>⁢
R
⁢
B

SB

*
12

R
2

*

R
1

*

⌋

)

wherein

$N_{PRB}^{SB}$

is the number of PRBs in one subband. R₂is the number of the second type of frequency domain units in one subband. R₁is the number of the first type of frequency domain units in one second type of frequency domain unit. S is the number of sub-carriers in one first type of frequency domain unit.

For each j, j=0, 1, . . . N−1, the w_t₁_,jhas ν columns each of which corresponds to one of ν layers and its l^thcolumn

$w_{t_{1}, j}^{l}$

has one of following format:

$\begin{matrix} w_{t_{1}, j}^{l} = [\begin{matrix} w_{t_{1}, 0, j}^{l} \\ w_{t_{1}, 1, j}^{l} \end{matrix}] = \frac{1}{β_{l, j}} [\begin{matrix} \overset{L_{j} - 1}{\sum_{i = 0}} v_{i, j} p_{l, 0, j}^{(1)} p_{l, j}^{(3)} φ_{l, j}^{(3)} y_{t_{1}, l, j}^{(1)} \overset{M_{j} - 1}{\sum_{f = 0}} y_{t_{2}, l, f, j}^{(2)} p_{l, i, f, j}^{(2)} φ_{l, i, f, j}^{(2)} \\ \overset{L_{j} - 1}{\sum_{i = 0}} v_{i, j} p_{l, 1, j}^{(1)} p_{l, j}^{(3)} φ_{l, j}^{(3)} y_{t_{1}, l, j}^{(1)} \overset{M_{j} - 1}{\sum_{f = 0}} y_{t_{2}, l, f, j}^{(2)} p_{l, i + L, f, j}^{(2)} φ_{l, i + L, f, j}^{(2)} \end{matrix}] & (4) \end{matrix}$

$\begin{matrix} w_{t_{1}, j}^{l} = [\begin{matrix} w_{t_{1}, 0, j}^{l} \\ w_{t_{1}, 1, j}^{l} \end{matrix}] = \frac{1}{β_{l, j}} [\begin{matrix} \overset{L_{j} - 1}{\sum_{i = 0}} v_{i, j} p_{l, 0, j}^{(1)} p_{l, j}^{(3)} φ_{l, j}^{(3)} φ_{j}^{(4)} y_{t_{1}, l, j}^{(1)} \overset{M_{j} - 1}{\sum_{f = 0}} y_{t_{2}, l, f, j}^{(2)} p_{l, i, f, j}^{(2)} φ_{l, i, f, j}^{(2)} \\ \overset{L_{j} - 1}{\sum_{i = 0}} v_{i, j} p_{l, 1, j}^{(1)} p_{l, j}^{(3)} φ_{l, j}^{(3)} φ_{j}^{(4)} y_{t_{1}, l, j}^{(1)} \overset{M_{j} - 1}{\sum_{f = 0}} y_{t_{2}, l, f, j}^{(2)} p_{l, i + L, f, j}^{(2)} φ_{l, i + L, f, j}^{(2)} \end{matrix}] & (5) \end{matrix}$

$\begin{matrix} w_{t_{1}, j}^{l} = [\begin{matrix} w_{t_{1}, 0, j}^{l} \\ w_{t_{1}, 1, j}^{l} \end{matrix}] = \frac{1}{β_{l, j}} [\begin{matrix} \overset{L_{j} - 1}{\sum_{i = 0}} v_{i, j} p_{l, 0, j}^{(1)} p_{l, j}^{(3)} y_{t_{1}, l, j}^{(1)} \overset{M_{j} - 1}{\sum_{f = 0}} y_{t_{2}, l, f, j}^{(2)} p_{l, i, f, j}^{(2)} φ_{l, i, f, j}^{(2)} \\ \overset{L_{j} - 1}{\sum_{i = 0}} v_{i, j} p_{l, 1, j}^{(1)} p_{l, j}^{(3)} y_{t_{1}, l, j}^{(1)} \overset{M_{j} - 1}{\sum_{f = 0}} y_{t_{2}, l, f, j}^{(2)} p_{l, i + L, f, j}^{(2)} φ_{l, i + L, f, j}^{(2)} \end{matrix}] & (6) \end{matrix}$

