Grating-Lobe Design in Phased Antenna Array

The famous λ/2 rule is safe. Designing λ/2 at the wrong frequency is not.

A 5.36 mm pitch supports ±60° near 30 GHz, but not across every higher band.

That distinction becomes critical in mm-Wave, Massive MIMO, AESA Radar, and SatCom.

A grating lobe is not simply another sidelobe.

It is spatial aliasing created by periodically sampling an electromagnetic wavefront. Analog Devices uses exactly this sampling analogy when explaining phased-array grating lobes. [Ref. 1]

And once spatial aliasing enters the visible region: tapering cannot change the fundamental sampling condition.

The problem begins with geometry.

First, Correct the λ/2 Rule

For a uniform linear array: d ≤ λ/2, guarantees grating-lobe-free steering throughout the entire visible hemisphere.

Analog Devices confirms λ/2 prevents spatial aliases even toward ±90°. [Ref. 1]. So half-wavelength spacing is not insufficient for ±60° scanning. In fact, it is slightly conservative.

For a restricted maximum scan angle:

d/λ ≤ 1 / [1 + |sinθmax|]

This relationship follows directly from the spatial-alias boundary. [Ref. 1]

Qorvo gives the same rectangular-lattice condition for active mm-Wave arrays. [Ref. 2]

For ±60° Scan, the Limit Is Not Exactly λ/2

Set: θmax = 60°

Then: sin60° = 0.866

Therefore:

d/λ ≤ 1/(1 + 0.866)

giving: d ≤ 0.536λ

So a rectangular array can theoretically exceed λ/2 slightly. That extra 7.2% pitch can matter enormously in hardware. Especially when BFICs, PAs, vias, and thermal structures need space.

At 30 GHz, the Number Becomes Very Real

Free-space wavelength is approximately: λ₀ ≈ 10.0 mm.

Therefore: dmax ≈ 0.536 × 10.0.

giving: dmax ≈ 5.36 mm.

That is your approximate unit-cell width for ±60° scanning.

Inside those 5.36 millimetres, you may need:

• antenna feed

• PA or LNA

• beamformer channel

• bias network

• ground-via structure

• thermal path

• control routing

This is why grating-lobe design becomes a packaging problem.

Analog Devices Identifies Exactly This Constraint

ADI gives approximately 0.54λ maximum spacing for ±60° scanning. It also highlights shrinking backside electronics area as frequency increases. [Ref. 3].

The problem therefore connects antenna physics directly to IC integration.

At high mm-Wave frequencies, the aperture dictates the PCB floorplan.

Key Point 1: Grating Lobes Are Spatial Aliases, Not Ordinary Sidelobes

For a steered uniform linear array:

sinθm = sinθ₀ + mλ/d

where:

• θ₀ = desired beam angle

• d = element spacing

• m = 0, ±1, ±2...

The m = 0 solution is the desired beam.

Any other real solution becomes another beam.

That is a grating lobe.

The Visibility Condition Is the Key

A beam physically exists when: |sinθm| ≤ 1.

Therefore, grating-lobe design is fundamentally about preventing m ≠ 0 solutions from entering that interval.

This is why broadside testing can be dangerously reassuring.

Consider d = 0.7λ at Broadside

At θ₀ = 0°, and d = 0.7λ, the first alias becomes sinθGL = ±1/0.7, giving: ±1.429.

That is nonphysical.

So, no visible grating lobe exists at broadside.

An engineer could measure this antenna and conclude everything looks excellent. Then steering begins.

Now Scan the Same Array to +30°

For the first opposite-side alias: sinθGL = sin30° − λ/d.

Therefore, sinθGL = 0.5 − 1/0.7, giving sinθGL ≈ −0.929.

Therefore, θGL ≈ −68.2°.

Suddenly, a second high-gain beam enters the visible hemisphere.

Analog Devices demonstrates almost this exact case. Its 0.7λ example develops another full-gain beam near −70°. [Ref. 1]

This is the essential lesson: An array can be grating-lobe-free at broadside and fail when scanned.

