RA‑RNTI is a temporary identifier used in 5G NR during the Random Access Procedure.
It uniquely represents a UE’s PRACH transmission occasion (defined by time index t_id and frequency index f_id), allowing the gNB to identify which UE sent the RA preamble.

Once calculated using the PRACH occasion, the gNB uses this RA‑RNTI to send the Random Access Response (RAR) to the correct UE.

• Qm/R selection: Choose the MCS table and index; Qm and target code rate R come from TS 38.214 §5.1.3.1 (Tables 1–3).
• RE accounting: For an allocation of Nsymb,sh symbols, the usable RE/PRB is N’RE = 12·Nsymb,sh − NDMRS − Noh, capped to 156 RE/PRB.
• TBS determination: Form Ninfo = NRE × R × Qm × ν × tbScaling, then apply the ≤ 3824 / > 3824 procedures in TS 38.214 §5.1.3.2. (This calculator uses the common 6‑bit quantization for small TBS; on request, I can switch to a spec‑exact discrete set.)

A Link‑Budget in 5G NR is a complete, end‑to‑end accounting of all gains and losses a radio signal experiences as it travels from the transmitter (gNB/UE) to the receiver (UE/gNB).

It answers two core engineering questions:

1. Will the received signal be strong enough to meet the required SNR for decoding?
2. What is the maximum coverage distance for a given transmit power, frequency, bandwidth, and environment?

Link‑budget is essential for:

• Cell planning & coverage prediction
• Network optimization
• gNB/UE sensitivity assessment
• Propagation model comparison
• Determining downlink vs uplink imbalance

Why Link‑Budget Matters in 5G NR

5G uses higher frequencies (FR1 up to 7.125 GHz, FR2 up to 52.6 GHz), massive MIMO antennas, beamforming, and wide bandwidths — all of which impact signal strength.

Higher frequencies → higher free‑space path loss
Wider bandwidth → higher thermal noise
Beamforming → higher antenna gain
NR numerology & MIMO → different SNR and performance targets

This makes link‑budget more important in NR compared to LTE.

Core Components of a 5G NR Link‑Budget

A link‑budget is normally expressed as:

Where:

• Ptx → Transmit power (dBm)
• Gtx / Grx → Antenna gains (dBi)
• Ltx / Lrx → Feeder, cable, and connector losses (dB)
• PL → Path loss (free‑space + environmental losses)

1. Path Loss (PL)

For a first‑order link‑budget, free‑space path loss (FSPL) from ITU‑R P.525 is used.
FSPL formula (GHz, km form):

This is directly from the ITU free-space attenuation model.

Engineers then add more losses:

• Penetration loss (indoor, vehicles)
• Body loss
• Shadowing
• Clutter / foliage loss
• Rain attenuation (especially mmWave)

2. Noise Floor (kTB)

Every receiver has thermal noise based on Boltzmann’s constant (k), temperature (T), and bandwidth (B):

The −174 dBm/Hz value at 290 K is a standard industry reference.

Noise floor increases with bandwidth — which is very important for 5G NR because NR supports up to 400 MHz in FR2.

3. Receiver Noise Figure (NF)

Noise Figure quantifies how much noise the receiver adds on top of thermal noise.

Lower NF → more sensitive receiver.

4. Required SNR (SNR_req)

To decode NR channels (PBCH, PDCCH, PDSCH), the UE or gNB needs a minimum SNR that depends on:

• Modulation order (QPSK/16QAM/64QAM/256QAM)
• Coding rate
• MIMO layers
• Channel conditions

Receiver sensitivity is computed as:

5. Link Margin

Once you compute received power (Prx) and sensitivity (Psens):

• Positive margin → Link is healthy
• Zero margin → Borderline coverage
• Negative margin → Out of coverage

DL vs UL Link‑Budget (Important in 5G)

In 5G NR, uplink is almost always weaker than downlink because:

• UE transmit power is low (23–26 dBm)
• gNB antenna arrays provide high DL gain
• UL beamforming at UE is limited

Therefore UL usually defines:

• Cell edge coverage
• Uplink-limited throughput

This is why UL link‑budget is considered the limiting path in NR planning.

