Modulation & MCS in 5G NR

Introduction

Modulation and the Modulation and Coding Scheme (MCS) are how NR matches the data rate of a transmission to the quality of the channel carrying it. Modulation, defined in TS 38.211 §5.1, maps coded bits onto complex I/Q symbols; the MCS index, defined through the tables in TS 38.214, is a compact 5-bit code that names both a modulation order and a target code rate at once. Together they are the output of link adaptation and the input to the transport-block-size calculation.

You meet them on every scheduled transmission. The gNB reads a UE's CQI feedback and HARQ history, picks an MCS index, and signals it in the scheduling DCI on PDCCH; the UE looks it up to recover the modulation and code rate it must use to demodulate and decode the PDSCH (or to transmit its PUSCH). The same index, retuned per slot, is what makes a 5G link speed up in good coverage and slow down at the cell edge.

It matters because this is the direct lever on user throughput and reliability. Choose too aggressive an MCS and the block fails, triggering HARQ retransmissions that lower effective rate; choose too conservative and you leave capacity on the table. Understanding how one index resolves into (modulation order, code rate) and then into a transport block size is the difference between reading a throughput number and knowing why it is what it is.

Why modulation and MCS are needed

The concrete problem is that one fixed modulation cannot serve a whole cell. A UE at the centre with 25 dB SINR could carry eight bits per symbol; a UE at the edge with 2 dB would drop every packet at that setting. Offering a graded ladder of modulation orders and code rates, and a compact index to select among them per transmission, lets the scheduler track each UE's instantaneous channel — extracting throughput where the SINR allows and staying decodable where it does not.

What modulation actually does

A modulation scheme maps a group of coded bits onto one complex symbol — a point in the I/Q plane. The number of bits per symbol is the modulation order Qm. Higher Qm packs more bits into each symbol, so you send more data in the same time-frequency resource — but the constellation points sit closer together, so the same amount of noise flips them into each other more easily. That is the whole tension of link adaptation in one sentence: bits-per-symbol versus distance-between-symbols.

It helps to separate two ideas that beginners often merge. Modulation order Qm is a physical-layer waveform property — how the constellation is drawn and how many bits map to one symbol. The MCS index is a scheduling concept — a compact code that names both a modulation order and a target code rate at once, so the gNB can convey the entire per-transmission rate decision in five bits of DCI. The rest of this page walks from the constellation up to that index and back down into the transport block size it produces.

The modulation ladder — Qm, bits and where each lives

Each rung buys you more bits per symbol at the cost of needing a cleaner channel. The SINR figures below are typical operating points, not spec thresholds — the actual switch points come from the CQI tables and the gNB's link-adaptation policy. Read the table top-to-bottom as "worse channel to better channel."

The uplink π/2-BPSK deserves a note. Ordinary BPSK places its two points on opposite ends of one axis; the π/2 variant rotates the constellation by 90 degrees on every alternate symbol. That rotation keeps the phase transitions from passing through the origin, which lowers the peak-to-average power ratio (PAPR) of the DFT-s-OFDM waveform. Lower PAPR lets the UE's power amplifier run closer to saturation without distortion, buying a few precious dB of link budget exactly where it is needed — a power-limited UE screaming from the cell edge.

Constellations and Gray mapping

A constellation is just the set of legal I/Q points. What matters for performance is not only how many points there are, but how bits are assigned to them. NR uses Gray mapping: adjacent constellation points differ by exactly one bit. Because noise most often nudges a received symbol into its nearest neighbour, a single-symbol error then corrupts only one bit rather than several — which is exactly what the channel decoder is best equipped to fix.

The mapping itself is defined bit by bit in TS 38.211 §5.1. For a square QAM constellation the coded bits split into two halves: the first half selects the in-phase (I) amplitude level and the second half selects the quadrature (Q) level, each half Gray-coded independently. That separability is why the picture is always a clean square grid and why the decoder can compute soft bits (log-likelihood ratios) per axis rather than searching all 2^Qm points. The constellation is also power-normalised — each order is scaled by a fixed factor so that the average symbol energy is the same regardless of Qm, which is precisely why higher orders squeeze the points closer together instead of spreading out.

The MCS index — one number, two meanings

The scheduler doesn't signal modulation and code rate separately. It signals a single 5-bit MCS index (values 0–31) in the DCI, and the UE looks it up in an MCS table to recover both the modulation order Qm and the target code rate R (listed in the table as R × 1024). That pair, together with the number of allocated resource elements and layers, determines the transport block size. One index, two meanings: modulation and coding, bundled.

Which table the UE consults is not fixed — it is selected by a combination of RRC configuration and the RNTI that scrambled the DCI. The precedence, from TS 38.214 §5.1.3.1, works like this:

• If PDSCH-Config carries mcs-Table set to qam256, and the DCI is a UE-specific format (for example 1_1) scrambled by C-RNTI, the UE uses the 256QAM table.
• If an MCS-C-RNTI is configured and scrambles the DCI, the UE uses the low-spectral-efficiency (qam64LowSE) table — this is the reliability/URLLC path.
• If mcs-Table is set to qam64LowSE for a search space, that low-SE table applies there.
• Otherwise the UE falls back to the baseline 64QAM table.

The uplink follows the same idea with its own IE, mcs-Table (and mcs-TableTransformPrecoder) inside PUSCH-Config, so a transform-precoded uplink can point at the table that contains π/2-BPSK. The takeaway is that the same 5-bit index means different things depending on which table is active — the index alone is meaningless without knowing the table selection rule.

The 38.214 MCS tables in detail

TS 38.214 §5.1.3.1 defines several tables for PDSCH, each an ordered ladder from rugged QPSK up to a maximum modulation order. The network tells the UE which one to use via RRC (mcs-Table) and/or the DCI/RNTI, as above.

