A Review of Codebooks for CSI Feedback in 5G New Radio and Beyond

Type I Codebook with Single-Panel is relatively straightforward as the reported PMI reflects the information of a single beam, including the beam selection and the co-phasing information among the dual-polarized antennas. Under the assumption of an uniform planar array (UPA) at the gNB as in [19], the chosen beam is selected from the set of 2D DFT vectors with spatial oversampling, indicated by $\left({{N_{1}},{N_{2}},{O_{1}},{O_{2}}}\right)$. These parameters are specified by Table 5.2.2.2.1-2 in [6]. Fig. 2 demonstrates the physical meanings of the PMI. Define the PMI vector as ${\mathbf{I}}{\text{ = }}\left[{\begin{array}[]{*{20}{c}}{{{\mathbf{I}}_{1}}}&{{{\mathbf{I}}_{2}}}\end{array}}\right]$, where ${{\bf{I}}_{1}}$ reports the chosen beam information and ${{\bf{I}}_{2}}$ indicates the corresponding phase information, respectively. ${{\bf{I}}_{1}}$ includes two indicators $i_{1,1}$ and $i_{1,2}$. The indicator $i_{1,1}$ maps the horizontal beam index $m_{1}$ and the indicator $i_{1,2}$ maps the vertical beam index $m_{2}$. The second part of the PMI ${{\bf{I}}_{2}}=i_{2}$ maps the co-phasing information by ${\varphi_{n}}={e^{j{{\pi n}\mathord{\left/{\vphantom{{\pi n}2}}\right.\kern-1.2pt}2}}}$. We should note that $n$ is binary, except when $\upsilon=1$, $n\in\left\{{0,1,2,3}\right\}$. When the layer limitation $\upsilon\leq 2$, the beam choice is indicated together by $i_{1,1},i_{1,2},i_{2}$, otherwise by $i_{1,1},i_{1,2}$.

The 2D antenna array structure and the PMI format of Type I Codebook are illustrated in Fig. 2. The 2D beam ${\bf{w}}_{m_{1},m_{2}}$ is a Kronecker product of the vertical beam ${{\bf{u}}_{m_{2}}}$ and the horizontal beam ${{\bf{g}}_{m_{1}}}$. And the neighboring 2D beam ${{{\widetilde{\bf{w}}}_{m_{1},m_{2}}}}$ consists of a different horizontal beam ${\widetilde{\bf{g}}_{m_{1}}}$ and the same vertical beam with ${\bf{w}}_{m_{1},m_{2}}$. The indices $m_{1}$ and $m_{2}$ are indicated by $i_{1,1}$ and $i_{1,2}$, respectively. Fig. 2 also demonstrates how to calculate the precoding matrix from the reported PMI and the equation is given

The precoding matrix ${\bf{W}}^{\left(\upsilon\right)}$ is made of the beam vector and phasing information, which are indicated by the 2D beam ${\bf{w}}_{m_{1},m_{2}}$ and the subband phase $\phi_{n}$, respectively. This procedure is relatively straightforward and only includes one beam and the co-phasing information. More specifically, the 2D beam ${\bf{w}}_{m_{1},m_{2}}$ is frequency-irrelevant and reported in wideband mode. In contrast, the co-phasing matrix ${\bf{W}}_{2}^{\left(\upsilon\right)}$ is frequency-dependent and needs to be reported per subband. The column vector of ${\bf{W}}_{2}^{\left(\upsilon\right)}$ characterizes the co-phasing information of each layer, which is specified in Table 5.2.2.2.1-(5-12) in [6]. However, when $N_{\rm{AP}}>16$ and $\upsilon\in\left\{3,4\right\}$, the matrix ${\bf{W}}_{2}^{\left(\upsilon\right)}$ also indicates a beam choice between the beam ${\bf{w}}_{m_{1},m_{2}}$ and another beam ${{{\widetilde{\bf{w}}}_{m_{1},m_{2}}}}$ which is defined in Table 5.2.2.2.1 of [6].

Evolved from LTE, this codebook is rather simple and works well in strong line of sight (LoS) scenarios. The number of reported coefficients is smaller compared to other codebooks. The computational complexity of calculating the precoding matrix from the PMI is the lowest. Due to the concise structure of Type I Codebook with Single-Panel, the layer limitation can be eight. However, the performance of this codebook is limited, particularly so in multipath scenarios, since only one beam is used for signal transmission.

