5G NR Beamforming Beam Count

Not absolutely necessarily, but typically low-band and mid-band 5G NR employs digital beamforming, whereas high-band employs analog beamforming. The explanation of the difference between them is out of scope of this article, though the key mainstay of analog beamforming is the cornerstone of the essence of this article - with analog beamforming, only a single beam can be active at any point in time, and the beams in analog beamforming are predefined in terms of their spacial properties, i.e. direction and directivity, as a beam grid.

This article aims to answer one and only one simple question - how to derive the number of wide SSB beams and number of narrow traffic beams of the cell from RRC signalling on the UE side only?

W.r.t. SSB count and even exact position in burst it is straightforward:

ssb-PositionsInBurst
?longBitmap: '0000110000111100000011000011110000000000000000000000000000000000'B,
??????????????? ssb-periodicityServingCell ms20,
??????????????? dmrs-TypeA-Position pos2,
??????????????? ssbSubcarrierSpacing kHz120,
??????????????? ss-PBCH-BlockPower 15        

In the example above the cell has 12 wide SSB beams and according to their position in burst their indexes are 4, 5, 10, 11, 12, 13, 20, 21, 26, 27, 28, 29.?Further down another way how to derive the number of and the indexes of the wide SSB beams will be presented as well in no uncertain terms.

W.r.t. narrow traffic beam a derivation would require a few consecutive steps. Let's begin!

Only the cell knows exactly everything about its narrow beams and controls them. The UE uses them without knowing which exactly fixed pre-defined beam it is using. But the cells can select the best beams based on a measurement report from the UE about the strongest beam(s), and that is where the clue on the narrow traffic beam quantity can be found.

In the example below the gNodeB transmits 6 and always 6 CSI reference signals for narrow traffic beam measurement and reporting purposes. The UE is supposed to report the indicator (CRI) of the strongest narrow traffic beam and its RSRP for the gNodeB to know how to best serve the UE. CRI is the method to identify beams in the pre-defined beam grid in analog beamforming. In digital beamforming case, like in low- or mid-band 5G NR, you will unlikely find CRI in the RRC Reconfiguration message altogether - digital beamforming forms user-specific beams instead of pre-defined grid beams.

Please note that the CRI can have the same 6 values (0…5) under any wide SSB beam, which is why it makes sense only in association with the serving parent SSB beam. For the gNodeB to know which wide SSB beam is the strongest one for a particular UE, the UE also reports the strongest SSB beam index and its RSRP. The reported SSB Index can have value 0…11, corresponding to the 12 available SSB beams in their ascending order: the actual indexes 4, 5, 10, 11, 12, 13, 20, 21, 26, 27, 28, 29 in our example would be reported as 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, or 11 correspondingly. The correspondence is simple and unambiguous. Similarly, the reported CRI values 0, 1, 2, 3, 4 and 5 unambiguously correspond to the CSI reference signals whose actual IDs are 24, 25, 26, 27, 28 and 29. But this clarification just for your information and does not directly impacts the derivation of the number of the wide and narrow beams.

First step. Find those CSI-ReportConfig that is intended for CRI_RSRP reporting. You can also pay attention to the CSI-ReportConfig that are intended for ssb_Index_RSRP reporting, though this is not really necessary - this would just open another way to derive the count and indexes of SSB present in the cell, as mentioned earlier.

csi-ReportConfigToAddModList {
???????????? CSI-ReportConfig {
?????????????? reportConfigId 1,
?????????????? resourcesForChannelMeasurement 0,
???????????? reportQuantity cri_RSRP : NULL,
???????????? timeRestrictionForChannelMeasurements configured,
???????????? timeRestrictionForInterferenceMeasurements configured,
???????????? groupBasedBeamReporting disabled : {
?????????????? nrofReportedRS n2
???????????? },
???????????? subbandSize value1
?????????? },
?????????? CSI-ReportConfig {
???????????? reportConfigId 2,
???????????? resourcesForChannelMeasurement 1,
???????????? reportQuantity ssb_Index_RSRP : NULL,
???????????? timeRestrictionForChannelMeasurements configured,
???????????? timeRestrictionForInterferenceMeasurements configured,
???????????? groupBasedBeamReporting disabled : {
?????????????? nrofReportedRS n4
???????????? },
???????????? subbandSize value1
?????????? }        

Second step. Link resourcesForChannelMeasurement # in the found CSI-ReportConfig in the first step to csi-ResourceConfigId # in the csi-ResourceConfigToAddModList. In our example the # is 0.

csi-ResourceConfigToAddModList {
????????????????? CSI-ResourceConfig {
??????????????????? csi-ResourceConfigId 0,
??????????????????? csi-RS-ResourceSetList nzp_CSI_RS_SSB : {
????????????????????? nzp-CSI-RS-ResourceSetList {
??????????????????????? NZP-CSI-RS-ResourceSetId 13
????????????????????? }
??????????????????? },
??????????????????? bwp-Id 0,
??????????????????? resourceType aperiodic
????????????????? },
????????????????? CSI-ResourceConfig {
??????????????????? csi-ResourceConfigId 1,
??????????????????? csi-RS-ResourceSetList nzp_CSI_RS_SSB : {
????????????????????? csi-SSB-ResourceSetList {
??????????????????????? CSI-SSB-ResourceSetId 0
????????????????????? }
??????????????????? },
??????????????????? bwp-Id 0,
??????????????????? resourceType aperiodic
????????? ????????}        

Supplementarily you can also link resourcesForChannelMeasurement # in the found CSI-ReportConfig corresponding to ssb_Index_RSRP reporting in the first step to csi-ResourceConfigId # in the csi-ResourceConfigToAddModList. Though this is not necessary, for the number of SSB beams can be easier derived in more straightforward way already described above. Either way, in our example the # is 1.

