# Why MUSIC algorithm fail when the antenna spacing is larger than half wavelength?

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?

• 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. Commented Oct 23, 2022 at 12:38
• 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. Commented Oct 23, 2022 at 13:37