This codebook may be applied when the antenna array at the gNB consists of multiple antenna panels instead of one. In order to facilitate the implementation, the number of antenna ports $N_{\rm{AP}}$ is limited to the set $\left\{{8,16,32}\right\}$ and the layer limitation descends to $\upsilon\leq 4$. In this codebook, additional co-phasing information needs to be reported.

Compared to Type I Codebook with Single-Panel, a new indicator vector ${\bf{i}}_{1,4}$ is introduced in Type I Codebook with Multi-Panel. The dimension of the vector ${\bf{i}}_{1,4}$ is associated with the number of antenna panels $N_{g}$ and the codebook mode $C_{m}$, varying from one to three. It indicates the inter-panel co-phasing information and the dual-polarization co-phasing information. Other indices in ${\bf{I}}_{1}$ are consistent with Type I Codebook with Single-Panel. However, the indicator ${{\bf{I}}_{2}}$ is reported in a different manner. When $C_{m}=2$, it consists of three indices, ${i_{2,0}}$, ${i_{2,1}}$ and ${i_{2,1}}$. Otherwise, it only includes one index $i_{2}$, as in Type I Codebook with Single-Panel.

The precoding matrix ${{\bf{W}}^{\left(\upsilon\right)}}$ of Type I Codebook with Multi-Panel is similar to Type I Codebook with Single-Panel. The main difference lies in the co-phasing matrix ${\bf{W}}_{2}^{\left(\upsilon\right)}$, which is jointly indicated by ${{\bf{I}}_{2}}$ and ${\bf{i}}_{1,4}$. It relies on the parameter combination $\left({{N_{g}},{C_{m}},\upsilon}\right)$, which is specified in Table 5.2.2.2.2-1 of [6]. Particularly, the additional co-phasing information is quantified by ${a_{p}}={e^{j{\pi\mathord{\left/{\vphantom{\pi 4}}\right.\kern-1.2pt}4}}}{e^{j{{\pi p}\mathord{\left/{\vphantom{{\pi p}2}}\right.\kern-1.2pt}2}}}$ and ${b_{n}}={e^{-j{\pi\mathord{\left/{\vphantom{\pi 4}}\right.\kern-1.2pt}4}}}{e^{j{{\pi n}\mathord{\left/{\vphantom{{\pi n}2}}\right.\kern-1.2pt}2}}}$. The indices $n\in{n_{0},n_{1},n_{2}}$ are indicated by ${\bf{I}}_{2}$ and $p\in{p_{1},p_{2}}$ are indicated by ${{\bf{i}}_{1,4}}$.

In general, the two sub-types of Type I Codebook mentioned above are both able to provide the beam information and the co-phasing information. It is particularly applicable in a single-user MIMO (SU-MIMO) scenario. Besides, Type I Codebook lays the foundation of the other codebooks in subsequent releases of 5G NR. However, the drawbacks of Type I Codebook are also explicit. Due to the large bandwidth in 5G NR, the channels of subbands differ a lot. Type I Codebook only allows for one spatial beam, which will be used in the whole BWP. Hence, it has limited capability to characterize the channel with multipath. As a result, the spectral efficiency performance of Type I Codebook is unsatisfactory, especially in massive MIMO. Therefore, other types of codebooks are naturally proposed as enhancements, such as Type II Codebook.

The PMI report for Type II Codebook turns out to be more complicated than Type I Codebook. As a tradeoff between the performance and the feedback overhead / complexity, the layer limitation $\upsilon$ is 2. Fig. 3 demonstrates the PMI format, which covers four kinds of beam information, i.e., the beam choice, the beam with the maximum amplitude, the beam amplitudes and the beam phases. The chosen $L\in\left\{2,3,4\right\}$ beams are indicated by ${{\bf{i}}_{1,1}}$ and ${i_{1,2}}$. We should note that all layers share the same beam choice. The indicator ${\bf{i}}_{1,1}$ contains two indices $q_{1},q_{2}$, where ${q_{1}}$ and ${q_{2}}$ map the oversampling parameter in the horizontal and vertical direction, respectively. The indicator ${i_{1,2}}$ indicates how to choose $L$ beams from the DFT vector set of size $N_{1}N_{2}$. The value of ${i_{1,2}}$ varies from $0$ to $C_{{N_{1}}{N_{2}}}^{L}-1$, where $C_{{N_{1}}{N_{2}}}^{L}$ represents the number of possibilities of selecting different $L$ beams from all ${N_{1}}{N_{2}}$ beams.

