Radio Frame, Subframe, Slot & Symbol in 5G NR

1. Why the Frame Structure Is Built This Way

LTE fixed one subcarrier spacing at 15 kHz and built everything on top of it. NR had to cover a 600 MHz IoT carrier and a 400 MHz millimetre-wave carrier with the same physical layer, and those two have irreconcilable requirements: the low band needs long symbols to survive multipath, the high band needs short symbols to survive phase noise and Doppler. The resolution was to make subcarrier spacing a parameter — a single exponent µ — and then to hold two things constant so that the parameter does not tear the system apart.

• The 10 ms radio frame and the 1 ms subframe never change. Whatever µ is, a subframe is 1 ms and a frame is ten of them. Numerology subdivides the subframe; it never touches the frame.
• A resource block is always 12 subcarriers. Its width in Hz scales with µ, but its width in subcarriers does not, so every allocation formula, every DCI field and every bitmap in the specification can be written in RBs without knowing µ.

Everything else — slot duration, symbol duration, cyclic prefix length, how many RBs fit in a carrier, how many slots exist per frame — follows mechanically from µ. That is why the first question to ask of any timestamp, slot number or PRB index in a log is which numerology it was counted in. A "slot 17" means 8.5 ms into the frame at 30 kHz and 2.125 ms at 120 kHz, and nothing in the number itself tells you which.

Table 1. The frame structure is not a topic in itself so much as the coordinate system every other topic is written in.

2. Time Units: T_c, T_s and the Constant κ

The specification does not define durations in seconds. It defines two time units and expresses everything as an integer multiple of one of them TS 38.211 cl. 4.1. This matters because it is why cyclic prefix lengths are the odd-looking integers they are, and why the timing advance granularity is what it is.

T_c = 1 / (Df_max * N_f)          Df_max = 480 000 Hz,  N_f = 4096
    = 1 / 1 966 080 000 s
    ~ 0.509 ns                    the NR basic time unit

T_s = 1 / (Df_ref * N_f,ref)      Df_ref = 15 000 Hz,  N_f,ref = 2048
    = 1 / 30 720 000 s
    ~ 32.552 ns                   the LTE basic time unit, kept for reference

kappa = T_s / T_c = 64            the constant that appears in every CP formula

Table 2. The four numbers behind every duration in NR. Note that T_c is defined from the largest numerology, so it is fine enough to express any symbol boundary at any µ as an integer.

The clearest place these units surface in practice is the timing advance command, converted with N_TA = T_A · 16 · 64 / 2^µ in units of T_c — where the 16 · 64 is 16 · κ, i.e. sixteen LTE samples. The step size therefore halves every time µ increments: 0.52 µs at 15 kHz, 0.26 µs at 30 kHz, 0.13 µs at 60 kHz. See the companion 04 Timing Advance document.

3. Frames, Subframes, Half-Frames and the SFN

A radio frame is 10 ms and contains ten 1 ms subframes, numbered 0 to 9. Frames are numbered by the System Frame Number, a 10-bit counter that runs 0..1023 and then wraps. Each frame is also divided into two half-frames of five subframes: half-frame 0 is subframes 0–4, half-frame 1 is subframes 5–9. The half-frame is not decoration — SSB burst sets are defined to fit inside one, and which one a given burst occupies is signalled by a single bit in the PBCH payload.

Table 3. The time hierarchy and where each level's index actually comes from. Only the frame and half-frame numbers are transmitted; everything finer is counted.

4. Numerology µ: the One Exponent That Scales Everything

The subcarrier spacing is SCS = 15 · 2^µ kHz. Everything else in the time domain scales as 2^-µ and everything in the frequency domain as 2^µ. There is no independent parameter: pick µ and the rest is determined TS 38.211 Table 4.2-1.

Table 4. The full numerology table. µ = 5 and 6 were added in Rel-17 for the 52.6–71 GHz range; µ = 4 has always been SSB-only. Extended CP exists at 60 kHz and nowhere else.

The trade being made is the classic OFDM one. Doubling the SCS halves the useful symbol duration T_u = 1/Δf, which halves the delay spread the cyclic prefix can absorb, and doubles the tolerance to Doppler shift and oscillator phase noise. At 3.5 GHz with a few microseconds of delay spread, 30 kHz is comfortable. At 28 GHz the phase noise makes 15 kHz unusable and the short propagation paths make the shorter CP harmless, so 120 kHz is the natural choice.

µ = 4 deserves a note of its own. It appears in the numerology table but is not a data numerology — it exists so that an FR2 cell can pack 64 SSB candidate positions into a 5 ms half-frame while its PDSCH runs at 120 kHz. A UE will therefore legitimately report a 240 kHz SSB measurement on a carrier whose active BWP is 120 kHz, and that is not an inconsistency in the log.

