A beam at mmWave needs a large array, and a large phased array needs a phase shifter and an RF chain behind almost every element. Holographic beamforming takes a different route to the same beam. I'll start with the cost problem it tries to solve, then explain how a holographic antenna steers a beam, and finish with a comparison against a phased array. The explanation below follows the general holographic antenna principle and does not describe any one product.

• What problem does holographic beamforming try to solve ?
• How does a holographic antenna steer a beam ?
• How is it different from a phased array ?
• Reference
• YouTube

What problem does holographic beamforming try to solve ?

Let's start with the size of the array, because the cost of beamforming grows with it. At mmWave the path loss is high, so the antenna has to give back that loss as gain.

The gain of an array grows with the number of elements. With N elements, the array gain is about 10log₁₀(N) dB over a single element. So 64 elements give about 18 dB, and 256 elements give about 24 dB. The elements are usually spaced by half a wavelength. At 28 GHz the wavelength is about 10.7 mm, so the spacing is about 5.4 mm, and a 16 x 16 array of 256 elements is only about 8.6 cm on a side. So the aperture itself is small. The electronics behind it are the difficult part.

In a phased array, each element needs its own phase shifter to steer the beam. An active phased array also puts a PA and an LNA behind each element or each small group of elements. So 256 elements can mean 256 phase shifters and 256 amplifier chains. Each chain costs money and power and produces heat, and at mmWave the phase shifters also have loss. This cost grows linearly with N, while the gain grows only with 10log₁₀(N). A larger array therefore becomes more expensive faster than it becomes better.

Holographic beamforming attacks exactly this part. It keeps a large aperture with many elements, but it removes the phase shifter from each element. Each element only has to change how strongly it radiates, and a single feed drives the whole aperture. The next section shows how a beam can still be steered under that restriction.

• Array gain grows only with the logarithm of N : 256 elements give about 24 dB over a single element.
• The aperture is small at mmWave : 256 elements at half wavelength spacing fit in about 8.6 cm x 8.6 cm at 28 GHz.
• The electronics per element are the cost : a phased array needs a phase shifter, and often a PA and an LNA, behind each element.
• Holographic beamforming removes the phase shifter per element : each element only controls how strongly it radiates.

How does a holographic antenna steer a beam ?

The name comes from optical holography, so let's borrow its idea first. In optical holography, a reference wave and an object wave interfere, and the film records their interference pattern. When you light the film with the reference wave again, the film radiates the object wave.

A holographic antenna uses the same idea along a surface. A feed wave travels along a waveguide under the elements, and it plays the role of the reference wave. The feed wave has a propagation constant β, so at position x its phase is -βx. The wanted beam at angle θ plays the role of the object wave, and along the surface its phase is -kx sinθ, where k = 2π/λ is the free space wavenumber. The hologram is the interference pattern of the two, m(x) = cos((β - k sinθ)x). Each element is tuned so that it radiates with a strength that follows this pattern.

Now let's check that this pattern really produces the beam. The feed wave, multiplied by the hologram, gives two terms. The first term has the phase -kx sinθ, which is exactly the wanted beam. The second term has the phase -(2β - k sinθ)x. The feed is normally a slow wave with β greater than k, so 2β - k sinθ is also greater than k. A wave with a propagation constant above k cannot radiate, so the second term stays bound to the surface. An element cannot radiate a negative amount, so a real design uses (1 + m(x))/2 as the element weight. The constant part only continues the feed wave, and that part does not radiate either.

Let's put numbers on it. Take β = 1.2k and a beam at θ = 30 deg. The hologram period is 2π/(β - k sinθ), which is λ/0.7, or about 1.43λ. At 28 GHz that is about 15.3 mm. The second term has 2β - k sinθ = 1.9k, so it does not radiate. A numerical array factor confirms this. An aperture of 20λ with elements every λ/8 and the weights (1 + m(x))/2 gives its main beam at 29.85 deg, within 0.2 deg of the 30 deg target. To steer the beam to another angle, the controller only loads a new pattern with a new period.

The diagram below shows this arrangement. The feed wave enters from the left and travels under a row of elements. The shading of each element shows its weight, which follows the hologram pattern. The arrows above the surface show the radiated beam at angle θ.

Figure 1. Holographic beam steering. The feed wave supplies the phase, and the element weights only set the amplitude. A new hologram period steers the beam to a new angle.

• The waveguide at the bottom carries the feed wave from left to right. Its phase changes as -βx along the surface.
• The dark elements radiate strongly and the light elements radiate weakly. The shading repeats with the hologram period.
• The red arrows are the radiated beam at angle θ from the normal of the surface.

• The feed wave is the reference wave : it supplies the phase at every element, so no element needs a phase shifter.
• The hologram is an amplitude pattern : the element weights follow (1 + cos((β - k sinθ)x))/2.
• The unwanted term does not radiate : with a slow feed wave, its propagation constant 2β - k sinθ is above k.
• Steering means loading a new pattern : with β = 1.2k, a 30 deg beam needs a period of about 1.43λ.

How is it different from a phased array ?

Both antennas produce a steerable beam from a flat array, so the difference is in what each element has to do. Let's line up the two on the points that decide cost and flexibility.

Let's compare the steering step more closely. In a phased array with half wavelength spacing, a beam at 30 deg needs a phase step of 360 x 0.5 x sin(30 deg), which is 90 deg, from one element to the next. The phase shifter at every element produces that step. In the holographic antenna, the feed wave already has a phase step between the elements. The pattern only decides which parts of that wave radiate strongly. So the same beam comes from amplitude control alone.

This saving has a price. An element that can only scale the passing wave cannot use the whole aperture as fully as an element with free phase control, because the weights have to follow the hologram pattern. Also, one feed drives the whole aperture, so the antenna does not have a separate RF chain per element. This makes digital beamforming per element impossible with this structure. The exact performance depends on the design, so compare the gain, the side lobes and the scan range of a real antenna with a measured pattern.

• A phased array steers with phase : at half wavelength spacing, a 30 deg beam needs a 90 deg phase step per element.
• A holographic antenna steers with amplitude : the feed wave supplies the phase step, and the pattern selects where the energy leaves.
• The saving is in the electronics per element : no phase shifter and no separate RF chain per element.
• The cost is flexibility : the weights must follow the hologram, and there is no per element digital beamforming.

Reference

[1] 

YouTube

[1] Holographic Beam Forming™ by Pivotal Commware

[2] Pivotal Commware Conducts First Public Demonstration

[3] Holographic beamforming; public safety LTE comms trends: Carrier Wrap Episode 77

[4] Advanced 5G, Game Changers! || mmWave problems solved!