In general, the gNB is equipped with dual-polarized antennas. In Type II Codebook, the same set of $L$ beams are shared for both polarizations. As a result, $2L$ beam coefficients corresponding to $L$ chosen beams are reported. These coefficients include the amplitudes and the phases. In order to reduce the complexity, only the phase information are reported in a subband manner, while the amplitudes can be reported in subband manner or wideband manner ( the reported amplitude for a certain beam is identical for all the subbands in the whole BWP), depending on configuration.

The wideband amplitude indicator ${{\bf{i}}_{1,4,l}}$ is a vector with $2L$ entries, which are denoted by $k_{l,i}^{{\rm{(1)}}}$, where $i\in\left\{{0,\cdots 2L-1}\right\}$ indicates the beam index and $k_{l,i}^{{\rm{(1)}}}\in\left\{{0,1,\ldots,7}\right\}$. The wideband amplitude of beam $i$ at layer $l$ is computed by $p_{l,i}^{({\rm{1}})}={\left({{1\mathord{\left/{\vphantom{1{\sqrt{2}}}}\right.\kern-1.2pt}{\sqrt{2}}}}\right)^{7-k_{l,i}^{({\rm{1}})}}}$. The phase information reported in every subband are indicated by ${\bf{i}}_{2,1,l}$. Its element $c_{l,i}$ quantizes phases in a N-phase shift keying (N-PSK) manner as ${e^{j2\pi{{{c_{l,i}}}\mathord{\left/{\vphantom{{{c_{l,i}}}{{N_{{\rm{psk}}}}}}}\right.\kern-1.2pt}{{N_{{\rm{psk}}}}}}}}$, where $N_{\rm{psk}}\in\left\{4,8\right\}$. The indicator ${i_{1,3,l}}$ maps the index of the beam with the maximum amplitude at layer $l$.

In fact, subband amplitude report can be supported in Type II Codebook and it is indicated by a binary parameter $I_{s}$. Specifically, $I_{s}=1$ means that subband amplitude report is enabled, while $I_{s}=0$ means it does not. If $I_{s}=1$, an additional indicator vector ${{\bf{i}}_{2,2,l}}$ is reported to quantize the subband amplitude information with its entries being $k_{l,i}^{\left(2\right)}\in\left\{0,1\right\}$. The reported subband amplitude is thus $p_{l,i}^{({\rm{2}})}={\left({{1\mathord{\left/{\vphantom{1{\sqrt{2}}}}\right.\kern-1.2pt}{\sqrt{2}}}}\right)^{1-k_{l,i}^{({\rm{2}})}}}$.

Type II Codebook supports multiple beams and subband-wise report. As a result, the feedback overhead becomes heavier compared to Type I Codebook. To balance the report accuracy and the overhead, Type II Codebook introduces a PMI report compression mechanism. The coefficients of beam with the strongest amplitude $k_{l,i_{l}^{*}}^{\left(1\right)}$ and the corresponding phase ${c_{l,i_{l}^{*}}}$ will not be reported, where the beam index $i_{l}^{*}$ is indicated by ${i_{1,3,l}}$. When Type II Codebook is configured to wideband mode, only the non-zero wideband amplitude $k_{l,i}^{{\rm{(1)}}}$ and the corresponding phase $c_{l,i}$ are reported to the gNB. The number of non-zero coefficients of each layer is $M_{\rm{nz}}^{l}<2L$. If subband mode is configured, the subband coefficients report is slightly different. The ${M_{\rm{vr}}^{l}}$ stronger subband coefficients are phase-quantized in a N-PSK manner, where $N_{\rm{psk}}\in{4,8}$. And the remaining ${M_{{\rm{nz}}}^{l}}-{M_{{\rm{vr}}}^{l}}$ non-zero subband coefficients are phase-quantized with $N_{\rm{psk}}=4$. The rest $2L-{M^{l}_{{\rm{vr}}}}$ subband coefficients are not reported, since they are very close to zero. In general, the core idea of PMI report compression lies in feeding back the information of the predominant beams, and the feedback overhead is reduced by ignoring the weak beams.

The precoding matrix calculation in Type II Codebook is different from Type I Codebook. The main difference is that Type II Codebook supports multiple beams. Fig. 3 shows how to map the precoding matrix from the PMI in Type II Codebook.

