Ferkans — Interactive Telecom Tutor

Definition:
Adaptive Modulation and Coding (AMC)

Adaptive modulation and coding (AMC) dynamically adjusts the modulation order and code rate on each OFDM subcarrier (or group of subcarriers) based on the instantaneous channel quality. Subcarriers with high SNR use high-order modulation (e.g., 64-QAM) and high code rates, while subcarriers with low SNR use low-order modulation (e.g., QPSK) and low code rates — or are left unused (null subcarriers).

The goal is to maximise throughput while maintaining a target bit error rate or block error rate:

$R = \sum_{k=0}^{N-1} r_k \cdot m_k \cdot \Delta f \cdot (1 - \eta_{\text{CP}})$

where $r_k$ is the code rate and $m_k = \log_2 M_k$ is the number of bits per symbol on subcarrier $k$ .

Definition:
Channel Quality Indicator (CQI)

The channel quality indicator (CQI) is a quantised measure of the channel quality on each subcarrier or subband, reported by the receiver to the transmitter. In LTE, CQI is a 4-bit index (0--15) that maps to a specific modulation and coding scheme (MCS):

CQI	Modulation	Approximate code rate	Spectral efficiency
1	QPSK	0.076	0.15 bits/s/Hz
7	16-QAM	0.369	1.48 bits/s/Hz
10	64-QAM	0.332	1.99 bits/s/Hz
15	64-QAM	0.926	5.55 bits/s/Hz

The receiver selects the highest CQI index for which the estimated block error rate is below a target (typically 10%).

Water-Filling Power Allocation

The capacity-achieving power allocation across OFDM subcarriers follows the water-filling principle (Chapter 11):

$P_k = \left(\mu - \frac{\sigma^2}{|H[k]|^2}\right)^+$

where $\mu$ is chosen so that $\sum_k P_k = P_{\text{total}}$ . Subcarriers with high channel gain receive more power; subcarriers with very low gain receive no power at all.

In practice, LTE and 5G NR use equal power allocation with AMC (varying modulation/coding rather than power), which is simpler and nearly as efficient when combined with modern channel codes.

Example: AMC Throughput Calculation

An OFDM system has $N = 12$ subcarriers (one LTE resource block) with subcarrier spacing $\Delta f = 15$ kHz and CP overhead $\eta_{\text{CP}} = 7\%$ . The measured SNR on each subcarrier is:

Subcarrier	0	1	2	3	4	5	6	7	8	9	10	11
SNR (dB)	5	8	12	15	18	20	22	19	14	10	6	3

Using the following AMC table:

SNR $< 5$ dB: no transmission
$5 \leq$ SNR $< 10$ dB: QPSK, rate 1/2 ( $m \cdot r = 1$ )
$10 \leq$ SNR $< 17$ dB: 16-QAM, rate 1/2 ( $m \cdot r = 2$ )
$17 \leq$ SNR $< 23$ dB: 64-QAM, rate 3/4 ( $m \cdot r = 4.5$ )

Calculate the total throughput of this resource block.

Solution

Assign MCS per subcarrier

Subcarrier	SNR (dB)	MCS	$m \cdot r$
0	5	QPSK, R=1/2	1
1	8	QPSK, R=1/2	1
2	12	16QAM, R=1/2	2
3	15	16QAM, R=1/2	2
4	18	64QAM, R=3/4	4.5
5	20	64QAM, R=3/4	4.5
6	22	64QAM, R=3/4	4.5
7	19	64QAM, R=3/4	4.5
8	14	16QAM, R=1/2	2
9	10	16QAM, R=1/2	2
10	6	QPSK, R=1/2	1
11	3	No TX	0

Calculate throughput

Total bits per symbol per RB: $\sum_k m_k r_k = 1 + 1 + 2 + 2 + 4.5 + 4.5 + 4.5 + 4.5 + 2 + 2 + 1 + 0 = 29$

Throughput: $R = 29 \times \Delta f \times (1 - \eta_{\text{CP}}) = 29 \times 15000 \times 0.93$ $= 404.55\;\text{kbits/s}$

Average spectral efficiency: $\eta = \frac{R}{12 \times 15000} = \frac{404550}{180000} = 2.25\;\text{bits/s/Hz}$

$\blacksquare$

Why This Matters: AMC in LTE and 5G NR

In LTE, AMC operates at the resource block (RB) level: each RB consists of 12 subcarriers $\times$ 7 OFDM symbols. The UE reports a wideband CQI and optionally sub-band CQI values (groups of RBs). The eNodeB scheduler selects the MCS index (0--28) for each scheduled RB.

5G NR extends this with finer granularity: up to 13 sub-band CQI reports, 256-QAM support (CQI table 2), and flexible numerology. The MCS tables in NR include entries for $\pi/2$ -BPSK (for coverage enhancement), QPSK, 16-QAM, 64-QAM, and 256-QAM with various LDPC code rates.

Quick Check

Why does OFDM naturally lend itself to adaptive modulation and coding, compared to single-carrier transmission?

OFDM has lower PAPR, making it easier to adapt modulation

The per-subcarrier flat-fading model allows independent MCS selection on each subcarrier or subband

OFDM signals are more robust to noise, allowing higher-order modulation

The cyclic prefix makes channel estimation unnecessary for AMC

Correction:

The per-subcarrier flat-fading model allows independent MCS selection on each subcarrier or subband

OFDM decomposes the frequency-selective channel into independent flat-fading sub-channels, each with a well-defined SNR. This allows the transmitter to optimise the modulation and coding independently for each subcarrier or group of subcarriers, exploiting the frequency-domain channel variation.

AMC

Adaptive Modulation and Coding — dynamically adjusting the modulation order and code rate based on the instantaneous channel quality to maximise throughput while meeting error rate targets.

CQI

Channel Quality Indicator — a quantised feedback index reported by the receiver indicating the supportable modulation and coding scheme. In LTE, it is a 4-bit index (0--15).

Adaptive Modulation and Coding in OFDM

Definition: Adaptive Modulation and Coding (AMC)

Definition: Channel Quality Indicator (CQI)