That Is Why a Grating Lobe Is More Dangerous Than a Sidelobe

A conventional uniformly excited finite aperture has ordinary sidelobes.

Analog Devices shows first sidelobes around −13 dBc for uniform weighting. [Ref. 4]

A grating lobe is fundamentally different. In the ideal array factor, it can approach main-beam amplitude.

Therefore, calling both phenomena “sidelobes” hides important physics.

Amplitude Tapering Does Not Change the Spatial-Aliasing Boundary

Taylor or Hamming taper changes aperture weighting. That can suppress ordinary sidelobes.

Analog Devices shows tapering reduces sidelobes while sacrificing gain and beamwidth. [Ref. 5]. But tapering does not change d/λ or the periodic sampling geometry.

Suppressing grating lobes requires additional electromagnetic mechanisms.

Key Point 2: The Highest Frequency Sets the Physical Pitch

This is one of the most common design-review mistakes. RF antenna engineer calculate d = 0.536λ at the centre frequency.

Then they assume the entire bandwidth remains grating-lobe-free.

It may not.

Physical Pitch Does Not Shrink When Frequency Increases

But wavelength does: λ = c/f.

Therefore: d/λ = df/c, increases with frequency.

That means grating-lobe margin becomes worse at the upper band edge.

Always design the lattice at fMAX, not merely at fCENTER.

A 30 GHz Design Example Exposes the Problem

Suppose you choose d = 5.36 mm.

This corresponds approximately to 0.536λ at 30 GHz.

So ±60° is near the theoretical grating-lobe boundary.

Now increase frequency.

At 32 GHz

The wavelength becomes approximately: λ ≈ 9.37 mm

Therefore, d/λ ≈ 0.572.

The maximum symmetric scan becomes:

θmax ≈ sin⁻¹(λ/d − 1)

giving approximately: θmax ≈ 48.4°.

Your mechanical PCB has not changed. But your grating-lobe-free scan volume just collapsed.

At 35 GHz

Now, λ ≈ 8.57 mm.

Therefore, d/λ ≈ 0.626.

The same calculation gives approximately: θmax ≈ 36.7°.

So an array designed for ±60° at 30 GHz can become severely compromised near 35 GHz.

That is why wideband grating-lobe design must use the upper frequency.

The Required Pitch Shrinks Rapidly With Frequency

For a rectangular lattice scanning to ±60°:

Qorvo specifically highlights this rapid lattice contraction above 28 GHz.  It notes the shrinking pitch leaves little room for T/R electronics and keeping electronics inside the lattice minimizes feed loss. [Ref. 2]

That directly protects both EIRP and receiver noise figure.

This Creates the Central mm-Wave Packaging Conflict

Electromagnetically, smaller pitch is safer.

Mechanically, larger pitch is easier.

The antenna wants:

• smaller spacing

• wider scan volume

• fewer grating lobes

The hardware wants:

• larger BFIC footprint

• wider RF routes

• more thermal copper

• easier power delivery

• simpler manufacturing

That conflict defines practical active-array architecture.

A Real 2025 30 GHz Array Demonstrated the Risk

A fabricated 8 x 8 slot array operated around 30 GHz. Its measured E-plane pattern showed strong radiation near ±60°. The authors identified those features as potential grating lobes. [Ref. 6]

Its E-plane slot spacing approached approximately one wavelength at 30 GHz. The paper links this spacing to reduced radiation efficiency. 

That is an excellent real-world warning.

Feed convenience can become radiation ambiguity.

Key Point 3: One-Dimensional Spacing Rules Are Not Enough

Real phased arrays are two-dimensional.

For a rectangular planar lattice, define direction cosines:

u = sinθ cosφ

v = sinθ sinφ

The desired beam sits at: (u₀,v₀).

Spatial replicas then occur approximately at:

um = u₀ + mλ/dx

vn = v₀ + nλ/dy

where: m,n = 0, ±1, ±2...

A replica becomes visible when: um² + vn² ≤ 1.

That unit circle is the real two-dimensional visibility boundary.

This Is Why Scan Azimuth Matters

A square array can tolerate one scan direction, then perform differently along the diagonal. The reciprocal-lattice geometry changes the nearest alias location.

