# What is the behaviour of this antenna array?

I have a subarray-based antenna system as shown here:

The four subarrays are arranged vertically. In each subarray there are six antenna elements. Only the bottom three in each subarray have a common phase shifter.

The inputs to each subarray are distinct: i1 ≠ i2 ≠ i3 ≠ i4.

The operating frequency is 3.5 GHz. The antenna elements are vertically arranged with half a wavelength spacing.

The phase shifters can take 4 distinct values, i.e., 2-bit phase shifters, for directions 0°, 15°, 25°, and 35° (vertically).

Can someone please explain the behaviour of this antenna? What happens to the un-phase-shifted signals, e.g. the top three antenna elements in each subarray?

If we want to direct the signals to a given direction, lets say, 15° (vertical), how do we do it? Can we achieve the full array gain in this case, i.e., from these 24 antenna elements? Or is each signal only supported by its subarray in terms of array gain?

• nobody can tell you that, because we don't know the physical arrangement of the individual antenna elements (especially, the relative positions distances of phase centers in wavelengths), nor the feedline lengths, nor what the phase shifters are configured to. Commented Jan 18 at 11:09
• @MarcusMüller thanks for your comment. I have edited my question with additional informations
– MGM
Commented Jan 18 at 12:23
• Thanks, but what's the relative phase of the patches? are all these lines length-matched? Commented Jan 18 at 12:51
• @MarcusMüller all three patches (bottom three) in each subarray has the same phase.
– MGM
Commented Jan 18 at 14:50
• huh, surprising! That makes the "unphased" 3 patches have a narrow beam at 0°, with little or no ability to do much steering with the lower array. You'd really have to use the DFT to calculate an array factor for that, because, as said, with a concentrated main beam with a phase center more than a wavelength away from the second half's phase center, you're essentially setting yourself up for something that looks like a very slightly slanted main beam at roughly 0° and weaker grating lobes. Not something you'd usually want to build. Commented Jan 18 at 17:05

Let's take this one step at a time. Consider first the behavior of one subarray.

The subarray can be considered as being composed of two elements (the two groups of three), separated by 1.5 lambda. Since half the subarray has a 2-bit phase shifter in its feed, you can steer the subarray beam to 4 different positions, corresponding to the 4 possible phase states of the phase shifter. The beam positions are 0 deg, 15 deg, 25 deg, & 35 deg, per you question.

What happens to the signals un-phase-shifted, e.g., the top three antenna elements in each subarray?

In your case, the fact that the upper 3 elements in each subarray are not phase shifted doesn't really matter, The subarray's beam is steered by the relative phase difference between the upper 3 elements and the lower 3 elements.

Keep in mind that the overall pattern of the steered subarray beam is a function (product) of the 3-elements that make up half the subarray and the 2 super elements (for lack of a better term) that make up the subarray.

If we want to direct the signals to a given direction, lets say, 15 degree (vertical), how do we do it?

Well, I explained above how that works at the subarray level. At the array level - 4 subarrays - it all depends on the relative phase shift between the 4 subarrays. You have all 4 subarrays steering to the same place, so now you have to bring those 4 subarrays into phase alignment. The spacing between the subarrays is 6 element spacings, or 3 lambda. This is 2X the spacing between the upper 3 and lower 3 elements of a subarray, So the phase shift between subarrays should be 2X that of the phase shift between the upper & lower halves of each subarray.

That means we can benefit from the array gain of total 24 antenna elements when we steer the beams (from all 4 subarrays) towards a given direction?

No, that won't work with the architecture you have. The basic issue is that the phase value of the upper half of each subarray is always zero. The illustration below shows what happens.

In order to steer and form a beam at a direction other than broadside, you would need a phase gradient (taper) across the array that's shown in blue. What your architecture gives you is something like what's shown in red, where the lower half of each subarray is phase aligned (at least to the quantization allowed by the phase shifter), but the upper half of each subarray is steered to boresight (perpendicular to the face of the array).

This really gives you two separate beams, one steered in the desired direction amd the other fixed at boresight.

• Thank you so much for your reply. It gives me answer to my questions. That means we can benefit from the array gain of total 24 antenna elements when we steer the beams (from all 4 subarrays) towards a given direction? Can you give me just a simple practical example of how to set the phase shift values of the four lower halves of the 4 subarrays if we want to steer the beams to 15 degree considering the fact that the phase shifters can take only 4 states. I am a very novice in this area.
– MGM
Commented Jan 19 at 2:22
• @MGM - Given the architecture you've shown, the answer is NO. You cannot make those 4 subarrays act like one 24 element array. The problem is that in order to steer the beam off broadside, the upper 4 elements in each subarray need to have a phase shift other than 0. I try to sketch something up & add it to my answer. Commented Jan 19 at 17:06
• Because each subarray is independently fed it should be possible to achieve a closer phase gradient by setting each delay line the same (e.g. 15 degrees) and then delaying the input signals by 30, 60 and 90 degrees. Commented Jan 19 at 17:56
• @user253751 - Yes, if you had that knob to turn. But OP's diagram does not show such an adjustment - either time delay or phase. Note that what you suggested is fairly common for large arrays where wide IBW is needed. Steer the indivudual subarrays with phase shifters, and steer the entire array with time delays at the subarray level. Commented Jan 19 at 19:28
• OP says each of the 4 input signals can be independent and the delay elements can be set to either 0, 15, 25 or 35 degrees. Commented Jan 19 at 21:56