Ferkans — Interactive Telecom Tutor

Why 5G NR Has Two Codebooks

In an FDD cell, the downlink channel cannot be reconstructed from uplink measurements — the UE must feed back a description of it. The feedback is necessarily a compressed version of the true channel because bit budgets are tight: a few tens to a few hundred bits per reporting instance. The design problem is what to quantize: the full channel vector? a beam direction? a set of DFT basis coefficients?

5G NR answers this differently for two operating points. For simple single-user deployments and cell-edge coverage, Type I codebooks quantize a single DFT beam plus a phase term — cheap, compatible with older hardware, and sufficient for SU-MIMO. For multi-user spatial multiplexing with 4-16 users sharing the same resource block, Type II codebooks quantize a linear combination of $L \in \{2,3,4\}$ DFT beams, giving much higher precoder resolution at the cost of 5-10x more feedback bits. Rel-17 eType II and Rel-18 ML-based codebooks push the resolution-versus-overhead trade-off further.

Definition:
Type I Single-Panel Codebook

A Type I single-panel codebook quantizes the precoder as a product of two beam indices $i_1 = (i_{1,1}, i_{1,2})$ and one co-phasing index $i_2$ : $\mathbf{v}(i_1, i_2) = \frac{1}{\sqrt{2}} \begin{bmatrix} \mathbf{v}_{i_{1,1}, i_{1,2}} \\ \phi_{i_2}\,\mathbf{v}_{i_{1,1}, i_{1,2}} \end{bmatrix},$ where $\mathbf{v}_{i_{1,1}, i_{1,2}}$ is a 2D DFT steering vector indexed over an oversampled $(O_1 N_1) \times (O_2 N_2)$ grid of azimuth/elevation beams, and $\phi_{i_2} \in \{1, j, -1, -j\}$ is a QPSK-valued cross-polarization phase correction. The total feedback payload is $B_{\text{Type I}} = \lceil \log_2(O_1 N_1) \rceil + \lceil \log_2(O_2 N_2) \rceil + \log_2 4 + O(1)$ which for a 32-port CSI-RS with $N_1 = 4$ , $N_2 = 4$ , oversampling $O_1 = O_2 = 4$ is about $12$ - $14$ bits per precoder report.

The factor of $\frac{1}{\sqrt 2}$ and the block-structured form reflect the fact that NR CSI-RS ports are typically organized in pairs of cross-polarized elements — each "port pair" is a dual-polarized antenna. The precoder decomposition is into a beam direction plus a polarization co-phasing.

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Definition:
Type II Linear-Combination Codebook

A Type II codebook represents the precoder as a linear combination of $L$ orthogonal DFT beams: $\mathbf{v}^{\text{Type II}} = \sum_{\ell=1}^{L} c_\ell\,\mathbf{v}_{i_{1,\ell}},$ where the beam indices $\{i_{1,\ell}\}_{\ell=1}^L$ are reported once per wideband report, and the complex combining coefficients $\{c_\ell\}$ (magnitude 3 bits, phase 8-PSK or 16-PSK) are reported per subband. The parameter $L \in \{2, 3, 4\}$ controls the precoder resolution.

Because $L$ beams can reproduce any angle within the beam-grid span via their convex combinations, Type II approaches Grassmannian optimality as $L$ grows — at the cost of feedback overhead that scales as $B_{\text{Type II}} \approx L \log_2(O_1 N_1 O_2 N_2) + L \cdot (b_{\text{mag}} + b_{\text{ph}}) \cdot N_{\text{SB}},$ where $N_{\text{SB}}$ is the number of subbands (typically 10-30) and $b_{\text{mag}} + b_{\text{ph}} = 3 + 4 = 7$ bits per coefficient. A typical Rel-15 Type II report is 300-800 bits.

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Theorem: Type II Sum Rate Gap to Ideal Precoding

Consider an MU-MIMO cell with an $N_t$ -element array serving $K$ users via ZF precoding. If each user feeds back a Type II precoder with $L$ beams, the per-user rate gap to ideal (unquantized) ZF precoding satisfies $R_k^{\text{ideal}} - R_k^{\text{Type II}} = \log_2\!\left(1 + \frac{\text{SNR}}{\sigma^2}\, \mathbb{E}\left[\sin^2 \theta_L\right]\right) + O(\text{SNR}^{-1}),$ where $\theta_L$ is the angle between the true channel direction and the best $L$ -beam linear combination in the codebook. For random channels under the one-ring model, $\mathbb{E}[\sin^2 \theta_L] \propto L^{-2}$ , so the rate gap shrinks quadratically with $L$ .