Therefore, “±60° scanning” is incomplete without specifying:

• azimuth plane

• elevation plane

• diagonal planes

• full 2D scan volume

The same lesson appeared in our previous scan-loss discussion.

Triangular Lattices Can Buy More Packaging Space

Qorvo gives a triangular-lattice criterion: d/λ < 1.15/[1 + sinθmax] for the specified wide-scan case. [Ref. 2]

For θmax = 60°, this becomes: d < 0.616λ. 

Compare that with rectangular: d < 0.536λ

That is approximately 15% more nearest-neighbour pitch.

At 30 GHz, That Difference Is Tangible

Rectangular: dmax ≈ 5.36 mm.

Triangular: dmax ≈ 6.16 mm.

That extra ≈ 0.8 mm may determine whether a BFIC package fits beneath the antenna.

At mm-Wave, 0.8 mm is not trivial.

At 39 GHz

Rectangular: dmax ≈ 4.12 mm.

Triangular: dmax ≈ 4.73 mm.

Again, ~0.6 mm additional nearest-neighbour pitch becomes available.

But triangular routing is more complicated.

There is no free packaging solution.

Triangular Lattices Are Already Used in High-Performance SATCOM Arrays

A 1024-element Ku-band SATCOM transmitter used an equilateral triangular grid. Its element spacing was approximately λ/2 at 14.4 GHz. [Ref. 7]

The array achieved approximately 75 dBm single-polarization EIRP. It also demonstrated scanning to approximately ±75° in all planes. 

That is a strong example of lattice architecture supporting real systems.

Triangular Lattices Can Also Reduce Required Element Count

A wide-scanning triangular-lattice array demonstrated over 30% bandwidth. It maintained approximately ±60° scanning across all azimuth planes. The authors specifically used triangular geometry with fewer elements than rectangular arrangements. [Ref. 8]

Its cavity-backed structure also suppressed surface-wave-driven scan blindness.

Again, grating-lobe engineering is not only about pitch. It is about the complete periodic electromagnetic environment.

Do Not Use Guided Wavelength for Free-Space Grating-Lobe Spacing

This is another important misconception. 

The visible grating-lobe condition is governed primarily by free-space wavelength λ₀ and the physical element phase-center spacing.

Do not simply substitute: λg = λ₀/√εeff, into the free-space array-sampling equation. That would usually over-constrain the lattice incorrectly.

So Does Dielectric Loading Matter? Absolutely

But differently.

Dielectric loading affects:

• element physical size

• surface-wave modes

• mutual coupling

• embedded pattern

• feed geometry

• scan blindness

These mechanisms can worsen usable scan performance. But they are not the same as the basic free-space sampling condition.

That distinction matters when selecting dielectric substrates.

Element Size Can Become the Hard Constraint

Suppose the grating-lobe limit is: d ≤ 5.36 mm, but the radiator requires 6.2 mm, including isolation and feed transition.

Now no amount of BFIC miniaturization solves the problem. The radiating element itself violates the required lattice.

That forces a different antenna topology.

Possible Alternatives Include

• tightly coupled dipole arrays

• magnetoelectric dipoles

• stacked patches

• slot antennas

• substrate-integrated cavity elements

• metasurface-assisted radiators

The right choice depends on bandwidth and polarization.

Wide scan must be designed into the element, not appended later.

Element Pattern Can Suppress a Grating Lobe, But Be Careful

Array factor determines where spatial replicas exist.

The embedded element pattern determines how strongly they radiate.

If an element has a deep pattern null at the alias direction, grating-lobe radiation may be reduced substantially.

This opens more advanced design strategies, but it becomes frequency and scan dependent.

Recent Research Is Exploiting Exactly This Principle

A large-spacing IEEE design used controllable higher-order element modes. It suppressed grating lobes below approximately −30 dB in tested conditions. It demonstrated wide scanning despite element spacing reaching 0.75λ. [Ref. 9]

That does not invalidate spatial sampling theory.

It engineers the element factor to suppress the alias.

