EP3251227A1

EP3251227A1 - Precoder design and use for massive mimo

Info

Publication number: EP3251227A1
Application number: EP16701956.1A
Authority: EP
Inventors: Bishwarup Mondal; Eugene Visotsky; Frederick Vook
Original assignee: Nokia Solutions and Networks Oy
Current assignee: Nokia Solutions and Networks Oy
Priority date: 2015-01-29
Filing date: 2016-01-29
Publication date: 2017-12-06
Also published as: WO2016120443A1

Abstract

A precoder is determined (e.g., at a base station) for a given layer and for a UE. The precoder includes a three-part product codebook structure. The determining uses CSI from the UE for the three-part product codebook structure, and the CSI corresponds to multiple antenna elements in at least a 2D array of cross-polarized antenna elements. The determined precoder is applied to information for the layer to be transmitted to the UE, and the precoded information for the layer is transmitted to the UE using the antenna elements in the at least 2D array of cross-polarized antenna elements. The UE can determine, using reference signal information transmitted using the antenna elements, the CSI corresponding to each part of a three-part product codebook structure for the layer, and report the determined CSI to the base station. Methods, apparatus, computer program products, and systems are disclosed.

Description

Precoder Design and Use for Massive MIMO

TECHNICAL FIELD

[0001] This invention relates generally to wireless communication and, more specifically, relates to using many antennas in wireless communication.

BACKGROUND

[0002] This section is intended to provide a background or context to the invention disclosed below. The description herein may include concepts that could be pursued, but are not necessarily ones that have been previously conceived, implemented or described.

Therefore, unless otherwise explicitly indicated herein, what is described in this section is not prior art to the description in this application and is not admitted to be prior art by inclusion in this section. It is noted that abbreviations that may be found in the specification and/or the drawing figures are defined below.

[0003] Multiple-antenna (e.g., MIMO) technology is becoming mature for wireless communications and has been incorporated into wireless broadband standards like LTE and Wi-Fi. Basically, the more antennas the transmitter/receiver is equipped with, the more the possible signal paths and the better the performance in terms of data rate and link reliability. The price to pay is increased complexity of the hardware (e.g., the number of RF amplifier frontends) and the complexity and energy consumption of the signal processing at both ends.

[0004] Massive MIMO uses a very large number of service antennas (e.g., hundreds or thousands) that are operated fully coherently and adaptively. Extra antennas help by focusing the transmission and reception of signal energy into ever-smaller regions of space. This brings improvements in throughput and energy efficiency, in particular when combined with simultaneous scheduling of a large number of user equipment (e.g., tens or hundreds). For additional details on massive MIMO, see, e.g., 3GPP TR 36.897 - Study on Elevation Beamforming/full-dimension MIMO (FD-MIMO) for LTE.

[0005] While massive MIMO has benefits, it also has drawbacks, particularly for codebook and precoder design.

BRIEF SUMMARY

[0006] This section is intended to include examples and is not intended to be limiting.

[0007] In one example, a method comprises: determining a precoder for a given layer and for a user equipment, wherein the precoder comprises a three-part product codebook structure, wherein the determining uses channel state information from the user equipment for the three-part product codebook structure, and wherein the channel state information corresponds to a plurality of antenna elements in at least a two-dimensional array of cross-polarized antenna elements; applying the determined precoder to information for the layer to be transmitted to the user equipment; and transmitting the precoded information for the layer to the user equipment using the plurality of antenna elements in the at least two-dimensional array of cross-polarized antenna elements.

[0008] An additional exemplary embodiment includes a computer program, comprising code for performing the method of the previous paragraph, when the computer program is run on a processor. The computer program according to this paragraph, wherein the computer program is a computer program product comprising a computer-readable medium bearing computer program code embodied therein for use with a computer.

[0009] A further exemplary embodiment is an apparatus comprising: means for determining a precoder for a given layer and for a user equipment, wherein the precoder comprises a three-part product codebook structure, wherein the determining uses channel state information from the user equipment for the three-part product codebook structure, and wherein the channel state information corresponds to a plurality of antenna elements in at least a two-dimensional array of cross-polarized antenna elements; means for applying the determined precoder to information for the layer to be transmitted to the user equipment; and means for transmitting the precoded information for the layer to the user equipment using the plurality of antenna elements in the at least two-dimensional array of cross-polarized antenna elements.

[0010] An exemplary apparatus includes one or more processors and one or more memories including computer program code. The one or more memories and the computer program code are configured to, with the one or more processors, cause the apparatus to perform at least the following: determining a precoder for a given layer and for a user equipment, wherein the precoder comprises a three-part product codebook structure, wherein the determining uses channel state information from the user equipment for the three-part product codebook structure, and wherein the channel state information corresponds to a plurality of antenna elements in at least a two-dimensional array of cross-polarized antenna elements; applying the determined precoder to information for the layer to be transmitted to the user equipment; and transmitting the precoded information for the layer to the user equipment using the plurality of antenna elements in the at least two-dimensional array of cross-polarized antenna elements. [0011] An exemplary computer program product includes a computer-readable storage medium bearing computer program code embodied therein for use with a computer. The computer program code includes: code for determining a precoder for a given layer and for a user equipment, wherein the precoder comprises a three-part product codebook structure, wherein the determining uses channel state information from the user equipment for the three-part product codebook structure, and wherein the channel state information corresponds to a plurality of antenna elements in at least a two-dimensional array of cross-polarized antenna elements; code for applying the determined precoder to information for the layer to be transmitted to the user equipment; and code for transmitting the precoded information for the layer to the user equipment using the plurality of antenna elements in the at least

two-dimensional array of cross-polarized antenna elements.

[0012] In a further exemplary embodiment, a method comprises: receiving at a user equipment reference signal information for a layer that has been transmitted from a base station, the reference signal information transmitted using a plurality of antenna elements in at least a two-dimensional array of cross-polarized antenna elements; determining, at the user equipment and using the reference signal information, channel state information corresponding to each part of a three-part product codebook structure for the layer; reporting by the user equipment the determined channel state information corresponding to each part of the three-part product codebook structure to the base station; and receiving at the user equipment previously precoded information for the layer transmitted from the base station using the plurality of antenna elements, where the previously precoded information is based on the reported channel state information.

[0013] An additional exemplary embodiment includes a computer program, comprising code for performing the method of the previous paragraph, when the computer program is run on a processor. The computer program according to this paragraph, wherein the computer program is a computer program product comprising a computer-readable medium bearing computer program code embodied therein for use with a computer.

[0014] An additional exemplary embodiment is an apparatus comprising: means for receiving at a user equipment reference signal information for a layer that has been transmitted from a base station, the reference signal information transmitted using a plurality of antenna elements in at least a two-dimensional array of cross-polarized antenna elements; means for determining, at the user equipment and using the reference signal information, channel state information corresponding to each part of a three-part product codebook structure for the layer; means for reporting by the user equipment the determined channel state information corresponding to each part of the three-part product codebook structure to the base station; and means for receiving at the user equipment previously precoded information for the layer transmitted from the base station using the plurality of antenna elements, where the previously precoded information is based on the reported channel state information.

