A circular transducer array operable to transmit or receive broad beams

Abstract

A method (100) for beamforming using a circular transducer array of equal transducer elements, comprising: in the circular transducer array, identifying (101) a circular first subarray of transducer elements with a first polarization (A) and a circular second subarray of transducer elements with a distinct, second polarization (B); transforming (102) the first subarray into a first virtual subarray with at most the number of elements as the first subarray, such that its steering vector has an approximate Vandermonde structure; similarly transforming (103) the second subarray into a second virtual subarray with as many elements as the first virtual subarray; forming (104) a broad beam by combining the first and second virtual subarrays in accordance with respective excitation weight vectors, which are such that the broad beam's power pattern is approximately equal in shape to a power pattern of one transducer element; and transmitting or receiving (106) signals using the broad beam.

Description

P112009WO011A CIRCULAR TRANSDUCER ARRAY OPERABLE TO TRANSMIT OR RECEIVE BROAD BEAMSTECHNICAL FIELD

[0001] Within the general field of multi-sensor technology, the present disclosure proposes 5 methods and devices for beamforming using a circular transducer array, such as a dual polarized circular antenna array. In particular, this disclosure presents techniques for generating broad beams.BACKGROUND

[0002] With Massive MIMO, throughput and network capacity can be increased by enabling user-specific beamforming of the data channel, forming narrow beams with high antenna gain pointed at a certain user. An example is shown in figure 11A, where 310 refers to user equipments and 320 to a base station. Transmission to a full cell - as shown in figure 1 IB - is still needed for broadcasting and certain control signaling, however. A common approach is to utilize Synchronization Signal Block (SSB) sweeping, wherein multiple narrow beams carrying control information are transmitted in sequence over the intended cell area. The downside of sweeping is that it leads to additional overhead, 15 resulting in lower capacity and lower peak rate. Full-cell transmission could, in theory, be achieved by broadcasting from a single antenna element, but this no economically viable option as the single antenna element would have to be fed by an oversized power amplifier that was used merely a small fraction of the total time.

[0003] The applicant’s prior disclosure W02017190811A1 introduced a dual-polarized20 beamforming (DPBF) approach, which enables an efficient realization of cell-specific transmission through the construction of a single broad SSB beam for Massive MIMO. A key element of DPBF is the simultaneous use of two antenna ports which have different polarizations, such that they are free from mutual wave interference, whether of the constructive or destructive kind. The contributions from the two antenna ports sum to a total power pattern shaped as the power pattern of one antenna element; see figures 6 to 8 in WO2017190811A1. A more complete description of the DPBF approach can be found in the research paperGP21 M. A. Gimyk and S. O. Petersson, “Efficient Cell-Specific Beamforming for Large Antenna Arrays,” IEEE Transactions on Communications, vol. 69 (2021), no. 12, pp. 8429-8442, doi: 10.1109 / TCOMM.2021.3113755.30

[0004] The disclosure WO2017190811A1 is concerned with (uniform) linear antenna arrays and (uniform) rectangular antenna arrays, and it more precisely addresses the problem of finding complex antenna weights that cause the array to have a power pattern approximately equal in shape to the power pattern of one antenna element. The choice of antenna weights according to WO2017190811A1 thus made it possible to disable, or at least suppress, the inherent directivity of a linear or rectangularP112009WO012antenna array. The use of such antenna weights thus counteracts the narrowing of the main lobe when the number of antenna elements increases, similar to the behavior of the Dirichlet kernel Dn(0) when n -> oo. Instead, when the antenna elements of an M x N array are fed with MN identical signals (such that the phase shifts are determined by the antenna weights only), the power pattern of the radiated 5 beam has the same shape as a single antenna element’s power pattern but an MN-fold magnitude.

[0005] It would be desirable to generalize the teachings ofW02017190811A1 beyond linear and rectangular antenna arrays, and notably to circular arrays. Uniform circular arrays (UCAs) are mainly deployed in small cell indoor environments due to their convenient and visually appealing form factor when attached to ceilings or suspended. Upward-pointing UCAs may also find other uses in future sixth-generation cellular systems (6G) for communicating with drones, High Altitude Platforms Stations (HAPS) and other airborne systems. The UCAs offer, compared to URAs and ULAs, a better sky coverage and beam tracking ability over wide zenith and azimuth angular ranges.

[0006] Another use case where UCAs excel is in indoor ceiling-mounted repeater or relay units. Such relay units may be transparent from an end-to-end link perspective, meaning that the relay does 15 not terminate the link but only amplifies and plays back the received signal. Broad beam transmission can alleviate the beam tracking issue between such relays and the UEs in 5G / 6G cellular systems. More precisely, the ‘second leg’ beamforming (pertaining to the link between the relay and the UE) may use a setting that is independent of the UE position, such that the user can move freely indoors with no need for relay’s beamformer to adapt.20 SUMMARY

[0007] One objective of the present disclosure is to propose methods and devices for generating broad beams using circular transducer arrays. Two particular objectives are to propose methods and devices for generating broad beams using a circular antenna array (e.g., in a radio transceiver) or a circular array of mechanical transducers (e.g., in a seismometer). A further objective is to propose methods and devices for generating broad beams using uniform circular arrays (UCAs) of transducers.

[0008] At least some of these objectives are achieved by the invention as defined in the independent claims. The dependent claims are directed to advantageous embodiments of the invention.

[0009] According to a first aspect of the present disclosure, there is provided a method for beamforming using a circular transducer array of equal transducer elements. The method comprises: in 30 the circular transducer array, identifying a circular first subarray of transducer elements with a first polarization A and a circular second subarray of transducer elements with a distinct, second polarization B; transforming the first subarray into a first virtual subarray with at most the number of elements as the first subarray, such that its steering vector has an approximate Vandermonde structure; transforming the second subarray into a second virtual subarray with as many elements as the firstP112009WO013virtual subarray, such that its steering vector has an approximate Vandermonde structure; forming a broad beam by combining the first and second virtual subarrays in accordance with respective excitation weight vectors wA, wB, which are such that the broad beam’s power pattern is approximately equal in shape to a power pattern of one transducer element; and transmitting or 5 receiving signals using the broad beam.

