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I am building a uniform linear antenna array (ULA) of Wi-Fi to extract channel state information, or channel matrix $H$.

With some literature search, as not familiar with antennas and electromagnetic wave, I found that antennas spacing $\Delta$ should be less than a half of wavelength. In my case, approximate wavelength $\lambda = \frac{3\times10^8}{2.4\times10^9} = 12.5cm$. Hence, $\Delta$ should be less than 6.25 cm, or grating lobes will appear [1]. Unfortunately, I misconfigured antenna spacing for the first attempt. I placed 3 antennas with $\Delta=6.5cm$.

The question is, does it matter to measure the exact channel matrix $H$? If ULA with 3 antennas is used as a receiver and it does not transmit a signal, then does grating lobes still in effect? In my opinion, I don't think so. But, as I am not familiar with it, I'd like to hear other expert's advices.

TL;DR

  1. Does antenna spacing of uniform linear array (ULA) receiver larger than a half of wavelength have an impact on grating lobes and measuring channel matrix?
  2. If so, is there any tolerance in spacing error? e.g., is it okay to set spacing 6.5 cm instead of 6.25 cm? (error is 4 percent)
Jeon
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  • Grating lobes are a function of the phase differences between the different antennas. This seems to be more related to a spatial sampling criterion and you would probably do slightly better with antenna spacing at the quarter wavelength (2x oversampling), but there is, of course, a limit to that, as you are getting ever higher correlations between the channels, which are good for obtaining SNR and smooth spatial responses but will require more hardware. As long as you are somewhat below the sampling criterion, you are theoretically OK, if not by much. – CuriousOne Jun 14 '16 at 07:53
  • So, to be clear, not only a transmitter but also a receiver should space antennas with a correct spacing. And in order to meet sampling criterion, I should place them 6.25 cm apart or closer. Is that right? – Jeon Jun 14 '16 at 08:25
  • The appearance of grating lobes is related not only to antenna spacing but also to steering angle. When talking about measuring the channel matrix you are probably talking about some kind of MIMO system and that is related to the correlation of the various multipath components. This phys group is probably not the right place to discuss that subject. – hyportnex Jun 14 '16 at 16:00
  • Thanks for your advice. Then, http://electronics.stackexchange.com/ seems more appropriate group? Actually, I've concerned which site is proper for this question. Or, Quora and Researchgate? – Jeon Jun 14 '16 at 16:13
  • For MIMO wider apart would actually be better, IMHO. You aren't gaining anything from highly correlated antennas in an application that needs them to be uncorrelated. The only saving grace there is that the environment helps you with that, a little. Having said that, doing MIMO and measuring the channel matrix, which is all about your environment, are two completely different tasks. – CuriousOne Jun 14 '16 at 18:23

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