Can you please try to expand a bit on the capabilities part, like effective range, number it can monitor, and how many it can simulaneosly track and engage. My undersatnding of X, S and L bands are very limited but ultimately it is about specfic capabilities and without them it is very difficult to place context and comparison against contemporaries.
My understanding of different bands are not anywhere near comprehensive either, however I'll give it a try (if I'm wrong anywhere, I would love to be corrected by anyone). But before we talk about that, it's obviously worth mentioning that the relative capability of a radar depends on the array and the processing systems behind the radar. Obviously a modern S band AESA like SAMPSON is far superior to an older phased array S band radar like SPS-48.
So keep in mind when I talk about the capability of 055's potential radar suite, it is in context of the radars all being competitive with current international peers in terms of array technology, processing, and back end integration (a reasonable expectation, given radars seem to be something the PLA's contractors and institutes can do quite well, say, compared to mass producing turbofan engines).
In terms of radar band, X band is one of the most common small wavelength radars for military use, often with relatively small array sizes compared to larger band radars, and provides good resolution but at shorter range. Most fighter radars operate in the X band, and terminal SAM illuminators/FCRs for naval ships also operate in this band, as well as FCRs for naval guns and the like. Modern X band APARs like the Thales APAR and the future AMDR-X will be able to do a variety of roles from illumination to gunfire guidance, and surface search, all at the same time. Also, X band radars tend to be able to achieve quite good performance for their properties with relatively small size, meaning each array can be placed higher on a ship's mast, so if the arrays are placed in a fixed style like Burke or 052C/D, then it means a ship will have longer radar horizon for detecting low altitude targets.
L band (and lower frequency/long wavelength radars like UHF or VHF) are usually used for long range surveillance and volume search roles, and is the preferred band for a variety of AEWC. Many L band radars have quite large array sizes compared to X band. As an aside, long wave radars also tend to have better anti stealth properties against a variety of stealth designs, but it is only recently that such radars have been designed to be more reliable in that role.
S band radars typically lie between X band and L band in terms of range, array size, and resolution, and that is why it is one of the most common radar bands aboard military ships, and is the band occupied by the USN's SPY-1, AMDR-S/SPY-6, the PLAN's 346/A, the RN's SAMPSON, the European EMPAR and Herakles, the Israeli MF-STAR, among others. This band provides a good compromise between the range, and target resolution. Note that S band generally is not good enough for terminal illumination of targets for SARH SAMs, but it is used for midcourse guidance of both SARH and ARH SAMs. The difference is that Active Radar Homing SAMs do not need terminal illumination by an offboard source, as they have an onboard radar that can do terminal illumination for themselves. This means they are not limited by terminal illumination from the ship and are really limited by the processing aboard the ship and number of midcourse guidance channels the ship can do at one time. For instance, Burkes and Ticos only 3 and 4 terminal illuminators of the older mechanically oriented type, respectively, which limits the number of targets that they can engage at one time using SARH SAMs. However many newer ships have X band AESAs as mentioned before, which can form multiple beams of terminal illumination at once, whereas the old terminal illuminators can only designate one target at a time, meaning ships with modern X band AESAs can engage many more targets at once using SARH SAMs than a ship forced to rely on older mechanically oriented illuminators.
(note, I don't think there is any inherent difference in the number of targets each radar band can monitor, that really depends on the kind of array the radar fields, and the back end processing, software, integration and overall computing power)
Now, obviously there is a difference between any "phased array" and a phased array MFR.You can have phased array radars but whose function is only terminal illumination or gunfire fire control. So when I spoke regarding 055 having multiple sets of phased array radars in multiple bands, I meant having multiple phased array MFRs. MFRs, Multi Function Radars, are just that -- they can do multiple roles, often at multiple roles at once especially for AESAs. Volume Search, Detection, Tracking, weather, surface search, midcourse guidance, illumination, fire control, are some of the roles that MFRs can do. And the take away message is that modern MFRs differ in their ability to do those different roles depending on which band they are, because different roles are done better with different properties of radar bands. E.g.: L band is better at volume search at long range but can't do practical terminal illumination, whereas X band radar can do terminal illumination but has shorter range.
I'm going to quickly go through some examples of ships and their radar suites, but keep in mind I won't go through all the roles their radars have.
Many modern ships tend to have one, or at most two phased array MFRs of each band:
European surface combatants like the Saschen class, De Zeven class, use L band and X band. the L band SMART L MFR is used for longer range volume search and X band Thales APAR MFR is used for closer in surface search, horizon search, and terminal illumination of targets for semi active radar homing missiles.
The USN in their current burke and tico class ships only have a single phased array MFR, the S band SPY-1 for volume search and midcourse guidance of their SARH SAMs, but rely on older mechanically oriented X band FCRs for terminal illumination of targets. The newer Flight III burkes will have an X band AESA as part of the AMDR package, meaning they will have similar multi target engagement capability for their SARH SAMs that European frigates equipped with the Thales X band APAR (TM) currently enjoy.
The British and French use S band MFR SAMPSON and EMPAR for volume search and midcourse guidance aboard their Type 45 and Horizon class ships -- they don't have any X band terminal illuminators or X band APARs for their SAMs, because their Aster SAMs are active radar homing, so no shipboard terminal illumination is needed. However they also have an L band radar for volume search and longer range work. I seen it said that there is no real need for a large L band MFR when a ship already has a perfectly capable S band MFR, but the truth is a radar in a different band means it can do different jobs with better results, and it also leaves your other radars to concentrate more on jobs that they can do better in. Think of it as division as labour.
Now, the PLAN's 052C and 052D only feature an S band AESA MFR, the 346/A. They have no X band terminal illuminators or X band MFR APARs, and over the years it has been speculated and agreed upon that the HHQ-9 SAMs on 052C are active radar guided. Similarly, I expect 052D's SAMs to be all ARH as well.
So what does this mean for 055?
Well, it means having multiple capable phased array MFRs that operate across different bands means the division of labour is more effective (assuming the ship has the computing power to support all of them, and assuming they can be integrated into a good overall combat picture), and each radar will be able to concentrate more on the tasks it is good at rather than having to multitask.
Some more fundamental properties are also beneficial, for instance a longer wave radar like L band or UHF band will physically have better anti stealth capability, and an X band radar means you can set your X band arrays higher on the mast, meaning you'll have a longer radar horizon meaning more reaction time against sea skimmers. Indeed, we all expect X band radars aboard 055's integrated mast.
Obviously not every ship can have three or even two sets of highly capable MFRs in different bands -- radars need power, cooling, processing, and integration into the combat system which needs a lot of space, and thus a larger ship. Fortunately, 055 seems to be quite a big ship and should have more than enough space to handle the rumoured three sets of radar.
Also, having multiple bands of radar on a single ship means more chance of electromagnetic interference with each radar set, meaning that is another challenge one has to solve. But if all the aforementioned issues can be resolved and one can fork up the money, then a ship with multiple sets of radars in different bands operating in harmony with one another will definitely have a more formidable radar suite than a ship with fewer bands, assuming array technology, processing, integration, etc are all equal.