GB2554910A - Beamforming in multiple input multiple output systems - Google Patents

Abstract

A beamforming method includes obtaining a channel matrix, factorizing the channel matrix to obtain a plurality of elements of an n x n matrix, where n is a number of antennas 108 used in the MIMO apparatus. A plurality of analogue phase shifts are then calculated for a plurality of antenna signals of the MIMO apparatus, based on the obtained elements of the n x n matrix. Beamforming is then performed by controlling the MIMO apparatus to apply the calculated analogue phase shifts to the plurality of antennas signals. Calculating the analogue phase shifts may comprise calculating first and second parameters from elements of the n x n matrix. The first and second parameters may relate to terms in a power function describing a difference in power between a desired signal and interfering signals. Apparatus for implementing the method are also described.

Description

(71) Applicant(s):

University of Surrey (Incorporated in the United Kingdom)

GUILDFORD, Surrey, GU2 7XH, United Kingdom (72) Inventor(s):

Mehdi Molu Pei Xiao Rahim Tafazolli (74) Agent and/or Address for Service:

Venner Shipley LLP

200 Aldersgate, LONDON, EC1A4HD,

United Kingdom (51) INT CL:

H04B 7/04 (2017.01) H04B 7/0456 (2017.01)

H04B 7/06 (2006.01) (56) Documents Cited:

WO 2017/021774 A2 WO 2013/169055 A1 US 8335167 B1

13th ISWCS, 20-23 September 2016, Poznan, Poland, A.Roze et al., Comparison between a hybrid digital and analogue beamforming system and a fully digital massive ΜΙΜΟ system with adaptive beamsteering receivers in millimeter-wave transmissions, pages 86-91.

IEEE transactions on wireless communications, Vol 15, No.11, November 2016, Date of publication August 11th 2016, Payami et al Hybrid beamforming for large antenna arrays with phase shifter selection, pages 7258-7271 (58) Field of Search:

INT CL H04B

Other: WPI, EPODOC, INSPEC, XPI3E, XP3GPP (54) Title of the Invention: Beamforming in multiple input multiple output systems

Abstract Title: Hybrid beamforming in multiple input multiple output antenna systems (57) A beamforming method includes obtaining a channel matrix, factorizing the channel matrix to obtain a plurality of elements of an η x n matrix, where n is a number of antennas 108 used in the ΜΙΜΟ apparatus. A plurality of analogue phase shifts are then calculated for a plurality of antenna signals of the ΜΙΜΟ apparatus, based on the obtained elements of the η x n matrix. Beamforming is then performed by controlling the ΜΙΜΟ apparatus to apply the calculated analogue phase shifts to the plurality of antennas signals. Calculating the analogue phase shifts may comprise calculating first and second parameters from elements of the η x n matrix. The first and second parameters may relate to terms in a power function describing a difference in power between a desired signal and interfering signals. Apparatus for implementing the method are also described.

FIG. 1

1/3

Ap

DIGITAL

BEAMFORMER

RF

2/3

Rate

Ο

15

SNR (dB)

3/3

Rate

SNR(dB) rlGi. 0

- 1 Beamforming in Multiple Input Multiple Output Systems

Technical Field

The present invention relates to beamforming in Multiple Input Multiple Output 5 (ΜΙΜΟ) systems. More particularly, the present invention relates to methods and apparatus for obtaining analogue phase shifts for use in ΜΙΜΟ beamforming.

Background

As a consequence of the growth of capacity-hungry wireless communication services over recent years, future wireless communication systems will be required to support higher data rates to permit greater numbers of users to be connected to the network. Two promising technologies that it is hoped could satisfy this ever-increasing demand for capacity are millimetre wave (mmWave) band systems and Massive Multiple Input Multiple Output (ΜΙΜΟ) systems. Operation in the mmWave band allows system designers to pack a large number of antennas more compactly, and achieve higher antenna gains.

Hybrid beamforming solutions, which combine digital and analogue beamforming, have been proposed for both mmWave and Massive ΜΙΜΟ systems. Hybrid beamforming involves the computation of phase shifts to be applied in the digital beamforming stage and the analogue beamforming stage. However, current solutions for designing hybrid beamformers are either system-specific or channel-specific.

For example, existing hybrid beamforming solutions for Massive ΜΙΜΟ systems calculate the digital beamformer as an identity matrix, and then determine the analogue beamformer as being equal to the phases of right/left eigenvector matrices of the channel. This approach relies on the assumption that H^HH ~ I, using the law of large numbers, and so is not applicable when a smaller numbers of antennas is used. Existing solutions for massive ΜΙΜΟ systems are therefore system-specific.