In general, the precoding matrix ${\bf{W}}^{\left(l\right)}$ is a weighted summation of multiple beams and is calculated by

For each beam, four types of beam information are reported, i.e., the beam choice ${\bf{w}}_{m_{1}^{(i)},m_{2}^{(i)}}$, the wideband amplitude $p_{l,i}^{({\rm{1}})}$, the subband phase $c_{l,i}$ and the subband amplitude $p_{l,i}^{{\rm{(2)}}}$. In Fig. 3, the chosen $L$ beams are denoted by ${\bf{B}}$. The block matrix $\text{diag}\left\{{\bf{B}},{\bf{B}}\right\}$ is introduced to represent the beams for both polarizations. The matrix ${\bf{B}}$ is composed of $L$ beams and each beam ${\bf{w}}_{m_{1}^{(i)},m_{2}^{(i)}}$ is similar to the vector ${{\bf{w}}_{m_{1},m_{2}}}$ in Type I Codebook. However, the indices $m_{1}^{\left(i\right)},m_{2}^{\left(i\right)}$ are mapped from ${\bf{i}}_{1,1}$ and $i_{1,2}$ as illustrated in Fig. 3. And the beam choice indices $n_{1}^{\left(i\right)}$, $n_{2}^{\left(i\right)}$ are calculated from $i_{1,2}$ through the algorithm in Sec. 5.2.2.2.3 of [6]. The wideband amplitude of each layer is defined by a diagonal matrix ${\bf{A}}_{w}^{\left(l\right)}$ and its element $p_{l,i}^{({\rm{1}})}$ is indicated by ${\bf{i}}_{1,4,l}$. The wideband amplitude matrix ${\bf{A}}_{w}^{\left(l\right)}$ is always reported. The diagonal matrix ${\bf{A}}_{s}^{\left(l\right)}$ is the subband amplitude matrix, which is valid only if subband mode is supported. The diagonal elements of ${\bf{A}}_{s}^{\left(l\right)}$ are indicated by ${\bf{i}}_{2,2,l}$. Correspondingly, the subband phase information is characterized by ${\bf{P}}_{s}^{\left(l\right)}$. The elements of ${\bf{P}}_{s}^{\left(l\right)}$ are mapped from ${\bf{i}}_{2,1,l}$. The matrix $I_{N_{1}N_{2}}$ is an $N_{1}N_{2}\times N_{1}N_{2}$ identity matrix.

Overall, Type II Codebook shows many significant improvements, especially the support of subband amplitude and multiple beams. As a result, the CSI feedback is more accurate, which facilitates the gNB to cancel inter-user interference and allocate resources. This is also why Type II Codebook is more suitable for multi-user MIMO (MU-MIMO) than Type I Codebook. Even though Type II Codebook introduces a PMI report compression scheme to reduce the overhead, the feedback still scales with the bandwidth and the number of UEs. This problem is particularly acute in FDD mode with large number of gNB antennas. Nowadays, the increasing number of antennas and wider bandwidth call for new codebooks with high accuracy and low feedback overhead. Fortunately, a better-performing codebook called “Enhanced Type II Codebook” is proposed in 5G NR R16.

The PMI format in Enhanced Type II Codebook is more complicated than Type II Codebook. As illustrated in Figure 4, the PMI format includes the beam indicators ${\bf{i}}_{1,1},i_{1,2}$, the delay indicators $i_{1,5},i_{1,6,l}$, the bitmap indicator $i_{1,7,l}$, the strongest beam indicator $i_{1,8,l}$, the wideband amplitude indicator ${{\bf{i}}_{2,3,l}}$, the feedback amplitude indicator ${{\bf{i}}_{2,4,l}}$ and the feedback phase indicator ${{\bf{i}}_{2,5,l}}$.