[0010] It is recalled that a steering vector is a vector of the phase delays experienced by a plane wave at the level of the subarray elements. A steering vector a(φ, θ), a function of the azimuth φ and zenith θ angles, has an approximate Vandermonde structure if its components form (within approximation, or within an absolute or relative tolerance) a geometric progression,10 a(φ, θ) = [1, ω, ω2, ω3, ... ], (1) where ω ∈ ℂ is such that |ω| = 1. A matrix has Vandermonde structure if for each row there exists a ωj such that the row has the form (1) for ω = ωj.

[0011] In this disclosure, the term “transducer array” (or sensor array) may refer to an array of antenna elements or an array of mechanical transducers. A transducer array with an approximate circular geometry is a “circular transducer array” in the sense of the claims. On the one hand, the imaginary curve on which the transducers are placed could be a nonperfect circle; on the other hand, the angular positions of the transducers could be distributed nonuniformly over said curve.

[0012] In the present disclosure, further, a beam emitted from or received by a transducer array is a “broad beam” if the beam’s power pattern is approximately equal in shape to a power pattern of one 20 transducer element. Alternatively, a “broad beam” is a beam with a spatially flat array factor (in the power domain).

[0013] The method according to the first aspect successfully enables broad beamforming from a circular transducer array because, as the inventors have realized, the approach originally disclosed in WO2017190811 A 1 is applicable to any subarray for which the steering vector has an approximate Vandermonde structure. As such, the excitation weight vectors according to WO2017190811A1 are applied not to the circular transducer array directly but to the first and second virtual subarrays.

[0014] The proposed solution provides a simple method for constructing broad beams for UCAs. This enables broadcasting of signals to multiple UEs simultaneously in environments of interest, such as in small-cell indoor deployments or 6G airborne communication systems. A further advantage, with 30 relevance notably for a UE with a channel with large angular spread, is that beamforming with a narrow beam may not lead to an increase in received signal power compared to beamforming with a broad beam due to unwanted distribution of the channel energy into several angular directions. In fact, broadening the signal energy to several multi-path components may lead to increased robustness, as a result of the diversity gain.P112009WO014

[0015] Different embodiments of the method of the first aspect implement the transformation of the circular first (second) subarray into the first (second) virtual subarray by different matrix operations, as will be described in a later section of this disclosure.

[0016] In some embodiments, the first and / or the second subarray is an approximate UCA. 5

[0017] In some embodiments, the first and / or the second subarray is a circular antenna array.

[0018] In some embodiments, the first and / or the second subarray is a circular array of mechanical transducers.

[0019] In some embodiments, the first polarization A is orthogonal to the second polarization B. In the present disclosure, two linear polarization states are considered orthogonal if the respective 10 polarization axes differ by approximately 90° in the plane, such as 90° + 15%, such as 90° + 10%, such as 90° + 5%, such as 90° + 2%. Common to electromagnetic and mechanical waves, the geometric orientation of the transverse oscillations determines the polarization. For electromagnetic waves, orthogonality also exists between a linear polarization state and a circular polarization state, between a left-circular and a right-circular polarization state, and so forth.

[0020] In some embodiments, the method includes forming a second broad beam by combining the first and second virtual subarrays in accordance with excitation weight vectors which are in a specific relationship with the excitation weight vectors wA, wBby which the (first) broad beam was formed. The polarization of the second broad beam is orthogonal to the polarization of the (first) broad beam. This provides two channels of polarization-division multiplexing into a broad angular range.20

[0021] In some embodiments, the excitation weight vectors are proportional to ε-complementary sequences, which may have been computed by numerically solving an optimization problem, or by reading them from a repository of ε-complementary sequences of different lengths. In other embodiments, the excitation weight vectors are proportional to a Golay complementary sequence pair.

[0022] In some embodiments, the teachings of this disclosure are combined with per se known techniques for narrowing beamforming. For example, the excitation weight vectors contain at least some elements which are related in phase to form a spatially flat radiation pattern in a limited angular range. This is to say, the broad beam is not used with its maximum angular width but with an adaptable, smaller width. This option is convenient in cellular communication systems for the purpose of broadcasting data (e.g., system information) to all users in a cell, when the broadcast data is of no 30 relevance outside the cell.

[0023] According to a second aspect of the present disclosure, there is provided a beamforming device for use with a transducer array of equal transducer elements. The beamforming device comprises processing circuitry configured to perform the method of the first aspect.P112009WO015

[0024] According to further aspects, there is provided a user equipment (UE), a radio base station, an indoor wireless access point, a communication satellite, and a radar, each comprising the beamforming device according to the second aspect, wherein the beamforming device is adapted for use with a circular antenna array.5

[0025] According to still further aspects, there is provided a sonar and a seismometer, each comprising the beamforming device according to the second aspect, wherein the beamforming device is adapted for use with a circular array of mechanical transducers.

[0026] This disclosure further relates to a computer program containing instructions for causing a computer, or the beamforming device in particular, to carry out the method of the first aspect. The computer program may be stored or distributed on a data carrier. As used herein, a “data carrier” may be a transitory data carrier, such as modulated electromagnetic or optical waves, or a non-transitory data carrier. Non-transitory data carriers include volatile and non-volatile memories, such as permanent and non-permanent storage media of magnetic, optical or solid-state type. Still within the scope of “data carrier”, such memories may be fixedly mounted or portable.15

[0027] Generally, all terms used in the claims are to be interpreted according to their ordinary meaning in the technical field, unless explicitly defined otherwise herein. All references to “a / an / the element, apparatus, component, means, step, etc.” are to be interpreted openly as referring to at least one instance of the element, apparatus, component, means, step, etc., unless explicitly stated otherwise. The steps of any method disclosed herein do not have to be performed in the exact order 20 described, unless this is explicitly stated.BRIEF DESCRIPTION OF THE DRAWINGS

