# `Grating Lobes in Antenna Arrays`

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 We saw previously that a uniformly-spaced array with weights selected to be:                       (1) will have the array steered towards the desired direction, . In equation (1), k is the wave number and d is the spacing between adjacent array elements. However, it is possible that the array will have equally strong radiation in other directions. These unintended beams of radiation are known as grating lobes. They occur in uniformly spaced arrays (arrays with an equal distance between adjacent elements) when the antenna element separation is too large. As an example, consider again the situation from the previous page, a group of N=5 uniformly spaced elements with half-wavelength separation on the z-axis. Supposed that the array is to be steered towards . This means the array is to be steered along its own axis, in the +z-direction; this type of radiation is known as an endfire pattern or endfire radiation. The weights can be easily determined from equation (1) above. The response of the array given these weights is shown in Figure 1. Recall that the response of the array is mathematically equivalent to the array factor. Figure 1. Response of array when weights are steered towards . Note that in Figure 1, the array does indeed have a response that is maximum towards the desired direction (0 degrees-or the +z axis). However, the array also produces a lobe of maximum radiation towards 180 degrees, which was unintended. This lobe is known as a grating lobe. For uniformly spaced arrays, this can be eliminated by decreasing the separation between the elements. For non-uniform arrays, grating lobes are much more difficult to predict. In the next section, we'll take a more mathematical look at the properties of uniformly spaced arrays using the phased-steering weighting scheme described by equation (1).

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