PDCCH Common refers to the parameters specified in PDCCH-ConfigCommon and it define how various common search spaces (e.g., for system information, paging, and random access) are signaled in NR (Refer to this page if you want to know of the details of various search space).  

NOTE : In terms of 3GPP, these are based on 38.331 and 38.213-10.1

The highlights of the configurations are as follows. If the network omits any of these optional fields (other than ra-SearchSpace, which must be present), the UE does not attempt to decode the corresponding common search space in that particular DL BWP.

• controlResourceSetZero : Interpreted in the same way as the MIB parameter pdcch-ConfigSIB1. Although it is only explicitly configured in the initial DL BWP (BWP#0), it may still be referenced by search spaces in other DL BWPs.
• commonControlResourceSet : Provides an extra CORESET for Random Access Response (RAR), paging, or additional system information. If configured, the network assigns it a non-zero ControlResourceSetId.
• searchSpaceZero : Mirrors the bits from pdcch-ConfigSIB1 in the MIB. Like controlResourceSetZero, it is configured in the initial BWP but can also be utilized in other DL BWPs.
• commonSearchSpaceList : A collection (size 1–4) of additional common search spaces, each assigned a non-zero SearchSpaceId, for purposes such as paging or system information reception.
• searchSpaceSIB1 : Designates a search space ID for SIB1. If absent, the UE does not monitor for SIB1 in this BWP.
• searchSpaceOtherSystemInformation : Designates a search space ID for other system information (SIB2 and beyond). If absent, the UE does not monitor for those SIBs in this BWP.
• pagingSearchSpace : Points to the search space ID where paging DCI is found. If absent, the UE does not monitor for paging on this BWP.
• ra-SearchSpace : Specifies the search space ID for receiving the Random Access Response (RAR). This field is mandatory in the DL BWP, ensuring the UE can perform random access.

NOTE : Why we need controlResourceSetZero searchSpaceZero while it is already defined in MIB ?

Even though CORESET #0 and SearchSpace #0 are initially defined in the MIB, the specification allows (and sometimes requires) these same parameters to be signaled again through controlResourceSetZero and searchSpaceZero in PDCCH-ConfigCommon. In other words, the duplication ensures that the same MIB-defined parameters for CORESET #0 and search space #0 can be referenced or tweaked at the RRC layer and reused across BWPs, rather than being tied solely to the initial-access settings from the MIB.

The main reasons are:

• Reusability in Other BWPs: MIB settings primarily apply to the initial downlink bandwidth part (BWP) for early access. By copying them into controlResourceSetZero and searchSpaceZero, the network can explicitly reuse—or reference—those same CORESET #0 and search space #0 definitions in additional BWPs if needed.
• RRC-Based Configuration: MIB transmission has strict payload limits and mainly provides “bootstrap” information. More comprehensive or revised signaling occurs via RRC. Placing controlResourceSetZero and searchSpaceZero within PDCCH-ConfigCommon lets the network adjust or reconfirm these parameters at the RRC level, rather than being locked into only what is signaled in the MIB.
• Consistency and Future Changes: By carrying over the same CORESET #0 and search space #0 definitions into PDCCH-ConfigCommon, the UE has a single, well-defined configuration source for all BWPs (not just the initial one). If the network ever needs to reconfigure aspects of CORESET #0 or search space #0, it can do so through RRC messages, without changing the MIB. This design also maintains consistency across different bandwidth parts and operational scenarios.

NOTE : Should MIB pdcch-ConfigSIB1 and controlResourceSetZero/searchSpaceZero always match ?

This is stated in 38.331 but I think this would need some interpretation. To me, it is a little bit ambiguous.

• controlResourceSetZero : Parameters of the common CORESET#0 which can be used in any common or UE-specific search spaces. The values are interpreted like the corresponding bits in MIB pdcch-ConfigSIB1. Even though this field is only configured in the initial BWP (BWP#0) controlResourceSetZero can be used in search spaces configured in other DL BWP(s) than the initial DL BWP if the conditions defined in TS 38.213, clause 10 are satisfied.
• controlResourceSetZero : Parameters of the common CORESET#0 which can be used in any common or UE-specific search spaces. The values are interpreted like the corresponding bits in MIB pdcch-ConfigSIB1. Even though this field is only configured in the initial BWP (BWP#0) controlResourceSetZero can be used in search spaces configured in other DL BWP(s) than the initial DL BWP if the conditions defined in TS 38.213 , clause 10 are satisfied.