[0015] An exemplary apparatus includes one or more processors and one or more memories including computer program code. The one or more memories and the computer program code are configured to, with the one or more processors, cause the apparatus to perform at least the following: receiving at a user equipment reference signal information for a layer that has been transmitted from a base station, the reference signal information transmitted using a plurality of antenna elements in at least a two-dimensional array of cross-polarized antenna elements; determining, at the user equipment and using the reference signal information, channel state information corresponding to each part of a three-part product codebook structure for the layer; reporting by the user equipment the determined channel state information corresponding to each part of the three-part product codebook structure to the base station; and receiving at the user equipment previously precoded information for the layer transmitted from the base station using the plurality of antenna elements, where the previously precoded information is based on the reported channel state information.

[0016] receiving at a user equipment reference signal information for a layer that has been transmitted from a base station, the reference signal information transmitted using a plurality of antenna elements in at least a two-dimensional array of cross-polarized antenna elements;

[0017] An exemplary computer program product includes a computer-readable storage medium bearing computer program code embodied therein for use with a computer. The computer program code includes: code for determining, at the user equipment and using the reference signal information, channel state information corresponding to each part of a three-part product codebook structure for the layer; code for reporting by the user equipment the determined channel state information corresponding to each part of the three-part product codebook structure to the base station; and code for receiving at the user equipment previously precoded information for the layer transmitted from the base station using the plurality of antenna elements, where the previously precoded information is based on the reported channel state information.

BRIEF DESCRIPTION OF THE DRAWINGS

[0018] In the attached Drawing Figures: [0019] FIG. 1 is a block diagram of an exemplary system in which the exemplary embodiments may be practiced;

[0020] FIG. 2 is a chart of sector Spectral Efficiency (SE) versus various Full Dimension (FD) MIMO methods for the 3D Urban Micro (3D UMi) environment with 10 0.5λ elevation ports with 2 azimuth cross polarization (Xpols);

[0021] FIG. 3 is a 3D planar antenna structure where each column is a cross-polarized array;

[0022] FIG. 4 is a logic flow diagram performed by a base station for combination of scalar quantization and codebooks for precoder design for massive MIMO, and illustrates the operation of an exemplary method, a result of execution of computer program instructions embodied on a computer readable memory, functions performed by logic implemented in hardware, and/or interconnected means for performing functions in accordance with exemplary embodiments;

[0023] FIG. 5 is a logic flow diagram performed by a user equipment for combination of scalar quantization and codebooks for precoder design for massive MIMO, and illustrates the operation of an exemplary method, a result of execution of computer program instructions embodied on a computer readable memory, functions performed by logic implemented in hardware, and/or interconnected means for performing functions in accordance with exemplary embodiments;

[0024] FIG. 6 is a logic flow diagram performed by a base station for precoder design and use for massive MIMO, and illustrates the operation of an exemplary method, a result of execution of computer program instructions embodied on a computer readable memory, functions performed by logic implemented in hardware, and/or interconnected means for performing functions in accordance with exemplary embodiments; and

[0025] FIG. 7 is a logic flow diagram performed by a user equipment for precoder design and use for massive MIMO, and illustrates the operation of an exemplary method, a result of execution of computer program instructions embodied on a computer readable memory, functions performed by logic implemented in hardware, and/or interconnected means for performing functions in accordance with exemplary embodiments.

DETAILED DESCRIPTION OF THE DRAWINGS

[0026] The word "exemplary" is used herein to mean "serving as an example, instance, or illustration." Any embodiment described herein as "exemplary" is not necessarily to be construed as preferred or advantageous over other embodiments. All of the embodiments described in this Detailed Description are exemplary embodiments provided to enable persons skilled in the art to make or use the invention and not to limit the scope of the invention which is defined by the claims.

[0027] The exemplary embodiments herein describe techniques for combination of scalar quantization and codebooks for precoder design for massive MIMO. Additional description of these techniques is presented after a system into which the exemplary embodiments may be used is described.

[0028] Turning to FIG. 1 , this figure shows a block diagram of an exemplary system in which the exemplary embodiments may be practiced. In FIG. 1, N UEs 110-1 through 110-N are in wireless communication with a wireless network 100. It is assumed the UEs 110 are similar and only a possible internal configuration of UE 110-1 will be discussed herein. The user equipment 110 (e.g., UE 110-1) includes one or more processors 120, one or more memories 125, and one or more transceivers 130 interconnected through one or more buses 127. Each of the one or more transceivers 130 includes a receiver, Rx, 132 and a transmitter, Tx, 133. The one or more buses 127 may be address, data, or control buses, and may include any interconnection mechanism, such as a series of lines on a motherboard or integrated circuit, fiber optics or other optical communication equipment, and the like. The one or more transceivers 130 are connected to one or more antennas 128. The one or more memories 125 include computer program code 123. The UE 110 includes a CSI F/B module 140, comprising one of or both parts 140-1 and/or 140-2, which may be implemented in a number of ways. The CSI F/B module 140 may be implemented in hardware as CSI F/B module 140-1 , such as being implemented as part of the one or more processors 120. The CSI F/B (feedback) module 140-1 may be implemented also as an integrated circuit or through other hardware such as a programmable gate array. In another example, the CSI F/B module 140 may be implemented as CSI F/B module 140-2, which is implemented as computer program code 123 and is executed by the one or more processors 120. For instance, the one or more memories 125 and the computer program code 123 may be configured to, with the one or more processors 120, cause the user equipment 110 to perform one or more of the operations as described herein. Each UE 110 communicates with eNB 170 via a wireless link 111, and there are N wireless links shown.

[0029] The eNB 170 is a base station that provides access by wireless devices such as the UE 110 to the wireless network 100. The eNB 170 includes one or more processors 152, one or more memories 155, one or more network interfaces (N/W I/F(s)) 161, and one or more transceivers 160 interconnected through one or more buses 157. Each of the one or more transceivers 160 includes a receiver, Rx, 162 and a transmitter, Tx, 163. The one or more transceivers 160 are connected to multiple (e.g., many) antennas 158. The one or more memories 155 include computer program code 153. The eNB 170 includes a MIMO module 150, comprising one of or both parts 150-1 and/or 150-2, which may be implemented in a number of ways. The MIMO module 150 may be implemented in hardware as MIMO module 150-1, such as being implemented as part of the one or more processors 152. The MIMO module 150-1 may be implemented also as an integrated circuit or through other hardware such as a programmable gate array. In another example, the MIMO module 150 may be implemented as MIMO module 150-2, which is implemented as computer program code 153 and is executed by the one or more processors 152. For instance, the one or more memories 155 and the computer program code 153 are configured to, with the one or more processors 152, cause the eNB 170 to perform one or more of the operations as described herein. The one or more network interfaces 161 communicate over a network such as via the links 176 and 131. Two or more eNBs 170 communicate using, e.g., link 176. The link 176 may be wired or wireless or both and may implement, e.g., an X2 interface.

[0030] The one or more buses 157 may be address, data, or control buses, and may include any interconnection mechanism, such as a series of lines on a motherboard or integrated circuit, fiber optics or other optical communication equipment, wireless channels, and the like. For example, the one or more transceivers 160 may be implemented as a remote radio head (RRH) 195, with the other elements of the eNB 170 being physically in a different location from the RRH, and the one or more buses 157 could be implemented in part as fiber optic cable to connect the other elements of the eNB 170 to the RRH 195.