On one hand, the beam indicators are similar to the ones in Type II Codebook. The beam selection is mapped by ${\bf{i}}_{1,1},i_{1,2}$ like Type II Codebook. The wideband amplitude indicator ${{\bf{i}}_{2,3,l}}$ consists of two coefficients, ${k_{l,0}^{\left(1\right)}}$ and ${k_{l,1}^{\left(1\right)}}$. They quantize the wideband amplitude in each polarization direction with 4 bits according to the mapping relationship in Table 5.2.2.2.5-2 of [6]. The quantified wideband amplitude at each polarization direction is denoted by $p_{l,0}^{\left(1\right)}$ and $p_{l,1}^{\left(1\right)}$. Compared with the wideband amplitude indicator ${\bf{i}}_{1,4,l}$ in Type II Codebook, the amplitude quantization in Enhanced Type II Codebook increases from 3 bits to 4 bits. Moreover, the subband beam information is always available in Enhanced Type II Codebook. It is reported in angle-delay domain. The coefficients $k_{l,i,f}^{\left(2\right)}$ of ${{\bf{i}}_{2,4,l}}$ quantize the feedback amplitude $p_{l,i,f}^{\left(2\right)}$ with 3 bits, outperforming the 1-bit quantization of the subband amplitude in Type II Codebook. Corresponding to the feedback amplitude $p_{l,i,f}^{\left(2\right)}$, the coefficients $\phi_{l,i,f}$ of indicator ${{\bf{i}}_{2,5,l}}$ quantize the feedback phase ${c_{l,i,f}}$ in a 4PSK manner. The indicator ${i_{1,8,l}}$ records the index of the strongest subband coefficient at layer $l$, similar to the indicator $i_{1,3,l}$ in Type II Codebook.

On the other hand, due to the compression in frequency domain and the report of delay information, several new indicators $i_{1,5},i_{1,6,l},{\bf{i}}_{1,7,l}$ are introduced. The subband amplitude and phase information is reported in $M_{\upsilon}$ dimension instead of $N_{3}$, due to the frequency domain compression. The frequency basis vectors are determined by a vector ${{\bf{n}}_{3,l}}\in{\mathbb{C}^{1\times{M_{\upsilon}}}}$. Each element of this vector, denoted by $n_{3,l}^{\left(f\right)}\in\left\{{0,1\cdots{N_{3}}-1}\right\},f\in\left\{{0,\cdots{M_{\upsilon}}-1}\right\}$, indicates the delay information of the corresponding frequency basis vector through the relationship $\tau_{{n_{f}},l}^{\left(f\right)}={e^{j{{2\pi{n_{f}}n_{3,l}^{\left(f\right)}}\mathord{\left/{\vphantom{{2\pi{n_{f}}n_{3,l}^{\left(f\right)}}{{N_{3}}}}}\right.\kern-1.2pt}{{N_{3}}}}}}$ is the subband index. The vector ${{\bf{n}}_{3,l}}$ is computed based on the indicators $i_{1,5},i_{1,6,l}$ that are fed back by the UE, according to the algorithm in Sec. 5.2.2.2.5 of [6]. Denote the index of the strongest frequency basis vector at the layer $l$ by $f^{*}_{l}$. The frequency basis vector ${\bf{n}}_{3,l}$ is reorganized with respect to $f^{*}_{l}$ such that $n_{3,l}^{\left(f\right)}=\left({n_{3,l}^{\left(f\right)}-n_{3,l}^{\left({f_{l}^{*}}\right)}}\right)\bmod{N_{3}}$. Thus, $n_{3,l}^{\left({f_{l}^{*}}\right)}=0$ after remapping. Likewise, the frequency basis vector index $f$ is reorganized with respect to $f^{*}_{l}$ such that ${f}=\left({{f}-f_{l}^{*}}\right)\bmod{M_{\upsilon}}$, and therefore, $f^{*}_{l}=0$.

Although the problem of feedback overhead is alleviated by IDFT based frequency domain compression in Enhanced Type II Codebook, the PMI report still consumes valuable time-frequency resources. In order to further reduce the overhead, some PMI compression mechanisms are introduced.