A 2025 Research Is Pushing This Further

A 2025 IEEE study used prephased metalens techniques. It targeted grating-lobe suppression in large-spacing phased subarrays.

A 16 × 16-unit design used 2 × 2-element subarrays. Its reported 2D sidelobe level remained below approximately −9.9 dB. [Ref. 10]

This represents a broader industry direction.

Future arrays may engineer spatial aliases instead of only avoiding them.

Another 2025 Research Approach Breaks Periodicity Itself

Rotated subarrays can intentionally disrupt periodic spacing.

A 2025 IEEE paper optimized these large-spacing configurations. Full-wave simulations validated improved grating-lobe suppression. [Ref. 11]

This is fundamentally different from a regular λ/2 array.

The array is no longer a simple periodic sampler.

Aperiodic Arrays Convert Grating Lobes Into Distributed Sidelobe Energy

This can be useful, but the energy does not disappear.

Instead of one strong coherent alias, energy spreads across more angular directions.

That creates different optimization problems:

• sidelobe floor

• calibration complexity

• manufacturing repeatability

• beamforming weights

So aperiodicity is not automatically superior.

Grating Lobes and Beam Squint Become Coupled in Wideband Arrays

Phase-shift beamforming creates beam squint across frequency.

Analog Devices shows beam direction changing with both frequency and scan angle. [Ref. 1]

Now combine that with frequency-dependent: d/λ.

The main beam moves. The grating-lobe locations move too.

Wideband scan-volume analysis must therefore include both phenomena.

True Time Delay (TTD) Fixes Squint, Not Spatial Aliasing

A TTD network provides frequency-independent delay. That can stabilize beam direction across bandwidth.

But if d/λ is too large at the highest frequency, grating lobes still exist.

Do not confuse beam-squint mitigation with grating-lobe mitigation.

They solve different physical problems.

A Real Ku-Band SATCOM Example Shows Frequency Matters

A wideband IEEE SATCOM array achieved at least ±60° downlink scanning. Its uplink scan range was approximately ±47°. Both scan loss and circular-polarization axial ratio used a ≤3 dB criterion. [Ref. 12]

The study involves more than grating lobes alone. But it illustrates an important system reality. 

Higher-frequency operation often contracts useful scan volume.

Grating Lobes Are Particularly Dangerous for Radar

A second high-gain beam creates angular ambiguity. A target in the grating-lobe direction can resemble another target.

In surveillance Radar, that can corrupt angular interpretation.

Tapering ordinary sidelobes is not enough and spatial aliasing must be controlled architecturally.

For 5G Infrastructure, They Waste EIRP

Energy radiated into a grating lobe is unavailable to users. It can also increase inter-cell interference.

Massive MIMO and Open RAN radios therefore need controlled scan sectors.

The required sector should determine lattice pitch.

Not the other way around.

For Satellite Communications, They Can Illuminate the Wrong Region

Grating lobes waste precious EIRP. They can also increase interference toward other satellites or terrestrial systems.

This becomes especially important during low-elevation scanning.

A wide-angle terminal needs both high gain and clean spatial spectrum.

For Aerospace & Defense, They Complicate Low-Probability-of-Intercept Design

A strong unintended beam can radiate energy elsewhere. That can increase detectability. It may also create interference with onboard RF systems.

MIL-STD-461 addresses system EMC.

It does not solve phased-array spatial aliasing. The electromagnetic aperture still requires dedicated analysis.

The Strategic Engineering Solution

Top-tier engineering teams should design the lattice first, not after BFIC placement.

1. Define the Full Scan Volume

Do not specify only ±60° elevation.

Define:

• θMAX

• φ coverage

• diagonal scan

• polarization

• frequency band

Grating-lobe limits are directional.

2. Use the Highest Operating Frequency

Calculate spacing at fMAX, not fCENTER.

For a rectangular lattice:

d/λMAX ≤ 1/[1 + sinθMAX],

where λMAX means wavelength at the highest frequency.

This is one of the simplest ways to prevent expensive redesign.

3. Choose the Lattice Architecture Early

Compare:

• rectangular

• triangular

• hexagonal

• aperiodic

• rotated subarrays

The lattice determines reciprocal-space alias positions.