Example (n78, 3.5 GHz)

• gNB EIRP: 61 dBm
• UE gain: 0 dBi
• Distance: 1 km
• BW: 20 MHz
• NF: 7 dB
• Required SNR: 5 dB

FSPL ≈ 103.4 dB (from ITU P.525)

Noise floor (20 MHz) ≈ −101 dBm (from kTB)

Sensitivity = −101 + 7 + 5 = −89 dBm
Prx = 61 − 103.4 = −42.4 dBm
Margin = 46.6 dB (very strong link)

Summary (Easy‑to‑Remember)

5G NR uses two separate numbering systems to identify frequencies:

• NR‑ARFCN → identifies carrier center frequencies (used for channels like PDSCH, PUSCH, SS/PBCH reference points, etc.)
• GSCN → identifies Synchronization Signal Block (SSB) frequencies (used for initial cell search and synchronization)

Although both map to frequencies, they serve different purposes, have different step sizes, and follow different equations.

1. NR‑ARFCN (Absolute Radio Frequency Channel Number)

NR‑ARFCN uniquely maps any RF channel frequency in the range 0–100 GHz.
The mapping is defined in 3GPP TS 38.104 §5.4.2.1.

 Purpose

• Identifies carrier center frequency
• Used in RF channel configuration, RRC signaling
• Used for Point A, BWP, PRB alignment, and scheduling
• Applies to FR1 and FR2

 Mapping Formula

(from 3GPP TS 38.104 Table 5.4.2.1‑1)

Depending on the frequency range:

(A) 0 – 3000 MHz

• ΔFGlobal = 5 kHz
• FREF-Offs = 0
• NREF-Offs = 0

(B) 3000 – 24250 MHz

• ΔFGlobal = 15 kHz
• FREF-Offs = 3000
• NREF-Offs = 600000

(C) 24250 – 100000 MHz

• ΔFGlobal = 60 kHz
• FREF-Offs = 24250.08
• NREF-Offs = 2016667

 Key Characteristics

• Very fine resolution (5 kHz / 15 kHz / 60 kHz)
• Covers all NR frequencies (usable for carriers, SSB, etc.)
• Used by both UE and gNB for tuning receivers/transmitters
• Exact alignment needed for spectrum planning and CA

2. GSCN (Global Synchronization Channel Number)

GSCN identifies where SSBs (PSS+SSS+PBCH) can be transmitted.
All SSBs must lie on a global synchronization raster defined in 3GPP TS 38.104 §5.4.3.

 Purpose

• Identifies the SSB center frequency, not carrier center
• Used for UE initial synchronization
• Reduces search complexity → UE searches only these discrete frequencies
• Defined differently for FR1 sub‑3 GHz, FR1 ≥3 GHz, and FR2

3. GSCN Frequency Mapping Rules

Mapping depends on the frequency region (above 3 MHz raster):

 (A) 0 – 3000 MHz region

M ∈ {1,3,5} ― small steps around 50 kHz

GSCN range: 2 – 7498

 (B) 3000 – 24250 MHz (FR1 mid-band)

GSCN range: 7499 – 22255

 (C) 24250 – 100000 MHz (FR2 mmWave)

GSCN range: 22256 – 26639

4. Summary Comparison Table

5. Why 5G Needs Both?

NR‑ARFCN handles everything

• Choosing carrier bandwidth
• Defining scheduling grids
• Setting PointA
• Calculating PRB boundaries
• Required for uplink & downlink channels

GSCN optimizes initial access

• UE doesn’t know bandwidth or numerology
• So it scans only pre‑defined SSB frequencies
• Much faster synchronization
• Reduces battery drain
• Ensures consistent SSB placement across bands

The GSCN raster is a coarse global marker, while
NR‑ARFCN is a fine-granularity universal channel marker.

6. Simple Example: n78 (3300–3800 MHz)

• In this range, SSB frequencies use 1.44 MHz steps
• Example from 3GPP-derived calculators:
  • GSCN = 7725 → f = 3325.44 MHz
• But the carrier center frequency will use ARFCN:
  • f = 3645.12 MHz → NR‑ARFCN = 643008 (15 kHz raster)

So SSB may not lie at the carrier center, and GSCN ≠ ARFCN.

This section explains the theory, assumptions, 3GPP references, formulas and logic used inside the 5G NR Throughput Calculator.

1. What Determines 5G NR Throughput?

The throughput in 5G NR fundamentally depends on:

• Allocated PRBs (N_PRB)
• Modulation Order (Qm)
• Coding Rate (R)
• Number of Layers (ν)
• Resource Elements (REs) per PRB
• Slots per second (depends on numerology μ)
• DL Duty Cycle (TDD only)
• Number of Component Carriers (CA)
• Overheads: DM‑RS, PDCCH, CSI‑RS, SSB etc.