Existing solutions for hybrid beamforming in mmWave systems require a codebook of different beam patterns to be defined in advance. During operation, the system exhaustively searches for the best analogue beamformer based on the existing codebook. Once the best value is obtained for the analogue beamformer, the digital beamformer is obtained either by using singular value decomposition or by pseudoinverting the overall channel. However, this approach relies on the assumption that the

- 2 channel is spatially sparse with a high path loss, meaning that a relatively small number of signals reach the receiver. Accordingly, existing hybrid beamforming solutions for mmWave systems are channel-specific.

It would therefore be desirable to have a general hybrid beamforming solution that can be applied to all types of ΜΙΜΟ systems.

The invention is made in this context.

Summary of the Invention

According to a first aspect of the present invention, there is provided a beamforming method for Multiple Input Multiple Output ΜΙΜΟ apparatus, the method comprising: obtaining a channel matrix; factorizing the channel matrix to obtain a plurality of elements of an η x n matrix, where n is a number of antennas used in the ΜΙΜΟ apparatus; calculating a plurality of analogue phase shifts for a plurality of antenna signals of the ΜΙΜΟ apparatus, based on the obtained elements of the η χ n matrix; and performing beamforming by controlling the ΜΙΜΟ apparatus to apply the calculated phase shifts to the plurality of antennas signals.

In some embodiments according to the first aspect, calculating each one of the plurality of analogue phase differences 3_mk may comprise: calculating a first parameter r_mk and a second parameter 5_mk from elements of the η x n matrix, where the first and second parameters relate to terms in a power function describing the difference in power between a desired signal and one or more interfering signals at the m^th antenna; and setting the analogue phase shift 0_mk according to the calculated values of the first and second parameters. The analogue phase shift 0_mk may be set so as to maximise the power function.

The first parameter r_mk and the second parameter Smk may be given by:

3k = Sign(lrn(v_r,v_m, )Jv_r,v_m,|, and

V ^rmk J where v_rk denotes the fc^th element in the r^th row of the η x n matrix, the r^th row being a reference row relative to which the phase shifts are calculated, and where v_mk denotes the fc^th element in the m^th row of the η x n matrix.

-3In some embodiments according to the first aspect, the channel matrix is factorized using singular value decomposition.

In some embodiments according to the first aspect, the ΜΙΜΟ apparatus is configured to operate as a transmitter, and n is the number of antennas used for transmitting signals at the ΜΙΜΟ apparatus.

In some embodiments according to the first aspect, the ΜΙΜΟ apparatus is configured 10 to operate as a receiver, and n is the number of antennas used for receiving signals at the ΜΙΜΟ apparatus.

According to a second aspect of the present invention, there is provided a computerreadable storage medium arranged to store computer program instructions which, when executed, perform a method according to the first aspect.

According to a third aspect of the present invention, there is provided beamforming apparatus for a Multiple Input Multiple Output ΜΙΜΟ apparatus, wherein the beamforming apparatus is configured to: obtain a channel matrix; factorize the channel matrix to obtain a plurality of elements of an η χ n matrix, where n is a number of antennas used in the ΜΙΜΟ apparatus; calculate a plurality of analogue phase shifts for a plurality of antenna signals of the ΜΙΜΟ apparatus, based on the obtained elements of the η χ n matrix; and perform beamforming by controlling the ΜΙΜΟ apparatus to apply the calculated phase shifts to the plurality of antennas signals.

In some embodiments according to the third aspect, the beamforming apparatus is configured to calculate each one of the plurality of analogue phase differences 3_mk by: calculating a first parameter r_mk and a second parameter 5,„k from elements of the η χ n matrix, where the first and second parameters relate to terms in a power function describing the difference in power between a desired signal and one or more interfering signals at the m^th antenna; and setting the analogue phase shift Q_mk according to the calculated values of the first and second parameters. The beamforming apparatus may, for example, be configured to set the analogue phase shift Q_mk so as to maximise the power function.

-4The beamforming apparatus may be configured to calculate the first parameter r_mk and the second parameter 8mk using:

r_mk = Sign(lm(v_(/v_m/ ))|v_r,v_mJ , and

V ^rmk ) where v_rk denotes the fc^th element in the r^th row of the η χ n matrix, the r^th row being a reference row relative to which the phase shifts are calculated, and where v_mk denotes the fc^th element in the m^th row of the η χ n matrix.