$\begin{matrix} w_{t_{1}, j}^{l} = [\begin{matrix} w_{t_{1}, 0, j}^{l} \\ w_{t_{1}, 1, j}^{l} \end{matrix}] = \frac{1}{β_{l, j}} [\begin{matrix} \overset{L_{j} - 1}{\sum_{i = 0}} v_{i, j} p_{l, 0, j}^{(1)} p_{l, j}^{(3)} φ_{j}^{(4)} y_{t_{1}, l, j}^{(1)} \overset{M_{j} - 1}{\sum_{f = 0}} y_{t_{2}, l, f, j}^{(2)} p_{l, i, f, j}^{(2)} φ_{l, i, f, j}^{(2)} \\ \overset{L_{j} - 1}{\sum_{i = 0}} v_{i, j} p_{l, 1, j}^{(1)} p_{l, j}^{(3)} φ_{j}^{(4)} y_{t_{1}, l, j}^{(1)} \overset{M_{j} - 1}{\sum_{f = 0}} y_{t_{2}, l, f, j}^{(2)} p_{l, i + L, f, j}^{(2)} φ_{l, i + L, f, j}^{(2)} \end{matrix}] & (7) \end{matrix}$

$\begin{matrix} w_{t_{1}, j}^{l} = [\begin{matrix} w_{t_{1}, 0, j}^{l} \\ w_{t_{1}, 1, j}^{l} \end{matrix}] = \frac{1}{β_{l, j}} [\begin{matrix} \overset{L_{j} - 1}{\sum_{i = 0}} v_{i, j} p_{l, 0, j}^{(1)} y_{t_{1}, l, j}^{(1)} \overset{M_{j} - 1}{\sum_{f = 0}} y_{t_{2}, l, f, j}^{(2)} p_{l, i, f, j}^{(2)} φ_{l, i, f, j}^{(2)} \\ \overset{L_{j} - 1}{\sum_{i = 0}} v_{i, j} p_{l, 1, j}^{(1)} y_{t_{1}, l, j}^{(1)} \overset{M_{j} - 1}{\sum_{f = 0}} y_{t_{2}, l, f, j}^{(2)} p_{l, i + L, f, j}^{(2)} φ_{l, i + L, f, j}^{(2)} \end{matrix}] & (8) \end{matrix}$

$\begin{matrix} w_{t_{1}, j}^{l} = [\begin{matrix} w_{t_{1}, 0, j}^{l} \\ w_{t_{1}, 1, j}^{l} \end{matrix}] = \frac{1}{β_{l, j}} [\begin{matrix} \overset{L_{j} - 1}{\sum_{i = 0}} v_{i, j} p_{l, 0, j}^{(1)} φ_{j}^{(4)} y_{t_{1}, l, j}^{(1)} \overset{M_{j} - 1}{\sum_{f = 0}} y_{t_{2}, l, f, j}^{(2)} p_{l, i, f, j}^{(2)} φ_{l, i, f, j}^{(2)} \\ \overset{L_{j} - 1}{\sum_{i = 0}} v_{i, j} p_{l, 1, j}^{(1)} φ_{j}^{(4)} y_{t_{1}, l, j}^{(1)} \overset{M_{j} - 1}{\sum_{f = 0}} y_{t_{2}, l, f, j}^{(2)} p_{l, i + L, f, j}^{(2)} φ_{l, i + L, f, j}^{(2)} \end{matrix}] & (9) \end{matrix}$

- wherein ν_i,jis spatial domain vector which can be referred to as a third type of vector and each element of ν_i,jcorresponds to an antenna of the CSI-RS port group j. That is, the ν_i,jincludes

$\frac{P_{j}}{2}$

elements, wherein P_jis the number of CSI-RS ports of CSI-RS port group j. In some implementations, ν_i,jid is a DFT/2D-DFT with

$\frac{P_{j}}{2}$

elements. In another implementation, ν_i,jis a vector with only one element that equals 1 and the remaining

$\frac{P_{j}}{2} - 1$

elements are 0.

$p_{l, q, j}^{(1)}, q = 0, 1$

is a phase value whose amplitude equals 1. If one of formulas (4)-(7) is adopted, for each j, one of

$p_{l, q, j}^{(1)}, q = 0, 1,$

with fixed phase 0 is not reported by UE.

$p_{l, j}^{(3)} and P_{l, i, f, j}^{(2)}$

are amplitude values whose phases equal 0.

$p_{l, q, j}^{(1)} and q = 0, 1,$

$P_{l, i, f, j}^{(2)} and p_{l, j}^{(3)}$

are amplitude values which are smaller than or equal to 1 and are larger than or equals to 0.

$φ_{l, i, f, j}^{(2)}, φ_{l, j}^{(3)} and φ_{j}^{(4)}$

are phase values whose amplitudes equal to 1.

$y_{t_{1}, l, j}^{(1)}$

is an element with index t₁, t₁=0, 1, . . . F₄of the first type of vector

$y_{l, j}^{(1)}$

which is specific to layer l and CSI-RS port group j.

$y_{t_{1}, l, j}^{(1)}$

corresponds to a first type frequency domain unit with index t₁.