5. Symbols and Cyclic Prefix: Where the Extra 16κ Goes

Each OFDM symbol consists of a useful part of duration T_u = 1/Δf preceded by a cyclic prefix — a copy of the end of the useful part, prepended to the front. The CP absorbs the multipath echoes of the previous symbol, so as long as the delay spread is shorter than the CP there is no inter-symbol interference and the channel stays diagonal in the frequency domain. The CP length is TS 38.211 cl. 5.3.1:

Normal CP:      N_CP,l = 144 * kappa * 2^-mu  +  16 * kappa   if l = 0 or l = 7*2^mu
                N_CP,l = 144 * kappa * 2^-mu                  otherwise

Extended CP:    N_CP,l = 512 * kappa * 2^-mu                  for every l

  l       is the symbol index within the SUBFRAME, 0 .. 14*2^mu - 1
  kappa   = 64
  lengths are in units of T_c

The two index values that get the extra 16·κ — l = 0 and l = 7·2^µ — are exactly the symbols that start the two 0.5 ms halves of the subframe. So every 1 ms subframe contains exactly two long-CP symbols, at 0 ms and 0.5 ms, whatever µ is. At 30 kHz that is the first symbol of every slot; at 60 kHz the first symbol of every second slot; at 120 kHz of every fourth.

Table 5. Symbol and CP durations, computed from the clause 5.3.1 formulas. Extended CP needs no top-up because 12 symbols × (2048+512)·κ·2^-µ already fills the subframe exactly.

The CP length is also the cell-size limit for anything that is not timing-advanced. PRACH gets its own, much longer CP precisely because the preamble is sent before any timing advance exists — see the companion 03 Random Access document, §6.1, where the preamble format's CP is what sets the maximum cell radius.

6. Resource Elements and Resource Blocks: CRB, PRB, VRB

A resource element is one subcarrier in one OFDM symbol, identified by the pair (k, l). It is the smallest addressable unit and carries one modulation symbol. A resource block is 12 consecutive subcarriers in the frequency domain TS 38.211 cl. 4.4.4 — note that the definition says nothing about time. An RB is a frequency-domain object; when people say "an RB" and mean 12 subcarriers across 14 symbols they mean an RB for the duration of a slot, which is 168 resource elements.

NR then defines three numbering schemes over resource blocks, and mixing them up is a genuine source of misread logs:

Table 6. The three RB numberings. A PRB index in a log is meaningless without the BWP it belongs to, and a CRB index is meaningless without the SCS its grid was drawn at.

The ceiling on all three is maxNrofPhysicalResourceBlocks = 275 per numerology, so a BWP is at most 275 PRBs and PRB indices never exceed 274. A "PRB" index above that in a log is a CRB index, a subcarrier index, or a decoder bug.

7. Point A, offsetToCarrier and the Common Resource Block Grid

Point A is the frequency-domain origin of the whole cell. It is not required to be inside the carrier, it is not the carrier centre, and it is not where anything is transmitted. It is simply the agreed zero from which every CRB grid is counted, so that the network and the UE can talk about absolute frequency positions without either of them having to know the other's bandwidth configuration.

absoluteFrequencyPointA

offsetToPointA

offsetToCarrier

SCS-SpecificCarrier

carrierBandwidth

SCS-SpecificCarrier

Table 7. Everything that positions the grid. offsetToPointA and k_SSB together are what let a UE bootstrap the entire frequency coordinate system from an SSB alone.

The two-step definition of point A is deliberate. Before SIB1, a UE knows only where the SSB is, because it found it by searching the synchronisation raster. offsetToPointA in SIB1 and k_SSB in the MIB let it work downward from the SSB to point A, and from there it can build the CRB grid and interpret every frequency-domain field in every subsequent message. Get either value wrong in configuration and the symptom is characteristic: the MIB decodes, CORESET#0 is found — it is defined relative to the SSB, not to point A — and then SIB1 or the initial BWP is in the wrong place. See the companion 18 MIB and SIB1 IEs document.

8. Carrier Bandwidth in PRBs: FR1 and FR2

How many RBs fit into a channel bandwidth is not calculated by the UE — it is tabulated per bandwidth and per SCS as the transmission bandwidth configuration N_RB TS 38.101-1 Table 5.3.2-1 and TS 38.101-2 Table 5.3.2-1, with the leftover spectrum becoming guard band. The numbers are what they are because the guard band has to satisfy the spectrum emission mask, not because of any clean formula.

Table 8. FR1 transmission bandwidth configuration N_RB. A dash means the combination is not defined — notably 15 kHz stops at 50 MHz, which is why a 100 MHz FR1 carrier is always 30 kHz or above.