First, the indices of the strongest beam at the layer $l$ are denoted by $i^{*}_{l}$. The coefficients of ${{\bf{i}}_{2,4,l}},{{\bf{i}}_{2,5,l}}$ corresponding to $i^{*}_{l},f^{*}_{l}$, as well as the wideband amplitude ${{\bf{i}}_{2,3,l}}$ with indices equal to $\left\lfloor{{{i_{l}^{*}}\mathord{\left/{\vphantom{{i_{l}^{*}}L}}\right.\kern-1.2pt}L}}\right\rfloor$ are not reported. Then, similar to Type II Codebook, only non-zero coefficients of ${\bf{i}}_{2,4,l}$ and ${\bf{i}}_{2,5,l}$ are reported. The indicator ${\bf{i}}_{1,7,l}$ serves as a bitmap with size $1\times 2LM_{\upsilon}$ in order to show whether the UE reports the corresponding coefficients in ${\bf{W}}_{\text{sb}}^{\text{(l)}}$ or not. Since some values in ${\bf{W}}_{\text{sb}}^{\text{(l)}}$ are negligible, this bitmap will help reduce the feedback overhead. The number of reported coefficients of all layers is denoted by ${M_{{\rm{nz}}}}=\sum\limits_{l=1}^{\upsilon}{M_{{\rm{nz}}}^{l}}$. The number of non-zeros coefficients ${M_{\rm{nz}}^{l}}$ is equal to the summation of the coefficients of the bitmap indicator ${\bf{i}}_{1,7,l}$ at layer $l$. As a result, $2L\upsilon{M_{v}}-{M_{\rm{nz}}}$ coefficients of ${{\bf{i}}_{2,4,l}},{{\bf{i}}_{2,5,l}}$ are not reported, where $\upsilon$ is the number of layers. Since in each layer, only relative values with respect to the coefficient with the maximum amplitude are needed for feedback, the number of all reported coefficients $k_{l,i,f}^{\left(2\right)},{c_{l,i,f}}$ is thus ${M_{\rm{nz}}}-\upsilon$.

In general, the precoding matrix calculation in Enhanced Type II Codebook has a lot in common with Type II Codebook. The precoding matrix ${{\bf{W}}^{\left({{n_{f}},l}\right)}}$ is similar to ${{\bf{W}}^{\left(l\right)}}$ in Fig. 3 The main difference lies in the frequency domain compression and the mapping of the delay information. Fig. 4 demonstrates the relationship between the PMI and the precoding matrix ${{\bf{W}}^{\left({{n_{f}},l}\right)}}$. The beam selecting matrix $\bf{B}$ is consistent with Type II Codebook. However, the wideband amplitude matrix ${\bf{A}}_{w}^{\left(l\right)}$ is different, as it is composed of a block diagonal matrix with the two blocks reflecting the wideband amplitudes for both polarization instead of reusing the same set of wideband amplitudes among the two polarizations as in Type II Codebook. The reconstruction of the subband phase and amplitude is also quite different from Type II Codebook, because of the frequency domain compression with IDFT basis vectors. The amplitude and phase information of all subbands are transformed to angle-delay domain, quantized, and fed back to the gNB. Then the gNB reconstructs the information by reverse transformation with the quantized coefficients.

Generally speaking, Enhanced Type II Codebook is more sophisticated than Type II Codebook. Despite the complexity, Enhanced Type II Codebook shows great potential in improving system spectral efficiency. The detailed PMI report in Enhanced Type II Codebook characterizes much more channel structure information, especially in the delay domain. The key lies in the exploitation of the multipath angle-delay structure of wideband massive MIMO by means of DFT and IDFT transformations. Thanks to the feedback overhead reduction in frequency domain, the maximum number of layers in Enhanced Type II Codebook increases to four. And the maximum number of beams $L$ increases from four to six compared to Type II Codebook. In fact, higher frequency band and larger antenna arrays are given great expectations for 5G NR and beyond. In such case, the angle and delay structure of the channel is more obvious and should be captured by the codebooks in order to facilitate the CSI feedback. No doubt that Enhanced Type II Codebook is a good choice in this circumstance. However, the feedback overhead of Enhanced Type II Codebook is still a serious problem, especially when the number of antennas and the bandwidth are large. Achieving more accurate CSI feedback with less overhead is an everlasting effort of industry.

According to the technical report [20], the relative gains of throughput for Enhanced Type II Codebook is demonstrated in Fig. 5. And four different feedback overhead compress ratios $\beta=\left\{{\frac{1}{8},\frac{1}{4},\frac{1}{2},\frac{3}{4}}\right\}$ are evaluated. The parameter $\left(L,M_{\upsilon}\right)$ stands for the number of the spatial-frequency basis vectors. Learned from Fig. 5, Enhanced Type II Codebook achieves better performance gains over the former codebooks as well as lighter feedback overhead. And the number of spatial-frequency basis vectors $\left(L,M_{\upsilon}\right)$ play an important role in feedback overhead and performance. Note that more evaluation results under different parameter configurations can be found in [21, 22].

These two codebooks are proposed together with the corresponding non-port selection codebooks in R15 and R16, respectively. We focus on analyzing the port selection indicators of both codebooks.