In some embodiments according to the third aspect, the beamforming apparatus is io configured to factorize the channel matrix using singular value decomposition.

In some embodiments according to the third aspect, the ΜΙΜΟ apparatus is configured to operate as a transmitter, and n is the number of antennas used for transmitting signals at the ΜΙΜΟ apparatus.

In some embodiments according to the third aspect, the ΜΙΜΟ apparatus is configured to operate as a receiver, and n is the number of antennas used for receiving signals at the ΜΙΜΟ apparatus.

Brief Description of the Drawings

Embodiments of the present invention will now be described, byway of example only, with reference to the accompanying drawings, in which:

Figure l illustrates apparatus for transmitting data over a wireless communication channel, according to an embodiment of the present invention;

Figure 2 illustrates apparatus for receiving data over a wireless communication channel, according to an embodiment of the present invention;

Figure 3 is a flowchart showing a beamforming method for a ΜΙΜΟ apparatus, according to an embodiment of the present invention;

Figure 4 is a graph illustrating simulation results for a mmWave channel with 10 scatterers in a ΜΙΜΟ system in which both the receiver and transmitter have 30 antennas and 5 RF chains, comparing the performance of a beamforming method according to an embodiment of the present invention against a prior art beamforming method; and

-5Figure 5 is a graph illustrating simulation results for a rich scattering channel in a ΜΙΜΟ system in which both the receiver and transmitter have 30 antennas and 5 RF chains, comparing the performance of a beamforming method according to an embodiment of the present invention against a prior art beamforming method.

Detailed Description

In the following detailed description, only certain exemplary embodiments of the present invention have been shown and described, simply by way of illustration. As those skilled in the art would realize, the described embodiments maybe modified in various different ways, all without departing from the scope of the present invention. Accordingly, the drawings and description are to be regarded as illustrative in nature and not restrictive. Like reference numerals designate like elements throughout the specification.

Referring now to Fig. 1, apparatus for transmitting data over a wireless communication channel is schematically illustrated, according to an embodiment of the present invention. The apparatus uses a hybrid architecture comprising a digital beamforming stage and an analogue beamforming stage. In the digital beamforming stage a precoder applies digital phase shifts to data streams. Data symbols in the analogue domain are then phase-shifted and combined in the analogue beamforming stage.

As shown in Fig. 1, the apparatus of the present embodiment comprises a digital beamformer 102, a plurality of RF chains 104, a plurality of analogue phase shifters 106, and an antenna array comprising a plurality of antennas 108. The analogue phase shifters 106 may be constant-modulus phase shifters. The digital beamformer 102 comprises a precoder configured to apply digital phase shifts to a plurality of data streams X, each of which comprises data to be transmitted over a wireless communication channel 120. The digital beamformer 102 outputs phase-shifted data streams to the plurality of RF chains 104, each of which is configured to modulate a carrier signal with the phase-shifted data stream received from the digital beamformer 102 to generate a data symbol.

The data symbols Si, S₂, S₃ are then sent to the plurality of antennas 108 via the plurality of analogue phase shifters 106. Each analogue phase shifter 106 receives one data symbol and applies a phase shift to the data symbol, before sending the phaseshifted data symbol to one of the antennas 108. The antennas 108 are configured to

-6transmit the phase-shifted data symbols over a wireless channel 120, which can be represented by a channel matrix H. In the present embodiment each RF chain 104 is connected to all of the antennas 108, such that each data symbol Si, S₂, S₃ is transmitted by every antenna 108 in the array. In other embodiments, each RF chain 104 may only be connected to a subset of the antennas 108. However, greater efficiency is achieved when all of the antennas are used to transmit each data symbol.

In general, the digital precoder 102 can be configured to process any number of input data streams, and the apparatus may include any number of RF chains 104. The antenna array comprises a number of antennas 108 greater than or equal to the number of RF chains 104. By using fewer RF chains than antennas 108, the cost and complexity of the apparatus can be reduced. This advantage may be particularly significant when the number of antennas is large, as is to be expected in the next generation of wireless communication systems. In contrast, in current communication systems the number of

RF chains is usually equal to the number of antennas.

