WO2015016331A1

WO2015016331A1 - A computer implemented simulator and method

Info

Publication number: WO2015016331A1
Application number: PCT/JP2014/070285
Authority: WO
Inventors: Thirukkumaran Sivahumaran
Original assignee: Nec Corporation
Priority date: 2013-07-31
Filing date: 2014-07-24
Publication date: 2015-02-05

Abstract

A computer implemented simulator is operable to determine a first correlation matrix (R) simulating transmission path correlation between a base station and user equipment antennas. The first correlation matrix (R) is determined for simulated wireless transmission paths of a plurality of antennas having the same polarization and arranged in a two-dimensional array. The simulator is configured to: determine second correlation matrices (R_k') for a subset of the antennas which form a first side of the array, determine third correlation matrices (R _k'') for a subset of the antennas which form a second side of the array, determine fourth correlation matrices (R_k), each fourth correlation matrix being determined based on a Kronecker product of each second correlation matrix (R_k') and a corresponding third correlation matrix (R_k''), and determine the first correlation matrix (R) simulating transmission path correlation by determining a weighted sum of the one or more fourth correlation matrices (R_k).

Description

DESCRIPTION

Title of Invention

A COMPUTER IMPLEMENTED SIMULATOR AND METHOD

Technical Field

[0001]

The present invention relates to a computer implemented simulator and a method for simulating transmission path correlation between a base station and user equipment antennas. More particularly, embodiments of the invention are directed to simulating mobile radio channels for evaluating, verifying, and validating radio access technologies, features, functionality and performance of wireless communication systems and equipment in relation to three dimensional beamforming and full dimensional multiple input multiple output (MIMO) technology, although the scope of the invention is not necessarily limited thereto.

Background Art

[0002]

MIMO enhancements in the third Generation Partnership Project (3GPP) Long Term Evolution (LTE) including Rel-11 were designed taking into account antenna configurations at the base station, such as LTE enhanced base station node (eNodeB), that are capable of adaptation in only one plane, for example the horizontal plane.

[0003]

Recently, antenna systems having a two-dimensional array structure have been studied by 3 GPP RAN-WGl as a potential option for enhancing system performance NPLl, NPL2 and NPL3.

[0004]

A two-dimensional antenna array enables adaptive control over an additional plane, for example, thus the vertical plane, enabling different strategies such as adaptation of a vertical beam pattern and/or tilt, vertical sectorization and user-specific elevation beamforming.

Citation List

Non Patent Literature

[0005]

NPL 1: ARTIST 4G, WP1, "D1.2 - Innovative advanced signal processing algorithms for interference avoidance", vl.O 31/12/2010

NPL 2: 3 GPP RP-121994, "Study on Downlink Enhancements for Elevation

Beamforming for LTE"

NPL 3: 3 GPP RP122015, "Study on Full Dimension MIMO for LTE"

NPL 4: 3GPP TS 36.101, "User Equipment (UE) radio transmission and reception

(Release 11)", vll.3.0 (2012-12)

NPL 5: Paul D. Teal, Thushara D. Abhayapala, "Spatial Correlation for General Distributions of Scatterers", IEEE Signal Processing Letters, Vol 9, Issue 10, Oct 2002, pp305-307

NPL 6: Su Khiong Yong, John S. Thompson, "Three-Dimensional Spatial Fading

Correlation Models for Compact MIMO Receivers", IEEE Trans on Wireless Comm, Vol4, Issue6, Nov2005, pp2856-2868

NPL 7: 3 GPP TR 25.996, "Spatial channel model for Multiple Input Multiple Output (MIMO) simulations (Release 11)", vl 1.0.0 (2012-09)

Summary of Invention

Technical Problem

[0006]

To verify the performance of these new technologies by a modelling simulation, it is necessary to emulate the mobile radio channels taking into account radio frequency propagation constructed by the two-dimensional antenna arrangement/configuration into a three-dimensional scattering environment.

[0007]

Embodiments of the present invention provide a simulator and method for simulating transmission path correlation between base station and user equipment antennas with sufficient accuracy, as well as computational and memory efficiency.

[0008]

It will be clearly understood that, if a prior art publication is referred to herein, this reference does not constitute an admission that the publication forms part of the common general knowledge in the art in Australia or in any other country.

Solution to Problem

[0009]

According to one aspect of the invention, a computer implemented simulator operable to determine a first correlation matrix (R) simulating transmission path correlation between a base station and user equipment antennas is provided, the first correlation matrix (R) being determined for simulated wireless transmission paths of a plurality of antennas having the same polarization and arranged in a two-dimensional array, the computer implemented simulator being configured to:

determine one or more second correlation matrices (Rt ) for a subset of the antennas which form a first side of the array,

determine one or more third correlation matrices (R* ) for a subset of the antennas which form a second side of the array,

determine one or more fourth correlation matrices (Rk), each fourth correlation matrix being determined based on a Kronecker product

Rt ® Rt ) of each second correlation matrix (Rj ) and a corresponding third correlation matrix (Rk^"),

and

determine the first correlation matrix (R) simulating transmission path correlation by determining a weighted sum of the one or more fourth correlation matrices (Rt).

[0010]

Advantageously, by using the Kronecker product of the third and fourth correlation matrices (Rk , Rt ) and the weighted sum of the fourth correlation matrices (Rt), the first correlation matrix (R) can be determined with sufficient accuracy and relatively low

computational complexity, thereby achieving computational and memory efficiency. This is particularly important in the event that the number of antennas is high.

[0011]

The array may be rectangular. In addition, the second side may be adjacent the first side. Moreover, the computer implemented simulator may be configured to:

determine a number of sets (K) for grouping the simulated wireless transmission paths, determine weight factors associated with the one or more sets (K), and

determine the weighted sum of the one or more fourth correlation matrices (Rt) using the weight factors.

[0012]

The computer implemented simulator may be configured to:

divide a three-dimensional transmission space of the transmission paths into a number of sectors equal to the number of sets (K), each sector being defined by an elevation angle range ( Θ) and an azimuth angle range ( φ ), and

group the transmission paths which have an elevation angle ( Θ) and an azimuth angle ( φ ) falling within the same sector so as to form K sets of transmission paths.

[0013]

The computer implemented simulator may be configured to determine the one or more second correlation matrices (R*) by determining a second correlation matrix

for each set (£) of transmission paths using the following equation:

2 ^Gfe> _' Ψη, )exp /^'2^;, cos 9_m sin <f>_m )

wherein d _y is a normalized distance with respect to a wavelength ( λ ) of a carrier between two antennas (i, j) along the first side of the two-dimensional array, 9_m is an angle that a sub-path (m) extends to a reference plane formed by the first side of the two-dimensional array and a direction perpendicular to the array, <p_m is an angle between the projection of the sub-path

(m) on the reference plane and the direction perpendicular to the array, and M_k is the number of transmission paths in a set ( k ).

[0014]

K ( k ) of transmission paths using the following equation:

α, = \ \ρ{θ,φ ρ{θ,φ)άφάθ

wherein d . is a normalized distance with respect to a wavelength ( λ ) of a carrier between two antennas along the first side of the two-dimensional array, Θ is an elevation angle above a reference plane formed by the first side of the two-dimensional array and a direction perpendicular to the array, φ is an angle measured from a direction perpendicular to the array on the reference plane, and a domain of integration 0_k , <j>_k correspond to set k .

[0015]

The computer implemented simulator may be configured to determine the second ri,o ^r,

correlation matrix R'_k = using the following equation:

'i.O

ΛΤ-1

' -a

wherein N' is the number of antennas along the first side of the array, and parameter a' is defined based on a required Ergodic capacity expectation.

[0016]

The computer implemented simulator may be configured to determine the one or more third correlation matrices (R* ) by determining a third correlation matrix

' 0,0 ' 0,1

n

1,0 1,1

K for each set ( k ) of transmission paths using the following equation:

n

' i.O

Q_k =∑G{e_m , <p_m )

m=l

wherein d" _j is a normalized distance with respect to a wavelength ( λ ) of a carrier between two antennas (i, j) along the second side of the two-dimensional array, 9_m is an angle that sub-path (m) extends to a reference plane formed by the first side of the two-dimensional array and a direction perpendicular to the array, <p_m is an angle between the projection of the sub-path (m) on the reference plane and the direction perpendicular to the array, and M_k is the number of transmission paths in a set ( k ).

