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Antennas and Beamforming

Radio astronomy interferometry and dish mapping

Owens Valley Radio Observatory, 6 dish submillimeter interferometer, managed by Caltech's Submillimeter Astronomy Group.

To evaluate the surface coherency of these telescopes, and hence to adjust the surface panels for best beam shape, used a holographic technique for surface mapping. Using one dish as a reference held pointed directly at a quasar, each of the other dishes is swept in a grid about the source. Since an interferometer measures complex cross-correlation, the grid response is related to the dish surface illumination amplitude and phase via a fourier transform.

Maps of the dish surfaces

In the phase map above, "+" marks where the hexagonal panels are anchored, and one particular panel (half way out at 7oclock) had intentionally been shifted via shims to verify the technique.

details on these techniques are in this paper

In addition to surface mapping and beam tuning, an improved antenna pointing model was created to reduce the pointing errors to 3 arc second RMS. An 11-term mounting model was developed, which compensated for azel axis misalignments, encoder biases, and gravitational sag (dish flex as a function of elevation angle). Since optical telescopes have a better angular resolution than microwave telescopes, a 4" telescope was mounted to each dish. Software was developed to automatically sample a large set of bright stars giving a good distribution in sky coverage, at each point an operator manually adjusted a pointing offset. These offsets vs az/el were used via a least-squares fit to determine coefficients for the pointing correction model.

77GHz terrestrial cellular communication

Cell tower antenna beam design for constant link margin vs distance from tower. This corresponds to first order as a cosecant antenna pattern, but then adjusted for atmospheric losses at 77GHz.
In azimuth, beam selectivity at these frequencies is most easily achieved with a rotman lens, with send/receive ports on one side and modified-cosecant antenna elements on the other. A rotman design tool was developed, outputting its design as an autocad DXF file for subsequent prototype testing.

Example rotman lens design

For the design tool, see Tools page, or follow direct link to java tool webpage.
A paper describing the entire analysis and design is here

UWB antennas

When using ultrawideband waveforms for ranging, it's important to choose sufficiently wideband antennas. For terrestrial ranging, we would like beam to be mostly in the horizontal plane, and amplitude and phase should be as aziumuthly symmetric as posssible. A bicone antenna is an excellent choice for this case

When the working volume is bounded and transceivers/beacons are along the perimeter facing inward, a hemi-directional azimuth beam is desired, to increase gain inward. Similar to the bicone, we'd like a narrower elevation beam since we are working mostly in the horizontal plane.  Since the fractional bandwidth of the system was only 30% of the carrier frequency, a short vertical bowtie array was found to be the best design.

Ground speed radar, with variation for cotton flow sensing

Dual horns, one forward, one backward, for pitch immunity

Suspended from the bottom of an agriculture vehicle, the speed measured both fore and aft is immune to vehicle pitch, and whose geometry can be corrected to determine accurate forward ground speed. This device is used in agriculture because the tires are often designed to slip in their contact to earth, so direct vehicle odometry in the form of wheel encoder motion is not accurate.

The angle of the two homodyne radar horns was chosen to minimize speed estimation error; horns pointed more directly down have better return SNR, but a smaller velocity component. More ground-grazing angles saw most of the velocity, but suffered from r^4 power loss. The optimum angle was a function of whether the ground was either isotropic or lambertian, and whether the radar noise was dominated by thermal noise or low-frequency sinc skirts (primary an artifact of homodyne doppler discrimination). The optimum angle varied from 45deg to 57.7deg depending on assumptions.,

While originally designed only for ground speed sensing, a separate application was found for measuring the flow of cotton through an internal harvesting duct. The speed and radar cross-section yields a total mass flow rate (with some assumptions on cotton moisture for backscattering). The optimum beam of the system depended on the mounting and the cotton flow geometry, and a special aperture plate was created to tailor to the cotton application without requiring a redesign of the product.

Horn antenna design

While a long horn would give nearly uniform aperture illumination and a sinc beam, it was desirable to create a corrective lens for the horn to:
  • shorten the length of the horn, to avoid large structures under the vehicle undercarriage and to reduce material cost
  • improve on the natural sinc sidelobes, by adjusting the phase and amplitude across the horn aperture
We started with a pyramidal horn, and experimented with ETFE, PTFE,  or polyurethane plastics for the correcting lens. The profile of the lens was initialized to a flat phase illumination, and then adjusted via a gradient search to minimize sidelobes. The resulting design was output to a cad standard for fabrication.