These relationships come from 3GPP:

• MCS Tables → Qm, R come from 3GPP TS 38.214 §5.1.3.1
• TBS / RE calculation → Defined in 3GPP TS 38.214 (TBS calculation)
• Slot duration & slots/sec → Defined by NR numerology in 3GPP TS 38.211 (frame/slot structure)
• Peak throughput formula → Referenced in 3GPP TS 38.306 (UE capability)

2. NR Numerology (μ) → Slots per Second

5G NR uses flexible numerology μ, where each step doubles the subcarrier spacing and halves slot duration.

According to 3GPP NR numerology rules:

• Slot duration = 1 ms / 2^μ
• Slots per 10 ms frame = 10 × 2^μ
• Slots per second = 1000 × 2^μ

Reference: 14 symbols/slot for Normal CP and slot duration scaling appear in 3GPP numerology descriptions.

Used in calculator formula:

SlotsPerSecond = 1000 × 2^μ

3. MCS → Modulation Order (Qm) + Code Rate (R)

The calculator implements MCS Tables 1, 2, and 3 from:
3GPP TS 38.214, Table 5.1.3.1‑1, 5.1.3.1‑2, 5.1.3.1‑3.

Each entry gives:

• Qm: bits per symbol → (QPSK=2, 16QAM=4, 64QAM=6, 256QAM=8)
• R: Target code rate = (value / 1024)

Example (from Table 1):
MCS 18 → Qm = 6, R = 466/1024

The plugin loads these values exactly and uses them in throughput formulas.

4. Resource Elements (RE) per PRB

Each PRB has 12 subcarriers × (# data symbols).

Since every slot has 14 OFDM symbols (Normal CP) (3GPP NR numerology):

N_RE' = 12 × (DataSymbolsPerSlot)

But DM‑RS and overhead must be removed. Using 38.214 logic:

N_RE = min(156, N_RE' – DMRS – Overhead)

The calculator uses the cap 156 RE/PRB, documented in open TBS calculations based on 3GPP rules.

5. Information Bits (Ninfo) and TBS Calculation (TS 38.214)

The transport block size (TBS) is based on the total number of REs across all PRBs:

N_RE_total = N_RE × N_PRB

Information bits:

Ninfo = N_RE_total × Qm × R × ν

The TBS algorithm in 3GPP TS 38.214 splits into two cases depending on Ninfo ≤ 3824 or > 3824. The calculator uses the standard engineering rounding:

TBS = 6 × floor(Ninfo / 6)

This rounding to 6‑bit multiples is also described in TBS computation workflows.

6. TBS-Based Throughput Formula (Per CC)

Once TBS/slot is known, the reachable throughput for one component carrier is:

Throughput_per_CC (bps) = TBS × SlotsPerSecond × DL_DutyCycle

DL duty cycle is applied only for TDD mode. Duty cycle logic comes from standard understanding of TDD dynamic DL/UL allocation.

Output shown in Mbps:

Throughput_Mbps = (TBS × SlotsPerSecond × DL_DutyCycle) / 1e6

7. Peak Throughput Formula (38.306‑Style)

3GPP TS 38.306 defines a UE maximum data rate depending on:

• PRBs allocated
• 12 subcarriers per PRB
• Qm
• R (often Rmax = 948/1024 at highest MCS)
• ν layers
• symbols/slot
• slots per second
• overhead factor

Engineers often summarize the relationship as:

BitsPerSlot = (PRB × (12 × DataSymbols) × Qm × R × ν × (1 – OH))

Then:

Throughput_per_CC_Mbps
= BitsPerSlot × SlotsPerSecond × DL_DutyCycle / 1e6

This aligns with the peak data-rate logic found in NR UE capability explanations.

8. Component Carrier Aggregation (CA)

Final throughput is the sum across all carriers:

Total_Throughput = Throughput_per_CC × J

Where J = number of aggregated carriers (up to 16 as per NR CA discussions).

 9. Summary Table of All Formulas Used

gNB‑ID & NCI: Concepts, Logic & Calculation Method (3GPP‑Aligned Notes)

These notes are aligned with:

• 3GPP TS 38.300 (NR Overall Architecture)
• 3GPP TS 38.413 (NGAP)
• 3GPP TS 38.331 (RRC)

You may cite those standards in your blog.