[0017]

The computer implemented simulator may be configured to determine the one or more third correlation matrices (ftt ) by determining a third correlation matrix e following equation:

wherein d"_j is the normalized distance with respect to a wavelength (λ ) of a carrier between two antennas (/^', j,) along the second side of the two-dimensional array, Θ is an elevation angle above a reference plane formed by the first side of the two-dimensional array and a direction perpendicular to the array, φ is an angle measured from the direction perpendicular to the array on the reference plane, and a domain of integration 0k, <>_k correspond to set k .

[0018]

The computer implemented simulator may be configured to determine a third

correlation matrix R"_k lowing equation:

wherein N" is the number of antennas along the second side of the array, and parameter a" is defined based on a required Ergodic capacity expectation.

[0019]

The computer implemented simulator may be further operable to determine spatially correlated coefficients for the simulated wireless transmission paths by being configured to: obtain a matrix square root of a receive correlation matrix, obtain a matrix square root of a transmit correlation matrix along direction 1,

R' = C'C "

obtain a matrix square root of a transmit correlation matrix along direction 2,

_R" ₌ Q

determine receiver correlation for each transmit antenna: determine transmit correlation along direction 1 for each transmit antenna along direction 2 and receive antenna

¾ = C¾ V/,/

determine transmit correlation along direction 2 for each transmit antenna along direction 1 and receive antenna

wherein H_{t j l} denotes uncorrelated input coefficients between a receive antenna , a transmit antenna given by index j along direction 1, and a transmit antenna given by index along direction 2.

[0020]

The computer implemented simulator may be further operable to determine a spatial correlation matrix ( R_SPO(/A/ ) for facilitating the designing, evaluating and testing of

three-dimensional beamforming, FD-MIMO algorithms in which a rectangular antenna array is used at a base station node and a linear antenna array is used at a user equipment, the spatial correlation matrix being determined based on the following Kronecker product formula:

H spatial ⁼ R'eAB ® ^"eNB ® ^UE

wherein

R._e'_NB is a correlation matrix of the rectangular antenna array at the base station node, and elements of matrix R'_EA¾ can be determined using a formula r . =a'^^N'~^ , is a further correlation matrix of the rectangular antenna array at the base station node, and elements of matrix R^ can be determined using a formula r". = " ,

RU_E is a correlation matrix of the linear antenna array at the user equipment,

'-j

and elements of matrix ^~R_UE can be determined using a formula: r. . =β^ι

N' , N" are the numbers of antennas at the base station node along two adjacent sides of the rectangular antenna array respectively,

N is the number of antennas at the user equipment, and

values for ' , a" and β for different correlation levels are selected from the following table 1 : [table 1]

[0021]

According to another aspect of the invention, a method for determining a first correlation matrix (R) simulating transmission path correlation between a base station and user equipment antennas is provided, the first correlation matrix (R) being determined for simulated wireless transmission paths of a plurality of antennas having the same polarization and arranged in a two-dimensional array, the method including the steps of:

determining one or more second correlation matrices (Rt ) for a subset of the antennas which form a first side of the array,

determining one or more third correlation matrices (R* ^") for a subset of the antennas which form a second side of the array adjacent the first side,

determining one or more fourth correlation matrices (Rt), each fourth correlation matrix being determined based on a Kronecker product (Rt- Rt ® Rt ) of each second correlation matrix (Rt ) and a corresponding third correlation matrix (Rt ), and

determining the first correlation matrix (R) simulating transmission path correlation by determining a weighted sum of the one or more fourth correlation matrices (Rt).

[0022]

The method may include:

determining a number of sets (K) for grouping the simulated wireless transmission paths,

determining weight factors associated with the one or more sets (K), and

determining the weighted sum of the one or more fourth correlation matrices (Rt) using the weight factors.

[0023]

The method may include:

dividing a three-dimensional transmission space of the transmission paths into a number of sectors equal to the number of sets (K), each sector being defined by an elevation angle range ( Θ ) and an azimuth angle range ( φ ), and grouping the transmission paths which have an elevation angle ( Θ) and an azimuth gle (φ ) falling within the same sector so as to form K sets of transmission paths.

[0024]

The method may include:

determining the one or more second correlation matrices (R*) by determining a second

correlation matrix R'_k for each set ( k) of transmission paths using the

followin equation:

Q_k =∑G(0_m ,<p_m )

m=l

wherein d'_j is a normalized distance with respect to a wavelength (λ ) of a carrier between two antennas (i, j) along the first side of the two-dimensional array, 0_m is an angle that a sub-path (m) extends to a reference plane formed by the first side of the two-dimensional array and a direction perpendicular to the array, φ_ιη is an angle between the projection of the sub-path

(m) on the reference plane and the direction perpendicular to the array, and M_k is the number of transmission paths in a set (k).

[0025]

The method may include:

determining the one or more second correlation matrices (R* ) by determining a second

Ό,ο ^ro,i '0,7

i,o Ί,ι

correlation matrix R'_k = for each set ( k ) of transmission paths using the

' ,0

following equation: r_u' = J j Ρ(θ, φ (θ, )exp(/27ztf ; _y cos Θ sin φ)άφάθ

wherein d'_j is the normalized distance with respect to a wavelength ( λ ) of a carrier between two antennas (/^', j) along the first side of the two-dimensional array, Θ is an elevation angle above a reference plane formed by the first side of the two-dimensional array and a direction perpendicular to the array, φ is an angle measured from the direction perpendicular to the array on the reference plane, and a domain of integration 9_k , _Ιι correspond to set k .

[0026]

The method may include determining a second correlation matrix

using the following equation:

wherein N' is the number of antenna along the first side of the array, and parameter defined based on a required Ergodic capacity expectation.

[0027]

The method may include determining the one or more third correlation matrices (R* ) ro,o Ό,Ι 'OJ

Ί,Ο ι

by determining a third correlation matrix R£ = for each set (k) of

Ί,Ο

transmission paths using the followin equation:

Q_k =∑G^_m ,<p_m )

m=l

wherein d " . is a normalized distance with respect to a wavelength ( λ ) of a carrier between two antennas (/^', j) along the second side of the two-dimensional array, 9_m is an angle that a sub-path m extends to a reference plane formed by the first side of the two-dimensional array and a direction perpendicular to the array, cp_m is an angle between the projection of the sub-path (m) on the reference plane and the direction perpendicular to the array, and M_k is the number of transmission paths in a set ( k ).

[0028] The method may include determining the one or more third correlation matrices (R* )

' 0,0 ' 0,1 '0,7

1,0 ' 1,1

by determining a third correlation matrix = for each set ( k ) of

'',0 '

transmission paths using the following equation:

¾ =— J J Ρ(θ, φ (θ, tp) x 2nd_u" *ιηθ)άφάθ

Q Λk θ_{ΙΙ ι},

wherein d"_} is a normalized distance with respect to a wavelength (λ ) of a carrier between two antennas (i, j,) along the second side of the two-dimensional array, Θ is an elevation angle above a reference plane formed by the first side of the two-dimensional array and a direction perpendicular to the array, ψ is an angle measured from a direction perpendicular to the array on the reference plane, and a domain of integration 6_k , <f>_k correspond to set k .

[0029]

The method may include determining a third correlation matrix

0,0 ^0,1

1,0 U

R: = using the following equation:

' ;,0 •

wherein N" is the number of antenna along the second side of the array, and parameter a" is defined based on a required Ergodic capacity expectation.

[0030]

The method may further include determining spatially correlated coefficients for the simulated wireless transmission paths by:

obtaining a matrix square root of a receive correlation matrix,

' C_SC_FT

obtaining a matrix square root of a transmitting correlation matrix along direction 1,

R' = C'^H

obtaining a matrix square root of a transmitting correlation matrix along direction 2, R' = CC^H

determining receiver correlation for each transmit antenna using the following formula:

H,., =c_fiH _;, vy,/

determining transmit correlation along direction 1 for each transmit antenna along direction 2 and receive antenna using the following formula:

determining transmit correlation along direction 2 for each transmit antenna along direction 1 and receive antenna using the following formula:

wherein H_{j j t} denotes uncorrelated input coefficients between a receive antenna , a transmit antenna given by index j along direction 1 , and a transmit antenna given by index / along direction 2.

