The real question is that even if you are able to use C-band for guidance, what makes you think its better to use than X-band? The case is really why use C-band when X-band is superior for this purpose. The HQ-9 seeker is still fairly small and X-band will still give you better angular accuracy. It should not be any bigger than the S-300 missiles like the 48N6 and 5V55 that it is very similar to, and it should be slightly smaller. Yet the 48N6 and 5V55 are both guided on X-band.
AN/MPQ-53 is intended to be able to operate as a self contained all in one unit.
The C in C-band stands for "compromise". As you answered your own question , it enables a MFR with search/track/engage capability.
Concerning target engagement. As you pointed out, TVM is not without advantages. It is a multistatic radar system. The fire control system gets to process two reflections from the target: I suspect this is enough to overcome the weaker angular resolution compared to X-band.
Coming back to the question of Type 346 and HHQ-9.
The fact that everything points to HHQ-9 being derived from HQ-9, a C-band TVM guided missile, is what led me hypothesize that HHQ-9 introduced on Type 052C maintained the same guidance system. This would most elegantly be supported by a MFR radar with search/track/engage and TVM missile quidance, just like what is provided by Patriot and HQ-9 SAM systems from which it is ostensibly derived. Let's call this hypothesis A.
As far as I know, there is no shot of the Type 346 phase array. There is however that of the Type 346A on 052D, showing two narrow strips at the upper and lower edge of the array.
One hypothesis is that these are C-band arrays sandwiched around the central S-band array. Given their geometry, it is unlikely that these would serve an illumination purpose. Rather, it seems that they may be used for high data rate communication with HHQ-9s. This would be consistent with TVM. But in absence of any other candidate for an illumination radar we are lead to conclude that HHQ-9s on 052D must have some form of autonomous guidance in the terminal phase. Let's call this hypothesis B1.
Another hypothesis is that the two strips are an extension of the same S-band array. The communication with the missiles would then be carried out in S-band, like it is on SPY-1. Or that function may be fulfilled by the antennae that sit on top of the superstructure, above the Type 346 panels. Let's call this hypothesis B2.
In either of hypothesis B, the HHQ-9s have autonomous terminal guidance. This could be ARH or IR.
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