Table 9. FR2-1 transmission bandwidth configuration N_RB. Rel-17 FR2-2 (52.6–71 GHz) adds 480 kHz and 960 kHz columns and channel bandwidths up to 2000 MHz.

Turned into a resource count, a 273-PRB carrier at 30 kHz carries 273 × 12 × 14 = 45 864 resource elements per slot, and there are 2 000 slots per second, so the raw grid is 91.7 million REs per second. Reference signals, control, synchronisation and guard consume a substantial fraction of that — commonly 15–25 % depending on DM-RS and CSI-RS density — before any user data is placed. When a throughput figure looks impossible, recompute the RE budget before suspecting the scheduler.

9. Bandwidth Parts

A bandwidth part is a contiguous set of PRBs on a carrier, with its own subcarrier spacing and cyclic prefix, within which a UE operates. It exists for two reasons that pull in the same direction: a UE that only has to receive 20 MHz of a 100 MHz carrier spends far less power in its RF and baseband, and a network that can give different UEs different BWPs can run several numerologies on one carrier without partitioning it statically.

9.1 What is configured, and what is active

• Up to four dedicated BWPs may be configured per serving cell per direction (maxNrofBWPs = 4), plus the initial BWP which always exists and carries bwp-Id 0. So bwp-Id ranges 0..4.
• Exactly one DL BWP and one UL BWP is active at any instant on a serving cell. In TDD they must have the same centre frequency and the same SCS; in FDD they are independent.
• The initial DL BWP is what a UE uses before it has dedicated configuration. Before SIB1 it is effectively CORESET#0's bandwidth and position; SIB1's initialDownlinkBWP then defines it explicitly for Msg2/Msg4 and SI reception.
• firstActiveDownlinkBWP-Id says which BWP to activate on applying a reconfiguration; defaultDownlinkBWP-Id says which to fall back to when bwp-InactivityTimer expires. If defaultDownlinkBWP-Id is absent, the fallback is the initial BWP.

9.2 locationAndBandwidth is a RIV, not a pair

locationAndBandwidth is a single INTEGER (0..37949) that encodes both the start RB and the length, using the resource indicator value formula from TS 38.214 cl. 5.1.2.2.2 evaluated with a fixed N_BWP^size = 275 regardless of the actual carrier width. This is why the numbers look arbitrary in a decoded configuration.

if (L_RBs - 1) <= floor(N / 2):
    RIV = N * (L_RBs - 1) + RB_start
else:
    RIV = N * (N - L_RBs + 1) + (N - 1 - RB_start)

  N        = 275 always, for locationAndBandwidth
  RB_start = start of the BWP, counted from the lowest usable PRB of the
             carrier at this BWP's SCS (i.e. from offsetToCarrier)
  L_RBs    = number of PRBs, 1 .. 275

9.3 Switching the active BWP

bwp-InactivityTimer

Table 10. The four ways an active BWP changes. Only the first is fast enough to be used per-burst; only the third happens without the network sending anything.

Table 11. BWP switch delay TS 38.133 Table 8.6.2-1. Which type applies is a UE capability. The UE is not required to transmit or receive anything during the delay, so a grant issued inside it is simply lost.

10. The SS/PBCH Block Inside the Grid

The SS/PBCH block is the only thing in NR whose position in the grid a UE must be able to find with no prior information at all. It therefore has a rigid, fully specified shape: four consecutive OFDM symbols by 240 contiguous subcarriers — 20 PRBs — with PSS, SSS and PBCH at fixed positions inside that rectangle TS 38.211 cl. 7.4.3.1.

Table 12. TS 38.211 Table 7.4.3.1-1, laid out by subcarrier range. In symbol 0 everything outside the PSS is set to zero; in symbol 2 only the two narrow guard regions are.

The PBCH DM-RS is interleaved with the PBCH data at a density of one RE in four, on subcarriers k = 4n + ν where ν = N_ID^cell mod 4. The cell identity therefore shifts the DM-RS comb, which is what lets a UE separate two overlapping SSBs from different cells. The DM-RS sequence itself is initialised from the three least-significant bits of the SSB index, so the beam identity is carried by the reference signal rather than by the payload.

systemFrameNumber

Table 13. The 32-bit PBCH payload. For L_max = 4 or 8 the SSB index fits entirely in the DM-RS sequence, so the three payload bits are used differently — one carries the k_SSB most-significant bit and the rest are reserved.

11. SSB Burst Sets, Candidate Positions and Periodicity

A cell transmits its SSBs as a burst set confined to the first or second 5 ms half-frame of a frame. Within that half-frame the specification defines a set of candidate positions — fixed first-symbol indices at which an SSB may start — and the cell transmits on some subset of them, one per beam. The candidate pattern depends on the SSB subcarrier spacing and the frequency range, and the five patterns are named Case A through Case E TS 38.213 cl. 4.1.