[0031] The wireless network 100 may include a network control element (NCE) 190 that may include MME/SGW functionality, and which provides connectivity with a further network, such as a telephone network and/or a data communications network (e.g., the Internet). The eNB 170 is coupled via a link 131 to the NCE 190. The link 131 may be implemented as, e.g., an SI interface. The NCE 190 includes one or more processors 175, one or more memories 171, and one or more network interfaces (N/W I/F(s)) 180, interconnected through one or more buses 185. The one or more memories 171 include computer program code 173. The one or more memories 171 and the computer program code 173 are configured to, with the one or more processors 175, cause the NCE 190 to perform one or more operations.

[0032] The wireless network 100 may implement network virtualization, which is the process of combining hardware and software network resources and network functionality into a single, software -based administrative entity, a virtual network. Network virtualization involves platform virtualization, often combined with resource virtualization. Network virtualization is categorized as either external, combining many networks, or parts of networks, into a virtual unit, or internal, providing network-like functionality to software containers on a single system. Note that the virtualized entities that result from the network virtualization are still implemented, at some level, using hardware such as processors 152 or 175 and memories 155 and 171, and also such virtualized entities create technical effects.

[0033] The computer readable memories 125, 155, and 171 may be of any type suitable to the local technical environment and may be implemented using any suitable data storage technology, such as semiconductor based memory devices, flash memory, magnetic memory devices and systems, optical memory devices and systems, fixed memory and removable memory. The processors 120, 152, and 175 may be of any type suitable to the local technical environment, and may include one or more of general purpose computers, special purpose computers, microprocessors, digital signal processors (DSPs) and processors based on a multi-core processor architecture, as non-limiting examples.

[0034] In general, the various embodiments of the user equipment 110 can include, but are not limited to, cellular telephones such as smart phones, personal digital assistants (PDAs) having wireless communication capabilities, portable computers having wireless

communication capabilities, image capture devices such as digital cameras having wireless communication capabilities, gaming devices having wireless communication capabilities, music storage and playback appliances having wireless communication capabilities, Internet appliances permitting wireless Internet access and browsing, tablets with wireless communication capabilities, as well as portable units or terminals that incorporate combinations of such functions.

[0035] Now that one possible system has been discussed, problems with massive MIMO are discussed. Massive MIMO is considered for study in 5G considering a large number of antenna ports (16 - 64 or more). In order to exploit such large arrays, MU-MIMO is considered as a necessary transmission mechanism. Initial studies (see FIG. 2 for a study with 40 ports) show that most of the gains come from MU-MIMO when employing such a system. In the study illustrated by FIG. 2, the product codebook concept was compared against the azimuth-only baseline and a system that has ideal knowledge of the covariance matrix (covMTX). The baseline was a system with four transmission antennas (4TX), using transmission mode 9 (TM9), single user (SU) and multi-user (MU) MIMO, with 4 bits of LTE codebook feedback. The LTE Rel-10 style product codebook versions used SU-MIMO with 40 ports (40 TX, 40 transmission antennas) or MU-MIMO with 40 ports, and 8 bits of codebook feedback. The term FD-MIMO is assumed to mean the same as the term massive MIMO.

[0036] One of the challenges in optimizing MU-MIMO performance is the need for very accurate channel state information (more accurate than what is necessary for SU-MIMO). Currently the LTE codebooks vary in size from 4 bits to 8 bits depending on the number of ports - the fidelity of CSI feedback in LTE lies between 1 -2 bits/port. Using this as a rough guide, supporting 16-64 ports will lead to codebook sizes of the order of 16-128 bits. Such codebook sizes are clearly prohibitive in terms of search complexity. It is also likely that the fidelity of CSI feedback will need to be increased beyond 2 bits/port considering MU-MIMO optimization. One problem is therefore how to quantize CSI information targeting MU-MIMO for large arrays with reasonable complexity. This disclosure proposes techniques for performing this.

[0037] In this disclosure, it is assumed that transmission ports (relevant to massive MIMO transmission) are in the form of a rectangular array with cross-polarized antenna elements. It is shown that a precoder for a rectangular array can be represented with a 3-part (W3W1W2) product codebook structure and one exemplary proposal is to use a combination of scalar quantization for Wi and vector quantization for W₂, W3 to increase the quantization resolution without affecting UE search complexity.

[0038] As is known, scalar quantization is a mapping of an input value x into a finite number of output values, y: Q: x→ y. Vector quantization works by dividing a large set of points (i.e., vectors) into groups having approximately the same number of points in and closest to them. Each group is represented by its centroid point.

[0039] The invention comprises the following in an exemplary embodiment.

[0040] 1) A precoder for a given layer is given by P = W₃W₁W₂.

[0041] 2) The matrix W₂ comprises co-phasing information (across polarization) and is intended to be quantized with very few bits (<= 2 bits per layer approximately) using vector quantization (e.g., codebook). It is envisioned that W₂ can change more rapidly (relative to Wi) and therefore W₂ feedback information can be obtained on a per sub-band level of granularity in frequency and 5- 10ms granularity in time. Therefore it is envisioned that a UE will use a short averaging window or filter for W₂ in time and frequency. The matrix comprises the correlation information in the channel - both in the horizontal and in the vertical dimensions. Structurally, this is constrained to a dual Kronecker structure, a Kronecker structure comprising azimuth and elevation and another Kronecker structure due to polarization. Note that in this document, the terms azimuth and horizontal (and their variations) are considered equivalent, as are elevational and vertical (and their variations). It is envisioned that W₁ does not change rapidly and needs to be refreshed in the order of hundreds of milliseconds. It may be sufficient to obtain a wideband characterization oi W^. It is envisioned that a UE will use a long averaging window or filter for in time and frequency. The matrix W₃ is a diagonal matrix that is intended for tracking small changes in W_i. It is envisioned that W₃ is quantized using very few bits (<=2 bits per layer) using vector quantization (e.g., codebooks) and can be obtained on a per sub-band level of granularity in frequency and 5- 10ms granularity in time. It is envisioned that a UE will use a short averaging window or filter for W₃ in time and frequency.

[0042] 3) We propose in an exemplary embodiment to use a high-resolution scalar quantization for W_i. W₂, W₃, are quantized with very few bits using vector quantization (e.g., codebooks) that help to track the channel. It is also possible to use high-resolution scalar quantization only for the azimuth dimension of the precoder part and vector quantization for the elevation dimension of the precoder or vice-versa (vector quantization only for the azimuth dimension of the W₁ precoder part and high-resolution scalar quantization for the elevation dimension of the precoder).

[0043] One may assume a rectangular array with cross-polarized antenna elements as shown in FIG. 3. FIG. 3 illustrates a 3D planar antenna structure 300 (e.g., a version of antennas 158) where each column is a cross-polarized array. The right leaning elements 310 are +45° polarized and the left leaning elements 320 are -45° polarized.

[0044] We denote by N_R the number of rows of antenna elements, and by N_c the number of columns of antenna elements. The total number of antenna elements is then 2N_RN_C including both +/-45⁰ (plus and minus 45 degrees) polarized antennas. The total number of transmit ports for massive MIMO is 2N_RN_C. Let us denote the covariance matrix by R which is of size 2N_RN_C x 2N_RN_C.