A corresponding apparatus for receiving the data transmitted by the apparatus of Fig. 1 is illustrated in Fig. 2, according to an embodiment of the present invention. The receiving apparatus of Fig. 2 is configured to perform a similar sequence of operations to the transmitting apparatus of Fig. 1, but in reverse. The receiving apparatus comprises a plurality of antennas 208 configured to receive data symbols transmitted over the wireless communication channel 120. The signal from each antenna is then divided and sent to a plurality of RF chains 204 via a plurality of phase-shifters 206.

The RF chains 204 convert the antenna signals into digital data streams which are sent to a digital beamformer 202. The digital beamformer 202 applies digital phase-shifts and recovers estimated data X, which is an estimate of the original data X.

As shown in Figs. 1 and 2, the transmitter and receiver both comprise a controller 110, 210 for controlling the respective digital beamformer 102, 202 and analogue phase shifters 106, 206. The controller 110 for the transmitter is configured to calculate a digital beamforming matrix Dt and an analogue beamforming matrix At, which define the phase shifts to be applied by the digital beamformer 102 and the analogue phase shifters 106 respectively. Similarly, the controller 210 for the receiver is configured to calculate a digital beamforming matrix Dr and an analogue beamforming matrix Ar,

-Ίwhich define the phase shifts to be applied by the digital beamformer 202 and the analogue phase shifters 206 respectively.

Embodiments of the present invention provide methods of calculating the analogue and 5 digital beamforming matrices At, D_T which are significantly less complex compared to existing solutions, and provide higher data rates. Moreover, unlike existing solutions, embodiments of the present invention provide generalised beamforming solutions that are applicable to any type of system regardless of the operating frequency or number of antennas.

An exemplary method of calculating the analogue and digital beamforming matrices A_T, D_T will now be described in detail, according to an embodiment of the present invention. In the following example, the number of antennas 108 at the transmitter is denoted by n_T, the number of RF chains 104 at the transmitter is denoted by/r, the number of antennas 208 at the receiver is denoted by n_R, and the number of RF chains 204 at the receiver is denoted by/?, where n_T^fr and n_R >f_R.

The signal y detected at the receiver can be written as follows:

y = HA_TD_TX (1) where A is a unit power data symbol vector, H is the channel matrix, Aris the analogue beamforming matrix, and Dr is the digital beamforming matrix. Using matrix factorization, equation (1) can be rewritten as:

y = ULV^HATDTx = ULV^HATS (2) where Vis an η_τ χ n_T matrix, Uis an n_R x n_R matrix, and S is the transmitted data symbol. In the present example the channel matrix H is factorized using singular value decomposition. In other embodiments another factorization technique may be used, for example eigenvalue decomposition. The ?ΐτ χ ?ΐτ matrix Vcan then be used to calculate the analogue beamforming matrix for the transmitter, A_T, and U can be used to calculate the analogue beamforming matrix for the receiver, A_R. From equation (2), a new parameter T can be defined as follows:

-8T = V^hA_tS (3)

Taking an example of a transmitter with three antennas 108 and two RF chains 104, such that the analogue beamforming matrix Ar is a 3 x 2 matrix, equation (3) can be rewritten as follows:

ail A 2		Δ	“1 0’	r^i Ί
a21 a22			0 1
n ft	_ 2 _		0 0	_ 2 _

(4)

Although in the present example the transmitter has three antennas 108 and two RF chains 104, it will be readily appreciated that equations (3) and (4) can be generalised for apparatus with any arbitrary number of antennas and RF chains, provided that the number of antennas is greater than or equal to the number of RF chains as explained above.

The elements of T relate to the SINR (signal to interference-plus-noise ratio) at each antenna. The expression on the right-hand side of equation (4) shows the ideal form of the solution, in which the 3x2 matrix has the diagonal elements in and i₂₂ equal to 1 and all off-diagonal elements equal to 0. Under real-world conditions this will not be achieved, meaning that the diagonal elements have a magnitude of less than 1 and the off-diagonal elements are greater than 0. In embodiments of the present invention, the elements of the analogue beamforming matrix Ar can be selected such that the performance of the system approaches that of the idealised example. In the following example, a method is described by which the elements of the analogue beamforming matrix Ar are optimised such that the diagonal elements in the 3x2 matrix of equation (4) are as close as possible to 1, and the off-diagonal elements are as close as possible to

0.