[0031]

The method may further include determining a spatial correlation matrix

(R^) for facilitating the designing, evaluating and testing of three-dimensional beamforming,

FD-MIMO algorithms in which a rectangular antenna array is used at a base station node and a linear antenna array is used at a user equipment, the spatial correlation matrix being determined based on the following Kronecker product formula:

^spatial ⁼ ^-eNB ® ^eNB ® ^UE

wherein

R^_B is a correlation matrix of the rectangular antenna array at the base station

i-j

node, and elements of matrix n be determined using the formula: r■ = '' ΛΤ-1

R^ ca

is a further correlation matrix of the rectangular antenna array at the base station node, and elements of matrix R^ can be determined using the formula: τ^*". =c " JV-l

^~R_UE is a correlation matrix of the linear antenna array at the user equipment and elements of matrix R^ can be determined using the formula: =fi

N' , N" are the numbers of antennas at the base station node along two adjacent sides of the rectangular antenna array, N is the number of antennas at the user equipment, and

values for a', a" and β for different correlation levels are selected from the following table 2:

[table 2]

[0032]

In one embodiment, the invention provides a method for generating a set of correlation matrices defining the correlation between the advanced base station antennas such as eNodeB and advanced user equipment antennas in the case of three dimensional multi-antenna systems supporting baseband implemented 3D beamforming and full dimension MIMO techniques. The set of correlation matrices defining the correlation between the advanced base station antennas such as eNodeB and advanced user equipment antennas generated may be standardized to be realized by computerised simulation in designing, evaluating and validating features/functions related to 3D-beam forming and/or full dimensional MIMO. Moreover, the set of correlation matrices defining the correlation between the advanced base station antennas such as eNodeB and advanced user equipment antennas generated may be further realized for being implemented as an apparatus in a laboratory validating advanced base station and user equipment supporting 3D beamforming and full dimension MIMO techniques.

[0033]

According to the embodiment, the method generates a transmit and/or receive correlation matrix for multiple transmit and/or receive antennas arranged in rectangular array. A computationally and memory efficient system that can be used to obtain spatially correlated coefficients when the correlation matrix is obtained is also provided.

[0034]

The method may include first obtaining the correlation matrices for two linear antenna arrays forming either side of the rectangular array, and then performing a Kronecker product to obtain the correlation matrix of the rectangular array of antennas.

[0035]

The method may include obtaining the correlation matrix of the rectangular array of antennas as the sum of correlation matrices, wherein each correlation matrix is formed while considering only a sub-set of non-overlapping scatterers.

[0036]

The generated transmit and/or receive correlation matrix may be used to generate a spatial correlation matrix of a MIMO channel for the emulation of MIMO wireless channel.

[0037]

Advantageously, embodiments of the invention provide a method for establishing a control environment such as computerized simulation for designing, evaluating and validating Active antenna system technologies including 3D beam forming and Full Dimensional MIMO.

[0038]

More particularly, embodiments of the present invention enable sufficiently accurate emulation of MIMO wireless channels to evaluate new technologies such as elevation beamforming and FD-MIMO. The method can advantageously be executed by a system in a manner that is computationally efficient for large number of antennas arranged in a rectangular array.

[0039]

Embodiments of the invention further provides a method to generate the transmit and/or receive correlation matrix for a rectangular antenna array that can advantageously be used for link level emulation of a MIMO wireless channel that is accurate enough for computerized evaluating and testing wireless systems/devices/algorithm that employ 3D elevation

beamforming and FD-MIMO technologies.

[0040]

Moreover, embodiments of the invention provides a computationally and memory efficient system that can be used to obtain spatially correlated coefficients when the correlation matrix is obtained based on the above method.

[0041]

Any of the features described herein can be combined in any combination with any one or more of the other features described herein within the scope of the invention.

[0042]

The reference to any prior art in this specification is not and should not be taken as an acknowledgement or any form of suggestion that the prior art forms part of the common general knowledge.

Advantageous Effects of Invention

[0043] According to the present invention, it is possible to provide a simulator and method for simulating transmission path correlation between base station and user equipment antennas with sufficient accuracy, as well as computational and memory efficiency. Brief Description of Drawings

[0044]

Preferred features, embodiments and variations of the invention may be discerned from the following Detailed Description which provides sufficient information for those skilled in the art to perform the invention. The Detailed Description is not to be regarded as limiting the scope of the preceding Summary of the Invention in any way. The Detailed Description will make reference to a number of drawings as follows:

[Fig. 1]

Fig. 1 is a schematic diagram illustrating wireless transmission paths between a transmitter and a receiver.

[Fig. 2]

Fig. 2 is a schematic diagram illustrating a tapped delay line system for emulating the transmission paths of Fig. 1.

[Fig. 3]

Fig. 3 is a schematic diagram of a tap coefficient generator for generating coefficients used in the tapped delay line system of Fig. 2.

[Fig. 4]

Fig. 4 is a schematic diagram illustrating wireless transmission paths between four transmitters and two receivers in a Multiple Input Multiple Output (MIMO) channel system. [Fig- 5]

Fig. 5 is a schematic diagram illustrating emulator system for emulating the

transmission paths of Fig. 4.

[Fig- 6]

Fig. 6 is a schematic diagram illustrating cross-polarized antenna configurations.

[Fig. 7]

Fig. 7 is a schematic diagram illustrating a linear antenna array.

[Fig. 8]

Fig. 8 is a schematic diagram illustrating 3 dimensional scattering of a group of transmission paths.

[Fig. 9] Fig. 9 is a schematic diagram illustrating a rectangular antenna array.

[Fig. 10]

Fig. 10 is a flow diagram illustrating a method for determining a first correlation matrix (R) simulating transmission path correlation between a base station and user equipment antennas according to an embodiment of the present invention.

[Fig. 11]

Fig. 11 is a schematic diagram of a system for introducing spatial correlation based on the first correlation matrix (R) determined using the method of Fig. 10. It describes the case where K=l.

Description of Embodiments

[0045]

The following table 3 provides an explanation of the abbreviations used in the present specification.

[table 3]

Abbreviation Description

3D Three Dimension

3 GPP 3^rd Generation Partnership Project

AAS Active Antenna Systems

AoA Azimuth angle of Arrival

AoD Azimuth angle of Departure

DL Down Link

EoA Elevation angle of Arrival

EoD Elevation angle of Departure eNB/eNodeB Enhanced Based Station Node (NodeB)

FD-MIMO Full Dimension - MIMO LTE Long Term Evolution

LTE-A LTE Advanced

MIMO Multiple Input Multiple Output

RF Radio Frequency rms Root Mean Square

UE User Equipment

[0046]

Traditionally, a single link of a wireless channel can be represented as illustrated in Fig. 1. A radio signal from a transmitter 121, due to the presence of various scattering objects 110, and 111 in the environment, propagates along multiple sub-paths 151-156 and reaches the receiver 131 at different delays with different phases and amplitudes. At a receiver, it is not possible to resolve the signals from the paths when they arrive with small relative delays. In Fig. 1, sub-paths 151-153 that arrive with small relative delays are clustered into one path 141 and sub-paths 154-156 that arrive with small relative delays are clustered into another path 142.

[0047]

Furthermore, the small scale (i.e. microscopic) fading of a single link of a wireless channel in a discretized time baseband can be emulated using a tapped delay line system 200 shown in Fig. 2. The taps in the tapped delay line correspond to the resolvable paths. The complex tap coefficients 221 to 224 correspond to the amplitude and phase of the signal along each resolvable path.

[0048]

Considering that each resolvable path consists of possibly many sub-paths, the tap coefficients 221-224 are generally characterized by an independent zero-mean complex valued Gaussian process.

[0049]

An exemplary system used to generate the tap coefficients 221-224 is further illustrated in Fig. 3. Each tap coefficient 221 to 224 in system 200 shown in Fig. 2 is generated by filtering the output of a complex white Gaussian noise generator 311 by a Doppler filter 321.

[0050]

The Doppler filter is introduced to take into account the variation of the tap coefficients with time due to the transmitter or receiver mobility. The Doppler filter is generally characterized by the Jakes power spectrum.

[0051]

Smart antenna technology such as MIMO has been shown to improve the performance of mobile radio systems and has been incorporated into the latest mobile standards, for example, 3rd Generation Partnership Project (3 GPP) LTE/LTE-A.

[0052]

Smart antenna technology generally uses multiple antennas at the transmitter and receiver and use spatial processing to combine the signals from the multiple antennas.

[0053]

In order to verify the performance and functionality of this technology it is necessary to emulate the channel between each of the transmit-receive antenna pairs. This channel is normally referred to as the MIMO channel.

[0054]

An exemplary antenna configuration forming a MIMO channel is illustrated in Fig. 4.