Table 14. SSB candidate position patterns. L_max — the maximum number of candidate positions in a half-frame — is 4 below 3 GHz, 8 from 3 to 7.125 GHz and 64 above 6 GHz, and it determines the length of the ssb-PositionsInBurst bitmap. Which case a band uses is fixed in TS 38.104 cl. 5.4.3.3.

The gaps in the Case D and Case E n sequences (no 4, 9, 14, 19 in Case D) are not arbitrary: they leave every fifth slot free so that the burst set does not consume the whole half-frame, and so that there is room for control and for the DL/UL switch in a TDD FR2 carrier.

ssb-periodicityServingCell

ssb-PositionsInBurst

ssb-SubcarrierSpacing

Table 15. SSB burst set configuration. ssb-PositionsInBurst is the field to check first when a UE reports fewer beams than the cell is believed to have.

12. GSCN and the Synchronisation Raster

A UE searching for a cell cannot try every frequency. NR therefore defines a coarse synchronisation raster of permitted SSB centre positions, each identified by a Global Synchronisation Channel Number TS 38.104 cl. 5.4.3. The raster is much sparser than the channel raster used for carrier centres, which is the whole point: fewer hypotheses to test.

Table 16. The three synchronisation raster regions. The M parameter exists only below 3 GHz, to give LTE-refarmed bands enough placement freedom; above 3 GHz the raster steps are chosen to be whole numbers of PRBs.

The raster step above 3 GHz being a whole number of PRBs is what keeps k_SSB small. Because 1.44 MHz = 4 × 360 kHz, an SSB placed on the raster is already nearly aligned to the 30 kHz CRB grid, so the residual misalignment k_SSB has to express is at most a few subcarriers. Below 3 GHz, where the 50 kHz M-offsets exist, the residual can be larger — which is why k_SSB is measured in 15 kHz units there and needs five bits rather than four.

13. TDD DL/UL Patterns and the Guard Period

Most NR deployments are TDD, so downlink and uplink share the frequency and are separated in time. Every OFDM symbol is therefore designated downlink (D), uplink (U) or flexible (F). The semi-static cell-wide designation comes from tdd-UL-DL-ConfigurationCommon in SIB1, which is where the phrase "TDD pattern" almost always refers to.

TDD-UL-DL-ConfigCommon ::= SEQUENCE {
    referenceSubcarrierSpacing   SubcarrierSpacing,
    pattern1                     TDD-UL-DL-Pattern,
    pattern2                     TDD-UL-DL-Pattern     OPTIONAL,
    ...
}

TDD-UL-DL-Pattern ::= SEQUENCE {
    dl-UL-TransmissionPeriodicity  ENUMERATED {ms0p5, ms0p625, ms1,
                                               ms1p25, ms2, ms2p5, ms5,
                                               ms10},
    nrofDownlinkSlots              INTEGER (0..maxNrofSlots),      -- 0..320
    nrofDownlinkSymbols            INTEGER (0..maxNrofSymbols-1),  -- 0..13
    nrofUplinkSlots                INTEGER (0..maxNrofSlots),
    nrofUplinkSymbols              INTEGER (0..maxNrofSymbols-1),
    ...,
    [[ dl-UL-TransmissionPeriodicity-v1530  ENUMERATED {ms3, ms4} OPTIONAL ]]
}

Listing 1. Abridged from TS 38.331. ... marks extension markers. ms3 and ms4 were added in Rel-15 late-drop as an extension, which is why they sit outside the original enumeration.

13.1 How the four counters divide a period

The encoding is positional and there is no bitmap. Within each period, counting in slots of referenceSubcarrierSpacing:

1. The first nrofDownlinkSlots slots are entirely downlink.

2. In the slot immediately after those, the first nrofDownlinkSymbols symbols are downlink.

3. The last nrofUplinkSlots slots are entirely uplink.

4. In the slot immediately before those, the last nrofUplinkSymbols symbols are uplink.

5. Everything left over — necessarily in the middle, and necessarily contiguous — is flexible. That leftover is the guard period.

DDDSU

DDDDDDDSUU

DSUUU

DDDSU

Table 17. Common patterns. The counters are the same numbers at FR1 and FR2 — what changes is what a slot is worth in microseconds, and therefore the cell radius the guard period allows.

14. Slot Format Indication: Who Wins

On top of the cell-wide semi-static pattern there are two further layers that can pin down flexible symbols: a UE-specific semi-static override, and a dynamic group-common indication. The precedence rules TS 38.213 cl. 11.1 are strict and asymmetric, and getting them the wrong way round is a standard source of confusion.

14.1 The three layers

Table 18. Precedence runs top to bottom and each layer may only act on what the layer above left flexible.