1. What is gNB‑ID?

The gNB-ID (gNodeB Identifier) uniquely identifies a gNB within a PLMN.

• It is a fixed-length binary identifier, where the length L is operator-configurable.
• Valid lengths according to 3GPP:

22 bits ≤ L ≤ 32 bits

The gNB‑ID is part of the NR Cell Identity (NCI) and therefore becomes part of NR‑CGI.

Purpose of gNB‑ID:

• Uniquely identify a gNB.
• Used in NGAP messages between gNB and 5GC.
• Part of NR‑CGI → used by UE during measurements and handovers.

2. What is NR Cell Identity (NCI)?

The NCI (NR Cell ID) is a 36‑bit globally unique cell identity.

NCI = 36 bits always, fixed by 3GPP.

The NCI is composed as:

[gNB-ID (L bits)] || [Cell ID (36 − L bits)]

Where:

• L = gNB‑ID length (22 to 32)
• Remaining bits = Cell ID

3. Why is NCI always 36 bits?

3GPP standardized 36 bits so that:

• The cell identity fits into RRC, NGAP, and OAM messages uniformly.
• Large deployments (dense NR networks) can allocate thousands of cells per gNB.

NCI Bit Structure:

Bit 35 -------------------------------- Bit 0
[ gNB-ID (L bits) | Local Cell ID (36-L bits) ]

Where Bit 35 is MSB (Most Significant Bit).

4. How many cells can a single gNB have?

Since the Cell ID portion = (36 − L) bits:

Number of local cells = 2^(36 − L)

Examples:

5. Forward Calculation: (gNB‑ID + Cell ID → NCI)

This is simply bit concatenation.

Formula:

NCI = (gNB_ID << (36 − L)) | CELL_ID

Where:

• << = Left Shift
• | = Bitwise OR

Example:

If:

• L = 28 bits
• gNB‑ID = 51234
• Cell ID = 15

Then:

cell_bits = 36 − 28 = 8
NCI = (51234 << 8) | 15

The shift moves the gNB‑ID into the upper 28 bits.
OR-ing places the Cell ID in the lower bits.

6. Reverse Calculation: (NCI → gNB‑ID + Cell ID)

This is the inverse of concatenation.

Formulas:

gNB_ID = NCI >> (36 − L)
CELL_ID = NCI & (2^(36 − L) − 1)

Where:

• >> = Right Shift
• & = Bitwise AND

Explanation:

1. Right shift drops lower bits → gives gNB‑ID.
2. Masking extracts only the lower (36 − L) bits → gives Cell ID.

7. Why shifting & masking works?

Because binary concatenation works as:

A || B  ===  (A << length(B)) | B

So the reverse operations naturally retrieve:

• Upper bits → A (gNB-ID)
• Lower bits → B (Cell ID)

This method is 100% bit-accurate and matches how signaling messages pack the identifiers.

8. Where are these identifiers used in 3GPP?

 RRC (TS 38.331)

• ServingCellConfigCommon includes NR‑CGI.
• UE uses NR‑CGI for measurements and reporting (e.g., MeasResult).

 NGAP (TS 38.413)

• NCI appears in messages like:
  • NG Setup
  • UE Context Setup Request
  • Handover Request

 OAM / O-RAN Management

• NCI is logged for:
  • Performance metrics
  • Fault logs
  • PCI/RSRP Coverage analysis

9. Example Bit-Level Construction

Let’s assume:

• gNB‑ID = 0xC85A → binary: 1100100001011010 (16 bits, but suppose padded to 28 bits)
• L = 28
• Cell ID = 0x0F (8 bits)

Final 36-bit NCI:

[ gNB-ID (28 bits) ][ Cell ID (8 bits) ]

Binary example:

1100100001011010 00000000 00001111

Hex packed:

0xC85A00F

Your plugin will output the exact decimal and hexadecimal form.

10. Why flexible gNB-ID length (22–32 bits)?

Operators need:

• Freedom to plan numbering for thousands of sites.
• Support for hierarchical cell identity structures.
• Efficient NMS/OAM identity mapping.

If an operator has:

• Few gNBs → larger Cell ID bits.
• Many gNBs → smaller Cell ID bits.

This flexibility is crucial for large nationwide deployments.

11. Summary (Perfect for blog conclusion)