There are four antennas 0,1,2 and 3 at the transmitters numbered 462 to 465 arranged linearly and two antennas 0 and 1 at the receivers numbered 472, 473. The channel between a

transmit-receive antenna pair is commonly referred to as a branch. For example a branch 7 representing the channel between transmit antenna 3 (465) and receive antenna 1 (473) is numbered as 481.

[0055]

An exemplary system 500 to emulate the MIMO channel in example of the antenna configuration 400 is illustrated in Fig. 5. The MIMO channel is commonly emulated using multiple tapped delay lines, i.e. one tapped delay line for example, tapped delay line system 200 to emulate one branch, for example, branch 481. The system also consists of multiple

sub-systems 510 each of which generates tap coefficients for each branch of a single tap.

[0056]

An exemplary system 510 to emulate the tap coefficients for a single tap of the MIMO channel in example of the antenna configuration 400 is illustrated in Fig. 5. It consists of multiple blocks 300 for generating independent Doppler-filtered white Gaussian noise for each branch of the MIMO channel. This is followed by a spatial correlator 520 to introduce correlation between the branches.

• [0057] The spatial correlator 520 performs linear filtering on the uncorrelated input coefficients to produce correlated coefficients.

[0058]

This operation can be mathematically expressed by the following formula, correlator

h = Ch

where h represents the input vector (of size 8(=4x2) in the example of the antenna

configuration 400) of uncorrelated tap coefficients and h represent the output vector (of size 8(=4x2) in the example of the antenna configuration 400) of correlated tap coefficients and C the linear filtering matrix (of size 8 by 8 in the example of the antenna configuration 400).

[0059]

The correlation between the tap coefficients h_t and A . is then given by the /th row and j th column of the following matrix R ;

R = £[hh^/i J= E[chh ^/C^ff ]= CE[hh^/i ]c^w = CC"

[0060]

The correlation matrix R for a MIMO channel is generally estimated based on antennas characteristics and the scattering environment, and then the linear filtering matrix C is calculated as the square root of the correlation matrix R using techniques such as Cholesky decomposition.

[0061]

For wireless fading channels, when the transmitter array is placed far away from the receiver array (as is the case of mobile systems) and when all the antennas have the same polarization (as in the example of the antenna configuration 400), it is possible to compute the correlation matrix R as

R = R_r ®R_S

where R_r is the transmit-side correlation matrix (of size 4 by 4 in the example of the antenna configuration 400), K_R is the receiver-side correlation matrix (of size 2 by 2 in the example of the antenna configuration 400) and <8> is the Kronecker product (NPL4). To use the above computation for R , the element of the input vector h (and consequently output vector h ) should be arranged in the following order, i.e.

h = [Ho ₀ , H_{1 0} , HQ ! , . . . H_! 3 f where H_l . . represents the tap coefficient between receive antenna i and transmit antenna j or in other words

h = vec(H)

where H is a matrix with elements H_fJ and operator vecQ represents stacking the columns of a matrix one below the other to form a vector.

[0062]

An example 600 of a cross polarized eNB antenna array and cross polarized UE antenna array is shown in Fig. 6. The eNB antenna array has four antennas 0,1,2 and 3 numbered 662-665. Antennas 0 (662) and 2 (664) have +45° polarization while antennas 1 (663) and 3 (665) have -45° polarization. The UE antenna array has two antennas 0 and 1 numbered 672 and 673. Antenna 0 (672) has horizontal polarization while antenna 1 (673) has vertical polarization.

[0063]

In the DL, when the cross polarized eNB antenna array is used for transmission and the cross polarized UE antenna array is used for reception, the correlation matrix R can be computed as

R = R_r ⁽8>r®R_s

where R_r is the transmit-side correlation matrix for the sub-array of a transmit antenna with the same polarization (of size 2 by 2 for the example in 600), K_R is the receiver-side correlation matrix for the sub-array of transmit antennas with the same polarization (of size 1 by 1 for the example in 600), Γ is the polarization correlation between the different polarizations (of size 4 by 4 for the example in 600) and ® is the Kronecker product (NPL4). Please note that to use the above computation for R , the element of the input vector h (and consequently output vector h ) should be arranged appropriately.

[0064]

The transmit-side correlation matrix for an array of transmit antenna with the same polarization is estimated based on the transmit antenna characteristics and the scattering environment around the transmitter. The receiver-side correlation matrix is estimated based on the receive antenna characteristics and the scattering environment around the receiver.

[0065]

Fig. 7 illustrates an array of four transmit antennas 0,1,2 and 3 numbered 751 to 754 for example on an eNB of a cellular system equally spaced along the axis 730.

[0066] Fig. 8 illustrates the multiple sub-paths of path 810 corresponding to a tap for which the transmit-side correlation matrix R_r or receive side correlation matrix is estimated .

[0067]

Path 810 has many sub-paths M . The direction of a sub-path m for example 820, can be specified with reference to the co-ordinate references 710, 720, 730 by two angles, elevation angle 6_m (821) and azimuth angle φ_η (822).

[0068]

The following methods were traditionally used to calculate the transmit (or receive) correlation matrix, R_r (or R_¾ ). Note that for the traditional evaluation of MIMO systems it was considered sufficient to characterize the scatterers only in the horizontal plane and thus in the below Method A and Method B only the azimuth angle of scatterers are considered in the computation.

[0069]

(Method A: Direct calculation considering only azimuth angle of scatterers)

The elements of the correlation matrix can be calculated using the following formula,

where,

G( 9_m) is the square of the radiation pattern along the azimuth angle ^^m in the plane formed by axis 720 and 730,

d_i j is the normalized (by the carrier wavelength) distance between the two antennas, and

[0070]

(Method B: Using distribution function for azimuth angle of scatterers)

The sub-path azimuth angle φ_ηι is commonly modelled using probability distributions.

For example, when the sub-path azimuth angles in degrees have Laplace distribution

where σ is the rms azimuth angle spread and φ is the AoA or AoD of the path.

[0071]

In this case, the elements of the correlation matrix can be calculated using the following general formula,

which can be evaluated using numerical integration or Bessel series expansion (NPL5).

[0072]

For example, a following table 4 is reproduced from NPL7, showing the complex correlation values and the magnitude for different antenna spacing, variance, AoD or AoA at eNB (3 -sector antenna pattern) and UE (omni-directional antenna pattern) where Laplacian distribution has been assumed for the azimuth angle of scatterers.

[table 4]

[0073]

(Method C: Pragmatic approach based on capacity)

To simplify the testing of mobile equipment, a pragmatic approach not based on antenna configurations, but rather based on "artificial" values is defined for the correlation matrix (NPL4).

[0074]

The elements of the correlation matrix are calculated as follows

'-J

N-l where N is the number of transmit antennas and parameter a is selected based on the required ergodic capacity expectation of the MIMO channel.

[0075]

For example, a following table 5 captures the a values used in NPL4, together with the expected capacity for different MIMO channels. In the table 5, C₀ is the capacity when the antennas are completely uncorrelated, C\ is the capacity when the antennas are fully correlated and C_x is the capacity when the antenna correlation is given by the selected values of a_eNB , ^aUE ·

[table 5]

[0076]

The performance of the cellular systems can be improved considerably by techniques such as elevation beamforming and FD-MIMO. Elevation beamforming is a technique where signal processing is used at the base station to adapt the transmit beam/(s) in both horizontal and vertical planes to improve the received signal level at a particular user while reducing the interference with other users. FD-MIMO is another technique where a large number of antennas are used at a base station to form narrow beams that can be adapted in both horizontal and vertical planes.

[0077]

AAS technology such as eNB antenna implementation is being considered for a base station. In AAS technology, the RF circuitry is integrated into the antenna. This technology makes it possible to have more antennas at eNB and allows flexibility in their arrangement that is controllable at a base-band level.

[0078]

Fig. 9 illustrates a scheme where 16 antennas are used at a base station such as eNB and arranged in a rectangular array.

[0079]

By arranging antennas in a rectangular array, it is now possible to perform spatial processing to adapt the transmit beams in both horizontal and vertical planes. Meanwhile, the eNB antenna arranged in a linear array as shown foran example in Fig. 7 is only able to adapt the transmit beams in the horizontal plane.

[0080]

To verify the performance of these new technologies by modelling simulation, it is necessary to emulate the mobile radio channels taking into account the antennas

arrangement/configuration and scattering environment in both the directions.

[0081]

To emulate this MIMO channel, it is possible to follow the same general method as in the case of linear antenna arrays where the antennas are arranged along one direction, i.e. tapped delay line model, 200 can be used to model each branch with tap coefficients generated for example as described with reference to the emulator system 500. The Doppler filtering approach used for linear antenna arrays can be used also for the case of rectangular antenna array.