[0045] A general form for the Rel-10 8Tx rank-1 precoder (as represented in the codebook) for a given layer can be (approximately) decomposed into two parts, Wi and W2 written as: where w denotes a vector of coefficients common to the +45° and the -45° antenna elements and a represents a co-phasing scalar, a £ QPSK. In the case of a rank-2 precoder, the W₂ matrix is a square unitary matrix.

[0046] Note that W₂ as mentioned in Equation (1) only shows the co-phasing entries, but W₂ as specified in Rel-10 comprises both selection entries and co-phasing entries. In general, one underlying design principle is that Wi entries are long-term and need to be updated less frequently than W₂ entries.

[0047] In Equation (1), the ~ indicates that the design principle behind the Rel-10 8TX rank- 1 precoder assumes that the precoder w_R1 for each layer represents azimuth coefficients only since the Rel-10 8Tx precoder was designed for azimuth-only antenna arrays.

[0048] In the following, we propose to use a 3-part precoder decomposition for each layer composed of Wi, W₂, W3 and written in a general form as (for rank-1) :

W₃WⁱW₂ = [D_ei<g>D_az]

where is a Kronecker structure diagonal matrix, a follows Equation (1) above, Dei and D_az are diagonal matrices of the form diag(exp(j*k*9)), where k=0, 1, 2, ..., and -π/Ν<θ<π/Ν, diag() indicates matrix diagonalization, exp(x) is e^x, and <g> is a Kronecker product. In the case of rank-2, the W₂ matrix is a square unitary matrix.

[0049] Note that in Equation (2), the Wi matrix has a block diagonal structure where the two non-zero blocks are identical (both equal to w_az®w_ei ). When both blocks are identical, the w_az and w_el in general are accounting for both polarizations identically, meaning that they can be computed from a single covariance matrix that is an average of a first covariance matrix for the +45 co-pol (co-polarized) antennas and a second covariance matrix for the -45 co-pol antennas. An alternative embodiment is to relax the constraint that the upper left and lower right block diagonal blocks in Wi are equal. This can be achieved by computing the w_az and w_el in the upper left diagonal block based on the first covariance matrix for the +45 co-pol antennas. Then the w_az and w_el in the lower right block diagonal block can be computed based on the second covariance matrix for the -45 co-pol antennas.

[0050] An exemplary proposal herein is to use a high resolution scalar quantization for one or more components of the Wi matrix - either w_az or w_ei or both may be scalar-quantized. The quantized coefficients are considered to be valid for a long term (compared to W₂ and W3) and will be updated less frequently (compared to W₂ and W3). It is known from internal results that the conventional VQ approach for precoder quantization using codebooks gets saturated at around 10 bits. Further increasing the size will also have serious search-complexity concerns (currently a maximum size of 8 bits is considered in LTE). Scalar quantization provides a method to increase the fidelity of implicit feedback significantly to a total of hundreds of bits with no computational concerns if more bits can be utilized (e.g., in the range of 1-4 bits/port, 2 bits per port x 64 ports = 128 bits).

Q(x^q) 0

[0051] Another specific example of Wi is: W_i , which is a matrix

0 Q(x^q).

of size 2N_RN_C x 2. The vector x^q is of size N_RN_C x 1 and represents correlation among the N_RN_C co-polar antenna elements. Note that the N_RN_C co-polar antenna elements include both horizontally (azimuth adaptive) and vertically (elevation adaptive) positioned antenna elements. This example removes the constraints imposed by a Kronecker product of azimuth and elevation vectors and is more generic to handle array types not conforming to FIG. 3. For example, the vector x^q can be computed based on an eigendecomposition of a covariance matrix that is computed to be the average of two covariance matrices, the first being a covariance matrix for the +45 co-polar antenna elements and the second being a covariance matrix for the -45 co-polar antenna elements.

[0052] As with the previous discussion, another example for Wi is where we relax the constraint that the upper left and lower right block diagonal components in Wi are identical. In this case Wi is given by: W₁ = , where the vector x^+q can for example be

0 Q(x-^q)_.

computed based on the first covariance matrix for the co-polarized +45 elements, and the vector x^~q can be computed based on the second covariance matrix for the co-polarized -45 elements. Note that the diagonal entries can also be matrices in certain cases and W₁ can be

expressed as W = In this case the terms

Q(Mi⁴⁵)' Q(M₂ ⁴⁵) ^can be obtained from the first and second dominant eigenvectors of the covariance matrix for the co-polarized +45 elements respectively. The terms

@(ΜΪ⁴⁵)' Q(M₂ ⁴⁵) ^can be obtained from the first and second dominant eigenvectors of the covariance matrix for the co-polarized -45 elements respectively. Note that the function Q{.) here represents scalar quantization even though it is expressed as operating on a vector argument. An example of such a function is an element by element independent quantization of the set of phases associated with the vector argument.

[0053] Another specific example of W is given by W =

<?(_Zi⁴⁵) <?( i⁴⁵) where the cross block diagonal terms are also non-zeros. In this case a composite covariance matrix is defined as a matrix comprised of correlations among all the +45 and -45 antenna elements. The term Q(u±⁴⁵) can be obtained from the first dominant eigenvector of the composite covariance matrix but only the elements of the eigenvector that are associated with the +45 antenna elements. The term Q(v±⁴⁵) can be obtained from the first dominant eigenvector of the composite covariance matrix but only the elements of the eigenvector that are associated with the -45 antenna elements. The term Q(u⁴⁵) can be obtained from the second dominant eigenvector of the composite covariance matrix but only the elements of the eigenvector that are associated with the +45 antenna elements. The term Q(u±⁴⁵) can be obtained from the second dominant eigenvector of the composite covariance matrix but only the elements of the eigenvector that are associated with the -45 antenna elements.

[0054] In the above discussion, the quantization function Q(.) quantizes the phases of each of the elements using an M-PSK constellation, where amplitude differences among the different elements is not retained (each element is of equal amplitude). Also note that the same value of Wi may be suitable for multiple layers (in conjunction with a different W₂ for each layer). Alternatively, Q(.) can also quantize both phase and gain of each element.

[0055] An exemplary proposal is to design W₂ only for co-phasing (across polarizations) and W3 for allowing small perturbations of Wi. Wi and W3 are considered to be valid over a short-term and expected to be updated more often (compared to W₂). The Kronecker structure of W3 allows optimization of the W3 entries for azimuth and elevation separately, for example D_ei may be confined to a smaller perturbation range (θ=+/-π/128) and Da_Z may be confined to a larger perturbation range (θ=+/-π/32).

[0056] It is envisioned as one embodiment that Wi will be determined and quantized first at the UE. The scalar quantization of can be obtained by operating a scalar independently on each element of one or more eigenvectors derived from the estimated channel. It is also possible to use a scalar quantizer, where the quantization of an element is dependent on the quantized or unquantized value of another element - this process may add some implementation complexity with certain performance benefits. Irrespective of exactly the process used at the UE to achieve quantization, an eNB will be allowed to assume that an independent element-by-element mapping of the quantization output to the quantized value is sufficient to reconstruct W_i. The determination of W₁ as stated here can be based on the eigenvectors of a covariance matrix obtained by averaging covariance matrices across a certain time and frequency window. Based on the quantized value of Wi, W₂ and W3 will be determined by an exhaustive search procedure considering a certain cost- function. An example of a cost-function for determining W₂ can be expressed as max{trace(I*V^r WlRW₁W₂)},

W2

where R is an estimate of an appropriately averaged covariance matrix and trace of a matrix is defined as the sum of the diagonal elements.