From equation (4), the individual elements of Tcan be written as:

h ^— Ghlhl + ^21^21 + ^31^31 )^1 + (^12^11 + ^22^21 + ^32^31 )^2 Ε ^— Oh Al2 + ^21^22 + ^31^32 )^1 + 0^12^12 + ^22^22 + ^32^32 )^2 t₃ — (fl_nV₁₃ + ^21^23 + ^31^33 )^1 + (^12^13 + ^22^23 + ^32^33 )^2 (5) (6) (7)

-9In the analogue beamforming matrix Ar, each element a$ can be defined in terms of a phase shift θ$, which is the phase shift applied to the J^th symbol at the I^th antenna, as follows:

fr-e (8)

For any given antenna and transmitted data symbol, it is possible to define a desired signal power, Aj, and interfering signal power, 1%, where i is the antenna index and j is io the symbol index. For the first symbol Si and the first antenna, the desired signal power Ai is given by the Si term in equation (5), multiplied by its complex conjugate. Similarly, the interfering signal powers A and I₃i are given respectively by the Si terms in equations (6) and (7), multiplied by their complex conjugates. In the present example, the desired signal power Du and interfering signal powers Ι₂ι, I31 for the first antenna and the first data symbol can be written as follows, using the trigonometric identities (&^θ + = 2cos0 and (&^θ - e~F) = 2sin0:

D_n = (l + 2cos(0_n -^₂₁)Re{v₁*₁v₂₁}-2sin(^₁₁ -θ^ +2cos(0_n -6>₃₁)Re{v₁*₁v₃₁}-2sin(6>₁₁ -^Jlmfov^} (9) + 2cos(0₂₁ -0₃₁)Re{v₂₁v₃₁}-2sin(0₂₁ -^₃₁)lm{v₂>₃₁})|S₁|²

Z₂i = (l + 2cos(0_n -^₂₁)Re{v₁>₂₂}-2sin(^₁₁ +2cos(0_n -^₃₁)Re{v₁>₃₂}-2sin(^₁₁ -0₃₁ (10) + 2cos(0₂₁ -0₃₁)Re{v₂₂v₃₂}-2sin(0₂₁ - 6>_3I)Im{w₂₂ v₃₂ |²

Z₃₁ = (l + 2cos(0_n -^₂₁)Re{v₁>₂₃}-2sin(^₁₁ -0₂₁ 20 +2cos(^_n-^₃₁)Re{v₁*₃v₃₃}-2sin(^₁₁-^₃₁)lm{v!*₃v₃₃} (11) + 2cos(#₂₁ -#₃₁)Re{v₂₃v₃₃}-2sin(#₂₁ -Θ_3Ϊ )lni{v₂₃v₃₃})|S₁|²

It is also possible to express the desired signal power and interfering signal powers in different forms, for example by using different trigonometric identities. As such, embodiments of the present invention are not limited to the specific forms of equations shown above, or to the specific forms of equations shown in the following description.

- 10 As shown in equations (9), (10) and (11), the magnitude of the desired signal and the interfering signals depend on the phase differences between the signal components transmitted by each antenna. For example, (Θ11 - θ₂₁) denotes the phase difference between the first data symbol Si at the first antenna and the first data symbol Si at the second antenna.

Furthermore, it is possible to define a power function that is related to the difference in power between the desired signal power and the interfering signal power, for each data symbol. A performance increase can be achieved by selecting values of the analogue phase shifts which increase the value of this power function. In the present embodiment, analogue phase shifts are selected which maximise the value of these power functions, so as to provide the optimum beamforming solution. In the present embodiment two RF chains are used, and so two power functions/1 and/₂ can be defined as follows:

/,=(^,-(/,, + /,,))^1² (12) /₂ = (d₂₂-(/„ + /₃₂))|s₂|² (13)

Using the trigonometric identity acos(x)-bsin(x) = rcos(<p+<5), equation (12) for example can then be expanded and simplified as follows:

f\ 4r₂, cos(y?₂, + <J₂,)+4r₃, cos(y?₃, + </,)+4r₂,₃, cos(y?₂,₃, ^21,31) (14) where ^rmk = Sign(lrn(v_r,v_m, ))|v_r,v_mJ (15) (16)

K = ^arccos

Re(v_riv_mi Γ

In equation (14), φ₂₁, <p₃i and </>21,31 are variables which can be controlled by setting 30 appropriate analogue phase shifts at the transmitter. Accordingly, the controller 110 at the transmitter can set appropriate phase shifts for the first data symbol Si in the analogue beamforming matrix Ar to maximise/. Similarly, the controller 110 at the transmitter can set appropriate phase shifts for the second data symbol S₂ in the

- 11 analogue beamforming matrix A_T to maximise^. For example, it follows from equation (14) that/i will be maximised when the following phase differences are chosen:

''mk

-π, ^rmk >° ^rmk (I?)