[0082]

The method for estimation of the correlation matrix used for 520 is described below.

Advantageously, the estimation method described below also allows for simpler implementation to handle large number of antennas.

[0083] The method estimates the correlation matrix R for a MIMO channel taking into account a rectangular antenna arrangement and three dimensional scattering environment.

Further, a system is presented that shows how this method could be implemented with a low computational complexity and memory requirement.

[0084]

Fig. 9 illustrates an example of a rectangular antenna array at a base station such as LTE's eNB in a cellular system to which the current invention may be applied.

[0085]

The rectangular antenna array in Fig. 9 includes antennas with identical polarisation numbered from 911 to 914, from 921 to 924, from 931 to 934, from 941 to 944 arranged in a rectangular pattern in a plane 740. The plane 740 is formed by two perpendicular axes 710 and 730 (i.e. same axes, plane as in Fig. 8).

[0086]

For example, the rectangular antenna array at an eNB can be positioned so that a axis 720 perpendicular to the plane 740 is pointing towards the middle of a sector served by the planar array.

[0087]

The main aspect of the current invention is a method to generate the transmit (or receive) correlation matrix of an array of identically polarized antennas arranged rectangularly instead of a traditional array of identically polarized antennas arranged linearly in one direction, for example, horizontally. For the evaluation of the correlation matrix, this method further considers 3D scattering where, for example, the scatterers are characterized by azimuth and elevation angles instead of 2D scattering where, for example, scatterers are characterized only by azimuth angles. This is an important feature for evaluating techniques such as 3D elevation beamforming and FD-MIMO.

[0088]

This transmit (or receive) correlation matrix can be used to obtain the spatial correlation matrix for implementation as the spatial correlator 520 in the exemplary system 500 to filter spatially uncorrelated tap coefficients of a tap to obtain spatially correlated tap coefficients. Some examples are provided below.

[0089]

(Example A)

In the UL of a cellular system where the eNB uses a vertically polarized rectangular antenna array and UE uses a vertically polarized linear (horizontal) antenna array, the spatial correlation matrix, ϋ_ψο„_α, is computed as,

H spatial = ^R T ® ^R ?

^■-■·

where R_r is the transmit correlation matrix for the antenna array at UE and R_s is the receive correlation matrix at eNB. The present method provides a means for computing R^ .

[0090]

(Example B)

In the DL of a cellular system where the eNB uses a cross polarized rectangular antenna array and UE uses a vertically polarized linear (horizontal) antenna array, the spatial correlation matrix, R_spalial is computed as,

R„_fl„,, = R_r ® r ® R,

where R_r is the transmit correlation matrix for the sub-array of transmit antennas with the same polarization, R^ is the receive correlation matrix and Γ is the polarization correlation between the different polarizations. The method also provides a means for computing R_r .

[0091]

The element η _} of a transmit (or receive) correlation matrix R represents the correlation between the complex envelope of the signal transmitted (or received) by antenna i and the complex envelope of the si nal transmitted (or received) by antenna j .

[0092]

In reference to the exemplary rectangular antenna array shown in Fig. 9, if the antennas

0, 1, 2 and 3 are numbered as 911, 912, 913 and 914 respectively, antennas 4, 5, 6 and 7 are numbered as 921, 922, 923 and 924 respectively, antennas 8, 9, 10 and 11 are numbered as 931, 932, 933 and 934 respectively and antennas 12, 13, 14 and 15 are numbered as 941, 942, 943 and 944 respectively, then the element r_{0 10} of the correlation matrix R represents the correlation between the complex envelope of the signal transmitted (or received) by antenna 0 (911) and antenna 10 (933).

[0093]

The elements η _} of the correlation matrix can be obtained using the following methods.

[0094]

(Method 1 : Direct calculation considering azimuth and elevation angles of scatterers) Referrence will now be made to the example propagation condition in Fig. 8. A path 810 has many sub-paths M . The direction of a sub-path m , for example, sub-path 820 can be specified with reference to the co-ordinate reference 81 1 , 812, 813 by two angles, elevation angle, 9_m (821) and azimuth angle, ^^m (822), and the elements of the correlation matrix can be calculated using the following general formula,

where,

k = 2π I λ , and λ is the wavelength of the carrier

G{G_m ,<p_m) is the square of the antenna radiation pattern along the direction

d, . = . - x, , and x, is the position vector of antenna / l(#_m , <p_m ) is the unit vector along the direction ( 6_m , <p_m )

M

Q is a normalization constant given by Q = G(0_m , (p_m ), and

(x,y) represent a dot product of two vectors x and y .

[0095]

(Method 2: Using distribution function for azimuth and elevation angles of scatterers) The sub-path directions ( θ_η,φ_Μ ) can be modelled using probability distributions. For example, when the sub-paths azimuth angle in degrees and elevation angle in degrees are modelled independently to have Laplace distribution, i.e.

Ρ(θ, φ) = Ρ(θ)ρ(φ)

where σ_θ , σ_φ are the rms elevation angle spread and rms azimuth angle spread and

θ , φ are EoA/EoD and AoA/AoD of the path.

[0096]

In this case, probability distribution is used to model the sub-paths. The elements of the correlation matrix can be calculated using the following general formulas,

Θ Φ α = \\ρ{θ, φ)ρ{θ,φ)άφάθ

where,

k = 2π/λ , where λ is the wavelength of the carrier

G{e, φ) is the square of the antenna radiation pattern along the direction ( θ,φ ) d, _j = x . - x, where x, is the position vector of the antenna i

1(6?, φ) is the unit vector along the direction (θ,φ ), and

(x,y) represent a dot product of two vectors x and y .

[0097]

The above expression can be evaluated using numerical integration or spherical harmonic series expansion (NPL5).

[0098]

The above Method 1 and Method 2 can be used to generate the correlation matrix where the multiple antennas have an arbitrary location. However, when the multiple antennas are arranged in a rectangular array, then an approximate generation of the correlation matrix can be obtained with a lower computational complexity (which is significant especially when the number of antennas is high) using Method 3 below.

[0099]

(Method 3: Kronecker method (1000) comprises the following steps)

Step 0 (1010): This is an optional step based on what method is used in Step 1.

[0100]

If Method 3-1-1 is used in Stepl, then this step consists of, grouping. Two examples are shown below.

[0101] Example 1 : K = 1

All the sub-paths are assumed to be in one set.

[0102]

Example 2: K = 4

Divide the solid angle formed by Θ π/ π/ φ = [- π, π] into Κ solid angles as

/2 2

set 3: Θ = )Θ Λ φ = [- π,φ]

21

[0103]

If the angle of a sub-path falls within the solid angle of the set, then that sub-path is considered to be in that set.

[0104]

Example 3: K = 16

Divide the solid angl φ = [- π,π] into K solid angles follows. In this example θ =

[table 6]

[0106]

If Method 3-1-2 is used in Step 1, then this step includes the steps of, dividing the total solid angle of integration into K non-overlapping solid angles. This can be done in a manner to that in Example 2 above. If K = 1 , then the integration is performed over the total solid angle.

[0107]

If Method 3-1-3 is used in Step 1 then this step is omitted and K = l [_s assumed.

[0108]

Step 1 (1020): For each set, calculate the correlation matrix for the row of the antenna array that forms one dimension of the rectangular array. In reference to the exemplary rectangular array system shown in Fig. 9, the linear array 950 along one direction of the rectangular array is formed by the antennas 911, 912, 913 and 914. If the antennas 0 (911), 1 (912), 2 (913) and 3 (914) are indexed as 0, 1, 2 and 3 respectively, then K'_k describes the following correlation matrix:

The following methods can be used for this calculation.

[0109]

Method 3-1-1 : Similar to Method 1 (i.e. "Direct calculation considering azimuth and elevation angle of scatterers"). But only the sub-paths within the corresponding set (as obtained in StepO) are used in the calculation, i.e. using notation similar to that in Method 1,

m=l where,

d'_j is the normalized distance between the two antennas along the considered dimension of the rectangular array (normalization is with respect to λ , the wavelength of the carrier), and M_k is the number of rays in set k .

[0110]

Method 3-1-2: Similar to Method 2 (i.e. "Using distribution function for azimuth and elevation angle of scatterers"). But the integration is performed over the solid angles of the set (as obtained in Step 0), i.e. using notation similar to that in Method 2,

cos Θ sin φ)άφάθ

where,

d'_j is the normalized distance between the two antennas along the considered dimension of the rectangular array (normalization is with respect to λ , the wavelength of the carrier), and domain of integration 0_k , φ_Ιί corresponds to set k .