[0057] Turning to FIG. 4, this figure is a logic flow diagram performed by a base station for combination of scalar quantization and codebooks for precoder design for massive MIMO. This figure illustrates the operation of an exemplary method, a result of execution of computer program instructions embodied on a computer readable memory, functions performed by logic implemented in hardware, and/or interconnected means for performing functions in accordance with exemplary embodiments. The blocks in FIG. 4 are performed by a base station such as eNB 170, e.g., under the control in part by the MIMO module 150. For ease of reference, the blocks are assumed herein to be performed by the eNB 170. It is noted that a cellular system is being used as an example, but the instant example is not limited to a cellular system. For instance, the exemplary embodiments could be applicable to Wi-Fi or other wireless systems.

[0058] In block 410, the eNB 170 transmits reference signals to UEs using (e.g., massive) MIMO. As previously described, MIMO uses an antenna array such as array 300 with cross-polarized antenna elements. In block 420, the eNB 170 receives CSI from the UEs. The CSI corresponds to each part (e.g., Wi, W₂, and W3) of a three-part product codebook structure, as the codebook structure is described above. For a single UE, in block 430, the eNB 170 determines a precoder for a given layer using the CSI of the three -part product codebook structure corresponding to that layer. In block 440, the eNB 170 repeats block 430 for each UE and each layer. The eNB 170 in block 450 applies the determined precoders to information to be transmitted to corresponding UEs, and then transmits precoded information to the UEs using (e.g., massive) MIMO (e.g., using an antenna array with cross-polarized antenna elements) in block 460.

[0059] Referring to FIG. 5, a logic flow diagram is shown that is performed by a user equipment for combination of scalar quantization and codebooks for precoder design for massive MIMO. FIG. 5 illustrates the operation of an exemplary method, a result of execution of computer program instructions embodied on a computer readable memory, functions performed by logic implemented in hardware, and/or interconnected means for performing functions in accordance with exemplary embodiments. The blocks in FIG. 5 are assumed to be performed by a single one (e.g., UE 110-1) of the UEs 110. For ease of reference, this UE will be referred to as UE 110. Note that the UE 110 may perform the blocks under control in part by the CSI F/B module 140.

[0060] In block 505, the UE 110 receives reference signals from a base station based on (e.g., massive) MIMO (e.g., using an antenna array with cross-polarized antenna elements). The UE 110 in block 510 determines CSI corresponding to each part of a three-part product codebook structure (W3W2W1). In block 515, the UE 110 reports the CSI corresponding to each part of a three-part product codebook structure to the base station. In block 520, the UE 110 receives previously precoded information from the base station using (e.g., massive) MIMO, which uses an antenna array with cross-polarized antenna elements. That is, the base station has (see block 450 of FIG. 4) performed precoding of information for the UE prior to transmitting (block 460 of FIG. 4) the precoded information. The previous precoding is based on the reported CSI. It is noted that the UE 110 would perform decoding of the received information, as is known.

[0061] As explained above, the reporting (e.g., blocks 505, 510, and 515) by the UE 110 may be performed based on certain feedback granularities (block 525). For instance, in block 530, in one example the UE 110 reports Wi at a faster rate relative to the rate(s) for W2 and W3. The rates of reporting for W2 and W3 may be the same or different. The rates are time granularities. As another example in block 535, the UE 110 reports Wi based on wideband and reports W2 and W3 based on narrow band (e.g., subband). These reports are frequency (i.e., bandwidth) granularities. There are multiple possibilities for reporting time and frequency granularities, and these are only examples.

[0062] For block 510, the UE 110 may determine CSI for the three-part product codebook in a number of ways. One of those ways is illustrated by blocks 540-555. In this example, the UE 110 in block 540 determines Wi and then quantizes Wi in block 545. The UE 110 performs in block 550 an exhaustive search procedure considering a certain cost-function to determine W2 and W3. Note that the search may take into account the quantized value of Wi. In block 555, the UE 110 quantizes W2 and W3.

[0063] Regarding quantization, a number of options are available, and FIG. 5 illustrates a non-limiting and non-exclusive set of these options. For block 545, the UE 110 can perform (block 560) scalar quantization (e.g., high resolution) for azimuthal and elevational directions in one example. In another example, the UE 110 performs (block 565) scalar quantization (e.g., high resolution) for the azimuthal direction, and performs (block 570) vector quantization for the elevational direction. Note that the opposite may be performed, e.g., vector quantization only for the azimuth dimension of the precoder part and

high-resolution scalar quantization for the elevation dimension of the precoder. For block 555, the UE 110 could perform (block 575) vector quantization for one or both of W₂ and W . Additionally, the UE could perform (block 580) such quantization using relatively few bits (e.g., <= 2 per layer) as compared to, e.g., the number of bits used for quantization of Wi.

[0064] Turning to FIG. 6, this figure is a logic flow diagram performed by a base station for precoder design and use for massive MIMO. This figure also illustrates the operation of an exemplary method, a result of execution of computer program instructions embodied on a computer readable memory, functions performed by logic implemented in hardware, and/or interconnected means for performing functions in accordance with exemplary embodiments. The blocks in FIG. 6 are performed by a base station such as eNB 170, e.g., under the control in part by the MIMO module 150. For ease of reference, the blocks are assumed herein to be performed by the eNB 170. It is noted that a cellular system is being used as an example, but the instant example is not limited to a cellular system. For instance, the exemplary embodiments could be applicable to Wi-Fi or other wireless systems.

[0065] In block 610, the eNB 170 determines a precoder for a given layer and for a user equipment. The precoder comprises a three-part product codebook structure. The determining uses channel state information from the user equipment for the three-part product codebook structure. Also, the channel state information corresponds to a plurality of antenna elements in at least a two-dimensional array of cross-polarized antenna elements. In block 620, the eNB 170 applies the determined precoder to information for the layer to be transmitted to the user equipment. In block 630, the eNB 170 transmits the precoded information for the layer to the user equipment using the plurality of antenna elements in the at least two-dimensional array of cross-polarized antenna elements.

[0066] Additional examples are presented below. In these examples, the flow of FIG. 6 is considered to be example 1.

[0067] Example 2. The method of example 1 , wherein the precoder for a layer is given by P = W₃W_tW₂.

[0068] Example 3. The method of example 2, wherein the matrix W₂ comprises co-phasing information.

[0069] Example 4. The method of example 3, wherein the channel state information for the matrix W₂ is quantized with a few bits using vector quantization. [0070] Example 5. The method of example 4, wherein the few bits are less than or equal to two bits per layer.

[0071] Example 6. The method of any one of examples 3 to 5, wherein the channel state information for the matrix W₂ is obtained on a per sub-band level of granularity in frequency and five to 10 milliseconds granularity in time.

[0072] Example 7. The method of any one of examples 2 to 6, wherein the matrix comprises correlation information in the channel, in both horizontal and vertical dimensions.

