In the most straightforward implementation, beamwidth is a function of antenna aperture size and number of phase shifting elements. For small X-band arrays like the one on Type 054, the beamwidth is not going to be any narrower than the much larger S-band Type 346 array.
Even much larger X-band radars, like AN/TPY-2 with 25,000 T/R elements can perform volume search. If such a radar was not capable of adjusting its beamwidth, it would have a very hard time performing that function with a pencil beam less than 0,5 degree wide and all of that at a range of 1000km which severely limits the number of pulses than can be emitted.
Here's a plot of the radiation pattern for a of 12 element linear active array. in this case, each element is emitting at maximum power (gain=1).
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Now, if the gain of each transmitting element is adjusted, a very different radiation pattern can be generated. Here's an example of a radiation pattern with binomial weighting of gain per transmitter
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With binomial weighting beamwidth is more than doubled and sidelobes virtually eliminated. The downside is that this halves the antenna efficiency.
Here's a table of beamwidths, sidelobes and antenna efficiencty, per gain weighting method. As you can see, it is possible to further extend the beamwidth, up to 27.7 degrees.
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If you have a small array, you're going to have a wider beam. Beamwidth is also a function of the frequency and you can shape the beam with an uneven distribution of power across the face. With AESA you can vary this pattern but in PESA, you have to build this through the feed design and in parabolics through a slightly uneven design of the parabolic.
You would think that removing the sidelobes would increase the antenna efficiency.
But enough this is out of topic.
These arrays will likely have search functions on their own as a collateral benefit. But they can never act as search primaries due to the limitations of range with X-band, and the power feed to these will also be limited, and the small size of the array limits their receiving gain. These kind of reminds me about the size of fighter radars, and the number of elements could be in the upper hundreds to over a thousand. RWS can still be in excess of 100km.
I also believe that these arrays will end up in the next gen frigate, 054B or 057, and it may end up embedded in an integrated mast.
But this is a hack on an existing ship, which already has in place, existing systems that will do search, and one that they want to get out fast through the gate with minimum modification. Its not a perfect situation and its not calling for perfection.