Since the analogue beamforming matrix A_T defines individual phase shifts to be applied to the separate antenna input signals, whereas equation (17) defines a phase difference cpmk between two antenna signals, a modified form of equation (17) can be used by the controller 110 to determine the individual phase shifts. An arbitrary row in the analogue beamforming matrix A_T can be chosen as a reference row, with the phase shifts in this row being set to a constant modulus vector. In the example shown below the first row is used as the reference row, but in other embodiments any row in the analogue beamforming matrix A_T can be chosen as the reference row:

15	II	1—1 —i —i 1_	1 eje^ ej6ii	1 ··· eje2nT ... β^3ηΤ
			e^2	... gj@nTnT

(18)

The remaining elements a_mk in the other rows of A_T can then be defined based on phase shifts relative to the reference rows α&, as follows:

^rmk>^{Q r}mk (IQ)

Equations (15) and (16) define a known relationship between the elements of matrix V and the parameters r_mk and S_mk, which can then be used to select appropriate analogue phase shifts. In equation (19) Q_rk denotes a reference phase, which is the phase of the k^th element in the r^th row, where r is the index of the row that has been selected as the reference row. It can be seen that 5,„k is related to the phase difference between the phase shift 0_mk and the reference phase 6_rk· When r_mk is positive, the phase shift θ,,,ι- is selected to produce a phase difference of 5,„k relative to the reference phase θ,·ι·_:· When r_mk is equal to zero or is negative, the phase shift 0_mk is selected to produce a phase

- 12 difference of (5,,,/- + π) relative to the reference phase θ,-k- As explained above, setting the phase shift 3_mk in this way provides the optimum beamforming solution by maximising the magnitude of the power functions fi and f₂. In other embodiments, sub-optimal values could be selected whilst still providing a performance improvement in comparison to known beamforming solutions.

Equations (15), (16) and (19) can be pre-programmed into the controllers 110, 210 of the transmitter and receiver, and used to adapt the analogue phase shifts whenever the channel matrix changes. It will be appreciated that the exact form of equations (15) and (16) will depend on the form in which equation (14) is written. Different expansions of equations (12) and (13) maybe possible, for example by choosing different trigonometric identities, and accordingly embodiments of the present invention are not limited to the specific forms shown in equations (15) and (16).

Furthermore, equation (19) defines a known relationship between the variables r_mk and S_mk, which depend only on certain elements of the decomposed channel matrix V. Equations (15) to (19) are defined in general forms, which can be applied to embodiments with any numbers of RF chains and antennas. Consequently, when the channel conditions change the controller no can calculate new values of r_mk and 5,„k from the relevant elements of the decomposed channel matrix V, and configure the analogue beamforming matrix Arby selecting appropriate phase shifts based on a known relationship such as the one illustrated in equation (19).

Specifically, the controller no can obtain the channel matrix H in a known manner, using any suitable channel estimation method. The controller no may perform channel estimation itself, or may receive the channel matrix from another source. Once the channel matrix has been obtained, the controller no decomposes the channel matrix to obtain the n_T x n_T matrix V, for example by using singular value decomposition or another suitable technique, such as eigenvalue decomposition. V can be written as follows:

-13^k12

In?

'2i ^z22 '2n_T

3n_T (20)

Πγ 1

ΠγΠγ

Once the elements of V have been calculated, the controller no can select appropriate phase shifts to maximise/i and/₂, and configure the analogue beamforming matrix Ar in order to apply the selected phase shifts to the respective antenna input signals.

The controller 210 in the receiving apparatus can follow a similar process to calculate the analogue beamforming matrix for the receiver Ar, using the hr x ?1r matrix [fin place of the ητ χ ητ matrix V. This process will give Af, and the receiver can then take the complex conjugate of Af to arrive at the analogue beamforming matrix Ar.