[0073] Example 8. The method of example 7, where channel state information for the matrix is refreshed in the order of hundreds of milliseconds.

[0074] Example 9. The method of any one of examples 7 to 8, wherein the channel state information for the matrix W₁ is obtained via a wideband characterization.

[0075] Example 10. The method of any one of examples 7 to 9, wherein the matrix W₁ is constrained to a dual Kronecker structure having one Kronecker structure comprising azimuth and elevation elements and another Kronecker structure due to polarization.

[0076] Example 11. The method of any one of examples 2 to 10, wherein the matrix W₃ is a diagonal matrix that tracks small changes in the matrix W^.

[0077] Example 12. The method of example 11, wherein the channel state information for the matrix W is quantized using a few bits using vector quantization.

[0078] Example 13. The method of example 12, wherein the few bits are less than or equal to two bits per layer.

[0079] Example 14. The method of any one of examples 11 to 13, wherein the channel state information for the matrix W₃ is obtained on a per sub-band level of granularity in frequency and five to 10 milliseconds granularity in time.

[0080] Example 15. The method of any one of examples 2 to 14, wherein the precoder is further given by the following:

[0081] W₃WiW₂ = [D_el®D_az]

[0082] where is a Kronecker structure diagonal matrix, a represents a co-phasing scalar, D_ei and D_az are diagonal matrices of a form diag(exp(j*k*9)), where k=0, 1, 2, ... , and -π/Ν<θ<π/Ν, diag() indicates matrix diagonalization, exp(x) is e^x, and <g> is a Kronecker product.

[0083] Example 16. The method of any of examples 1 to 15, wherein: [0084] determining a precoder is performed for a plurality of layers for each of a plurality of user equipment;

[0085] applying the determined precoder to information for the layer is performed for each of the plurality of layers; and

[0086] transmitting comprises transmitting the precoded information for all of the plurality of layers and plurality of user equipment.

[0087] Example 17. The method of any of examples 1 to 16, further comprising, prior to the determining the precoder:

[0088] transmitting to the user equipment reference signal information for the layer using the plurality of antenna elements in the at least the two-dimensional array of cross-polarized antenna elements; and

[0089] receiving the channel state information from the user equipment in response to the transmitting of the reference signal information.

[0090] Referring to FIG. 7, this figure is a logic flow diagram performed by a user equipment for precoder design and use for massive MIMO. This figure further illustrates the operation of an exemplary method, a result of execution of computer program instructions embodied on a computer readable memory, functions performed by logic implemented in hardware, and/or interconnected means for performing functions in accordance with exemplary embodiments. The blocks in FIG. 7 are assumed to be performed by a single one (e.g., UE 110-1) of the UEs 110. For ease of reference, this UE will be referred to as UE 110. Note that the UE 110 may perform the blocks under control in part by the CSI F/B module 140.

[0091] In block 710, the UE 110 receives reference signal information for a layer that has been transmitted from a base station. The reference signal information was transmitted using a plurality of antenna elements in at least a two-dimensional array of cross-polarized antenna elements. In block 720, the UE 110 determines, using the reference signal information, channel state information corresponding to each part of a three-part product codebook structure for the layer. In block 730, the UE 110 reports the determined channel state information corresponding to each part of the three-part product codebook structure to the base station. In block 740, the UE 110 received previously precoded information for the layer transmitted from the base station using the plurality of antenna elements, where the previously precoded information is based on the reported channel state information.

[0092] Additional possible examples are outlined below. In these examples, the flow in FIG. 7 is referred to as example 18. [0093] Example 19. The method of example 18, wherein the precoder for a layer is given by P = W₃W₁W₂.

[0094] Example 20. The method of example 19, wherein the matrix W₂ comprises co-phasing information.

[0095] Example 21. The method of example 20, wherein determining the channel state information further comprises quantizing the channel state information for the matrix W₂ with a few bits using vector quantization.

[0096] Example 22. The method of example 21, wherein the few bits are less than or equal to two bits per layer.

[0097] Example 23. The method of any one of examples 20 to 22, wherein determining the channel state information further comprises obtaining the channel state information for the matrix W₂ on a per sub-band level of granularity in frequency and five to 10 milliseconds granularity in time.

[0098] Example 24. The method of any one of examples 19 to 23, wherein the matrix W₁ comprises correlation information in the channel, in both horizontal and vertical dimensions.

[0099] Example 25. The method of example 24, wherein determining the channel state information further comprises refreshing channel state information for the matrix in the order of hundreds of milliseconds.

[00100] Example 26. The method of any one of examples 24 to 25, wherein determining the channel state information further comprises obtaining the channel state information for the matrix via a wideband characterization.

[00101] Example 27. The method of any one of examples 24 to 26, wherein the matrix is constrained to a dual Kronecker structure having one Kronecker structure comprising azimuth and elevation elements and another Kronecker structure due to polarization.

[00102] Example 28. The method of any one of examples 19 to 27, wherein the matrix W₃ is a diagonal matrix that tracks small changes in the matrix W^.

[00103] Example 29. The method of example 28, wherein determining channel state information further comprises quantizing the channel state information for the matrix W₃ using a few bits using vector quantization.

[00104] Example 30. The method of example 29, wherein the few bits are less than or equal to two bits per layer. [00105] Example 31. The method of any one of examples 28 to 30, wherein determining channel state information further comprises obtaining the channel state information for the matrix W₃ on a per sub-band level of granularity in frequency and five to 10 milliseconds granularity in time.

[00106] Example 32. The method of any one of examples 18 to 31 , wherein the precoder is further given by the following:

[00107] W₃WiW₂ = [D_el ®D_az]

[00108] where is a Kronecker structure diagonal matrix, a represents a co-phasing scalar, D_ei and D_az are diagonal matrices of a form diag(exp(j *k*9)), where k=0, 1 , 2, . . . , and -π/Ν<θ<π/Ν, diag() indicates matrix diagonalization, exp(x) is e^x, and <g> is a Kronecker product.

[00109] Example 33. The method of any of examples 18 to 32, wherein:

[00110] receiving reference signal information, determining channel state information and reporting are performed for each of a plurality of layers; and

[00111] receiving previously precoded information further comprises receiving the previously precoded information for each of the plurality of layers.

[00112] The following are additional examples.

[00113] Example 34. A computer program, comprising code for performing any of the methods in claims 1 to 33, when the computer program is run on a processor. Example 35. The computer program according to example 34, wherein the computer program is a computer program product comprising a computer-readable medium bearing computer program code embodied therein for use with a computer.

[00114] Example 36. An apparatus, comprising:

[00115] means for determining a precoder for a given layer and for a user equipment, wherein the precoder comprises a three-part product codebook structure, wherein the determining uses channel state information from the user equipment for the three-part product codebook structure, and wherein the channel state information corresponds to a plurality of antenna elements in at least a two-dimensional array of cross-polarized antenna elements;

[00116] means for applying the determined precoder to information for the layer to be transmitted to the user equipment; and [00117] means for transmitting the precoded information for the layer to the user equipment using the plurality of antenna elements in the at least two-dimensional array of cross-polarized antenna elements.

[00118] Example 37. The apparatus of example 36, wherein the precoder for a layer is given by P = W₃W_iW₂.

