Grating Lobes

R2026b

Grating lobes are unintended radiation maxima of equal magnitude to the main beam that appear at angles away from the desired direction, as predicted by the pattern multiplication theorem. Grating lobes reduce antenna performance by directing energy into unwanted directions, causing ambiguity in direction finding and reducing gain in the desired direction. When the array spacing is less than or equal to $$\lambda /2$$, only the main lobe exists in the visible space (the range of angles from 0° to 180° relative to the array broadside), with no other grating lobes. Grating lobes appear when the array spacing is greater than $$\lambda /2$$. For large spacing, grating lobes can appear in the visible space even at a zero scan angle.

Consider a linear array of seven elements spaced one-half wavelength apart. This array contains no grating lobes.

When you increase the element spacing to one wavelength, the number of side lobes increases and a grating lobe appears at the edge of the visible region.

When you increase the element spacing to 1.5 wavelengths, the grating lobes move fully into the visible region.

As element spacing (d) increases or the beam is scanned away from broadside, grating lobes can move into the visible region. To avoid grating lobes while steering a uniform linear array to a maximum scan angle ​θ_max, the element spacing must satisfy $$d\le \frac{\lambda }{\left(1+\left|\sin {\theta }_{\max }\right|\right)}$$

References

[1] Stutzman, W.L. Thiele, G.A. Antenna Theory and Design, 3rd Edition. New York: Wiley, 2013, p. 307.