$y_{t_{2}, l, f, j}^{(2)}$

is an element with index t₂, t₂=0, 1, . . . F₃of the ƒ^thsecond type vector

$y_{l, f, j}^{(1)}$

which is specific to a layer l and CSI-RS port group j. Each

$w_{t_{1}, j}^{l}$

is based on one first type of vector, M_jsecond type of vectors and L_jthird type of vector ν_i, wherein M_jis a positive integer. In some implementations,

$y_{t_{1}, l, j}^{(1)} = e^{j \frac{2 π n_{4, l, j} t_{1}}{F_{4}}}, n_{4, l, j} \in {0, 1 \dots, F_{4} - 1}, t_{1} = 0, 1 \dots, F_{4} - 1$

$y_{t_{2}, l, j}^{(2)} = e^{j \frac{2 π n_{3, l}^{f} t_{2}}{F_{3}}}, n_{3, l, j}^{f} \in {0, 1, \dots F_{3} - 1}, t_{2} = 0, 1, \dots F_{3} - 1, f = 0, 1, \dots M_{j} - 1$

$or y_{t_{2}, l, j}^{(2)} = e^{j \frac{2 π (n_{3, l, j}^{f} * R_{1}) t_{2}}{F_{3} * R_{1}}}, n_{3, l, j}^{f} \in {0, 1, \dots F_{3} - 1}, t_{2} = 0, 1, \dots F_{3} - 1, f = 0, 1, \dots M_{j} - 1$

$or y_{t_{2}, l, j}^{(2)} = e^{j \frac{2 π (n_{3, l, j}^{f} * R_{1}) t_{2}}{F_{4}}}, n_{3, l, j}^{f} \in {0, 1, \dots F_{3} - 1}, t_{2} = 0, 1, \dots F_{3} - 1, f = 0, 1, \dots M_{j} - 1$

F₄is the number of the first type of frequency domain units and F₃is the number of the second type of frequency domain units, where F₄≥F₃. In some implementations, F₄is a multiple of F₃.

In a first implementation for reporting information of the first type of vector and the second type of vector, the

$n_{3, l, j}^{0} = 0$

and is not reported by the UE. The remaining M_j−1 of

$n_{3, l, j}^{f}$

is reported by the UE using

$C_{F_{3}}^{M_{j} - 1}$

which represents a sequence of indices of M_j−1

$n_{3, l, j}^{f}$

selected from F₃index values, wherein ƒ=1, 2, . . . M_j−1. Alternatively, the remaining M_j−1 of

$n_{3, l, j}^{f}$

is reported by the UE using

$C_{2 * M_{j} - 1}^{M_{j} - 1}$

which represents a sequence of indices of M_j−1

$n_{3, l, j}^{f}$

selected from 2*M_j−1 index values, wherein the UE also reports a value of M_initial∈{−2M_ν+1, −2M_ν+2, . . . , 0} by which the continuous 2*M_jsecond type of vector is determined. The reported M_j−1 of

$n_{3, l, j}^{f}$

is

$n_{3, l, j}^{f}$

after remapping operation, wherein the remapping operation refers to one of

$n_{3, l, j}^{f} = (n_{3, l, j}^{f} - n_{3, l, j}^{f^{*}})$

mod F₃,

$n_{3, l, j}^{f} = (n_{3, l, j}^{f} - n_{3, l, j}^{0}), n_{3, l, j}^{f} = ((n_{3, l, j}^{f} - n_{3, l, j_{i}^{*}}^{f_{l}^{*}}) * R_{1})$

mod F₄.

$n_{3, l, j}^{f^{*}}$

corresponds to the strongest

$p_{l, i, f, j}^{(2)},$

that is

$p_{l, i^{*} f^{*}, j}^{(2)} = \max_{i, f} p_{l, j, f, j}^{(2)} \cdot f^{*} = 0$

after the remapping operation. The n_4,l,jis reported using ┌log₂F₄┐ bits. If the remapping operation refers to

$n_{3, l, j}^{f} = (n_{3, l, j}^{f} - n_{3, l, j}^{0}),$

the UE reports

$f_{l, j}^{*}$

for each layer and each j.

In a second implementation for reporting information of the first type of vector and the second type of vector, the UE reports M_jindices of

$n_{3, l, j}^{f}$

using

$C_{F_{3}}^{M_{j}}$

or using

$C_{2 * M_{j}}^{M_{j}}$

and M_initial. The reported M_jindices of

$n_{3, l, j}^{f}$

without remapping operation. The UE also reports a value x using ┌log₂R₁┐, wherein R₁is the number of the first type frequency units in one second frequency domain unit.