[0028] Aspects and embodiments are now described, by way of example, with reference to the accompanying drawings, on which:figure 1 is a flowchart of a method for beamforming using a circular transducer array of equal transducer elements;figure 2 illustrates a circular array of polarized transducers and an associated beamforming device; figures 3A, 3B, 3C, 3D and 3E respectively show a user equipment, a radio base station, an indoor wireless access point, a communication satellite and a radar device;figures 4A and 4B respectively show a sonar and a seismometer;30 figure 5 shows a uniform linear array (ULA) and a corresponding coordinate system;figure 6 shows a uniform circular array (UCA) and a corresponding coordinate system;P112009WO016figure 7A is a three-dimensional plot of an angular radiation pattern of a downward-pointing UCA when excitation weights according to embodiments herein are applied;figure 7B illustrates the effect of a 5% random perturbation on the angular radiation pattern; figure 8 shows the data from figure 7A as a function of azimuth p for constant zenith angle 9 = 90° 5 (i.e., the (x,y) plane).figure 9 is a three-dimensional plot of an angular radiation pattern of an identical downward-pointing UCA when conventional (DFT-type) excitation weights are applied;figure 10 shows the data from figure 9 as a function of azimuth p for 9 = 90°; andfigures 11A and 1 IB illustrate simulation data for a use case of the teachings herein.DETAILED DESCRIPTION

[0029] The aspects of the present disclosure will now be described more fully hereinafter with reference to the accompanying drawings, on which certain embodiments of the invention are shown. These aspects may, however, be embodied in many different forms and should not be construed as limiting; rather, these embodiments are provided by way of example so that this disclosure will be 15 thorough and complete, and to fully convey the scope of all aspects of the invention to those skilled in the art. Like numbers refer to like elements throughout the description.Overview

[0030] Figure 5 shows, by way of background, a uniform linear array (ULA) 500 and a corresponding coordinate system, including cartesian coordinates (x, y, z) and equivalent polar 20 coordinates (, 9). The shown ULA 500 contains antenna elements 210 that are dual polarized, such that some antenna elements (solid line) have a first polarization A and the remaining antenna elements (hollow line) have a second polarization B. The first polarization A is orthogonal to the second polarization B in the sense discussed above. Each antenna element of polarization A is substantially co-located with an antenna element of polarization B.

[0031] One of the benefits of an antenna array is the ability to focus the radiated energy in an angular sector, thereby improving the received power of a receiver located in said sector. This is achieved by forming a narrow beam from the antenna array by exciting the antennas with a beamforming weight vector. Dual-polarized beamforming provides a way to create beams with larger half-power beam width (HPBW). When an antenna array operates with a pair of orthogonal30 polarizations (A, B), and, assuming that the receiver has a pair of antennas, one for each polarization, a radiation pattern in the power domain can be formed byG(φ, θ) = |A(φ, θ)|2G0(φ, θ),P112009WO017where G0(φ, θ) is the radiation pattern of a single array element in a direction given by the azimuth-elevation tuple (φ, θ), and the array factor is given byM|A(φ,θ)|2= |wATa(φ,θ)|2+ |wBTa(φ,θ)|2,with wAand wBbeing the excitation weight vectors of size N. The steering vector for a uniform linear 5 array (ULA) located on the y-axis is given byafc / gO') = [1, ejkd sin 0 sin^,...)eJOv-1-)kd sin 0 sin0]Tgf(2) with k = — being the wave number, A being the wavelength and d being the antenna spacing.

[0032] Conventional beamforming is typically unable to provide broad beam shapes, instead resulting in narrower beams when the number of antennas utilized grows. A broad beam can be defined as a radiation pattern whose array factor is flat over the observation angles associated with the designated coverage area. In other words, the (power-domain) array factor, i.e.,|A(φ, θ)|2= const,where (φ, θ) belong to the 2D angular region defining the service area. The radiation pattern of the array thus becomes a scaled version of the radiation pattern of a single array element.15

[0033] To achieve this, it was proposed in [GP21] to choose the beamforming weights from a pair of polyphase Golay complementary sequences. The main property of these pairs is the complementarity of their sum aperiodic autocorrelation function (AACF). That is, the sum AACF of the weight matrices is equal to zero everywhere, except for the zeroth lag, i.e.,+ RWB(T) = 2N6(T),20 where Rw(j) is the AACF of a sequence w of length N (cf. equation 7), and 5(r) is the Kronecker delta function. This property is equivalent to having a constant sum power spectral density of the two arrays. Therefore, picking such sequences as the per-polarization beamforming weight vectors results in a constant array factor for the beamforming, which is the desired property for achieving broad-beam transmission.

[0034] The above can be done by either picking an array pair from a list of known Golay sequence / array pairs (see Appendix 1 of W02017190811A1), or by using one of the existing constructions to obtain complementary arrays of a larger size from Golay sequences or Golay arrays of a smaller size. More details are found in W02017190811A1 and [GP21], which are hereby incorporated by reference in their entirety. A review of the theory of Golay array pairs is found in 30 JP07 J. Jedwab and M. G. Parker, “Golay complementary array pairs”, Des. Codes Cryptogr. vol. 44 (2007), pp. 209-216, doi: 10.1007 / sl0623-007-9088-zP112009WO01

[0035] A pair of complementary sequences of the appropriate size (corresponding to the ULA configuration, with the same number of entries as there are dual-polarized radiating elements) used as beamforming vectors in two polarizations will produce a radiation pattern with an omnidirectional array factor in the power domain. Unfortunately, the known complementary pairs are only known for a 5 limited set of lengths given by IV = 2“+^+13b5Clld13e, where f < c + e, b + c + d + e < a + 2 / + 1 and a, b, c, d, e,f £ No. To find sequences for arbitrary lengths, heuristic algorithms can be used based on the relaxation of the zero AACF sidelobes requirements, such as by the Modified Great Deluge Algorithm (MGDA) [GP21], The working solution is then referred to as e -complementary sequence pairs.

[0036] The inventors have realized that a sufficient condition for an array to be susceptible of the approach of [GP21] is that the steering vector has Vandermonde structure. This is fulfilled for an ULA since the steering vector (2) is equal to (1) with ω = ejkd sin θ sin φ.