Once the analogue beamforming matrices A_T,A_R have been obtained, the overall ‘equivalent’ channel H_eq observed by the RF chains can be written as follows:

H_eq=A_RHA_T (21)

This can then be factorized using a suitable matrix decomposition technique, for example singular value decomposition or eigenvalue decomposition, as follows:

U„ = D_T Σ„ V (22)

The controllers 110, 210 of the transmitter and receiver can then select suitable digital beamformers as follows:

D_T = V_eq (23)

D_r = Uf_q (24)

Referring now to Fig. 3, a flowchart is illustrated to show a method of determining analogue phase shifts to be applied in a ΜΙΜΟ apparatus. The ΜΙΜΟ apparatus may

-14be a transmitter or a receiver. The method uses the principles described above to improve the system performance, by selecting appropriate phase shifts which will increase the desired signal power at an antenna relative to the interfering signal powers. The method shown in Fig. 3 maybe implemented by either of the controllers

110, 210 illustrated in Figs. 1 and 2. Depending on the embodiment, a hardware or software implementation may be used. When a software implementation is used, the controller 110, 210 may include computer-readable memory arranged to store computer program instructions which, when executed, perform the method, and may also include one or more processors for executing the stored instructions.

First, in step S301 the controller 110, 210 obtains the channel matrix H. As explained above, any suitable channel estimation technique for a ΜΙΜΟ system may be used to obtain the channel matrix H. Next, in step S302 the controller 110, 210 factorizes the channel matrix H to obtain a plurality of elements of the η x n matrix V, where n is the number of antennas used in the ΜΙΜΟ apparatus. Following the notation used in the above-described examples, if the apparatus is a transmitter then n=n_T, and if the apparatus is a receiver then n=n_R. As explained above, any suitable factorization technique may be used in step S302, for example SVD or eigenvalue decomposition.

Next, in step S303 the controller 110, 210 calculates a plurality of analogue phase differences between antenna signals of the ΜΙΜΟ apparatus, based on the obtained elements of the η χ n matrix. This can be achieved using a predefined known relationship between the phase difference, relative to a reference phase, and corresponding elements of the η χ n matrix. In the example shown in equation (19) above, the phase difference is calculate to be either 5_mk or (8_mk + π), depending on the value of r_mk.

Then, in step S304 the controller 110, 210 controls the analogue phase shifters in order to provide the calculate phase differences between the antennas signals in the ΜΙΜΟ apparatus. In the example disclosed above, this is achieved by setting the matrix elements ay in the analogue beamforming matrix Ar, A_R according to equations (18) and (19), and then controlling each analogue phase shifter 106, 206 to provide the desired phase shift indicated by the corresponding element ay.

Embodiments of the present invention, such as the method shown in Fig. 3, provide a closed-form solution for determining analogue phase shifts to be applied in a ΜΙΜΟ

-15apparatus. By closed-form, it is meant that the analogue phase shifts can be calculated directly from the channel matrix H, whereas prior art solutions typically require an exhaustive search to be performed of all possible solutions before selecting the best solution for current channel conditions. Additionally, embodiments of the present invention provide generalized beamforming solutions that can be applied to ΜΙΜΟ apparatus with any number of antennas and RF chains, and for any operating frequency. In contrast, prior art solutions are typically either system-specific (e.g. massive ΜΙΜΟ) or channel-specific (e.g. mmWave/sparse channel).

Referring now to Figs. 4 and 5, graphs of simulation results are plotted which illustrate the improvement in performance in comparison to an idealised solution and prior art beamforming solutions. In Figs. 4, and 5, the transmission rate is plotted as a function of the signal-to-noise ratio (SNR). The graph shown in Fig. 4 illustrates simulation results for a mmWave channel with 10 scatterers in a ΜΙΜΟ system in which both the receiver and transmitter have 30 antennas and 5 RF chains. As shown in Fig. 4, the method according to the present invention provides comparable performance to the prior art mmWave beamforming method, but includes the added benefit that the method is generally applicable to any channel conditions, whereas existing mmWave beamforming solutions are only applicable to sparse channels.

The graph shown in Fig. 5 illustrates simulation results for a rich scattering channel in a ΜΙΜΟ system in which both the receiver and transmitter have 30 antennas and 5 RF chains. As shown in Fig. 5, the method according to the present invention provides a significant performance improvement over the prior art ΜΙΜΟ beamforming method under rich scattering channel conditions.

Whilst certain embodiments of the invention have been described herein with reference to the drawings, it will be understood that many variations and modifications will be possible without departing from the scope of the invention as defined in the accompanying claims.