A Type II codebook approximates the true channel by its projection onto the subspace spanned by the $L$ chosen DFT beams. The residual (what the projection misses) is what causes inter-user interference after ZF precoding. As $L$ grows, the subspace becomes richer and the residual shrinks — but the quadratic decay in $\sin^2 \theta_L$ hits diminishing returns beyond $L = 4$ for typical channels.

Show Hint

Write ZF precoding as $\mathbf{W} = \hat{\mathbf{H}}(\hat{\mathbf{H}}^H \hat{\mathbf{H}})^{-1}$ where $\hat{\mathbf{H}}$ is the quantized estimate.

Apply the high-SNR rate approximation $R \approx \log_2(\text{SNR}) - \log_2(\text{distortion})$ .

For one-ring channels, the angular spread and the codebook DFT-beam width determine $\sin^2 \theta_L$ .

Proof

ZF precoder with quantized CSI

The quantized precoder is the pseudoinverse of the quantized channel matrix. The user's received signal decomposes into the intended signal plus residual interference from the imperfect nulling of other users' signals. In the high-SNR limit the interference is proportional to the squared sine between the true and quantized channel directions.

Subspace projection

With an $L$ -beam Type II codebook, $\hat{\mathbf{h}}_k$ is the best projection of $\mathbf{h}_k$ onto the $L$ -dimensional subspace spanned by the chosen DFT beams. The residual is $\mathbf{h}_k - \hat{\mathbf{h}}_k$ , and its magnitude is controlled by how well the DFT basis matches the channel covariance eigenvectors.

One-ring asymptotics

Under the one-ring model, the channel covariance has a well-defined principal eigenspace. The $L$ -best DFT beams capture a fraction $1 - O(L^{-2})$ of the channel energy, so $\sin^2 \theta_L = O(L^{-2})$ on average. Substituting into the rate gap and expanding in high-SNR yields the claim. $\blacksquare$

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Type I vs Type II: Sum Rate and Feedback Payload

Sum rate achieved by Type I and Type II codebooks versus the user count $K$ and the Type II beam parameter $L$ . The feedback payload is shown on a secondary axis; Type II rates approach ideal-CSI at a feedback cost 5-10x that of Type I.

Parameters

Users

K

4

Type II beams

L

4

SNR (dB)15

CSI-RS ports

N_t

32

Example: Feedback Payload for Rel-15 Type II

A 32-port CSI-RS cell uses Rel-15 Type II codebook with $L = 4$ beams, $N_{\text{SB}} = 13$ subbands (for a 20 MHz allocation at $\mu = 1$ ), and wideband amplitude (3 bits) plus 8-PSK phase (3 bits) per coefficient. Compute the CSI report payload in bits.

Solution

Beam indices (wideband)

$L = 4$ beams out of an $N_1 N_2 O_1 O_2 = 4\cdot 2\cdot 4\cdot 4 = 128$ grid. Rel-15 reports a rotation of the 4 beams as a single wideband index of $\binom{128}{4}$ combinations, using about $\log_2 \binom{128}{4} \approx 23$ bits.

Coefficients (per subband)

Each of the $L = 4$ coefficients is amplitude (3 bits) + phase (3 bits) = 6 bits. Per subband payload: $4 \cdot 6 = 24$ bits. Across $N_{\text{SB}} = 13$ subbands: $13 \cdot 24 = 312$ bits.

Rank and CQI overhead

Adding the rank indicator (1-2 bits), CQI (4 bits per CW), and the wideband amplitude reference (3 bits per beam), the total payload is about $23 + 312 + 20 \approx 355$ bits per CSI report.

Comparison with Type I

A Type I report for the same configuration is about $14$ bits. Type II is about $25\times$ larger, but typically delivers $2$ - $4$ dB higher MU-MIMO SINR at the same port count. $\blacksquare$

Definition:
eType II (Rel-17 Enhanced Type II)

Rel-17 introduces eType II, which applies a DCT-like compression along the frequency dimension to the Type II coefficient matrix. The original $L \times N_{\text{SB}}$ coefficient grid is written as $\mathbf{C} \in \mathbb{C}^{L \times N_{\text{SB}}}$ and approximated by its $M$ -term principal components: $\mathbf{C} \approx \mathbf{U}_L\,\mathbf{D}\,\mathbf{V}^H,$ where $\mathbf{U}_L$ holds the spatial beams (as in Type II) and $\mathbf{V} \in \mathbb{C}^{N_{\text{SB}} \times M}$ holds $M \leq N_{\text{SB}}/2$ frequency-domain DFT basis vectors. Only the coefficients of the $M$ principal components are reported, yielding a feedback compression factor of $N_{\text{SB}}/M \approx 2$ - $4\times$ .

