What causes grating lobes in a phased array?

Grating lobes are additional beams of the same magnitude as the main beam that appear when array element spacing is large enough for the array factor to repeat within visible space. For a linear array scanned to θ₀ from broadside, they are avoided when d/λ < 1/(1+|sinθ₀|): d ≤ λ/2 permits scanning to endfire, while d = 0.6λ limits scan to about ±42°.^[1][2]

Why do grating lobes appear?

The array factor is periodic in ψ with period 2π. When kd(1+|sinθ₀|) exceeds 2π, a second maximum (ψ = ±2π) enters real angles. The grating lobe direction satisfies sinθ_g = sinθ₀ − mλ/d.^[1]

How are grating lobes managed?

• Keep spacing ≤ λ/2 at the highest frequency, or ≤ λ/(1+sinθ_max).
• Use triangular lattices to reduce element count for a given scan volume.
• Use element patterns that suppress radiation where grating lobes would fall.
• Use randomized or aperiodic subarrays to break up quantization and subarray lobes.^[1][3]

What are quantization lobes?

Digital phase shifters with few bits produce periodic phase errors across the aperture, generating quantization lobes and raised sidelobes; the RMS sidelobe from a B-bit phase shifter scales with 2^−B. Phase randomization spreads these errors.^[1]

Frequently asked questions

See also

• Phased arrays
• Array factor
• Antenna arrays
• Array tapering

References

Online sources accessed October 21, 2026; printed works cited by edition. See all sources.

1. “Phased Array Antenna Handbook, 3rd ed.”. R. J. Mailloux, Artech House. 2017.
2. “Antenna Theory: Analysis and Design, 4th ed.”. C. A. Balanis, Wiley. 2016.
3. “Phased Array Antennas, 2nd ed.”. R. C. Hansen, Wiley. 2009.