First, the port sampling parameter $d$ is configured by the gNB. The indicator ${i_{1,1}}$ denotes the selected port sample group at each polarization. This indicator is different from the one in non-port selection codebooks. The value of ${i_{1,1}}$ varies from zero to $\left\lceil{{{{N_{\rm{AP}}}}\mathord{\left/{\vphantom{{{N_{\rm{AP}}}}{2d}}}\right.\kern-1.2pt}{2d}}}\right\rceil-1$. The port selection index $q^{\left(i\right)}$ is mapped by $i_{1,1}$ as $q^{\left(i\right)}={i_{1,1}}d+i$. Finally, the $q^{\left(i\right)}$-th entry of the reported port selection vector ${\bf{w}}_{q^{\left(i\right)}}\in{\mathbb{C}^{\frac{{N_{\rm{AP}}}}{2}\times 1}}$ is one and the rest are zero.

The remaining indicators and the precoding matrix calculation of these two codebooks are consistent with the corresponding non-port selection codebooks. Therefore, the PMI of these two codebooks can be obtained in a way similar to the corresponding non-port selection codebooks, and the details are omitted.

This port selection codebook is first supported in the recent 5G NR R17. Its most intriguing characteristic lies in the exploitation of the partial angle-delay reciprocity of the channel in FDD massive MIMO. Even though the complete channel reciprocity does not hold in FDD, the frequency-irrelevant parameters, e.g., the multipath angle and delay distributions of the downlink and uplink channels are very close. Such a property is exploited in Further Enhanced Type II Port Selection Codebook and the feedback overhead is reduced. The core idea of Further Enhanced Type II Port Selection Codebook is elaborated in [17]. This codebook is enabled by a joint spatial-frequency domain precoding scheme for the transmission of the downlink CSI-RS. The joint spatial-frequency precoders are also referred to as “wideband precoders”. They are computed based on the uplink channel estimates, and the partial reciprocity is exploited therein. The choices of the wideband precoders can be flexible depending on different ways of implementation [17]. The specific form of wideband precoders includes, however not limited to, the DFT vectors and the eigenvectors of the joint spatial and frequency domain channel covariance matrix.

Thanks to the partial channel reciprocity, Further Enhanced Type II Port Selection Codebook has the potential to achieve better system performance with less feedback coefficients, and the computational complexity at the UE side is also greatly reduced.

Further Enhanced Type II Codebook extends the number of beams to ${{\alpha{N_{{\rm{AP}}}}}\mathord{\left/{\vphantom{{\alpha{N_{{\rm{AP}}}}}2}}\right.\kern-1.2pt}2}$, where $\alpha$ is the ratio of the chosen antenna ports to the total antenna ports. The maximum reported beams is 6 according to Table 5.2.2.2.7-1 in [6]. However, in frequency domain, the number of frequency basis vectors $M_{\upsilon}\in\left\{1,2\right\}$ is smaller than in Enhanced Type II Port Selection Codebook.

The PMI format of Further Enhanced Type II Port Selection Codebook is similar to Enhanced Type II Port Selection Codebook. However, it may report more beams compared to its predecessor. In frequency domain, the PMI report of Further Enhanced Type II Port Selection Codebook is quite different. Particularly, the frequency basis indicating vector ${{\bf{n}}_{3}}\in\mathbb{C}^{1\times M}$ is defined like in Enhanced Type Port Selection Codebook, however it is identical across layers, rather than layer-dependent. A new indicator $i_{1,6}$ reflects the non-zero values of ${{\bf{n}}_{3}}$.

According to the technical report [25], Further Enhanced Type II Port Selection Codebook is evaluated in terms of the relative throughput gains compared to the former codebooks in Fig. 7. Five parameter configurations of codebooks [6] are evaluated, except Type I Codebook. The numerical results demonstrate that Further Enhanced Type II Port Selection Codebook outperforms the other codebooks due to the exploitation of the partial reciprocity in the spatial-frequency domain. Moreover, the eigen-based Further Enhanced Type II Port Selection Codebook achieves a higher gain than the DFT-based one. For more details and simulation results of Further Enhanced Type II Codebook, one may refer to the technical reports [26, 27].

Generally speaking, port selection codebooks leads to a more flexible beam set than non-port selection codebooks. To be more specific, the beams can be chosen from DFT vectors, or the eigenvectors of covariance matrix, etc. It is not limited to a certain antenna array topology. On the contrary, the non-port selection codebooks generally assume a UPA or ULA topology at the gNB, and the beams are generated from DFT vectors. However, the port selection codebooks require a more intelligent gNB algorithm to find the proper beams based on limited information, e.g., the partial reciprocity. In the non-port selection codebooks, since the UEs have the DL channel estimation, the beams are readily obtained with DFT transformations.