A slot format is an index into TS 38.213 Table 11.1.1-1, which enumerates the useful D/F/U arrangements of 14 symbols. Format 0 is all downlink, format 1 all uplink, format 2 all flexible; the remaining defined formats are the practical mixtures — leading downlink with a trailing gap, leading gap with trailing uplink, and so on. DCI 2_0 does not carry a format directly: it carries an index into a configured list of slotFormatCombinations, each of which is a sequence of formats covering the SFI monitoring periodicity, so one DCI can describe several slots at once.

Flexible symbols left flexible are not wasted — they are simply available. A UE will use a flexible symbol for whatever it is scheduled to do there: receive a PDSCH if a DCI says so, transmit a PUSCH if a grant says so, or nothing at all. The value of leaving symbols flexible is that the scheduler keeps the choice; the cost is that the UE must monitor for both possibilities and cannot micro-sleep through them.

15. Mini-Slots and Non-Slot-Based Scheduling

A transmission does not have to occupy a slot. NR defines two PDSCH time-domain mapping types, and the second one is what "mini-slot" informally means:

Table 19. PDSCH mapping types TS 38.214 cl. 5.1.2.1. PUSCH has the analogous split, with type B allowing lengths 1..14.

The cost of mini-slots is DM-RS overhead: a 2-symbol allocation still needs at least one DM-RS symbol, so half the allocation is reference signal. That is an acceptable price for a 4-symbol URLLC transmission and an unacceptable one for bulk data, which is exactly why both mapping types exist rather than one replacing the other. See the companion 08 Scheduling document for how the time-domain resource allocation tables encode (S, L) pairs.

16. Parameter Reference: ASN.1 and Ranges

ServingCellConfigCommonSIB ::= SEQUENCE {
    downlinkConfigCommon        DownlinkConfigCommonSIB,
    uplinkConfigCommon          UplinkConfigCommonSIB      OPTIONAL,
    ssb-PositionsInBurst SEQUENCE {
        inOneGroup                  BIT STRING (SIZE (8)),
        groupPresence               BIT STRING (SIZE (8))  OPTIONAL
    },
    ssb-PeriodicityServingCell  ENUMERATED {ms5, ms10, ms20, ms40,
                                            ms80, ms160},
    tdd-UL-DL-ConfigurationCommon  TDD-UL-DL-ConfigCommon  OPTIONAL,
    ss-PBCH-BlockPower          INTEGER (-60..50),
    ...
}

FrequencyInfoDL-SIB ::= SEQUENCE {
    frequencyBandList           MultiFrequencyBandListNR-SIB,
    offsetToPointA              INTEGER (0..2199),
    scs-SpecificCarrierList     SEQUENCE (SIZE (1..maxSCSs)) OF
                                    SCS-SpecificCarrier,
    ...
}

SCS-SpecificCarrier ::= SEQUENCE {
    offsetToCarrier             INTEGER (0..2199),
    subcarrierSpacing           SubcarrierSpacing,
    carrierBandwidth            INTEGER (1..maxNrofPhysicalResourceBlocks),
    ...                                       -- maxNrofPhysicalResourceBlocks = 275
}

BWP ::= SEQUENCE {
    locationAndBandwidth        INTEGER (0..37949),
    subcarrierSpacing           SubcarrierSpacing,
    cyclicPrefix                ENUMERATED {extended}      OPTIONAL
}

BWP-DownlinkDedicated ::= SEQUENCE {
    pdcch-Config                SetupRelease {PDCCH-Config}  OPTIONAL,
    pdsch-Config                SetupRelease {PDSCH-Config}  OPTIONAL,
    ...
}

-- inside ServingCellConfig:
--   downlinkBWP-ToAddModList  SEQUENCE (SIZE (1..maxNrofBWPs)) OF BWP-Downlink
--   firstActiveDownlinkBWP-Id BWP-Id                   -- BWP-Id ::= INTEGER (0..4)
--   defaultDownlinkBWP-Id     BWP-Id
--   bwp-InactivityTimer       ENUMERATED {ms2, ms3, ms4, ms5, ms6, ms8,
--                                         ms10, ms20, ms30, ms40, ms50,
--                                         ms60, ms80, ms100, ms200, ms300,
--                                         ms500, ms750, ms1280, ms1920,
--                                         ms2560, spare10 ... spare1}

Listing 2. Abridged from TS 38.331. Enumerations are quoted in full where they matter for reading a log and marked with ... where they are cut.

subcarrierSpacing

cyclicPrefix

offsetToPointA

offsetToCarrier

carrierBandwidth

locationAndBandwidth

bwp-Id

bwp-InactivityTimer

referenceSubcarrierSpacing

dl-UL-TransmissionPeriodicity

ss-PBCH-BlockPower

Table 20. Frame-structure parameters, their ranges, and what breaks when they are wrong. Typical values are what many vendors ship, not specification requirements.

ssb-periodicityServingCell

dl-UL-TransmissionPeriodicity

bwp-InactivityTimer

ra-ResponseWindow

Table 21. Periodicities and delays whose wall-clock value depends on the numerology. Every one of these is a slot count or a frame count somewhere in the specification, not a duration.