[0111]

Method 3-1-3 : A pragmatic approach, i.e. the elements of the correlation matrix are calculated as follows

where N' is the number of transmit antennas along the considered direction and parameter a' is defined based on the required Ergodic capacity expectation.

[0112]

Step 2 (1030): For each set, calculate the correlation matrix for the column of the antenna array that forms the other side (refer to Step 1 above) of the rectangular array. In reference to the exemplary rectangular array system shown in Fig. 9, the linear array 960 along the other direction is formed by the antennas 911 , 921 , 931 and 941. If the antennas 0 (91 1), 4 (921), 8 (931) and 12 (941) are indexed 0, 1, 2 and 3 respectively, then R"_k describes the following correlation matrix: ro,o ^ro,i ^■ - >"0,3

ri,o ^ru ^■ ·· la [0113]

Depending on which method Method 3-1-1, Method 3-1-2, or Method 3-1-3 is used in Step 1, Method 3-2-1, Method 3-2-2 or Method 3-2-3 is respectively used in Step 2. Method 3-2-1, Method 3-2-2 and Method 3-2-3 are similar to Method 3-1-1, Method 3-1-2 and Method 3-1-3 respectively.

[0114]

Method 3-2-1 : Similar to Method 1 (i.e. "Direct calculation considering azimuth and elevation angle of scatterers"). But only the sub-paths within the corresponding set (as obtained in Step 0) are used in the calculation, i.e. using notation to that in Method 1,

Q_k =∑G{e_m ,9_m ) where,

d"_j is the normalized distance between the two antennas along the considered dimension of the rectangular array (normalization is with respect to λ , the wavelength of the carrier), and M_k is the number of rays in set k and contains the same set of rays as that in Step 1.

[0115]

Method 3-2-2: Similar to Method 2 (i.e. "Using distribution function for azimuth and elevation angle of scatterers"). But the integration is performed over the solid angles of the set (as obtained in Step 0), i.e. using notation to that in Method 2, r'_j = - - j J Ρ(θ, φ)ρ(θ, ₉)∞djlnd sin θ)άφάθ

where,

d"

is the normalized distance between the two antennas along the considered dimension of the rectangular array (normalization is with respect to λ , the wavelength of the carrier), and domain of integration 9_k , φ_Ι[ corresponds to set k .

[0116]

Method 3-2-3: A pragmatic approach, i.e. the elements of the correlation matrix are calculated as follows

where N" is the number of transmit antennas along the considered direction and parameter a" is defined based on the required Ergodic capacity expectation.

[0117]

Step3 (1040): For each set, obtain the following per set correlation matrix of the rectangular array as the Kronecker product of the two correlation matrices calculated in Step 1 and Step 2:

R* = R; ® R;

[0118]

In reference to the exemplary rectangular array system shown in Fig. 9, the above

Kronecker product can be explained as follows. The correlation, r, between the antenna 911 and the antenna 933 for set k is given as the product of the correlation, r! between the antenna 911 and the antenna 913 and the correlation, νζ between the antenna 911 and the antenna 931, i.e. r_t = r." . [0119]

Step 4 (1050): The final correlation matrix is given as a weighted sum of the per set correlation matrices.

[0120]

(Evaluations and suggestion for values)

If Method 3-1-2 is used in Step 1, the following table 7 captures the maximum (over different AoAs and EoAs) absolute error in the estimation of the correlation values of using Method3 as compared to the exact calculation using Method 2 between 2 antennas along the

d' ~ d"

diagonal of the rectangular array (i.e. ^{i ~ i} ). 3-sector antenna pattern at eNB and Laplacian distribution for the azimuth and elevation of scatterers were assumed. From the results, the following observations were made:

The accuracy improves as K increases. In general, the accuracy improves for lower inter antenna distances.

In general, the accuracy improves for lower rms angular spreads.

K=l give reasonable accuracy when the angle of spread is low (2 degrees) and the rectangular array span is less than 4 ^λ on either direction.

[table 7]

[0121]

If Method 3-1-3 is used in Step 1, the following table 8 captures the capacity for different values of a', a" in Step 1 and Step 2. From the results, it is proposed that the same values for ' and a" can be used to test the system at different correlation levels and ', can be assigned the same value of as defined in NPL4 for low, medium and high

correlations.

[table 8]

Correlation a' a" ^aUE = ^C° ^C"

(Stepl) (Step2) C ⁰— C ¹ for different configurations of

[(Number of eNB antennas direction 1, N _x

Number of eNB antennas direction 2, ^ ) x

Number of UE antennas] (2x2)x2 (4x2)x2 (4x4)x2 (4x4)x4

Low 0 0 0 0 0 0 0

Medium 0.3 0.3 0.9 0.4849 0.5493 0.5834 0.8405

High 0.9 0.9 0.9 0.7650 0.8122 0.8501 0.9424

[0122]

(System (1100) for implementation of Method 3)

The calculation of the correlation matrix as per Method 3 advantageously allows more efficient implementation of the spatial correlator. An example of the spatial correlator's system 1100 is shown in Fig. 11 for the case of 4 transmit antennas with the same polarization arranged in a 2x2 rectangular fashion and 2 receive antennas with the same polarization arranged linearly. Also K=l in Step 0 of Method 3 is shown in the example.

[0123]

The system 1100 has three separate spatial correlators 11 10, 1120 and 1130 which are used to successively correlate the input coefficients.

[0124]

If the uncorrelated input coefficients between the receive antenna , and a transmit antenna given by index / along direction 1 and index / along direction 2 are denoted by

H_j , , then the operations of 1110, 1120 and 1130 are shown below.

[0125]

The notation A. refers to the vector

where index ¹ has the following range 0,1,· ·· / - ! .

[0126]

Receive Spatial Correlator (1110) performs the following operation:

[0128]

Transmit Spatial Correlator 2 (1130) performs the following operation: [0129]

The implementation shown in this example can be similarly extended to other values of K in Step 0 and can be similarly extended to handle cross polarized antenna arrays. This implementation allows the order of the correlators 1110, 1120, 1130 to be interchanged and thus is computationally efficient and requires lower memory resources.

[0130]

Accordingly, the method can be used to obtain spatially correlated coefficients when the correlation matrix is obtained as described above. The uncorrelated input coefficients between the receive antenna , and transmit antenna given by index j along direction 1 and index along direction 2 are denoted by H, . _; .

[0131]

The method includes obtaining the matrix square root of a receive correlation matrix, a transmit correlation matrix along direction 1 , and a transmit correlation matrix along direction 2 using Cholesky decomposition:

R' = C'C

R" = C^ffC"

[0132]

Introducing receiver correlation for each transmit antenna:

K_M = C_RH._M Vj,l

[0133]

Introducing transmit correlation along direction 1 for each transmit antenna along direction 2 and receive antenna:

[0134]

Introducing transmit correlation along direction 2 for each transmit antenna along direction 1 and receive antenna:

[0135]

The order of introducing the correlation above can be arbitrary. Pragmatic spatial correlation matrices can also be determined based on Method 3. The pragmatic spatial correlation matrices are used for the designing, evaluating and testing of 3D beamforming, FD-MIMO algorithms where a rectangular antenna array is used at eNB and a linear array is used at UE:

R spatial ⁼ ^'eNB ® ^ "eNB ® ^UE where r'j =a'^^{N lj} are the elements of matrix R'_eNB , r'j =a"^^{N lj} are the elements of matrix R"_ws and η . =β^{ΙΝ 1J} are the elements of matrix . N¹ , N" are the number of eNB antennas along the two adjacent sides of the rectangular antenna array and N is the number of antennas at the UE.

[0137]

The values for a! , a" and β for different correlation levels are proposed in the following table 9:

[table 9]

[0138]

Advantageously, the set of correlation matrices determined above can be used in realizing a computerised simulation system for designing, evaluating and validating

featoes/functions related to 3D-beam forming and/or full dimensional MIMO.

[0139]

In addition, the correlation matrices can also be used in implementing apparatus such as test equipment utilized in a laboratory for validating an advanced base station and user equipment supporting 3D beamforming and full dimension MIMO techniques.

[0140]

Advantageously, the method can be used for generating a transmit (or receive) correlation matrix for a rectangular antenna array that can be used for link level emulation of a MIMO wireless channel that is accurate enough for evaluating and testing wireless systems that employ 3D elevation beamforming and FD-MIMO technologies and yet computationally efficient for a large number of antennas.