$n_{4, l, j} = R_{1} n_{3, l, j}^{0} + x$

or

$n_{4, l, j} = R_{1} n_{3, l, j}^{f_{i, j}^{*}} + x,$

wherein the UE reports

$f_{l, j}^{*}$

corresponds to strongest amplitude of

$p_{l, i, f, j}^{(2)},$

that is,

$p_{l, i^{*}, f^{*}, j}^{(2)} = \max_{i, f} p_{l, i, f, j}^{(2)} \cdot f_{l, j}^{*}$

may not be 0 and should be reported to gNB. In another implementation, the n_4,l,jis reported using ┌log₂F₄┐ bits. For each j, M_jindices of

$n_{3, l, j}^{f}$

increase while ƒ increases.

In a first implementation for reporting coefficient

$p_{l, q, j}^{(1)}, p_{l, j}^{(3)}, φ_{l, j}^{(3)}, p_{l, i, f, j}^{(2)}, φ_{l, i, f, j}^{(2)},$

the UE reports index

$i_{l, j}^{*}$

or index

$i_{l, j}^{*}$

and

$f_{l, j}^{*}$

corresponding to strongest amplitude for each layer l and each CSI-RS port group j. Then for each layer l and each CSI-RS port group

$j, p_{l, ⌊ i_{l, j}^{*} / L_{j} ⌋, j}^{(1)} = 1, p_{l, i_{l, j}^{*}, f_{l, j}^{*}, j}^{(2)} = 1$

and are not reported by the UE for each j. The UE reports j*_lcorresponding to maximum value of

$p_{l, j}^{(3)}$

for each layer l, l∈{1, 2, . . . ν}, that is,

$p_{l, j_{l, j}^{*}}^{(3)} = \max_{j} p_{l, j}^{(3)} .$

Then

$p_{l, j_{l}^{⋆}}^{(3)} = 1, φ_{l, j_{l}^{⋆}}^{(3)} = 1$

and

$p_{l, j_{l}^{⋆}}^{(3)}$

and

$φ_{l, j_{l}^{⋆}}^{(3)}$

are not reported by the UE. The remaining N−1 of

$p_{l, j}^{(3)}$

and

$φ_{l, j}^{(3)}$

should be reported by the UE for

$j \neq j_{l}^{*} .$

In this case, one of formulas (4)-(7) is optimal. There are N strongest

$p_{l, i_{l, j}^{*}, f_{l, j}^{*}, j}^{(2)}$

whose values equal 1 and are not reported to gNB for each layer. Furthermore, if

$φ_{l, i_{l, j}^{*}, f_{l, j}^{*}, j}^{(2)} = 1$

and is not reported to gNB, then formula (4) or (5) is adopted. If

$φ_{l, i_{l, j}^{*}, f_{l, j}^{*}, j}^{(2)}$

is reported to gNB, then formula (6) or (7) is adopted.

In a second implementation for reporting coefficient

$p_{l, q, j}^{(1)}, p_{l, j}^{(3)}, φ_{l, j}^{(3)}, p_{l, i, f, j}^{(2)}, φ_{l, i, f, j}^{(2)},$

the UE reports i*_l, ƒ*_l, j*_lcorresponding to maximum value for each layer l, that is

$p_{l, i_{l}^{*}, f_{l}^{*}, j_{l}^{*}}^{(2)} = \max_{i, f, j} p_{l, j, f, j}^{(2)}, then p_{l, i_{l}^{*}, f_{l}^{*}, j_{l}^{*}}^{(2)} = 1, p_{l, ⌊ i_{l}^{*} / L_{j}^{*} ⌋, j_{l}^{*}}^{(1)} = 1, p_{l, j_{l}^{*}}^{(3)} = 1, φ_{l, j_{l}^{*}}^{(3)} = 1$

and aren't reported by the UE. The UE should report the remaining 2N−1 of

$p_{l, q, j}^{(1)}, j \neq j^{*}, q \neq ⌊ i / L_{j^{*}} ⌋$

and the remaining N−1 of

$p_{l, j}^{(3)}$

and

$φ_{l, j}^{(3)}$

for j≠j*. In this case one of formula (4-9) is optimal. There is only one strongest

$p_{l, i_{l}^{*}, f_{l}^{*}, j_{l}^{*}}^{(2)}$

whose value equals to 1 and is not reported to gNB for each layer. Furthermore, if

$φ_{l, i_{l}^{*}, f_{l}^{*}, j_{l}^{*}}^{(2)} = 1$

and isn't reported to gNB, then one of formula (4) or (5) is adopted. If

$φ_{l, i^{*}, f^{*}, j^{*}}^{(2)}$

is reported to gNB, then one of formulas (6)-(9) is adopted.