The statement mentions about a specific condition 'if the conditions defined in TS 38.213 , clause 10 are satisfied'. What would it mean ?

My guess is it refers to the following statement of TS 38.213-10.1

If the active DL BWP and the initial DL BWP for a UE have same SCS and same CP length and the active DL BWP includes all RBs of the CORESET with index 0, or the active DL BWP is the initial DL BWP, or the active DL BWP includes all RBs of an MBS frequency resource provided by cfr-ConfigMCCH-MTCH as described in clause 18, the CORESET configured for Type0-PDCCH CSS set has CORESET index 0 and the Type0-PDCCH CSS set has search space set index 0.

This can be interpreted as follows

There are specific technical requirements—mostly around subcarrier spacing, cyclic prefix type, and frequency coverage—that must be met before CORESET #0 (originally defined in the initial BWP) can be validly reused in another DL BWP. These conditions ensure that the same CORESET #0 resources (i.e., frequency and time allocations) make physical sense in the new bandwidth part.

• For example, clause 10 in TS 38.213 describes that, to reuse CORESET #0 in another BWP:
• The active DL BWP must have the same subcarrier spacing and CP length as the initial BWP.
• The active DL BWP must cover all the RBs (resource blocks) used by CORESET #0.
• Certain additional checks (e.g., for broadcast or MBS usage) may apply.

RRC Parameters

PDCCH-ConfigCommon ::=                  SEQUENCE {
    controlResourceSetZero                ControlResourceSetZero OPTIONAL, 
    commonControlResourceSet              ControlResourceSet OPTIONAL, -- Need R
    searchSpaceZero                       SearchSpaceZero OPTIONAL, -- Cond InitialBWP-Only
    commonSearchSpaceList                 SEQUENCE (SIZE(1..4)) OF SearchSpace OPTIONAL, 
    searchSpaceSIB1                       SearchSpaceId OPTIONAL, -- Need S
    searchSpaceOtherSystemInformation     SearchSpaceId OPTIONAL, -- Need S
    pagingSearchSpace                     SearchSpaceId OPTIONAL, -- Need S
    ra-SearchSpace                        SearchSpaceId
    ...

}
ControlResourceSetZero ::= INTEGER (0..15)

controlResourceSetZero : Parameters of the common CORESET#0. The values are interpreted like the corresponding bits in MIB pdcch-ConfigSIB1. Even though this field is only configured in the initial BWP (BWP#0) controlResourceSetZero can be used in search spaces configured in other DL BWP(s) than the initial DL BWP

commonControlResourceSet : An additional common control resource set which may be configured and used for RAR/paging/system information. If the network configures this field, it uses a ControlResourceSetId other than 0 for this ControlResourceSet.

searchSpaceZero : Parameters of the common SearchSpace#0. The values are interpreted like the corresponding bits in MIB pdcch-ConfigSIB1. Even though this field is only configured in the initial BWP (BWP#0) searchSpaceZero can be used in search spaces configured in other DL BWP(s) than the initial DL BWP

commonSearchSpaceList : A list of additional common search spaces. If the network configures this field, it uses the SearchSpaceIds other than 0.

searchSpaceSIB1 :

• 38.331 states ID of the search space for SIB1 message. If the field is absent, the UE does not receive SIB1 in this BWP.
• 38.213-10.1 states : For a DL BWP, if a UE is not provided searchSpaceSIB1 for Type0-PDCCH CSS set by PDCCH-ConfigCommon, the UE does not monitor PDCCH candidates for a Type0-PDCCH CSS set on the DL BWP. The Type0-PDCCH CSS set is defined by the CCE aggregation levels and the number of PDCCH candidates per CCE aggregation level given in Table 10.1-1.

searchSpaceOtherSystemInformation : ID of the Search space for other system information, i.e., SIB2 and beyond. Corresponds to L1 parameter 'osi-SearchSpace'. If the field is absent, the UE does not receive other system information in this BWP.

pagingSearchSpace : ID of the Search space for paging. Corresponds to L1 parameter 'paging-SearchSpace'. If the field is absent, the UE does not receive paging in this BWP

ra-SearchSpace: ID of the Search space for random access procedure. Corresponds to L1 parameter 'ra-SearchSpace'. If the field is absent, the UE does not receive RAR in this BWP. This field is mandatory present in the DL BWP(s)

Reference

[1] Type0-PDCCH common search space