A Rel-17 eType II payload is about 40-60% of Rel-15 Type II for the same rate performance, and the per-subband coefficient reporting is replaced by a frequency-basis reporting scheme.

5G NR Codebook Families

Feature	Type I	Type II (Rel-15)	eType II (Rel-17)	ML-based (Rel-18+)
Precoder form	Single DFT beam + QPSK co-phasing	Linear combination of $L$ DFT beams	Compressed Type II via frequency DCT	Autoencoder-decoder CsiNet style
Typical $L$	1 (implicit)	2, 3, 4	2, 3, 4, 6	N/A (latent dim)
Feedback payload	10-14 bits	300-800 bits	150-400 bits	50-200 bits (learned)
Target use case	SU-MIMO, cell edge	MU-MIMO up to 8 users	MU-MIMO up to 12 users	Research; AI-driven UEs
Rate vs ideal ZF gap	3-5 dB	1-2 dB	1-1.5 dB	$<$ 1 dB claimed
First release	Rel-15	Rel-15	Rel-17	Rel-18 study, Rel-19 spec
UE complexity	Low	Medium	Medium-high	High (NN inference)

🎓CommIT Contribution(2013)

JSDM as an Alternative to High-Overhead FDD Codebooks

A. Adhikary, J. Nam, J.-Y. Ahn, G. Caire — IEEE Transactions on Information Theory, vol. 59, no. 10, pp. 6441-6463

The CommIT group's 2013 JSDM paper (treated in Chapters 7 and 8 of this book) pre-dates the 5G NR codebook design by five years, but offers a structurally different approach to FDD massive MIMO. Rather than quantize the channel in a fixed DFT codebook, JSDM exploits the long-term statistics of the channel to pre-beamform the CSI-RS into a reduced-dimension effective channel, and then applies a small feedback on the reduced channel. The result is FDD with feedback overhead that scales as $O(K)$ rather than $O(N_t)$ .

Commercial NR Type II codebooks reach a similar operating point by a different route — a fixed DFT basis with linear combination — but the spirit is the same: compress the channel via structure rather than via raw quantization. eType II's frequency compression explicitly uses statistical structure (the frequency correlation function) that JSDM used in the spatial dimension. The NR community is effectively revisiting the JSDM philosophy with each new release.

jsdmfddcsi-feedbackcodebookView Paper →

Common Mistake: Type II Beams Are Not Data Streams

Mistake:

A common error is to interpret the Type II parameter $L$ as the maximum number of data streams the BS can transmit to the user.

Correction:

$L$ is the number of DFT basis vectors used to represent the precoder as a linear combination — not the number of data streams. The number of streams is the rank indicator (RI), which is separately fed back and takes values in $\{1, 2, 3, 4\}$ (Rel-15 Type II only supports rank 1 and 2, extended to rank 4 in Rel-16). Confusing these two concepts leads to massively overestimated feedback payloads and a misreading of the codebook design.

Historical Note: Type II: The Codebook Debate of 2017

2017-2018

During Rel-15 standardization in 2017, the introduction of Type II was contentious. One camp argued that Type I was sufficient for MU- MIMO at the overhead budget available, and that Type II's 20x payload was wasted on marginal SINR gains. The other camp ran field simulations showing that at $K = 8$ - $16$ with 32-port CSI-RS, Type I left 3-5 dB of SINR on the table compared to ideal ZF — a gap too large to ignore at the beginning of the 5G deployment era. After heated debate at the August 2017 RAN1 meeting in Berlin, both codebooks were standardized as optional UE capabilities, with Type II explicitly targeted at multi-user deployments.

PMI (Precoding Matrix Indicator)

The index in the UE's CSI report that identifies the recommended downlink precoder from the configured codebook. For Type I it is a tuple of beam-grid indices; for Type II it is a compressed description of the beam combination and coefficient matrix.

CSI Subband

A contiguous set of resource blocks over which the UE reports one CSI measurement. For a 20 MHz carrier at $\mu = 1$ , the typical subband size is 8 RBs, giving $\approx 13$ subbands per component carrier. Wideband reports average across all subbands.

Quick Check

Which is the primary reason Type II codebook reports are 5-10x larger than Type I reports?

Type II uses more beam indices

Type II reports linear-combination coefficients per subband

Type II is for FDD only

Type II requires more CSI-RS ports