17. Failure Modes and Misconfigurations

Table 22. Frame-structure failures. Note how many of them are silent on the side that causes them — the frame structure is agreed by configuration, not negotiated, so a mismatch shows up as absence rather than as an error.

18. Illustrative Traces

18.1 Cell search: from SSB detection to a frame number

09:41:22.104  [PHY] SSB search, GSCN 7947 (3645.12 MHz), SCS 30 kHz, Case C
              PSS correlation peak    N_ID2 = 1     RSRP -88.4 dBm
              SSS decode              N_ID1 = 143
              -> N_ID_cell = 3 * 143 + 1 = 430
              DM-RS sequence -> i_SSB = 2           -- 3 LSBs of SSB index
              L_max = 8 (3-7.125 GHz) -> SSB index = i_SSB = 2
              first symbol of block   = 2 + 14*1 = 16  -> slot 1, symbol 2

09:41:22.107  [PHY] PBCH decode OK, 56 bits, Polar, E = 864
              payload (non-MIB bits)
                SFN LSBs (4) ......... 0b0110  = 6
                half-frame bit n_hf .. 0            -- first half-frame
                k_SSB MSB ............ 0
              MIB
                systemFrameNumber .... 0b010011 = 19    -- SFN MSBs
                subCarrierSpacingCommon  scs30or120
                ssb-SubcarrierOffset . 6
                dmrs-TypeA-Position .. pos2
                pdcch-ConfigSIB1
                  controlResourceSetZero  9
                  searchSpaceZero ....... 0
                cellBarred ........... notBarred
                intraFreqReselection . allowed

09:41:22.107  [PHY] SFN assembled = (19 << 4) | 6 = 310
              k_SSB = (0 << 4) | 6 = 6  -> 6 * 15 kHz = 90 kHz above the CRB grid
              frame boundary located; slot and symbol counting can begin

Listing 3. The SFN is assembled from two places and the SSB index from two places. Both splits exist so that PBCH can be re-encoded rarely and still carry fine timing.

18.2 The frame structure as SIB1 describes it

SIB1
 servingCellConfigCommon
  downlinkConfigCommon
   frequencyInfoDL
    offsetToPointA ................. 86         -- in 15 kHz RBs, FR1
    scs-SpecificCarrierList[0]
     offsetToCarrier ............... 0
     subcarrierSpacing ............. kHz30
     carrierBandwidth .............. 273        -- 100 MHz at 30 kHz
   initialDownlinkBWP
    genericParameters
     locationAndBandwidth .......... 12952      -- RIV: L=48, RB_start=27
     subcarrierSpacing ............. kHz30
    pdcch-ConfigCommon ............. (CORESET#0 + searchSpaceZero)
  uplinkConfigCommon
   frequencyInfoUL
    scs-SpecificCarrierList[0]
     offsetToCarrier ............... 0
     subcarrierSpacing ............. kHz30
     carrierBandwidth .............. 273
  ssb-PositionsInBurst
   inOneGroup .................... 0b10101010  -- 4 of 8 candidates used
  ssb-PeriodicityServingCell ...... ms20
  ss-PBCH-BlockPower .............. 18          -- dBm per RE
  tdd-UL-DL-ConfigurationCommon
   referenceSubcarrierSpacing ..... kHz30
   pattern1
    dl-UL-TransmissionPeriodicity . ms2p5
    nrofDownlinkSlots ............. 3
    nrofDownlinkSymbols ........... 10
    nrofUplinkSlots ............... 1
    nrofUplinkSymbols ............. 2

-- derived by the UE:
--   5 slots per period, 4 periods per frame, 20 slots per frame
--   slots 0,1,2 D | slot 3 = 10D + 2F + 2U | slot 4 U   (repeat x4)
--   SSB lowest RB = 86 / 2 = CRB 43 on the 30 kHz grid, so CRB 43..62
--   CORESET#0 (controlResourceSetZero 9) = 48 RB, offset 16 -> CRB 27..74
--   initial DL BWP = CRB 27 .. 74, i.e. the same 48 RB as CORESET#0
--   RIV check: 275 * (48-1) + 27 = 12925 + 27  ->  12952

Listing 4. Everything a UE needs in order to start counting slots and to know which of them it may transmit in. offsetToPointA is in 15 kHz RBs even though the carrier is 30 kHz — a standing source of off-by-two errors.

