# ` Introduction to Antenna Array Geometry`

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 We've discussed the basics of antenna arrays and weighting methods in arrays. The performance of an array will depend on the number of elements in the array (generally more elements yields better performance), the weighting vector used, and the geometry of the array. Observing the Array Factor, you will note that the array's output (or reception pattern) is a strong function of the geometry (positions of the antenna elements that make up the array). In this section, we'll discuss array geometry. There are a few basic rules, but its not as well understood as the weighting methods, which are extensively studied. In general, if the inter-element spacing between elements for an N element array is increased, the beamwidth decreases. However, as seen on the grating lobes page, increasing the size of the array will eventually produce grating lobes - undesirable directions of maximum radiation. For uniformly spaced arrays (either 1D, 2D, or 3D arrays with a constant spacing between elements), the maximum spacing is a half-wavelength to avoid grating lobes. This effect is sometimes called "aliasing", which is a term that is borrowed from the signal processing field. Aliasing occurs when plane waves from two distinct direction of arrivals (DOAs) produce the same set of phases across the array. Since an antenna array manipulates signals based on the phase differences that it observes across the array, aliasing results in the array being unable to distinguish signals from distinct DOAs. If the array has non-uniform spacing (the spacing between adjacent elements is not uniform), aliasing can be avoided - particularly if the spacings are not multiples of each other. For instance, an N=3 element linear array defined by positions will not exhibit aliasing: No matter how large the parameter C grows, this 3 element array will not exhibit aliasing. No two distinct directions of arrival will produce the same set of propagation delays across the array. However, the lack of aliasing does not imply that grating lobes will not exist. In fact, if C is very large (>10), for any scan angle there will exist multiple grating lobes. Hence, aliasing is not a criteria to focus on; rather, the existance of grating lobes is a more solid criterian. Non-uniform arrays do not solve the grating lobe problem, but they do enable extra degrees of freedom in designing the array. In general, there is no quick method of determining if an array will exhibit grating lobes. However, any array geometry can be quickly analyzed to determine if grating lobes will occur. In the next section, we'll look at the most popular 2D array: the hexagonally sampled array.

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