[0141]

Moreover, a computationally efficient and memory efficient system is advantageously provided for implementing the spatial correlation based on the method.

[0142]

In the present specification and claims (if any), the word 'comprising' and its derivatives including 'comprises' and 'comprise' include each of the stated integers but does not exclude the inclusion of one or more further integers.

[0143]

Reference throughout this specification to One embodiment' or 'an embodiment' means that a particular feature, structure, or characteristic described in connection with the embodiment is included in at least one embodiment of the present invention. Thus, the phrases 'in one embodiment' or 'in an embodiment' in various places throughout this specification are not necessarily all referring to the same embodiment. Furthermore, the particular features, structures, or characteristics of the various embodiments may be combined in any suitable manner in one or more combinations.

[0144]

In compliance with the statute which one, the invention has been described in language more or less specific to structural or methodical features. It is to be understood that the invention is not limited to specific features shown or described since the means herein described comprises preferred forms of putting the invention into effect. The invention is, therefore, claimed in any of its forms or modifications within the proper scope of the appended claims (if any) appropriately interpreted by those skilled in the art.

[0145]

Various other modifications will be apparent to those skilled in the art and thus will not be described in further detail here.

[0146]

This software can be stored in various types of non-transitory computer readable media and thereby supplied to computers. The non-transitory computer readable media includes various types of tangible storage media. Examples of the non-transitory computer readable media include a magnetic recording medium (such as a flexible disk, a magnetic tape, and a hard disk drive), a magneto-optic recording medium (such as a magneto-optic disk), a CD-ROM (Read Only Memory), a CD-R, and a CD-R/W, and a semiconductor memory (such as a mask ROM, a PROM (Programmable ROM), an EPROM (Erasable PROM), a flash ROM, and a RAM (Random Access Memory)). Further, the program can be supplied to computers by using various types of transitory computer readable media. Examples of the transitory computer readable media include an electrical signal, an optical signal, and an electromagnetic wave. The transitory computer readable media can be used to supply programs to computer through a wire communication path such as an electrical wire and an optical fiber, or wireless

communication path.

[0147]

This application is based upon and claims the benefit of priority from Australian

Provisional Patent Application No.2013902848 filed on 31 July, 2013, the disclosure of which is incorporated herein in its entirety by reference.

Reference Signs List

[0148]

100 wireless transmission paths

110 scattering object

111 scattering object

121 transmitter

131 receiver

141 path

142 path

151 sub-path

152 sub-path

153 sub-path

154 sub-path

155 sub-path

156 sub-path

200 tapped delay line system

210 delay

221 tap coefficient

222 tap coefficient

223 tap coefficient

224 tap coefficient 230 SUM

300 tap

311 complex white Gaussian noise ;

321 Doppler filter

400 antenna configuration

462 transmitter

463 transmitter

464 transmitter

465 transmitter

472 receiver

473 receiver

481 channel

500 system

510 sub-system

520 spatial correlator

521 Kronecker product

522 Cholesky decomposition

600 antenna array

662 antenna

663 antenna

664 antenna

665 antenna

672 antenna

673 antenna

700 linear antenna array

710 axis

720 axis

730 axis

740 plane

751 transmit antenna

752 transmit antenna

753 transmit antenna

754 transmit antenna

800 group of transmission paths 810 path

811 co-ordinate reference

812 co-ordinate reference

820 sub-path

821 elevation angle

822 azimuth angle

900 rectangular antenna array

911 antenna

912 antenna

913 antenna

914 antenna

921 antenna

931 antenna

933 antenna

941 antenna

950 linear array

960 linear array

970 horizontal array antennae

980 horizontal array antennae

990 vertical array antennae

1100 system

1110 receive spatial correlator transmit spatial correlator transmit spatial correlator

Claims

[Claim 1]

A computer implemented simulator operable to determine a first correlation matrix (R) simulating transmission path correlation between a base station and user equipment antennas, the first correlation matrix (R) being determined for simulated wireless transmission paths of a plurality of antennas having the same polarization and arranged in a two-dimensional array, the computer implemented simulator being configured to:

determine one or more third correlation matrices (Rjt ) for a subset of the antennas which form a second side of the array,

determine one or more fourth correlation matrices (Rt), each fourth correlation matrix being determined based on a Kronecker product (Rt= Rt ® Rt ) of each second correlation matrix (R ) and a corresponding third correlation matrix (Rt ), and

[Claim 2]

A computer implemented simulator as claimed in claim 1, wherein the array is rectangular and the second side is adjacent the first side, the computer implemented simulator being configured to:

determine a number of sets (K) for grouping the simulated wireless transmission paths, determine weight factors associated with the number of sets (K) , and

[Claim 3]

A computer implemented simulator as claimed in claim 2, wherein the computer implemented simulator is configured to:

divide a three-dimensional transmission space of the transmission paths into a number of sectors equal to the number of sets (K), each sector being defined by an elevation angle range (Θ ) and an azimuth angle range (φ ), and group the transmission paths which have an elevation angle (Θ) and an azimuth angle (<p ) falling within the same sector so as to form K sets of transmission paths.

[Claim 4]

A computer implemented simulator as claimed in claim 3, wherein the computer implemented simulator is configured to determine the one or more second correlation matrices

(Rjt ) by determining a second correlation matrix for each set ( k ) of

transmission paths using the followin equation: r'j = ^G(°m > 9 )exp(./27 j cos 6_m sin φ_η )

m=l

wherein d'_j is a normalized distance with respect to a wavelength ( λ ) of a carrier between two antennas (/, j) along the first side of the two-dimensional array, 9_m is an angle that sub-path (m) extends to a reference plane formed by the first side of the two-dimensional array and a direction perpendicular to the array, φ_πι is an angle between the projection of the sub-path

(m) on the reference plane and a direction perpendicular to the rectangular array, and M_k is the number of transmission paths in a set ( k ).

[Claim 5]

A computer implemented simulator as claimed in claim 3, wherein the computer implemented simulator is configured to determine one or more second correlation matrices (Rvt )

by determining a second correlation matrix for each set ( k ) of

transmission paths using the following equation: r_f'j =— J j Ρ(θ, φ)β(θ, φ)βχρ /2τκί_υ' cos Θ sin φ)άφάθ

Qk Θ,Φ,

wherein d'_j is a normalized distance with respect to a wavelength ( λ ) of a carrier between two antennas (/^', J) along the first side of the two-dimensional array, Θ is an elevation angle above a reference plane formed by the first side of the two-dimensional array and a direction perpendicular to the array, ψ is an angle measured from a direction perpendicular to the array on the reference plane, and a domain of integration 6_k , φ_Ιι corresponds to set k .

[Claim 6]

A computer implemented simulator as claimed in claim 1, wherein the computer implemented simulator is confi ured to determine the second correlation matrix

[Claim 7]

A computer implemented simulator as claimed in claim 3, wherein the computer implemented simulator is configured to determine one or more third correlation matrices (Rjt ) ro,o ^ro,i

1,0 'U

by determining a third correlation matrix for each set ( k ) of

Ί.0 'J

transmission paths using the following equation:

M,

Q_k =∑G(0_m ,<p_m ) wherein d"_j is a normalized distance with respect to a wavelength ( λ ) of a carrier between two antennas (/, j) along the second side of the two-dimensional array, G_m is an angle that sub-path (m) extends to a reference plane formed by the first side of the two-dimensional array and a direction perpendicular to the array, φ_η is an angle between the projection of the sub-path on the reference plane and the direction perpendicular to the array, and M_k is the number of transmission paths in a set ( k ).

[Claim 8]

A computer implemented simulator as claimed in claim 3, wherein the computer implemented simulator is configured to determine one or more third correlation matrices (Rt )

'0,0 '0,1

' 1,1

by determining a third correlation matrix Rl for each set ( k ) of

' ,0

transmission paths usin the following equation:

<2, = \\ρ{θ,φΡ(θ,φ)άφάθ

wherein d- j is the normalized distance with respect to a wavelength ( λ ) of a carrier between two antennas (i, j,) along the second side of the two-dimensional array, Θ is an elevation angle above a reference plane formed by the first side of the two dimensional array and a direction perpendicular to the array, φ is the angle measured from a direction perpendicular to the array on the reference plane, and a domain of integration 9_k , φ_Ι( corresponds to set k .