It also determines PCB routing opportunity.

4. Perform a Reciprocal-Lattice Check

For planar arrays, plot spatial replicas in u-v space.

Confirm every unwanted replica remains outside: u² + v² ≤ 1 across:

• frequency

• scan angle

• azimuth

This is much stronger than checking one one-dimensional equation.

5. Design the Embedded Element Pattern Together

Do not optimize the isolated element only.

Evaluate:

• embedded gain

• active VSWR

• mutual coupling

• surface-wave modes

• polarization

The element factor can either suppress or expose spatial aliases.

6. Use HFSS or CST Before Layout Freeze

Model:

• infinite unit cell

• Floquet modes

• scan impedance

• lattice modes

• finite-array edges

Then validate a realistic finite aperture.

Unit-cell periodic boundaries reveal infinite-array physics.

Finite models expose edge behaviour and packaging effects.

7. Bring the BFIC Package Into the EM Model

At mm-Wave, the electronics live inside the lattice.

Include:

• package ground

• RF transitions

• thermal vias

• copper coin

• shielding structures

These can perturb the antenna environment.

An RFIC is not electromagnetically invisible.

8. Co-Design Thermal Routing

Smaller pitch reduces thermal spreading area.

That can raise PA junction temperature.

Thermal derating then reduces EIRP.

So shrinking pitch solves one problem.

It can create another.

The best lattice balances RF, antenna, thermal, and manufacturability.

9. Recheck After Any Frequency-Band Change

Changing 28 GHz → 30 GHz without changing physical pitch increases d/λ.

A seemingly small frequency update can reduce scan margin.

Never reuse a lattice blindly across bands.

10. Quantify Grating-Lobe Level, Not Only Presence

For each scan state, report:

• main-beam gain

• highest grating-lobe level

• ordinary sidelobe level

• beam angle

• polarization

Binary “grating lobe/no grating lobe” is insufficient.

A −25 dBc alias is very different from −2 dBc.

11. Measure the Complete Scan Volume OTA

Simulate first, then confirm θ x φ x frequency through OTA measurement.

Do not validate only:

• broadside

• centre frequency

• one principal plane

That misses exactly where spatial aliases often emerge.

The Procurement Implication

A specification saying “Element spacing = λ/2” is incomplete.

Ask:

• λ at which frequency?

• physical pitch in millimetres?

• rectangular or triangular lattice?

• maximum scan direction?

• full azimuth coverage?

• highest grating-lobe level?

• scan bandwidth?

• element phase-center definition?

Without those answers, the spacing number has little procurement value. 

A Better Array Specification Would Say

For example:

24–30 GHz operating frequency

±60° 2D electronic scan

rectangular lattice

d ≤ 5.36 mm

no visible grating lobe across specified scan volume

highest unwanted beam < −15 dBc

Now the RF hardware team knows what must physically fit.

That is an actionable engineering requirement.

The Summary Takeaway

The first-order rectangular-lattice condition is:

d/λ ≤ 1/[1 + |sinθMAX|]

For θMAX = 60°, that gives: d ≤ 0.536λ.

At 30 GHz, that becomes approximately: d ≤ 5.36 mm.

At 39 GHz, it falls to approximately: d ≤ 4.12 mm

A triangular lattice can extend the theoretical spacing further.

Qorvo gives approximately:

d/λ < 1.15/[1 + sinθMAX] [Ref. 2]

For ±60°:

d < 0.616λ

But none of these equations replaces full-wave analysis.

A real array still contains:

• embedded element patterns

• mutual coupling

• surface-wave modes

• finite edges

• packaging

• beam squint

• active impedance

And recent measured hardware demonstrates what happens when spacing approaches λ.

A 30 GHz 8 x 8 slot array showed strong ±60° radiation consistent with potential grating lobes. [Ref. 6]

So the right question is not:

“Did we follow the λ/2 rule?”

It is:

“Is the complete scan volume spatially alias-free at the highest frequency?”

Because in a real phased array:

element pitch is not a PCB dimension, it is an electromagnetic system constraint.