantially symmetrical.

Comparing the antenna patterns from antenna 100 to antenna 300, at low and medium frequency bands, antenna patterns 500 and 501 are comparatively similar to patterns 200 and 201. However, at the high frequency band, antenna pattern 502 is much more symmetrical and parallel to the z axis than that of pattern 202. This is because the parasitic beam focussing element 305 of antenna 300 electromagnetically couples to driven dipoles 301 and linear parasitic radiators 303 when they are radiating at the high frequency bands. This corrects the distortion observed in the antenna pattern 202 to produce a pattern 502 which is more consistent with the patterns observed in the low and medium frequencies. Furthermore, having four planar discs 307 separated by a distance a further improves the pattern 502 because the planar discs 307 are able to mutually couple to one another.

Figure 6 illustrates an embodiment of a base station 600 comprising three dual polarised directional antennas 610, 620 and 630. Each antenna 610, 620 and 630 further comprises two driven dipoles 612 printed around the centre (around the main boresight direction z of each antenna) of a square flat plate substrate 611. The dipole 612a printed on the front of the substrate being polarised at linear 45° and the dipole 612b on the back is -45° polarisation. The substrate is transparent for illustration purposes only. The dipoles 612 are both 116mm in length. Also printed in the centre of each substrate 611 are four linear parasitic radiators 613 orientated at vertical and horizontal polarisations and 30mm in length. Each antenna 610, 620 and 630 further comprises a parasitic beam focussing element 614 mounted onto the substrate 611 and aligned with the antenna's main boresight direction z. Each beam focussing module 614 comprises four planar discs held within a tubular mount such that the circular cross sections of the discs are parallel to and separated from each other and the substrate 611.

Each antenna 610, 620 and 630 comprises a winged ground plane 615 which comprises three flat metal plates adjoined at their edges. The substrate 611 is parallel to and separated from the central flat plate. The outer flat plates are angled at 60° to form a winged ground plane 615. The ground plane 615 of each antenna 610, 620 and 630 are adjoined to each other such that the outer flat plates are back-to-back forming a triangular shaped base station 600 whereby each antenna 610,

620 and 630 covers a different 120° azimuth section at the same elevation.

In use, the base station 600 has three modes of operation including: single sector only radiating as a 'precision mode' of operation; all segments radiating to provide an omnidirectional capability (the fields from each segment are combined in phase to give higher gain radiation across all azimuth angles) and a receive only mode to acquire Direction Finding / Direction of Arrival / line of bearing type information.

The parasitic beam focussing element 614 couples with the dipoles 612 and linear parasitic radiators 613 at the high frequency bands used within the 2G, 3G, 4G and 5G protocols. This results in a stable and consistent directional beam pattern from each antenna 610, 620 and 630 across all frequency bands as observed in other embodiments.

Turning to Figure 7, there is provided the 2D omnidirectional antenna patterns (360° in azimuth, at a single elevation angle along the antenna's main boresight direction z) generated when modelling the base station 600 at different frequency bands. In the low frequency band, the antenna pattern 700, the 360° gain profile is fairly smooth, maintaining approximately + 4 to OdBi gain at all azimuth angles, without any significant nulls at the side of each mainlobe where the directional beams meet. Within the mainlobes of each antenna 610, 620, 630, there is some additional gain of around 4dBi. Similarly, at a medium frequency band the antenna pattern 701 also has a fairly smooth 360° gain profile with slightly higher gain (around 4dBi within the mainlobes). At a high frequency band, the antenna pattern 702 is less smooth than that of 700 or 701; however the variation in the 360° gain pattern is 3dB or less. The base station 600 therefore provides a relatively consistent, high gain, omnidirectional pattern across the frequency bands utilised by 2G, 3G, 4G and 5G protocols.

Note that absolute values stated above include worst case combining losses. Whilst the embodiments show printed dipole antennas, this is not intended to be limiting. Other antenna designs may be configured in a back-to-back arrangement and operated with different polarisations if a beam focussing module is mounted onto the antenna. In addition, a base station may be designed with an alternative number of antennas covering different angular sectors. A plurality of base stations may be mounted together to increase bandwidth. For example a first base station may be used for covering 2G, 3G and 4G protocols and a second base station providing 5G protocols. The base station antennas may be vertically mounted to each other so as to not obstruct their respective omnidirectional performances.