In a third implementation for reporting coefficient

$p_{l, q, j}^{(1)}, p_{l, j}^{(3)}, p_{l, i, f, j}^{(2)}, φ_{l, i, f, j}^{(2)},$

the UE reports i*, ƒ*, j* corresponding to maximum value for each layer l, that is

$p_{l, i^{*}, f^{*}, j^{*}}^{(2)} = \max_{i, f, j} p_{l, i, f, j}^{(2)},$

then

$p_{l, i^{*}, f^{*}, j^{*}}^{(2)} = 1,$

$φ_{l, i^{*}, f^{*}, j^{*}}^{(2)} = 1, p_{l, ⌊ i^{*} / L^{*} ⌋, j^{*}}^{(1)} = 1, p_{l, j^{*}}^{(3)} = 1$

and aren't reported by the UE. The UE should report the remaining 2N−1 of

$p_{l, q, j}^{(1)}, j \neq j^{*}, q \neq ⌊ i / L_{j^{*}} ⌋$

and the remaining N−1 of

$p_{l, j}^{(3)}$

for j≠j*. In this case formula (6-7) is optimal.

In a fourth implementation for reporting coefficient

$p_{l, q, j}^{(1)}, p_{l, i, f, j}^{(2)}, φ_{l, i, f, j}^{(2)},$

the UE reports i*, ƒ*, j* corresponding to the maximum value for each layer l, that is

$p_{l, i^{*}, f^{*}, j^{*}}^{(2)} = \max_{i, f, j} p_{l, i, f, j}^{(2)},$

then

$p_{l, i^{*}, f^{*}, j^{*}}^{(2)} = 1,$

$φ_{l, i^{*}, f^{*}, j^{*}}^{(2)} = 1,$

$p_{l, ⌊ i^{*} / L_{j}^{*} ⌋, j^{*}}^{(1)} = 1$

and are not reported by the UE. The UE should report the remaining 2N−1 of

$p_{l, q, j}^{(1)}, j \neq j^{*}, q \neq ⌊ i / L_{j^{*}} ⌋ .$

In this case, formulas (8)-(9) are optimal.

In the third and fourth implementations, i*, ƒ*, j* can also be referred to as i*_l, ƒ*_l, j*_lbecause it is reported for each layer.

In a first implementation for reporting the non-zero values of

$p_{l, i, f, j}^{(2)}$

and

$φ_{l, i, f, j}^{(2)},$

a bitmap indication is indicated for each

$w_{t_{1}, j}^{l}$

respectively. For each layer l and j, the UE reports a bitmap with 2*L_j*M_jor 2*L_j*M_j−1 bits where the bitmap has no bit corresponding to

$p_{l, i_{l, j}^{*}, f_{l, j}^{*}, j}^{(2)}$

and

$φ_{l, i_{l, j}^{*}, f_{l, j}^{*}, j}^{(2)} .$

If a bit corresponding to i, ƒ is indicated to be 1 in the bitmap, then the UE will report

$p_{l, i, f, j}^{(2)}$

and

$φ_{l, i, f, j}^{(2)}$

except at least one of

$p_{l, i_{l, j}^{*}, f_{l, j}^{*}, j}^{(2)}, φ_{l, i_{l, j}^{*}, f_{l, j}^{*}, j}^{(2)}, p_{l, i_{l, j}^{*}, f_{l, j}^{*}, j}^{(2)},$

or

$φ_{l, i_{l, j}^{*}, f_{l, j}^{*}, j}^{(2)} .$

If a bit corresponding to i, ƒ is indicated to be 0 in the bitmap, then the UE doesn't report

$p_{l, i, f, j}^{(2)}$

and

$φ_{l, i, f, j}^{(2)}$

where

$p_{l, i, f, j}^{(2)} = 0.$

The number of non-zeros values in the bitmap for each layer and each j.

In a second implementation for reporting the non-zero values of

$p_{l, i, f, j}^{(2)}$

amd

$φ_{l, i, f, j}^{(2)},$

for each layer l, the UE reports a bitmap with

$\sum_{j = 0}^{N - 1} 2 * L_{j} * M_{j} or \sum_{j = 0}^{N - 1} 2 * L_{j} * M_{j} - 1 bits,$

one bit of the bitmap corresponds to one layer l, one ƒ and one j. If a bit corresponding to i, ƒ, j is indicated to be 1 in the bitmap, then the UE will report

$p_{l, i, f, j}^{(2)}$

and

$φ_{l, i, f, j}^{(2)}$

except at least one of

$p_{l, i_{l, j}^{⋆}, f_{l, j}^{⋆}, j}^{(2)}, φ_{l, i_{l, j}^{⋆}, f_{l, j}^{⋆}, j}^{(2)}, p_{l, i_{l, j}^{⋆}, f_{l, j}^{⋆}, j}^{(2)}, or φ_{l, i_{l, j}^{⋆}, f_{l, j}^{⋆}, j}^{(2)} .$

If a bit corresponding to i, ƒ, j is indicated to be 0 in the bitmap, then the UE doesn't report