[0037] Figure 6 shows a uniform circular array (UCA) 600 and a corresponding coordinate system. For a UCA with N antenna elements 210 and radius R. lying in the (x, y) plane, the nearest- 15 neighbor spacing is given by2nRd=~tT- The azimuth directions of the antenna elements are given by2tr(n - l)φn= 2π(n-1) / N, n ∈ [1, ..., N],as indicated for the example value n = 5 in figure 6. The steering vector of the UCA readsa(0, 0) = ejkR sin0[COS(0-0IU XOS(0-0N)]T20=[ejkR sinθ cos(φ-φ)... ejkR sinθ cos(φ-φ)]T∈ ℂN. (3) Given a pair of per-polarization beamforming weight vectors wAand wB, the array factor for a UCA is given by|A(φ,θ)|2= |wATa(φ,θ)|2+ |wBTa(φ,θ)|2.Assuming omnidirectional array elements, which is the most likely practical case in the indoor ceiling deployments, the radiation pattern G(p, 0) is given by the above array factor. The above array factor is furthermore valid, within approximation, as long as the array elements are substantially omnidirectional (e.g., in the sense that there is an azimuthal variation of at most 30%, such as at most 20%, such as at most 10%). A beam with a pointing direction (φ0, θ0) can be generated by setting both beamforming vectors wA, wBequal to30 IV(0O, 0O) = e~jkR sin9° [COS(0O-0IX -XOS(0O-0N)]7’P112009WO01

[0038] Because a UCA’s steering vector (3) does not exhibit a Vandermonde structure, the broad-beam solution according to [GP21] cannot be applied to this type of arrays. The proposed method is thus based on the extraction of phase modes of the UCA, thereby converting the UCA into a virtual ULA. This is done by multiplying the above steering vector by a transformation matrix T = JF, 5 where∈ ℂ(2h+1)×(2h+1)(4a) ∈ ℂ(2h+1)×N(4b)-1 6 N ••• e N with Jnbeing the Bessel function of the first kind of order n. and with 2h + 1 the number of elements of the virtual ULA (virtual subarrays), which is such that 2h + 1 < N. It is noted that the matrix F is 10 proportional to a submatrix formed by extracting the 2h + 1 middle rows of a discrete Fourier transform (DFT) matrix of dimension N X N. It is further noted that the multiplication by the diagonal matrix J is equivalent to multiplying each element by a radially varying coefficient. If each element of the steering vector, after a DFT transformation (multiplication by F), has an angle-dependent phase and a radially varying (and angle-independent) phase / amplitude factor, the radially varying coefficient in J is chosen such that it cancels the radially varying phase / amplitude factor. In other words, the angle-dependent phase is preserved, such that the steering vector assumes a Vandermonde structure. It is proved in the research paperWS94 M. Wax and J. Sheinvald, “Direction finding of coherent signals via spatial smoothing for uniform circular arrays,” IEEE Transactions on Antennas and Propagation, vol. 42 20 (1994), no. 5, pp. 613-620, doi: 10.1109 / 8.299559that such an approximate cancellation is achieved if the coefficients are set proportional to inverted Bessel functions of different orders, for example:1 1 1 1 1 11 / J-h(·), 1 / J-h+1(·), ..., 1 / J-1(·), 1 / J0(·), 1 / J1(·), ..., 1 / Jh(·)P112009WO0110In particular, the orders of the inverted Bessel functions may form an integer sequence centered at zero and they may be scaled as shown in equation (4a). To the authors of [WS94], the approximate cancellation was of interest to enable a spatial smoothing technique, and it is proved by Bessel- expanding the elements of (3) as per5n=-∞ It turns out that the approximate cancellation holds for a coefficient 1 / Jn(α) if n ≫ α.

[0039] For the purposes of the present disclosure, the condition n » a may limit the allowable order of the inverted Bessel functions and thus the number of elements of the virtual ULA. The number of elements 2h + 1 of the virtual ULA may be selected such that, for each element of the 10 DFT-transformed steering vector of the virtual ULA, that element’s radially varying factor has a single dominant term. If more precisely the limiting case is considered to be the outer perimeter of the UCA (radius R). this condition is fulfilled as soon as the radially varying factor of the DFT-transformed steering vector has a single dominant term at a = kR. This corresponds to settingh = max{h ∈ ℕ: h ≤ (N-1) / 2, Jh-N(kR) / Jh(kR) ≤ ε'}, (5)( 2 Jh(kR) ) 15 where ε' > 0 is a predetermined tolerance. The quotient in (5) is derived from the Bessel expansion of the hthelement of the steering vector of the virtual ULA; it is the ratio of the second greatest and the greatest (dominant) term, corresponding to l = −1 and l = 0 in equation 23 of [WS94], If the second greatest term is no longer negligible (i.e., if the ratio is greater than the tolerance ε'), the virtual ULA should preferably not grow further. The same choice of h applies to both the first and second subarray; if the antenna elements have an irregular geometry, the antenna elements with the maximum distance Rmaxfrom the origin should determine the value of R in (5).

[0040] Two ε-complementary sequences ŵAand ŵBcan be determined according to any the approaches in [GP21], after which the beamforming weights for the UCA are chosen aswA= TTŵA, wB= TTŵB, (6) 25 and the array factor reads|A(φ,θ)|2= |wATa(φ,θ)|2+ |wBTa(φ,θ)|2= \TwAa(([),d')\2+ |Tiv£ a(0, e)|2.The array factor is spatially flat in the power domain and / or the power pattern is approximately equal in shape to a power pattern of one transducer element.P112009WO0111

[0041] Figure 7A is a three-dimensional plot of an angular radiation pattern of a downwardpointing UCA when excitation weights TTWA, TTWBobtained by this approach are applied. For comparison, figure 9 is a three-dimensional plot of an angular radiation pattern of an identical downward-pointing UCA when conventional, DFT-type excitation weights are applied.5

[0042] The plotted data was obtained by a simulation of a ceiling-mounted UCA of radius R = 1 cm with N = 8 antennas operating at a frequency of 7 GHz. The two figures illustrate two examples of beams designed forbroadcasting information across the coverage area. Figure 9 shows an example of a conventional UCA beam tilted to 90= 180° zenith angle (hence, pointing downwards). Figure 7A shows a beam designed with the proposed method with a choice of h = 3, and hence M = 2h + 1 = 7 virtual antennas, which were excited in accordance with the following pair of complementary sequences:wA= [-0.5421 - 0.57274, -0.2835 - 0.14014, 0.2410 + 0.73734, -0.2639 - 0.10744,-0.9896 - 1.32124, -0.5227 - 0.54034, 0.3502 + 0.91994,0.1297 + 0.55114]7’,15 wB= [-0.0534 - 0.94894, -0.2487 + 0.60364, -0.2029 + 0.23894,-0.0675 - 0.83724, -0.1623 - 0.08384, -0.3069 + 1.06604, -0.1763 + 0.02774, 0.0283 - 1.59844]7.The excitation weights actually applied to the antenna elements of the UCA were given by (6), where the J matrix in T = JF had been computed for the stated value R = 1 cm. By comparing figures 7A 20 and 9, it can be seen that the proposed approach (figure 7A) creates a broad radiation pattern, in contrast to the conventional beamforming method (figure 9).