[Claim 9]

A computer implemented simulator as claimed in claim 1, wherein the computer implemented simulator is configured to determine a third correlation matrix

' 0,0 ' 0,1

n r, it ,

K using the following equation:

' ί,Ο r IJ =a wherein N" is the number of antennas along the second side of the array, and parameter a" is defined based on a required Ergodic capacity expectation.

[Claim 10]

A computer implemented simulator as claimed in claim 1, wherein the computer implemented simulator is further operable to determine spatially correlated coefficients for the simulated wireless transmission paths by being configured to:

obtain a matrix square root of a receive correlation matrix,

^^■R ~ C^C_S

obtain a matrix square root of a transmit correlation matrix along direction 1 ,

R' = C'C'^H

obtain a matrix square root of a transmit correlation matrix along direction 2,

R" = CC^H

determine a receiver correlation for each transmit antenna:

determine a transmit correlation along direction 1 for each transmit antenna along direction 2 and receive antenna:

determine a transmit correlation along direction 2 for each transmit antenna along direction 1 and receive antenna:

wherein H_{t J} denotes uncorrected input coefficients between a receive antenna i , a transmit antenna given by index j along direction 1 , and a transmit antenna given by index / along direction 2.

[Claim 11]

A computer implemented simulator as claimed in claim 1, wherein the computer implemented simulator is further operable to determine a spatial correlation matrix ( R_spalial ) for facilitating the designing, evaluating and testing of three-dimensional beamforming, FD-MIMO algorithms in which a rectangular antenna array is used at a base station node and a linear antenna array is used at a user equipment, the spatial correlation matrix being determined based on the following Kronecker product formula:

R spatial ⁼ R'eNB ® ^"eNB ® ^UE wherein

R'_eNB is a correlation matrix of the rectangular antenna array at the base station node, and elements of matrix R^_s can be determined using formula r_{t J} =a'^lN~l1 ,

R'_jvg is a further correlation matrix of the rectangular antenna array at the base station node, and elements of matrix can be determined using formula r,". = "'

R_UE is a correlation matrix of the linear antenna array at the user equipment, and

>-j

elements of matrix _UE can be determined using formula: r_i . = ? N-\

N , N" are the numbers of antennas at the base station node along two adjacent sides of the rectangular antenna array, respectively,

N is the number of antennas at the user equipment, and

values for a! , a" and β for different correlation levels are selected from the following table:

[table 1]

[Claim 12]

A method for determining a first correlation matrix (R) simulating transmission path correlation between a base station and user equipment antennas, the first correlation matrix (R) being determined for simulated wireless transmission paths of a plurality of antennas having the same polarization and arranged in a two-dimensional array, the method including the steps of: determining one or more second correlation matrices (Rt ) for a subset of the antennas which form a first side of the array,

determining one or more third correlation matrices (R* ) for a subset of the antennas which form a second side of the array adjacent the first side,

determining one or more fourth correlation matrices (Rt), each fourth correlation matrix being determined based on a Kronecker product (Rt = Rt <8> R* ) of each second correlation matrix (Rt ) and a corresponding third correlation matrix (Rt ), and determining the first correlation matrix (R) simulating transmission path correlation by determining a weighted sum of the one or more fourth correlation matrices (Rt).

[Claim 13]

The method as claimed in claim 12, wherein the array is rectangular and the second side is adjacent the first side, the method including:

determining a number of sets (K) for grouping the simulated wireless transmission paths, determining weight factors associated with the number of sets (K), and

determining the weighted sum of the one or more fourth correlation matrices (R*) using the weight factors.

[Claim 14]

The method as claimed in claim 13, including:

dividing a three-dimensional transmission space of the transmission paths into a number of sectors equal to the number of sets (K), each sector being defined by an elevation angle range ( Θ) and an azimuth angle range ( φ ), and

grouping the transmission paths which have an elevation angle ( Θ) and an azimuth angle (φ ) falling within the same sector so as to form K sets of transmission paths.

[Claim 15]

The method as claimed in claim 14, including

correlation matrix = for each set ( k) of transmission paths using the

following equation:

U = ^~∑^G(⁰ _m ^_m )exp0^'2 , c°s0_m sin^ )

wherein d\_j is a normalized distance with respect to a wavelength ( λ ) of a carrier between two antennas (i, j) along the first side of the two-dimensional array, 9_m is an angle that sub-path (m) extends to a reference plane formed by the first side of the two-dimensional array and a direction perpendicular to the two-dimensional array, φ_ηι is an angle between a projection of the sub-path (m) on the reference plane and a direction perpendicular to the array, and M_k is the number of transmission paths in a set ( k ).

[Claim 16]

The method as claimed in claim 14, including

determining one or more second correlation matrices (R* ) by determining a second

correlation matrix = for each set ( k ) of transmission paths using the

following equation: "2?B¾∞%θύΆφ)άφάθ

wherein d _i is the normalized distance with respect to a wavelength ( A ) of a carrier between two antennas (/, j) along the first side of the two-dimensional array, Θ is an elevation angle above a reference plane formed by the first side of the two-dimensional array and direction perpendicular to the array, ψ is an angle measured from a direction perpendicular to the array on the reference plane, and a domain of integration 9_k , φ_Ιί corresponds to set k .

[Claim 17]

hod as claimed in claims 12, including determining a second correlation matrix

K =

wherein N' is the number of antennas along the first side of the array, and parameter ' is defined based on a required Ergodic capacity expectation.

[Claim 18]

The method as claimed in claim 14, including determining one or more third correlation

matrices (Rjt ) by determining a third correlation matrix R for each set

( k ) of transmission paths using the followin equation:

wherein d^* _} is a normalized distance with respect to a wavelength ( A ) of a carrier between two antennas ( , f) along the second side of the two-dimensional array, θ_η is an angle that sub-path (m) extends to a reference plane formed by the first side of the two-dimensional array and a direction perpendicular to the array, φ_η is an angle between a projection of the sub-path (m) on the reference plane and the direction perpendicular to the array, and M_k is the number of transmission paths in a set ( k ).

[Claim 19]

The method as claimed in claim 14, including determining the one or more third n it r\,o ^r\,\

correlation matrices (R* ) by determining a third correlation matrix R"_k =

'ifi

for each set (£) of transmission aths using the following equation:

wherein d"_j is a normalized distance with respect to a wavelength (/I ) of a carrier between two antennas (/, j,) along the second side of the two-dimensional array, Θ is an elevation angle above a reference plane formed by the first side of the two-dimensional array and a direction perpendicular to the array, φ is an angle measured from a direction perpendicular to the array on the reference plane, and a domain of integration 0_k , <fi_k corresponds to set k .

[Claim 20]

The method as claimed in claim 12, including determining a third correlation matrix

'0,0 '0,1

1.0 ' 1,1

K using the following equation:

r =a

[Claim 21]

The method as claimed in claim 12, further including determining spatially correlated coefficients for the simulated wireless transmission paths by:

obtaining a matrix square root of a receive correlation matrix, obtain a matrix square root of a transmitting correlation matrix along direction 1 ,

R' = C'C'^H

obtain a matrix square root of a transmitting correlation matrix along direction 2,

R" = C'C'^fl

determimng transmit correlation along direction 1 for each transmit antenna along direction 2 and receive antenna using the following formula:

H_{i ;} = C H_i V ,7 wherein H, _{s t} denotes uncorrelated input coefficients between a receive antenna / , a transmit antenna given by index j along direction 1 , and a transmit antenna given by index / along direction 2.

[Claim 22]

The method as claimed in claim 12, further including determining a spatial correlation matrix ( R_spalia! ) for facilitating the designing, evaluating and testing of three-dimensional beamforming, FD-MIMO algorithms in which a rectangular antenna array is used at a base station node and a linear antenna array is used at a user equipment, the spatial correlation matrix being determined based on the following Kronecker product formula:

R spatial R: eNB ® KNB UE

wherein

R'_eNB is a correlation matrix of the rectangular antenna array at the base station node, and elements of matrix can be determined using the formula: . =a'^{lN 1J} ,

is a further correlation matrix of the rectangular antenna array at the base station node, and elements of matrix R^_B can be determined using the formula: r"■ =a"^[-^{N 1}

R_UE is a correlation matrix of the linear antenna array at the user equipment, and elements of matrix R^ can be determined using the formula: r_{; /} = ?^{Lii lJ} ,

N' , N" are the numbers of antennas at the base station node along two adjacent sides of the rectangular antenna array,

N is the number of antennas at the user equipment, and

[table 2]

Correlation levels a' a" β

Low 0 0 0

Medium 0.3 0.3 0.9

High 0.9 0.9 0.9