$p_{l, i, f, j}^{(2)}$

and

$φ_{l, i, f, j}^{(2)}$

where

$p_{l, i, f, j}^{(2)} = 0.$

The number of non-zeros values in the bitmap for each layer and each j. In formulas (5), (7), and (9), the UE needs to report a phase coefficient

$φ_{j}^{(4)}$

which is common to all layers, the UE reports

$j_{l}^{⋆}$

corresponding to the strongest value of

$p_{l, j}^{(3)}$

for each layer. Then, for a predefined layer, such as the first layer

$l = 1, φ_{j_{1}^{⋆}}^{(4)} = 1$

is not reported by the UE. The UE reports the remaining N−1 of

$φ_{j}^{(4)}, j \neq j_{1}^{*},$

wherein

$j_{1}^{*}$

corresponds to the strongest value among N of

$p_{1, j}^{(3)}$

for a first layer. In another implementation,

$φ_{0}^{(4)} = 1$

is not reported by the UE. The UE reports the remaining N−1 of

$φ_{j}^{(4)}, j \neq 0.$

In a first implementation for reporting

$φ_{j}^{(4)}, j \neq j_{1}^{*}, or j \neq 0,$

the period of reporting

$φ_{j}^{(4)}$

and the period of reporting other information such as

$v_{i, j}, y_{l, j}^{(1)}, y_{l, f, j}^{(2)}, p_{l, q, j}^{(1)}, p_{l, i, f, j}^{(2)}, φ_{l, i, f, j}^{(2)}, p_{l, j}^{(3)}, φ_{l, j}^{(3)}$

can be the same. In a second implementation for reporting

$φ_{j}^{(4)}, j \neq j_{1}^{*}, or j \neq 0,$

the period of reporting

$φ_{j}^{(4)}$

and the period of reporting other information such as

$v_{i, j}, y_{l, j}^{(1)}, y_{l, f, j}^{(2)}, p_{l, q, j}^{(1)}, p_{l, i, f, j}^{(2)}, φ_{l, i, f, j}^{(2)}, p_{l, j}^{(3)}, φ_{l, j}^{(3)}$

can be different, for example, the former is shorter than the latter. One latter period includes multiple former periods. In a third implementation for reporting

$φ_{j}^{(4)}, j \neq j_{1}^{*}, or j \neq 0,$

the first period of reporting

$φ_{j}^{(4)}$

and at least one of

$p_{l, q, j}^{(1)}, p_{l, i, f, j}^{(2)}, φ_{l, i, f, j}^{(2)}, p_{l, j}^{(3)}, φ_{l, j}^{(3)}$

and the second period of reporting

$v_{i, j}, y_{l, j}^{(1)}, y_{l, f, j}^{(2)}$

can be different. The first period is shorter than the second period. The second period includes multiple first periods. In a fourth implementation for reporting

$φ_{j}^{(4)}, j \neq j_{1}^{*}, or j \neq 0,$

the first period of reporting

$φ_{j}^{(4)} p_{l, q, j}^{(1)}, p_{l, i, f, j}^{(2)}, φ_{l, i, f, j}^{(2)}, p_{l, j}^{(3)}, φ_{l, j}^{(3)}$

and the second period of reporting

$v_{i, j}, y_{l, j}^{(1)}, y_{l, f, j}^{(2)}$

can be the same, but

$φ_{j}^{(4)}, j \neq j_{1}^{*}, or j \neq 0$

of multiple occasions of the N CSI-RS port groups can be reported together using a set of fourth type of vectors. Each of the fourth type of vectors includes multiple elements each of which corresponds to one occasion of the N CSI-RS port groups. For example, there are 4 occasions of the N CSI-RS port groups. Each of the 4 occasions includes N CSI-RS port groups. The fourth type of vector include 4 elements or more than 4 elements each of which corresponds to one time domain unit. For example,

$φ_{j, t}^{(4)} = \sum_{𝓏 = 0}^{Z_{j} - 1} p_{j}^{(4)} e^{\frac{j * 2 * π n_{5, j}^{𝓏} t}{T}}, n_{5, j}^{𝓏} \in {0, 1, \dots, T - 1}, t = 0, 1, \dots, T - 1,$

wherein

$φ_{j, t}^{(4)}$

is

$φ_{j}^{(4)}$

corresponding to time domain unit t. Similarly for other information of

$p_{l, q, j}^{(1)}, p_{l, i, f, j}^{(2)}, φ_{l, i, f, j}^{(2)}, p_{l, j}^{(3)}, φ_{l, j}^{(3)}$

can also be reported using a respective vector. Each element of the vector corresponds to one time unit index t. For the 4 occasions or more than one occasion, each of

$v_{i, j}, y_{l, j}^{(1)}, y_{l, f, j}^{(2)}$

is the same, i.e., each of

$v_{i, j}, y_{l, j}^{(1)}, y_{l, f, j}^{(2)}$

only has the same value for the more than one occasion and does not change while the time domain unit index changes

In some implementations, the first type of frequency domain unit and the second type of frequency domain unit are the same, then t₁=t₂, F₃=F₄, the R₁₁is the number of the first type of frequency domain units in one subband. The R₁₁depends on at least one of: N, the bandwidth of BWP, sub-carrier space, or cp (cyclic prefix) length. The larger the N is, the larger R₁₁is. For example, R₁₁can be larger than 2. The size of first type of frequency domain unit can be one PRB or smaller than one PRB. The

$w_{t_{1}, j}^{l}$

has one of the following formats.