18.3 A BWP switch, done correctly

10:02:17.4405  [MAC] C-RNTI 0x4A11  active DL BWP = 1 (273 PRB)
10:02:17.4405  [MAC] no PDCCH for this UE since 10:02:17.3405
10:02:17.4405  [MAC] bwp-InactivityTimer (ms100) expired
               -> switch to defaultDownlinkBWP-Id = 2 (51 PRB from CRB 100)
               -> UE unavailable for 2 slots (type 1 delay, mu=1) = 1.0 ms

10:02:19.1200  [MAC] DL data arrival, 1.4 MB buffered
10:02:19.1205  [PHY-DL] DCI 1_1, C-RNTI 0x4A11, on BWP 2
                 bandwidthPartIndicator ...... 1        -- switch to BWP 1
                 freqDomainResourceAssignment  (interpreted on BWP 1)
                 timeDomainResourceAssignment  k0 = 2
10:02:19.1205  [MAC] BWP switch 2 -> 1 requested
               -> UE retunes; no Tx/Rx expected for 2 slots
10:02:19.1215  [PHY-DL] first PDSCH on BWP 1, 264 PRB, MCS 22
10:02:19.1225  [PHY-UL] HARQ-ACK received  -- switch completed cleanly

-- note: the DCI at .1205 both commanded the switch AND scheduled data.
-- k0 = 2 places the PDSCH exactly one switch delay after the DCI, which
-- is the minimum legal value here. k0 = 1 would have been lost.

Listing 5. A correct DCI-triggered switch. The scheduler's k0 has to be at least the BWP switch delay, and here it is exactly that.

18.4 A failure: uplink grant on a downlink symbol

11:37:02.0000  [RRC] tdd-UL-DL-ConfigurationCommon applied
                 referenceSubcarrierSpacing .. kHz15      -- (!) cell is 30 kHz
                 pattern1  ms2p5 / 3 DL slots / 10 DL sym / 2 UL sym / 1 UL slot

11:37:02.0000  [UE-MAC] reference SCS kHz15, active UL BWP SCS kHz30
                 period ms2p5 at 15 kHz = 2.5 slots -> non-integer
                 -> pattern cannot be expressed; configuration rejected
11:37:02.0010  [UE-RRC] RRCReconfigurationFailure, no cause IE
               -> UE reverts to the previous configuration

-- second, subtler variant of the same class of fault --

11:44:18.2500  [gNB-MAC] UL grant issued, C-RNTI 0x4A11
                 slot 3, symbols 8..13, 6 PRB
11:44:18.2500  [UE-MAC] slot 3 symbols 0..9 are semi-static DOWNLINK
                 grant overlaps 8 and 9 -> UL transmission not permitted
                 (TS 38.213 cl. 11.1: UE does not transmit in a symbol
                  configured as downlink)
11:44:18.2500  [UE-MAC] grant dropped, nothing transmitted
11:44:18.2600  [gNB-MAC] PUSCH decode failed, no energy detected
11:44:18.2600  [gNB-MAC] -> HARQ retransmission scheduled, same symbols
11:44:18.2700  [gNB-MAC] PUSCH decode failed, no energy detected
               ... repeats to maxHARQ-Tx ...

-- the gNB sees 'no energy', which reads as coverage. It is arithmetic:
-- nrofDownlinkSymbols = 10 means symbols 0..9 of slot 3 are DL, and the
-- earliest legal UL symbol in that slot is 12.

Listing 6. Two frame-structure faults with completely different signatures: one fails loudly at configuration time, the other silently as uplink that never arrives.

19. Release Deltas: Rel-15 to Rel-18

Table 23. Frame-structure changes by release. Feature presence should always be confirmed against the UE capability exchange — see the companion 26 UE Capability document.

20. Reading Frame Structure in Logs: A Checklist

1. Establish µ first, for each direction and each BWP. Every slot and symbol index in the log is relative to it. If the log prints a timestamp and a slot number, check that they agree: slot n starts at n × 1/(2^µ) ms into the frame.

2. Convert the SFN to a wall clock and check for a wrap. SFN wraps every 10.24 s. If you are comparing events across more than ten seconds, or across a node restart, the SFN alone is ambiguous.

3. Reconstruct the TDD pattern symbol by symbol from the four counters (§13). Write out the D/F/U string for one period. Almost every "unexplained uplink failure" resolves here.

4. Check `referenceSubcarrierSpacing` against every BWP's SCS. It must be no larger. A mismatch either fails at configuration time or silently shifts every boundary by a factor of two.

5. Compute the guard period in microseconds and convert it to kilometres. Compare against the largest timing advance you see in the cell. If UEs exist beyond the guard-period radius, their uplink cannot work and no amount of power will fix it.