[0043] To visualize the spatial flatness of the array factor in detail, figure 8 shows the data from figure 7A as a function of azimuth p for constant zenith angle 9 = 90° (i.e., the (x, y) plane).Similarly, figure 10 is a re-plot of the data from figure 9, which is considerably non-flat. It is evident that the novel approach proposed herein represents a significant improvement over conventional beamforming in UCAs.

[0044] Figure 7B is linked to the earlier observation that an approximate circular geometry constitutes a “circular transducer array” in the sense of the claims. Here, the same 6-complementary sequences wAand wBwere used, but a random 5% perturbation was superimposed on the elements of 30 the transformation matrix T:Tr= T + 0.05 x rand^size T)^,where rcmd(-) is a function which samples from a uniform probability distribution on [0,1], Using T' instead of T models a 5% deviation from an ideal UCA geometry. Because the radiation pattern in figure 7B remains substantially flat, it may be concluded that the proposed beamforming approach isP112009WO0112robust to deviations of at least this magnitude. To the extent the perturbation deforms the radiation pattern, there is no preferred direction and the inherent directivity of the UCA shows no sign of reappearing. The data in figure 7B corroborate the claim that the teachings herein are applicable to circular transducer arrays, whether they have an ideal and or merely an approximate circular geometry.5 Beamforming method

[0045] A method 100 for performing beamforming using a circular transducer array 200 of equal transducer elements 210 will now be described with reference to the flowchart in figure 1. The method 100 may be executed by any processing circuitry with authority to configure the excitation weights of the transducer array 200.10

[0046] In particular, the method 100 may be implemented in the beamforming device 290 shown in figure 2. The top portion of figure 2 shows an approximately circular transducer array 200 with eight transducer elements 210 with polarization A (drawn in solid line) and eight transducer elements 210 with polarization B (drawn in hollow line). The transducer elements 210 are distributed with approximately uniform angular spacing over the imaginary curve drawn in dashed line. Within the approximation, the transducer array 200 can be modeled as a UCA.

[0047] Each transducer element 210 is connected to an individual digital or analog beamformer configured to apply a phase shift and optionally to vary the amplitude of an electric signal. It is recalled that mechanical (including acoustic) transducers provide an electric signal, and an electric signal representing a mechanical excitation can be processed in the same way as an electric signal 20 representing an electromagnetic wave or the like.

[0048] In the depicted example, beamformers for A-polarized and B-polarized transducer elements are collected in respective feeder networks 220A, 220B. In transmit mode, the feeder networks 220A, 220B accept excitation weights wA, wBand a signal x to be transmitted. In receive mode, the feeder networks 220A, 220B accept excitation weights wA, wBand output a received signal x. If the transducer elements are antenna elements, then for each choice of excitation weights wA, wB, the A-polarized transducer elements and the corresponding feeder network 220A may be considered as a first antenna port and the B-polarized transducer elements and the corresponding feeder network 220B may be considered as a second antenna port.

[0049] The signal x to be transmitted may be generated by a radio chain (not shown) configured 30 for baseband processing. In a wireless communication system, the signal x may carry user data or control data. In a radar or sonar, the signal x to be transmitted may be a radio-frequency or acoustic excitation wave which impinges on an object to be observed and gives rise to a reflected wave, which is the received signal. In a seismometer (or geophone), the received signal represents a mechanical excitation of the transducer elements.P112009WO0113

[0050] The excitation weights wA, wBare determined by a beamforming device 290, which comprises processing circuitry 291 and a memory 292 storing computer-executable code (computer program) 293. The beamforming device 290 may be a standalone device, or it may be integrated in another device with a different main purpose. The processing circuitry 291 in the beamforming device 5 290 is configured to process instructions and data and may be configured to implement any sequential state machine operative to execute instructions stored as machine-readable computer programs in the memory 292. The processing circuitry 291 may be implemented as one or more hardware- implemented state machines (e.g., in discrete logic, field-programmable gate arrays (FPGAs), application specific integrated circuits (ASICs), etc.); programmable logic together with appropriate 10 firmware; one or more stored computer programs, general-purpose processors, such as a microprocessor or digital signal processor (DSP), together with appropriate software; or any combination of the above. For example, the processing circuitry 291 may include multiple central processing units (CPUs).

[0051] Although the example array 200 in figure 2 comprises, for each A-polarized transducer element 210, a substantially co-located B-polarized transducer element 210, this configuration is not an essential feature of the invention. For instance, the A-polarized transducer elements 210 and B- polarized transducer elements 210 can be arranged in a staggered fashion on the approximately circular curve, with nonnegligible angular separation between A- and B-polarized transducer elements 210. Additionally or alternatively, the A-polarized transducer elements 210 and the B-polarized transducer elements 210 can be arranged on two different, approximately circular imaginary curves, which need not coincide, or overlap, or be concentric. Indeed, the wanted add-up of the power contributions from the two polarizations in DPBF occurs in the far-field region (Fraunhofer zone), not in the immediate vicinity of the transducer elements.

[0052] In a first step 101 of the beamforming method 100, a circular first subarray of transducer 25 elements with a first polarization A and a circular second subarray of transducer elements with a distinct, second polarization B are identified. The distinct polarizations A and B may optionally be orthogonal polarizations; see above. In the example of figure 2, the first subarray may be identified as all A-polarized transducer elements, and the second subarray may be identified as all B-polarized transducer elements. The first and second subarrays are preferably disjoint in the sense that no transducer element 210 belongs to both subarrays.