[00119] Example 38. The apparatus of example 37, wherein the matrix W₂ comprises co-phasing information.

[00120] Example 39. The apparatus of example 38, wherein the channel state information for the matrix W₂ is quantized with a few bits using vector quantization.

[00121] Example 40. The apparatus of example 39, wherein the few bits are less than or equal to two bits per layer.

[00122] Example 41. The apparatus of any one of examples 38 to 40, wherein the channel state information for the matrix W₂ is obtained on a per sub-band level of granularity in frequency and five to 10 milliseconds granularity in time.

[00123] Example 42. The apparatus of any one of examples 37 to 41, wherein the matrix comprises correlation information in the channel, in both horizontal and vertical dimensions.

[00124] Example 43. The apparatus of example 42, where channel state information for the matrix W₁ is refreshed in the order of hundreds of milliseconds.

[00125] Example 44. The apparatus of any one of examples 42 to 43, wherein the channel state information for the matrix is obtained via a wideband characterization.

[00126] Example 45. The apparatus of any one of examples 42 to 44, wherein the matrix W₁ is constrained to a dual Kronecker structure having one Kronecker structure comprising azimuth and elevation elements and another Kronecker structure due to polarization.

[00127] Example 46. The apparatus of any one of examples 37 to 45, wherein the matrix W₃ is a diagonal matrix that tracks small changes in the matrix W^.

[00128] Example 47. The apparatus of example 46, wherein the channel state information for the matrix W is quantized using a few bits using vector quantization.

[00129] Example 48. The apparatus of example 47, wherein the few bits are less than or equal to two bits per layer. [00130] Example 49. The apparatus of any one of examples 46 to 48, wherein the channel state information for the matrix W₃ is obtained on a per sub-band level of granularity in frequency and five to 10 milliseconds granularity in time.

[00131] Example 50. The apparatus of any one of examples 37 to 49, wherein the precoder is further given by the following:

[00132] W₃WiW₂ = [D_el®D_az]

w_az®w_el

[00133] where is a Kronecker structure diagonal matrix, a represents a co-phasing scalar, D_ei and D_az are diagonal matrices of a form diag(exp(j*k*9)), where k=0, 1, 2, ... , and -π/Ν<θ<π/Ν, diag() indicates matrix diagonalization, exp(x) is e^x, and <g> is a Kronecker product.

[00134] Example 51. The apparatus of any of examples 36 to 50, wherein:

[00135] the means for determining determines a precoder for a plurality of layers for each of a plurality of user equipment;

[00136] the means for applying the determined precoder to information for the layer performs the applying for each of the plurality of layers; and

[00137] the means for transmitting comprises means for transmitting the precoded information for all of the plurality of layers and plurality of user equipment.

[00138] Example 52. The apparatus of any of examples 36 to 51, further comprising, prior to determining the precoder:

[00139] means for transmitting to the user equipment reference signal information for the layer using the plurality of antenna elements in the at least the

two-dimensional array of cross-polarized antenna elements; and

[00140] means for receiving the channel state information from the user equipment in response to the transmitting of the reference signal information.

[00141] Example 53. An apparatus, comprising:

[00142] means for receiving at a user equipment reference signal information for a layer that has been transmitted from a base station, the reference signal information transmitted using a plurality of antenna elements in at least a two-dimensional array of cross-polarized antenna elements;

[00143] means for determining, at the user equipment and using the reference signal information, channel state information corresponding to each part of a three-part product codebook structure for the layer; [00144] means for reporting by the user equipment the determined channel state information corresponding to each part of the three-part product codebook structure to the base station; and

[00145] receiving at the user equipment previously precoded information for the layer transmitted from the base station using the plurality of antenna elements, where the previously precoded information is based on the reported channel state information.

[00146] Example 54. The apparatus of example 53, wherein the precoder for a layer is given by P = W₃W_iW₂.

[00147] Example 55. The apparatus of example 54, wherein the matrix W₂ comprises co-phasing information.

[00148] Example 56. The apparatus of example 55, wherein the means for determining the channel state information further comprises means for quantizing the channel state information for the matrix W₂ with a few bits using vector quantization.

[00149] Example 57. The apparatus of example 56, wherein the few bits are less than or equal to two bits per layer.

[00150] Example 58. The apparatus of any one of examples 55 to 57, wherein the means for determining the channel state information further comprises means for obtaining the channel state information for the matrix W₂ on a per sub-band level of granularity in frequency and five to 10 milliseconds granularity in time.

[00151] Example 59. The apparatus of any one of examples 54 to 58, wherein the matrix comprises correlation information in the channel, in both horizontal and vertical dimensions.

[00152] Example 60. The apparatus of example 59, wherein the means for determining the channel state information further comprises means for refreshing channel state information for the matrix W₁ in the order of hundreds of milliseconds.

[00153] Example 61. The apparatus of any one of examples 59 to 60, wherein the means for determining the channel state information further comprises means for obtaining the channel state information for the matrix W₁ via a wideband characterization.

[00154] Example 62. The apparatus of any one of examples 59 to 61, wherein the matrix W₁ is constrained to a dual Kronecker structure having one Kronecker structure comprising azimuth and elevation elements and another Kronecker structure due to polarization. [00155] Example 63. The apparatus of any one of examples 54 to 62, wherein the matrix W₃ is a diagonal matrix that tracks small changes in the matrix W^.

[00156] Example 64. The apparatus of example 63, wherein the means for determining channel state information further comprises means for quantizing the channel state information for the matrix W₃ using a few bits using vector quantization.

[00157] Example 65. The apparatus of example 61, wherein the few bits are less than or equal to two bits per layer.

[00158] Example 66. The apparatus of any one of examples 63 to 65, wherein the means for determining channel state information further comprises means for obtaining the channel state information for the matrix W₃ on a per sub-band level of granularity in frequency and five to 10 milliseconds granularity in time.

[00159] Example 67. The apparatus of any one of examples 53 to 66, wherein the precoder is further given by the following:

[00161] where is a Kronecker structure diagonal matrix, a represents a co-phasing scalar, D_ei and D_az are diagonal matrices of a form diag(exp(j*k*9)), where k=0, 1, 2, ... , and -π/Ν<θ<π/Ν, diag() indicates matrix diagonalization, exp(x) is e^x, and <g> is a Kronecker product.

[00162] Example 68. The apparatus of any of examples 53 to 67, wherein:

[00163] the means for receiving reference signal information, means for determining channel state information and means for reporting operate for each of a plurality of layers; and

[00164] the means for receiving previously precoded information further comprises means for receiving the previously precoded information for each of the plurality of layers.

[00165] Example 69. A base station comprising any of the apparatus of examples 36 to 52.

[00166] Example 70. A user equipment comprising any of the apparatus of examples 53 to 68.

[00167] Example 71. A system comprising any of the apparatus of examples 36 to 52 and any of the apparatus of examples 53 to 68. [00168] Embodiments herein may be implemented in software (executed by one or more processors), hardware (e.g., an application specific integrated circuit), or a combination of software and hardware. In an example embodiment, the software (e.g., application logic, an instruction set) is maintained on any one of various conventional computer-readable media. In the context of this document, a "computer-readable medium" may be any media or means that can contain, store, communicate, propagate or transport the instructions for use by or in connection with an instruction execution system, apparatus, or device, such as a computer, with one example of a computer described and depicted, e.g., in FIG. 1. A computer-readable medium may comprise a computer-readable storage medium (e.g., memories 125, 155, 171 or other device) that may be any media or means that can contain or store the instructions for use by or in connection with an instruction execution system, apparatus, or device, such as a computer. A computer-readable storage medium does not comprise propagating signals.