$\begin{matrix} w_{t_{1}, j}^{l} = [\begin{matrix} w_{t_{1}, 0, j}^{l} \\ w_{t_{1}, 1, j}^{l} \end{matrix}] = \frac{1}{β_{l, j}} [\begin{matrix} \overset{L_{j} - 1}{\sum_{i = 0}} v_{i, j} p_{l, 0, j}^{(1)} p_{l, j}^{(3)} φ_{l, j}^{(3)} \overset{M_{j} - 1}{\sum_{f = 0}} y_{t_{1}, l, f, j}^{(2)} p_{l, i, f, j}^{(2)} φ_{l, i, f, j}^{(2)} \\ \overset{L_{j} - 1}{\sum_{i = 0}} v_{i, j} p_{l, 1, j}^{(1)} p_{l, j}^{(3)} φ_{l, j}^{(3)} \overset{M_{j} - 1}{\sum_{f = 0}} y_{t_{1}, l, f, j}^{(2)} p_{l, i + L, f, j}^{(2)} φ_{l, i + L, f, j}^{(2)} \end{matrix}] & (10) \end{matrix}$

$\begin{matrix} w_{t_{1}, j}^{l} = [\begin{matrix} w_{t_{1}, 0, j}^{l} \\ w_{t_{1}, 1, j}^{l} \end{matrix}] = \frac{1}{β_{l, j}} [\begin{matrix} \overset{L_{j} - 1}{\sum_{i = 0}} v_{i, j} p_{l, 0, j}^{(1)} p_{l, j}^{(3)} φ_{l, j}^{(3)} φ_{j}^{(4)} \overset{M_{j} - 1}{\sum_{f = 0}} y_{t_{1}, l, f, j}^{(2)} p_{l, i, f, j}^{(2)} φ_{l, i, f, j}^{(2)} \\ \overset{L_{j} - 1}{\sum_{i = 0}} v_{i, j} p_{l, 1, j}^{(1)} p_{l, j}^{(3)} φ_{l, j}^{(3)} φ_{j}^{(4)} \overset{M_{j} - 1}{\sum_{f = 0}} y_{t_{1}, l, f, j}^{(2)} p_{l, i + L, f, j}^{(2)} φ_{l, i + L, f, j}^{(2)} \end{matrix}] & (11) \end{matrix}$

$\begin{matrix} w_{t_{1}, j}^{l} = [\begin{matrix} w_{t_{1}, 0, j}^{l} \\ w_{t_{1}, 1, j}^{l} \end{matrix}] = \frac{1}{β_{l, j}} [\begin{matrix} \overset{L_{j} - 1}{\sum_{i = 0}} v_{i, j} p_{l, 0, j}^{(1)} p_{l, j}^{(3)} \overset{M_{j} - 1}{\sum_{f = 0}} y_{t_{1}, l, f, j}^{(2)} p_{l, i, f, j}^{(2)} φ_{l, i, f, j}^{(2)} \\ \overset{L_{j} - 1}{\sum_{i = 0}} v_{i, j} p_{l, 1, j}^{(1)} p_{l, j}^{(3)} \overset{M_{j} - 1}{\sum_{f = 0}} y_{t_{1}, l, f, j}^{(2)} p_{l, i + L, f, j}^{(2)} φ_{l, i + L, f, j}^{(2)} \end{matrix}] & (12) \end{matrix}$

$\begin{matrix} w_{t_{1}, j}^{l} = [\begin{matrix} w_{t_{1}, 0, j}^{l} \\ w_{t_{1}, 1, j}^{l} \end{matrix}] = \frac{1}{β_{l, j}} [\begin{matrix} \overset{L_{j} - 1}{\sum_{i = 0}} v_{i, j} p_{l, 0, j}^{(1)} p_{l, j}^{(3)} φ_{j}^{(4)} \overset{M_{j} - 1}{\sum_{f = 0}} y_{t_{1}, l, f, j}^{(2)} p_{l, i, f, j}^{(2)} φ_{l, i, f, j}^{(2)} \\ \overset{L_{j} - 1}{\sum_{i = 0}} v_{i, j} p_{l, 1, j}^{(1)} p_{l, j}^{(3)} φ_{j}^{(4)} \overset{M_{j} - 1}{\sum_{f = 0}} y_{t_{1}, l, f, j}^{(2)} p_{l, i + L, f, j}^{(2)} φ_{l, i + L, f, j}^{(2)} \end{matrix}] & (13) \end{matrix}$