[0053] In a step 102. the first subarray is transformed into a first virtual subarray with at most the number of elements as the first subarray. If the first subarray has N elements each, the first virtual subarray shall have 2 / 1 + 1 <elements. The transformation is such that the steering vector of the first virtual subarray assumes an approximate Vandermonde structure; see equation 1. It follows from 35 equation (6) that any excitation weights wA, wBwhich provide a desired beamforming on one of theP112009WO0114subarrays of the circular transducer array 200 must be transformed back before they are applied to the corresponding virtual subarray, as follows:

[0054] wA= TWA, WB= TWBAn some embodiments of the method 100, the transformation is carried out by a first left multiplication by a submatrix F of a DFT matrix, which yields a DFT- 5 transformed steering vector of the first subarray, F a(<p, 0). Next, the elements of the DFT- transformed steering vector are multiplied by respective coefficients, preferably radially varying coefficients each of which is adapted to substantially cancel a radially varying factor of a respective element of a DFT-transformed steering vector. The multiplications may be represented as a multiplication by a diagonal matrix / , where the coefficients are the diagonal elements, which changes 10 the steering vector into JF a(<p, 0). The coefficients may be fractions with Bessel functions in the denominator, i.e., the coefficients are inverted Bessel functions. In particular, the coefficients may be chosen proportional to inverted Bessel functions of the first kind, the orders of which form an integer sequence centered at zero, — h, —h + 1,..., —1,0,1,..., h, as per equation (4). The number of elements in the virtual subarray is determined by the number h. which is chosen such that, for each element of the DFT-transformed steering vector of the first and second subarray, that element’s radially varying factor has a single dominant term; see equation (5).

[0055] In other embodiments, the transformation is carried out by a single left matrix multiplication T. where T is a matrix product JF, in which one factor J is a diagonal matrix of inverted Bessel functions of different orders, and a further factor F is a submatrix of a DFT matrix. It is 20 appreciated that the first and second subarrays, as well as their steering vectors, are represented as column matrices.

[0056] In a third step 103. the second subarray is transformed into a second virtual subarray with an equal number of elements 2h + 1 as the first virtual subarray. It is understood that the number N2of elements of the second subarray also limits the size of the second virtual subarray, i.e., 2h + 1 < N2. The transformation is carried out as for the first subarray.

[0057] After completion of steps 102 and 103, the steering vector of each virtual subarray has an approximate Vandermonde structure, like for a ULA of the same size. As the inventors have realized, this property is sufficient to enable application of the DPBF technique.

[0058] In a next step 104. thus, a broad beam is formed by combining the first and second virtual 30 subarrays in accordance with respective excitation weight vectors wA, wB, which are such that the broad beam’s power pattern is approximately equal in shape to a power pattern of one transducer element. The broad beam’s power pattern is made approximately equal in shape to a power pattern of one transducer element by combining the first and second virtual subarrays in accordance with respective excitation weight vectors wA, wBas if they were ULAs.P112009WO0115

[0059] The prior application W02017190811A1, the research paper [GP21] as well as the further prior application WO2016141961A1 disclose several algorithms for determining such excitation weight vectors, and numerical examples of usable excitation weight vectors, as well as operations for modifying, combining or extending the excitation weight vectors while preserving the 5 spatially flat array factor.

[0060] In one embodiment, the excitation weight vectors wA, wBare proportional to E- complementary sequences. The ε-complementary sequences are such that, for any non-zero integer T,|^(T) + R»B(T)| < £,where R®A(T) and R®B(T) are autocorrelation functions of the excitation weight vectors and E > 0 is a 10 small tolerance, which is independent of T. It is recalled that the aperiodic autocorrelation function for a sequence u = (u1;u2,..., uN) can be defined as:Um+T / 0 — T < IV 1,(7)um-rum <—A + 1 < T < 0,0, T < —N or T > N. For T = 0, the expression R(VA( ) + R(VB( ) can have any nonzero value. After rescaling, setting the excitation weight vectors wA, wBproportional to ε-complementary sequences provides, for any integer T,= 2M<5(T).

[0061] To find excitation weight vectors wA, wBwhich are proportional to ε-complementary sequences, an optimization process configured to minimize \RA(T) + RwB(T) | for non-zero integer values of T may be executed. In particular, the optimization process may be configured to determine 20 the phases of the excitation weights. The optimization process may be, for example, a Great Deluge algorithm or modified Great Deluge algorithm (MGDA), a CANARY algorithm, a Majorization- Minimization (MM) algorithm, or a Simulated Annealing (SA) algorithm. The CANARY, MM and SA algorithms are described in W02017190811A1.

[0062] The following pseudocode illustrates the MGDA.Algorithm 1. Iterative algorithm for computing polyphase 6-complementary sequencesRequire: Rain intensity V > 0, phase scaling factor a G (0, 1], tolerance threshold e > 0, max number of unsuccessful steps dmax.Initiate phase vector (p ~ 'U[0, 2TT)2M.Initiate phase increments vector A0 ~ ‘lt[0, 2TT)2M.Set water level A <- U (0).Initialize unsuccessful step counter d <- 0.while U ((p) > e dofor i = 1 -> 2M dowhile U (0) < A doIncrement phase <pi <- <pi + A0;.if U ((p) > A thenAccept new phase (pi.elseStep backwards <pi <- <pi — &( / )[.if U (jpA) > A thenAccept new phase (pi.elseScale down step size A0;<- ahcpi.end ifend ifIncrease water level A <- A + V.if d > dmaxthenReinitialize step size A0 ~ 2TT)2M.Move to new neighborhood (p <- (p + A0.Reset water level A <- U (0).Reset unsuccessful step counter d <- 0.end ifend whileObtain beamforming weights: wA= and ivB=.In Algorithm 1, the utility function for the optimization can be computed ast ( ) = - [max(| ( i, 0)|2) - min(| ( i,e)|2)]whereM(< M)I2= |ivja(0,e)|2+ |iv£ a(0,e)|2,P112009WO0117or, alternatively{pM-1I- + W< LJT=1Jwhere p is a design parameter chosen for faster convergence. The utility function is evaluated for a set of azimuth samples (pi G [— n, n] for the current iteration’s pair of weights5 wA= eJ= [ej< Pi...ej<pM]TandwB= = [ej<pM+1...ej< P2M]T,where M = 2h + 1. The tolerance threshold may for example be set to 1% of the main sum-AACF lobe, that is, e = 0.02M.10

[0063] The MGDA is discussed more generally in [GP21],

[0064] Still with reference to step 104, in one embodiment the excitation weight vectors wA, wBare proportional to a Golay complementary sequence pair.