[00169] If desired, the different functions discussed herein may be performed in a different order and/or concurrently with each other. Furthermore, if desired, one or more of the above-described functions may be optional or may be combined.

[00170] Although various aspects are set out above, other aspects comprise other combinations of features from the described embodiments, and not solely the combinations described above.

[00171] It is also noted herein that while the above describes example embodiments of the invention, these descriptions should not be viewed in a limiting sense. Rather, there are several variations and modifications which may be made without departing from the scope of the present invention.

[00172] The following abbreviations that may be found in the specification and/or the drawing figures are defined as follows:

2D two-dimension or two-dimensional

3D three-dimension or three-dimensional

3 GPP third generation partnership project

5G fifth generation

az azimuth

CBOOK codebook

co-pol, co-polar co-polarized, wherein two elements are co-polarized if both of them are polarized at the same degree (e.g., both elements are +45 degree polarized) CQI channel quality indicator

CSI channel state information

dB decibels

DL downlink

el elevation

eNB or eNodeB base station, evolved Node B

F/B feedback

FD full dimension

LTE long term evolution

LTE-A long term evolution - advanced

MIMO multiple-input, multiple output

MME mobility management entity

M-PSK M-ary phase-shift keying

ms milliseconds

MU-MIMO multi-user MIMO

NCE network control element

QPSK quadrature phase-shift keying

Rel release

RI Rank Indicator

Rx or RX reception

SE spectral efficiency

SGW serving gateway

SU-MIMO single-user MIMO

TM transmission mode

TS technical specification

TR technical report

Tx or TX transmission

UE user equipment (e.g., a mobile station)

UL uplink

UMi urban micro

VQ vector quantization

Wi-Fi wireless fidelity, s local area wireless technology xpol cross polarizations

Claims

CLAIMS What is claimed is:

1. A method, comprising:

determining a precoder for a given layer and for a user equipment, wherein the precoder comprises a three-part product codebook structure, wherein the determining uses channel state information from the user equipment for the three-part product codebook structure, and wherein the channel state information corresponds to a plurality of antenna elements in at least a two-dimensional array of cross-polarized antenna elements;

applying the determined precoder to information for the layer to be transmitted to the user equipment; and

transmitting the precoded information for the layer to the user equipment using the plurality of antenna elements in the at least two-dimensional array of cross-polarized antenna elements.

2. The method of claim 1, wherein the precoder for a layer is given by P = W₃W₁W₂.

3. The method of claim 2, wherein the matrix W₂ comprises co-phasing information.

4. The method of any one of claims 2 to 3, wherein the matrix comprises correlation information in the channel, in both horizontal and vertical dimensions.

5. The method of claim 4, wherein the matrix is constrained to a dual Kronecker structure having one Kronecker structure comprising azimuth and elevation elements and another Kronecker structure due to polarization.

6. The method of any one of claims 2 to 5, wherein the matrix W is a diagonal matrix that tracks small changes in the matrix W^.

7. The method of any one of claims 2 to 6, wherein the precoder is further given by the following:

where is ^a ronecker structure diagonal matrix, a represents a

co-phasing scalar, D_ei and D_az are diagonal matrices of a form diag(exp(j*k*9)), where k=0, 1, 2, and -π/Ν<θ<π/Ν, diag() indicates matrix diagonalization, exp(x) is e^x, and <g> is a Kronecker product.

The method of any of claims 1 to 7, wherein:

determining a precoder is performed for a plurality of layers for each of a plurality of user equipment;

applying the determined precoder to information for the layer is performed for each of the plurality of layers; and

transmitting comprises transmitting the precoded information for all of the plurality of layers and plurality of user equipment.

The method of any of claims 1 to 8, further comprising, prior to the determining the precoder:

transmitting to the user equipment reference signal information for the layer using the plurality of antenna elements in the at least the two-dimensional array of cross-polarized antenna elements; and

receiving the channel state information from the user equipment in response to the transmitting of the reference signal information.

A method, comprising:

receiving at a user equipment reference signal information for a layer that has been transmitted from a base station, the reference signal information transmitted using a plurality of antenna elements in at least a two-dimensional array of cross-polarized antenna elements;

determining, at the user equipment and using the reference signal information, channel state information corresponding to each part of a three-part product codebook structure for the layer; reporting by the user equipment the determined channel state information

corresponding to each part of the three-part product codebook structure to the base station; and

receiving at the user equipment previously precoded information for the layer

transmitted from the base station using the plurality of antenna elements, where the previously precoded information is based on the reported channel state information.

11. The method of claim 10, wherein the precoder for a layer is given by P = W₃ W] W₂.

The method of claim 11 , wherein the matrix W₂ comprises co-phasing information.

The method of any one of claims 11 to 12, wherein the matrix W_t comprises correlation information in the channel, in both horizontal and vertical dimensions.

The method of claim 13, wherein the matrix is constrained to a dual Kronecker structure having one Kronecker structure comprising azimuth and elevation elements and another Kronecker structure due to polarization.

The method of any one of claims 11 to 14, wherein the matrix W₃ is a diagonal matrix that tracks small changes in the matrix W^.

The method of any one of claims 10 to 15, wherein the precoder is further given by the following:

where is a Kronecker structure diagonal matrix, a represents a

17. The method of any of claims 10 to 16, wherein:

receiving reference signal information, determining channel state information and reporting are performed for each of a plurality of layers; and

receiving previously precoded information further comprises receiving the previously precoded information for each of the plurality of layers.

18. An apparatus, comprising:

means for determining a precoder for a given layer and for a user equipment, wherein the precoder comprises a three -part product codebook structure, wherein the determining uses channel state information from the user equipment for the three-part product codebook structure, and wherein the channel state information corresponds to a plurality of antenna elements in at least a two-dimensional array of cross-polarized antenna elements;

means for applying the determined precoder to information for the layer to be

transmitted to the user equipment; and

means for transmitting the precoded information for the layer to the user equipment using the plurality of antenna elements in the at least two-dimensional array of cross-polarized antenna elements.

19. The apparatus of claim 18, further comprising means for performing any one of the methods of claims 2 to 9.

20. An apparatus, comprising:

means for receiving at a user equipment reference signal information for a layer that has been transmitted from a base station, the reference signal information transmitted using a plurality of antenna elements in at least a two-dimensional array of cross-polarized antenna elements;

means for determining, at the user equipment and using the reference signal

information, channel state information corresponding to each part of a three-part product codebook structure for the layer;

means for reporting by the user equipment the determined channel state information corresponding to each part of the three-part product codebook structure to the base station; and receiving at the user equipment previously precoded information for the layer transmitted from the base station using the plurality of antenna elements, where the previously precoded information is based on the reported channel state information.

21. The apparatus of claim 20, further comprising means for performing any one of the methods of claims 11 to 17.

22. A system comprising any of the apparatus of claims 18 to 19 and any of the apparatus of claims 20 to 21.