Third step. Link NZP-CSI-RS-ResourceSetId # in the found CSI-ResourceConfig in the second step to nzp-CSI-ResourceSetId # in the nzp-CSI-RS-ResourceSetToAddModList. In our example the # is 13 for narrow traffic beams and 0 for wide SSB beams.

NZP-CSI-RS-ResourceSet {
??????????????????? nzp-CSI-ResourceSetId 13,
??????????????????? nzp-CSI-RS-Resources {
????????????????????? NZP-CSI-RS-ResourceId 24,
????????????????????? NZP-CSI-RS-ResourceId 25,
????????????????????? NZP-CSI-RS-ResourceId 26,
????????????????????? NZP-CSI-RS-ResourceId 27,
????????????????????? NZP-CSI-RS-ResourceId 28,
??????????????? ??????NZP-CSI-RS-ResourceId 29
??????????????????? },
??????????????????? repetition off,
??????????????????? aperiodicTriggeringOffset 4
????????????????? }

csi-SSB-ResourceSetToAddModList {
????????????????? CSI-SSB-ResourceSet {
??????????????????? csi-SSB-ResourceSetId 0,
??????????????????? csi-SSB-ResourceList {
????????????????????? SSB-Index 4,
????????????????????? SSB-Index 5,
????????????????????? SSB-Index 10,
????????????????????? SSB-Index 11,
????????????????????? SSB-Index 12,
????????????????????? SSB-Index 13,
????????????????????? SSB-Index 20,
????????????????????? SSB-Index 21,
????????????????????? SSB-Index 26,
????????????????????? SSB-Index 27,
????????????????????? SSB-Index 28,
????????????????????? SSB-Index 29
??????????????????? }
????????????????? }
??????????????? }        

And now you can finally see that the UE is supposed to measure six CSI reference signals for CRI reporting purposes - their IDs being 24, 25, 26, 27, 28, and 29. That is the answer to the question - there are 6 narrow traffic beams per each wide SSB beam in the cell! Voila!

Please note, even though a pre-defined narrow traffic beam is mainly associated with, or belongs to, a certain one wide SSB beam, there is no absolutely exclusive association. A traffic beam on the boundary of two wide SSB beams may be associated with either of them, i.e. the gNodeB may ask UE to measure and report the same pre-defined narrow beam as one of 6 belonging to an SSB beam X and as one of six belonging to a neighbouring SSB Y, when it makes sense. That is why in fact the total number of the pre-defined narrow traffic beams in a cell may be lower than number of wide SSB beams multiplied by the number of nzp-CSI-RS-Resources transmitted for CRI measurement and reporting. In our example, the total number of traffic beams may or may not be exactly 12x6=72, it may be a bit lower than 72, this is up to the vendor's implementation.

Please note, with analog beamforming, only a single beam can be active at any point in time, so the CSI reference signals 24..29 in our example cannot be frequency or code multiplexed because they correspond to different predefined beams, hence only time multiplexing is allowed. For example, the CSI measurement configuration stipulates these six nzp-CSI-RS-Resource’s to have the following properties:

NZP-CSI-RS-Resource {
?????????????????? nzp-CSI-RS-ResourceId [24,25,26,27,28,29],
?????????????????? resourceMapping {
???????????????????? frequencyDomainAllocation row1 : '0010'B,
???????????????????? nrofPorts p1,
???????????????????? firstOFDMSymbolInTimeDomain [8,9,10,11,12,13],
???????????????????? cdm-Type noCDM,
???????????????????? density three : NULL,
???????????????????? freqBand {
?????????????????????? startingRB 0,
?????????????????????? nrofRBs 68
???????????????????? }
?????????????????? },
?????????????????? powerControlOffset 0,
?????????????????? scramblingID 315
???????????????? },        

For simplicity nzp-CSI-RS-ResourceId are listed as an array [24,25,26,27,28,29] in the example above, so are firstOFDMSymbolInTimeDomain listed as an array [8,9,10,11,12,13]. In the RRC Reconfiguration message they come as six separate NZP-CSI-RS-Resource elements of course.

The figure depicts the time and frequency domain allocation of these six CSI-RS in one physical resource block:

As you can see, at any point in time, i.e. at any symbol, only one CSI-RS is transmitted because all the PRBs during this symbol are transmitted in one and the same direction, i.e. in the direction of one and the same narrow traffic beam.

Want to dive deeper and see how and what these CSI-RS are used for? Check out 5G NR Aperiodic CSI Reporting for Beam Refinement.