[0065] Because of the transformation (6), the excitation weight vectors to be applied to the circular transducer array in step 104 (cf. feeder networks 220A, 220B) are given by15 wA= TTWA, WB= TTWB.where TT= FTJT. Accordingly, excitation weight vectors wA, wBwhich are recognizable as being vectors in accordance with W02017190811A1 or [GP21] (such as the simple Golay sequences (1,1,1, —j,j) and (1, / , —1,1, — / )) will undergo - when the beamforming device 290 determines the vectors wA, wBwhich are to be applied to the circular transducer array - an element-wise rescaling ]2ltfollowed by an inverse DFT for e~~N~ (inverse of length-lV DFT). It may be possible to determine the weight vectors by measurements during a transmission of an identical signal from one transducer element while muting the other transducer elements. If the transformation (6) is undone, as per wA= TWA, WB= TWB,for excitation weight vectors wA, wBmeasured in this way, then the familiar structure according to 25 W02017190811A1 or [GP21] should reappear.

[0066] In a further step 106. the broad beam formed in step 104 is used for transmitting or receiving signals. The subarrays were combined in step 104 in the sense that they are designated for use during simultaneous transmission or simultaneous reception, as illustrated by the parallel path of signal %; the excitation weight vectors wA, wBare applied to the subarrays but themselves do notP112009WO01change. In the case of an antenna array, the transmission or the reception is performed using two antenna ports simultaneously, wherein the A-polarized transducer elements and the corresponding feeder network 220A may be considered as a first antenna port and the B-polarized transducer elements and the corresponding feeder network 220B may be considered as a second antenna port. 5

[0067] Optionally, step 106 includes post-processing the excitation weight vectors to achieve amplitude tapering and / or phase tapering. This involves small modifications to the excitation weight vectors, which substantially preserve the spatially flat array factor; see section VII. A of [GP21], In some embodiments, the post-processing aims to provide a desired pointing direction; a significant angular range can be covered by just a small number of broad beams pointing in different directions. In other embodiments, the post-processing aims to limit the angular range of the broad beam, that is, the excitation weight vectors are modified such that they contain at least some elements which are related in phase to form a spatially flat radiation pattern in a limited angular range. After such postprocessing, the broad beam is not used with its maximum angular width but with an adaptable, smaller width. The spatially flat radiation pattern is narrower than the power pattern of one transducer 15 element. This option is convenient for broadcasting cell-specific signals in cellular communication systems, while limiting transmissions outside the cell.

[0068] Optionally, the beamforming method 100 according to some embodiments further comprises a step 105 of forming a second broad beam by combining the first and second virtual subarrays in accordance with respective excitation weight vectors (— EMwB*, EMw ). and a step 107 of 20 transmitting or receiving signals using the second broad beam. Here, EMis an order-flipping operator of size M = 2h + 1, which can be represented by the antidiagonal matrix0 1 '.1 0.To obtain the second broad beam, one thus applies the following excitation weights vectors to the circular transducer array:(W^WB' ) = -TTEMW^TEMW )- The two broad beams can be used simultaneously. The polarization of the second broad beam is orthogonal to the polarization of the (first) broad beam. This provides two channels of polarizationdivision multiplexing into a broad angular range.Use cases30

[0069] Figures 3 and 4 illustrate a number of envisioned use cases of the teachings herein. The circular transducer array is an antenna array in the examples in figure 3 and it is an array of mechanical (in particular acoustic) transducers in figure 4.P112009WO0119

[0070] Figure 3A shows a user equipment (UE) 310 which incorporates an approximately circular antenna array 311 and a beamforming device 290 with the functionalities described above. In particular, the UE 310 is configured to perform the beamforming method 100. As used herein, a UE refers to a device capable, configured, arranged and / or operable to communicate wirelessly with 5 network nodes and / or other UEs. Examples of a UE include, but are not limited to, a smart phone, mobile phone, cell phone, voice over IP (VoIP) phone, wireless local loop phone, desktop computer, personal digital assistant (PDA), wireless cameras, gaming console or device, music storage / playback device, wearable terminal device, wireless endpoint, mobile station, tablet, laptop, laptop-embedded equipment (LEE), laptop-mounted equipment (LME), an Augmented Reality (AR) or Virtual Reality 10 (VR) device, wireless customer-premise equipment (CPE), vehicle, vehicle-mounted or vehicle embedded / integrated wireless device, etc. Other examples include any UE identified by the 3rd Generation Partnership Project (3GPP), including a narrow band internet of things (NB-IoT) UE, a machine type communication (MTC) UE, and / or an enhanced MTC (eMTC) UE. A UE may support device-to-device (D2D) communication, for example by implementing a 3GPP standard for sidelink communication, Dedicated Short-Range Communication (DSRC), vehicle-to-vehicle (V2V), vehicle- to-infrastructure (V2I), or vehicle-to-everything (V2X). In other examples, a UE may not necessarily have a user in the sense of a human user who owns and / or operates the relevant device. Instead, a UE may represent a device that is intended for sale to, or operation by, a human user but which may not, or which may not initially, be associated with a specific human user (e.g., a smart sprinkler controller). Alternatively, a UE may represent a device that is not intended for sale to, or operation by, an end user but which may be associated with or operated for the benefit of a user (e.g., a smart power meter).

[0071] Figure 3B shows a radio base station 320 which incorporates an approximately circular antenna array 311 and is associated with a beamforming device 290 as described above. A radio base station may be a Node B, evolved Node B (eNB), NR Node B (gNB) or a base station for 6G or 25 higher. Radio base stations may be categorized based on the amount of coverage they provide (or, stated differently, their transmit power level) and so, depending on the provided amount of coverage, may be referred to as femto base stations, pico base stations, micro base stations, or macro base stations. A radio base station may be a relay node or a relay donor node controlling a relay. A network node may also include one or more (or all) parts of a distributed radio base station such as centralized digital units, distributed units (e.g., in an O-RAN access node) and / or remote radio units (RRUs), sometimes referred to as Remote Radio Heads (RRHs). Such remote radio units may or may not be integrated with an antenna as an antenna integrated radio. Parts of a distributed radio base station may also be referred to as nodes in a distributed antenna system (DAS).

[0072] Figure 3C shows an indoor wireless access point 330 which incorporates an35 approximately circular antenna array 311 and is associated with a beamforming device 290 as described above. A pico base station and a radio dot are examples of an indoor wireless access pointP112009WO0120330. The indoor wireless access point 330 may in particular be suspended from or mounted on a ceiling in an indoor environment 339.