-ι6-

Claims (14)

1. Claims

   l. A beamforming method for Multiple Input Multiple Output ΜΙΜΟ apparatus, the method comprising:

   5 obtaining a channel matrix;

   factorizing the channel matrix to obtain a plurality of elements of an η χ n matrix, where n is a number of antennas used in the ΜΙΜΟ apparatus;

   calculating a plurality of analogue phase shifts for a plurality of antenna signals of the ΜΙΜΟ apparatus, based on the obtained elements of the η χ n matrix; and 10 performing beamforming by controlling the ΜΙΜΟ apparatus to apply the calculated phase shifts to the plurality of antennas signals.
2. 2. The method of claim l, wherein calculating each one of the plurality of analogue phase differences Q_mk comprises:

   15 calculating a first parameter r_mk and a second parameter S_mk from elements of the η χ n matrix, where the first and second parameters relate to terms in a power function describing the difference in power between a desired signal and one or more interfering signals at the m* antenna; and setting the analogue phase shift θ,,,ί- according to the calculated values of the

   20 first and second parameters.
3. 3. The method of claim 2, wherein the analogue phase shift θ,,,ι, is set so as to maximise the power function.
4. 4. The method of claim 2 or 3, wherein the first parameter r_mk and the second parameter S_mk are given by:

   r_mk = Sign(lrn(v_r,v_m, )Jv_r,v_m,|, and d_mk = arccos

   V ^rmk ) where v_rk denotes the fc^th element in the r^th row of the η χ n matrix, the r^th row being a reference row relative to which the phase shifts are calculated, and where v_mk denotes the fc^th element in the m^th row of the η x n matrix.
5. 5. The method of any one of the preceding claims, wherein the channel matrix is factorized using singular value decomposition.

   -176. The method of any one of the preceding claims, wherein the ΜΙΜΟ apparatus is configured to operate as a transmitter, and n is the number of antennas used for transmitting signals at the ΜΙΜΟ apparatus.
6. 7. The method of any one of claims l to 5, wherein the ΜΙΜΟ apparatus is configured to operate as a receiver, and n is the number of antennas used for receiving signals at the ΜΙΜΟ apparatus.

   10
7. 8. A computer-readable storage medium arranged to store computer program instructions which, when executed, perform the method of any one of the preceding claims.
8. 9. Beamforming apparatus for a Multiple Input Multiple Output ΜΙΜΟ apparatus,

   15 wherein the beamforming apparatus is configured to:

   obtain a channel matrix;

   factorize the channel matrix to obtain a plurality of elements of an η x n matrix, where n is a number of antennas used in the ΜΙΜΟ apparatus;

   calculate a plurality of analogue phase shifts for a plurality of antenna signals of

   20 the ΜΙΜΟ apparatus, based on the obtained elements of the η χ n matrix; and perform beamforming by controlling the ΜΙΜΟ apparatus to apply the calculated phase shifts to the plurality of antennas signals.
9. 10. The beamforming apparatus of claim 9, wherein the beamforming apparatus is

   25 configured to calculate each one of the plurality of analogue phase differences Qmk by:

   calculating a first parameter r_mk and a second parameter S_mk from elements of the η χ n matrix, where the first and second parameters relate to terms in a power function describing the difference in power between a desired signal and one or more interfering signals at the m^th antenna; and

   30 setting the analogue phase shift 0_mk according to the calculated values of the first and second parameters.
10. 11. The beamforming apparatus of claim 10, configured to set the analogue phase shift 0_mk so as to maximise the power function.

    -ι812. The beamforming apparatus of claim 10 or n, wherein the beamforming apparatus is configured to calculate the first parameter r_mk and the second parameter Smk using:

    r_mk = Sign(lm(v_(/v_m/ ))|v_r,v_mJ , and d_mk =

    V ^rmk J where v_rk denotes the k^th element in the r^th row of the η χ n matrix, the r^th row being a reference row relative to which the phase shifts are calculated, and where v_mk denotes the fc^th element in the m^th row of the η χ n matrix.

    io 13. The beamforming apparatus of any one of claims 9 to 12, wherein the beamforming apparatus is configured to factorize the channel matrix using singular value decomposition.
11. 14. The beamforming apparatus of any one of claims 9 to 13, wherein the ΜΙΜΟ
12. 15 apparatus is configured to operate as a transmitter, and n is the number of antennas used for transmitting signals at the ΜΙΜΟ apparatus.

    15. The beamforming apparatus of any one of claims 9 to 13, wherein the ΜΙΜΟ apparatus is configured to operate as a receiver, and n is the number of antennas used
13. 20 for receiving signals at the ΜΙΜΟ apparatus.

    Intellectual

    Property

    Office

    Mr James Richards
14. 23 March 2017

    GB1617390.8

    1-15