Within any of these, low indices map to QPSK with a low code rate (maximum robustness), the middle to 16QAM and 64QAM, and the top to the highest modulation with code rates approaching ~0.93. Here is a representative excerpt of the baseline 64QAM table (Table 5.1.3.1-1). Spectral efficiency in the last column is simply Qm × R, and the "R × 1024" column is how the standard actually prints the target code rate.

Two structural features jump out. First, the table is monotonic in spectral efficiency across the data-carrying rows — walk up the index and bits/RE rises, which is exactly what makes it a clean adaptation ladder. Second, notice the overlap around indices 16–17: the network can deliver almost the same spectral efficiency either as high-rate 16QAM or low-rate 64QAM. That is deliberate — the lower-order option at a similar efficiency is more resilient to phase noise and estimation error, so the scheduler has a choice of "same speed, different robustness."

From (Qm, R) to transport block size

The MCS index is only half the throughput story; the resource allocation is the other half. TS 38.214 §5.1.3.2 turns the (Qm, R) pair plus the grant size into a concrete transport block size (TBS) in bits. The intuition is a two-step estimate then a quantisation.

Reading the pieces: N_RE is how many usable resource elements sit in one RB after you subtract DMRS and configured overhead; multiply by the number of allocated PRBs (n_PRB), by the code rate R, by the bits-per-symbol Qm, and by the number of layers ν, and you get a raw bit count N_info. The standard then quantises N_info to a valid TBS — snapping to a table of allowed sizes for small blocks, or to a byte- and LDPC-friendly value for large ones — so the transport block aligns with the channel-coding chain. This is why two different MCS indices on the same allocation can yield different transport block sizes, and why the same index on a bigger allocation scales the block up.

Two fixed pieces are worth pinning down. N_sc^RB = 12 subcarriers always — a resource block is 12 subcarriers wide by definition. The overhead term N_overhead is not free-form: it takes one of the RRC-configured values 0, 6, 12 or 18 from xOverhead in PDSCH-ServingCellConfig (defaulting to 0 when absent), and the per-RB count N_RE the standard actually uses is additionally capped at 156. That cap keeps the TBS calculation stable regardless of how many symbols the allocation spans.

The CQI cross-link and link adaptation

Modulation and MCS are not chosen in a vacuum — they are the output of link adaptation. The chain is: the UE measures CSI-RS, and reports a CQI that recommends the highest efficiency keeping block error rate at or below the target (typically 10%, or 0.001% for the URLLC CQI table). The gNB maps that CQI to a starting MCS, then refines with an outer-loop offset driven by real HARQ ACK/NACK feedback (too many NACKs → back off; a run of ACKs → push higher). The final MCS index goes out in the scheduling DCI.

The CQI tables in TS 38.214 §5.2.2.1 mirror the MCS tables: there is a 64QAM CQI table, a 256QAM CQI table, and a URLLC (low-SE) CQI table, and the UE is told which to use so its report and the eventual grant speak the same language. Each CQI index itself already names a modulation and a code rate — so CQI-to-MCS is really a translation between two ladders indexed by spectral efficiency. The CQI field is 4 bits (indices 0–15, where 0 means "out of range / no transmission").

The mapping shown is conceptual, not normative — each vendor's link-adaptation logic sets the exact CQI→MCS correspondence and the outer-loop bias — but the principle is fixed: both ladders are ordered by spectral efficiency, so translating between them is a matter of matching bits/RE and then applying the HARQ-driven correction.

Reserved indices and HARQ retransmissions

Look again at indices 28–31 in the excerpt: their code-rate cell reads "reserved." These are not throughput rungs at all. When the gNB schedules a HARQ retransmission, the transport block size must not change — the receiver has to combine the retransmission with the soft bits it already stored from the first attempt (chase combining or incremental redundancy). But the earlier code rate was what set that TBS, and recomputing it from a fresh (Qm, R) could land on a different size.

The reserved indices solve this cleanly. An MCS index of 28–31 (in the 64QAM/low-SE tables; 28–31 with Qm from 2/4/6/8 in the 256QAM table) signals only a modulation order — no target code rate. The UE keeps the TBS from the original transmission of that HARQ process and simply re-decodes with the indicated modulation. The gNB can thus retune the modulation for the retransmission (say drop from 64QAM to QPSK because the channel worsened) while guaranteeing the transport block size is byte-for-byte identical to the first send.

So the five bits of MCS carry two regimes in one field: indices 0–27 (or 0–28) are (modulation, code rate) pairs that define a brand-new transport block, and the top handful are modulation-only overrides that preserve an in-flight block for HARQ combining. It is a small piece of encoding economy that keeps retransmissions soft-combinable without a separate signalling field.

Summary

Modulation order Qm is bits per symbol — the ladder runs π/2-BPSK (UL only), QPSK, 16QAM, 64QAM, 256QAM and 1024QAM, each with 2^Qm Gray-mapped, power-normalised constellation points. The MCS index is the scheduling shorthand: a single 5-bit code that a TS 38.214 table resolves into a (Qm, target code rate R) pair, where the table itself is chosen by mcs-Table RRC config and the scrambling RNTI. Neither the index nor the modulation means anything without the other half of the pair.

From there, (Qm, R) plus the allocation (PRBs, symbols, DMRS/overhead, layers) quantises into the transport block size — efficiency times quantity. The whole selection is link adaptation: the UE's CQI sets the starting rung (inner loop), HARQ ACK/NACK trims it to hold BLER at target (outer loop), and the reserved indices 28–31 signal modulation-only overrides that preserve an in-flight TBS for HARQ combining. Chasing peak modulation beyond the channel's SINR budget backfires — the right MCS is the highest one that still decodes.