[0073] Figure 3D shows a communication satellite 340 equipped with an approximately circular antenna array 311 and is associated with a beamforming device 290 as described above.5

[0074] Figure 3E shows a radar device 350 which is equipped with an approximately circular antenna array 311 and is associated with a beamforming device 290 as described above.

[0075] Figures 4A shows a sonar 410 mounted on a ship hull 412. The sonar 410 has an approximately circular array of acoustic transducers 411 and is associated with a beamforming device 290 as described above.10

[0076] Figure 4B shows a seismometer (or geophone) 420, which includes an approximately circular array of mechanical transducers 411 secured to ground. The seismic measurements are carried out using a beamforming device 290 as described above.

[0077] The aspects of the present disclosure have mainly been described above with reference to a few embodiments. However, as is readily appreciated by a person skilled in the art, other15 embodiments than the ones disclosed above are equally possible within the scope of the invention, as defined by the appended patent claims.

Claims

P112009WO0121CLAIMS1. A method (100) for beamforming using a circular transducer array of equal transducer elements (210), the method comprising:in the circular transducer array, identifying (101) a circular first subarray of transducer elements with a 5 first polarization (A) and a circular second subarray of transducer elements with a distinct, second polarization (B);transforming (102) the first subarray into a first virtual subarray with at most the number of elements as the first subarray, such that its steering vector has an approximate Vandermonde structure; transforming (103) the second subarray into a second virtual subarray with as many elements as the first virtual subarray, such that its steering vector has an approximate Vandermonde structure; forming (104) a broad beam by combining the first and second virtual subarrays in accordance with respective excitation weight vectors (wA, wB), which are such that the broad beam’s power pattern is approximately equal in shape to a power pattern of one transducer element; andtransmitting or receiving (106) signals using the broad beam.15 2. The method of claim 1, wherein transforming (102, 103) the first and second subarrays into the respective virtual subarrays comprises multiplying (102.1, 103.1) by a submatrix (F) of a discrete Fourier transform, DFT, matrix.

3. The method of claim 2, wherein transforming (102, 103) the first and second subarrays into the respective virtual subarrays further comprises subsequently multiplying (102.2, 103.2) by radially 20 varying coefficients, each coefficient adapted to substantially cancel a radially varying factor of a respective element of a DFT-transformed steering vector of the first and second subarray.

4. The method of claim 2 or 3, wherein the coefficients are inverted Bessel functions of different orders.

5. The method of claim 4, wherein the coefficients are inverted Bessel functions of the first kind, the orders of which form an integer sequence centered at zero.

6. The method of any of claims 3 to 5, wherein the number of elements of the first and second virtual subarray is selected such that, for each element of the DFT-transformed steering vector of the first and second subarray, that element’s radially varying factor has a single dominant term.

7. The method of any of the preceding claims, wherein:30 the first and second subarrays are represented as column matrices; andP112009WO0122transforming (102, 103) the first and second subarrays into the respective virtual subarrays comprises multiplying by a matrix product (JF) from the left, in which one factor (J) is a diagonal matrix of inverted Bessel functions of different orders, and a further factor (F) is a submatrix of a DFT matrix.

8. The method of any of the preceding claims, wherein the first and / or the second subarray is an 5 approximate uniform circular array, UCA.

9. The method of any of the preceding claims, wherein the first and / or the second subarray is a circular antenna array.

10. The method of any of the preceding claims, wherein the first and / or the second subarray is a circular array of mechanical transducers.

11. The method of any of the preceding claims, wherein the first polarization (A) is orthogonal to the second polarization (B).

12. The method of any of the preceding claims, further comprising:forming (105) a second broad beam by combining the first and second virtual subarrays in accordance with respective excitation weight vectors (— EMwB, EMwA). where EMis an order-flipping operator; 15 andtransmitting or receiving (107) signals using the second broad beam.

13. The method of any of the preceding claims, wherein the excitation weight vectors (wA, wB) are proportional to ε-complementary sequences such that, for any non-zero integer T,+ Su>BW| < £,20 where RA(T) and RB(T) are autocorrelation functions of the excitation weight vectors and E > 0 is a small tolerance independent of T.

14. The method of claim 13, wherein the excitation weights (wA, wB) are determined by an optimization process configured to minimize |R^A(T) + R^B(T) | for non-zero integer values of T.

15. The method of claim 14, wherein the optimization process is a Great Deluge algorithm, in particular a modified Great Deluge algorithm, MGDA.

16. The method of any of the preceding claims, wherein the excitation weight vectors (wA, wB) are proportional to a Golay complementary sequence pair.

17. The method of any of the preceding claims, wherein the excitation weight vectors (wA, wB) contain at least some elements which are related in phase to form a spatially flat radiation pattern in a 30 limited angular range.P112009WO012318. The method of claim 17, wherein the spatially flat radiation pattern is narrower than the power pattern of one transducer element.

19. A beamforming device (290) for use with a transducer array (200) of equal transducer elements (210), wherein the beamforming device comprises processing circuitry (291) configured to:5 in the circular transducer array, identify a circular first subarray of transducer elements with a first polarization (A) and a circular second subarray of transducer elements with a distinct, second polarization (B);transform the first subarray into a first virtual subarray with at most the number of elements as the first subarray, such that its steering vector has an approximate Vandermonde structure;10 transform the second subarray into a second virtual subarray with as many elements as the first virtual subarray, such that its steering vector has an approximate Vandermonde structure;form a broad beam by combining the first and second virtual subarrays in accordance with respective excitation weight vectors (wA, wB), which are such that the broad beam’s power pattern is approximately equal in shape to a power pattern of one transducer element; andtransmit or receive signals using the broad beam.

20. The beamforming device (290) of claim 19, adapted to perform the method of any of claims 2- 18.

21. A user equipment (310) or a radio base station (320) or an indoor wireless access point (330) or a communication satellite (340) or a radar (350), each comprising the beamforming device (290) of 20 any of claims 19 to 20 arranged to be used with a circular antenna array (311).

22. A sonar (410) or a seismometer (420), each comprising the beamforming device (290) of any of claims 19 to 20 arranged to be used with a circular array of mechanical transducers (411).

23. A computer program (293) comprising instructions for causing the beamforming device (290) of claim 19 to carry out the method according to any of claims 1 to 18.25 24. A computer-readable medium (292) storing the computer program of claim 23.

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