One of the major challenges in massive MIMO is the mobility problem. The shorter coherence time in mobility scenarios leads to a serious degradation on the spectral efficiency [28]. Recently, some research work focused on this dilemma from the theoretical perspective [29, 30, 31, 32]. In industry, the topic of mobility enhancement had been considered and discussed in R17 from the perspective of mobility management with a type of non-zero power (NZP) CSI-RS for mobility management, as well as synchronization signal block (SSB)-based handover between cells. In future R18 version or 5G-advanced, the enhancement of mobility performance will be an integral part and has been added to the agenda [33]. However in the 5G NR standards, no codebook has ever been particularly designed for the non-negligible UE mobility, which causes serious deterioration of the system spectral efficiency. The main reason lies in the fast variation of the channel, and in particular, the Doppler of the paths. Unfortunately, the codebooks supported in R17 cannot solve this challenge. They are not designed to characterize the Doppler frequency shift of the multipath of the channel, nor can they report timely CSI for high mobility scenarios.

In order to design an enhanced codebook for mobility scenarios, we believe that three constraints should be considered. First, the codebook should characterize the Doppler frequency shift information of the channel. Second, the time-varying channel demands a timely CSI feedback framework. Introducing a channel prediction scheme in CSI report may be a solution. Third, the compatibility with the existing codebooks is also vital and will facilitate the implementation. The mobility enhanced codebook proposed in [34] is a candidate, which provides an effective approach to obtain the CSI in high mobility scenarios by applying a joint-angle-delay-Doppler (JADD) channel prediction scheme. The core idea is to track the multipath Doppler frequency shifts with a few channel samples. Moreover, the timely CSI feedback is enabled by a partial reciprocity based wideband precoding scheme for the pilots and the feedback-based CSI prediction at the gNB.

Recently, a distributed multiple antenna system or cell-free massive MIMO system has drawn much attention by academia [35] and industry. Compared to cell-centric massive MIMO, cell-free massive MIMO aims to serve the UEs simultaneously through widely distributed access points (APs) instead of the centralized antenna array at the base station [36]. This cell-free massive MIMO mainly shows the advantage in exploiting diversity against shadow fading at the expense of high backhaul requirements. It may lead to performance improvements in respect of the coverage probability, the energy efficiency and the spectral efficiency [37].

In cell-free massive MIMO, the channel environments between the distributed APs and a certain UE are quite different. There is little correlation between the distributed BS antennas, which makes the CSI compression more challenging. In fact, the codebooks mentioned in this paper all rely on the channel structure, e.g., the spatial-domain structure of the multipath angular response and the frequency-domain structure of the multipath delay response. The structure makes the channel correlated and therefore compressible. In cell-free massive MIMO however, such structures are not available. Hence, it is more challenging to characterize the channel parameters of each path, and the current codebook framework may not be suitable for cell-free massive MIMO. Therefore, the major challenge of designing the codebook for cell-free massive MIMO lies in how to reduce the feedback overhead, which scales with the number of distributed antennas.

Nowadays, 6G is widely discussed and many emerging technologies are considered candidates to be used in 6G [38, 39], including ultramassive MIMO, which helps to meet the extremely high rate acquirement. One of the most tricky problem of ultramassive MIMO is the CSI acquisition due to the massive antenna arrays. We believe that the challenges are mainly reflected in the following three aspects. First, the channel propagation nature is coherently changed. Due to the increasing antenna dimension, the channel radiating environment tends to exhibit a near-field effect. Hence, current codebook which is based on far-field radiating condition may fail to characterize the channel environment. Second, the dimension of the CSI and the precoder increase significantly. Therefore, the complexity of precoding and signal processing in ultramassive MIMO increase exponentially. Third, future codebooks for ultramassive MIMO should be easy to implement in real communication system. Some state-of-the-art methods specialize in dealing with the overwhelming CSI, such as artificial intelligence (AI) [40], compressed sensing method [41], two-stage beamforming [42] and hybrid beamforming [43]. They are promising solutions to utramassive MIMO codebook design. Nevertheless, how these methods would be standardized and deployed in real communication systems is a problem that needs to be solved in the future.