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I'm studying MUSIC algorithm for far-field DOA estimation. I found that when the antenna spacing $d$ is larger than half wavelength $(\frac{\lambda}{2})$, the algorithm fails and the spatial spectrum shows multiple peaks.

In 5G beyond and 6G wireless communications/localizations, mmWave or even higher THz band can be utilized, and thus the wavelengh might be smaller than a millimeter. However, it is quite challenging to manufacture an antenna array with such small element spacings in practice.

So my question is: why MUSIC algorithm fail when the antenna spacing is larger than a half wavelength? Is there an intuitive explanation for this?

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  • $\begingroup$ This is strictly speaking a physics, not a signal processing question. Look at the antenna pattern of a linear array of parallel antennas, and you'll see these multiple lobes. Your problem simply doesn't have a unique solution anymore, and thus, MUSIC also can't solve the problem. $\endgroup$ Commented Oct 23, 2022 at 12:38
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    $\begingroup$ Easy enough: it's spatial aliasing. The sampling theorem applies in space the same way as it does in time. Since your not sampling densely enough you get mirror images in spatial frequency. $\endgroup$
    – Hilmar
    Commented Oct 23, 2022 at 13:37
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    $\begingroup$ @Hilmar, you should add that as an answer. $\endgroup$
    – Peter K.
    Commented Oct 23, 2022 at 17:36

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