6. Verify point A independently. From the SSB's GSCN, offsetToPointA and k_SSB, compute where CRB 0 must be, and check that CORESET#0 and the initial BWP land where the configuration says. MIB-decodes-but-SIB1-fails is the signature of getting this wrong.

7. Track the active BWP as a state variable over time. Note every DCI with a BWP indicator, every bwp-InactivityTimer expiry and every RACH trigger. A PRB index means nothing until you know which BWP was active when it was printed.

8. After any BWP switch, allow for the switch delay (§9.3) before expecting the UE to respond. A DTX gap exactly one switch delay long is not a radio event.

9. Cross-check the SSB burst. ssb-PositionsInBurst says how many beams the cell claims; the UE's measurement reports say how many it found. A persistent shortfall is either a beam that is not being transmitted or a measurement window that does not cover it — see the companion 21 Measurement Gaps and SMTC document.

10. When a symbol appears unused, enumerate the reasons in order: semi-static flexible and unscheduled; SFI marked it unused; a Rel-16 LBT failure on an unlicensed carrier; uplink cancellation by DCI 2_4; or the BWP switch delay. They look identical and have nothing in common.

21. Glossary

22. References

• 3GPP TS 38.211 — Physical channels and modulation. Clause 4.1 (basic time units T_c, T_s, κ), 4.2 (numerologies, Table 4.2-1), 4.3 (frames, subframes, slots, Tables 4.3.2-1 and 4.3.2-2), 4.4 (resource grid, CRB/PRB/VRB, point A), 5.3.1 (OFDM baseband generation and cyclic prefix lengths), 7.3.1.6 (VRB-to-PRB mapping), 7.4.3.1 (SS/PBCH block resource mapping, Table 7.4.3.1-1).
• 3GPP TS 38.213 — Physical layer procedures for control. Clause 4.1 (SSB candidate positions, Cases A–E, the 20 ms initial-access assumption), 11.1 (slot configuration, D/F/U determination, slot formats, Table 11.1.1-1), 12 (bandwidth part operation), 13 (CORESET#0 and searchSpaceZero, and the k_SSB no-SIB1 encoding).
• 3GPP TS 38.214 — Physical layer procedures for data. Clause 5.1.2.1 (PDSCH mapping types A and B), 5.1.2.2 (resource allocation, including the RIV formula used by locationAndBandwidth), 6.1.2 (the PUSCH equivalents).
• 3GPP TS 38.104 — Base station radio transmission and reception. Clause 5.4.2 (NR-ARFCN and the channel raster), 5.4.3 (the synchronisation raster and GSCN), 5.4.3.3 (which SSB case applies per band).
• 3GPP TS 38.101-1 / TS 38.101-2 — UE radio transmission and reception, Range 1 / Range 2. Clause 5.3.2 (transmission bandwidth configuration N_RB), 5.3.3 (minimum guard band).
• 3GPP TS 38.133 — Requirements for support of radio resource management. Clause 8.6.2 (bandwidth part switch delay, Table 8.6.2-1).
• 3GPP TS 38.331 — RRC protocol specification. ServingCellConfigCommon and ServingCellConfigCommonSIB, FrequencyInfoDL and FrequencyInfoDL-SIB, SCS-SpecificCarrier, BWP / BWP-Downlink / BWP-Uplink, BWP-Id, TDD-UL-DL-ConfigCommon and TDD-UL-DL-ConfigDedicated, MIB.
• 3GPP TS 38.300 — NR overall description. Clause 5.1 (physical layer overview), 5.3 (bandwidth parts), 6 (channel structure).

Companion documents in this set

• 03 Random Access — PRACH occasions are (s_id, t_id, f_id) triples indexed into this structure; the preamble format's CP is the same cell-radius argument as §5 and §13.
• 04 Timing Advance — N_TA is expressed in T_c and its step size scales with 2^-µ (§2).
• 05 HARQ / 08 Scheduling — k0, k1 and k2 are slot offsets in the numerology of the relevant BWP.
• 06 Channel Mapping — where PBCH, PDSCH, PDCCH, PUSCH and PUCCH sit in the grid this document defines.
• 11 DRX — on-durations and cycles interact with bwp-InactivityTimer (§9.3).
• 17 System Information / 18 MIB and SIB1 IEs — the source of offsetToPointA, k_SSB, CORESET#0 and tdd-UL-DL-ConfigurationCommon; §7, §10 and §13 all depend on them.
• 19 Paging — paging frames and occasions are SFN arithmetic (§3).
• 20 Measurements and Events / 21 Measurement Gaps and SMTC — SMTC windows are placed against the SSB burst set of §11.
• 22–25 Handover documents — target-cell SSB indices and SFN offsets are what makes a handover land in the right slot.
• 26 UE Capability — which numerologies, bandwidths, BWP switch delay type and SSB cases a given UE actually supports.