$\begin{matrix} w_{t_{1}, j}^{l} = [\begin{matrix} w_{t_{1}, 0, j}^{l} \\ w_{t_{1}, 1, j}^{l} \end{matrix}] = \frac{1}{β_{l, j}} [\begin{matrix} \overset{L_{j} - 1}{\sum_{i = 0}} v_{i, j} p_{l, 0, j}^{(1)} \overset{M_{j} - 1}{\sum_{f = 0}} y_{t_{1}, l, f, j}^{(2)} p_{l, i, f, j}^{(2)} φ_{l, i, f, j}^{(2)} \\ \overset{L_{j} - 1}{\sum_{i = 0}} v_{i, j} p_{l, 1, j}^{(1)} \overset{M_{j} - 1}{\sum_{f = 0}} y_{t_{1}, l, f, j}^{(2)} p_{l, i + L, f, j}^{(2)} φ_{l, i + L, f, j}^{(2)} \end{matrix}] & (14) \end{matrix}$

$\begin{matrix} w_{t_{1}, j}^{l} = [\begin{matrix} w_{t_{1}, 0, j}^{l} \\ w_{t_{1}, 1, j}^{l} \end{matrix}] = \frac{1}{β_{l, j}} [\begin{matrix} \overset{L_{j} - 1}{\sum_{i = 0}} v_{i, j} p_{l, 0, j}^{(1)} φ_{j}^{(4)} \overset{M_{j} - 1}{\sum_{f = 0}} y_{t_{1}, l, f, j}^{(2)} p_{l, i, f, j}^{(2)} φ_{l, i, f, j}^{(2)} \\ \overset{L_{j} - 1}{\sum_{i = 0}} v_{i, j} p_{l, 1, j}^{(1)} φ_{j}^{(4)} \overset{M_{j} - 1}{\sum_{f = 0}} y_{t_{1}, l, f, j}^{(2)} p_{l, i + L, f, j}^{(2)} φ_{l, i + L, f, j}^{(2)} \end{matrix}] & (15) \end{matrix}$

$y_{t_{1}, l, f, j}^{(2)} = e^{j \frac{2 π n_{4, l, j}^{f} t_{2}}{F_{4}}}, n_{4}^{f} \in {0, 1, \dots F_{4} - 1}, t_{1} = 0, 1, \dots F_{4} - 1, f = 0, 1, \dots M_{j} - 1.$

In a first implementation case for reporting

$n_{4, l, j}^{f}, f = 0, 1, \dots, M_{j} - 1,$

the UE reports M_jof

$n_{4, l, j}^{f}, f = 0, 1, \dots, M_{j} - 1$

for each j=0, 1, . . . N−1. The reported M_jof

$n_{4, l, j}^{f}, f = 0, 1, \dots, M_{j} - 1$

for each j=0, 1, . . . N−1 is without remapping. If N is 1, then the UE can report M_j−1 of

$n_{4, l, j}^{f}, f = 1, \dots, M_{j} - 1$

after remapping operation and does not report

$n_{4, l, j}^{0} = 0.$

If N is larger than 1, the UE reports M_jof

$n_{4, l, j}^{f}, f = 0, 1, \dots, M_{j} - 1$

for each j=0, 1, . . . N−1. The reported M_jof

$n_{4, l, j}^{f}, f = 0, 1, \dots, M_{j} - 1$

for each j=0, 1, . . . N−1 is without remapping operation.

In a second implementation case for reporting

$n_{4, l, j}^{f}, f = 0, 1, \dots, M_{j} - 1,$

the UE reports M_jof

$n_{4, l, j}^{f}, f = 0, 1, \dots, M_{j} - 1$

for each j=0, 1, . . . N=1, j≠j*_iand the UE reports M_j−1 of

$n_{4, l, j}^{f}, f = 0, 1, \dots, M_{j} - 1,$

ƒ≠ƒ*_lfor j≠j*_l. The reported

$n_{4, l, j}^{f}, f = 0, 1, \dots, M_{j} - 1$

is after remapping operation which refers to

$n_{4, l, j}^{f} = (n_{4, l, j}^{f} - n_{4, l, j_{l}^{*}}^{f_{l}^{*}}) \mod F_{4} .$

In some implementations, the N CSI-RS port groups can include the same or different numbers of antenna ports. If they include the same number of antenna ports, then the subscript of P_jcan be ignored, that is P_j=P.

In the above implementation, the