Non-linear phased array -- Spatial Harmonics

Phased-arrays, or direct-radiating arrays, have elements which are driven by non-linear amplifiers, which create interesting beam artifacts. For spacecraft, where power is at a premium, it's even more important to drive amplifiers at least partly into saturation, since that is where they are most power efficient.
When phased-arrays are used to carry multiple simultaneous traffic to distinct formed beams, the individual beams create intermod spatial harmonics of the intended beams, as shown here:

When individual intended beams are unlucky enough to land in a regular array, the intermod beams can be directed at users, causing reduced signal to noise for that users link budget.

This problem becomes a complex trade-off between spacecraft bus power usage, choice of amplifiers, traffic management and power control, and beam illumination (such as variation on Taylor illumination). These trades were successfully performed as part of the Teledesic system design.

E&M simulators

FDTD simulation

Finite-difference time-domain simulation of E&M propogation is a powerful yet simple approach to solving system radiation design trade-offs.
We have performed many of these analyses, sometimes with custom tools as appropriate. For instance, the next diagram shows the shadow created by a GPS survey antenna of an RTK antenna link in an existing product, with pronounced nulls at 2 different azimuth angles in the far field. This quick analysis resulted in a design modification of the material dimensions and antenna location to spread the shadow of the pole more uniformly, thus improving the worst-case link budget.

Here is an example of a co-frequency transceiver with receive and transmit antennas at opposite ends of the box. The container was plastic (ABS), and choke spools were placed strategically to create most isolation between xmt and rcv. This was an UWB product, so a solution in the time domain via FDTD was greatly preferred.
Finally, here are two movies of propagation, the first of the UWB design above, the second a simple dipole field which is suddenly turned on. Note the use of "absorbing boundary conditions" at the walls ("numeric echosorb")

UWB Transponder sim, choke rings, ABS tube

Simple dipole field

Kirchhoff diffraction simulation

Simple Kirchhoff diffraction modeling can be a more productive E&M simulation approach for complex designs (vs large FDTD simulations). Also, they can provide a better understanding of the basic behavior of the device.
For instance, this approach was used to design the transmits/receive isolation structure shown below

The idea is that the possible paths between transmit and receive cancel, because of a carefully constructed phase decoherence of the path integrals.
A prototype, with 2 different decoherence plates is shown below

Greater technical information, from a patent derived from this work, is given below.

Operation of the device relies on isolation between the transmit and receive antennas only. This can be a combination of directivities between the antennas, path loss (physically separated antennas), and possibly polarization isolation. One innovative technique developed for this system to reduce antenna coupling is the use of decoherence plates. Rather than relying on arbitrarily large ground planes to separate the two antennas, judicious selection of the ground plane boundary shape will result in mutual cancellation of signals traveling between the two antennas, allowing a much smaller ground plane for the same isolation. To illustrate this phenomenon, consider radiation paths that only graze the edge the ground plane, on their way to the receive antennas, as shown in the figure above.

With a sawtooth edge with triangular teeth, the edge diffracts all paths between the longest length and shortest length with uniform distribution. If the path difference is about 1 wavelength, for every path there is another path with a 180deg phase shift, which mutually cancel. In this way, the special ground plane causes a decoherence of signal between the two antennas. This description was just for illustration, as paths beyond the ground plane edge are also possible. When the full path integration is performed, there is a significant quantitative difference in ground plane boundary that leads to best decoherence, and extra constraints on radius and shape, but qualitatively the result is the same: deep nulls of decoherence when the plate is chosen correctly. In addition to a star shape like above, a gear shape also works well, with teeth width, length, and gear radius as free parameters

Surface integral is performed over elements which pass radiation. Obliquity terms are generalizations of fresnel obliquity based on the Kirchhoff formulation, and include near field terms.

For multiple surfaces, break contributions into segments, corresponding to radiation in direction of surface, spherical wave diffusion to surface, obliquity at surface in direction of observation point, but NOT the spherical wave diffusion to the observation point. In this manner, multiple surfaces can be chained together.

For materials that pass some radiation, with a phase shift and attenuation, we can generalize the above integral to include and amplitude and phase term vs surface element position:

Radome -- wind loading and MTB issues

Radome design for antenna enclosures is a strong function of operating conditions, in particular wind. The following analysis was for ground radome design for use anywhere in the world, with a particular design point of 9mph wind speed limit.

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