Multibeam antenna system and method

Abstract

An antenna beam forming circuit for the transmission and reception of directional electromagnetic radiation, the circuit including: a series of m input / output ports for input / output of transmission / reception signals; a series of n antennas; a series of directional couplers and associated phase shifters arranged in matrix form in order to form multiple and individually and independently steerable beams.

Description

Multibeam antenna system and method RELATED APPLICATION

[0001] The present disclosure claims benefit of priority to Australian Provisional Patent Application Number: 2023201214 filed 28 February 2023, titled: “Multibeam antenna system and method”, the contents of which are incorporated herein by reference. In jurisdictions where incorporation by reference is not permitted, the applicant reserves the right to add any or the whole of the contents of the Application 2023201214 as an Appendix hereto, forming part of the specification. FIELD OF THE INVENTION

[0002] The present invention relates to antenna system and methods for wireless communications and sensing systems such as satellite communications and the six generation (6G) wireless communications systems as well as wireless Internet of Things (IoT). REFERENCES

[0003] [1] Y. Jay Guo, Maral Ansari and Nelson J. G. Fonseca, “Circuit Type Multiple Beamforming Networks for Antenna Arrays in 5G and 6G Terrestrial and Non-Terrestrial Networks,” IEEE Journal of Microwaves, Vol. 1, No. 3, July, 2021, pp. 704-722, DOI: 10.1109 / JMW.2021.3072873.

[0004] [2] Y. Jay Guo, Maral Ansari, Richard W. Zilkowski and Nelson J. G. Fonseca, “Quasi- optical Multi-beam Antenna Technologies for B5G and 6G mmWave and THz Networks: A Review,” IEEE Open Journal of Antennas and Propagation, DOI: 10.1109 / OJAP.2021.3093622.

[0005] [3] Y. Jay Guo and Bevan Jones, Base Station Antennas, in John Volakis ed., Chapter 40, Antenna Engineering Handbook, Fifth Edition, McGraw-Hill, 2018.

[0006] [4] C. Tsokos et al., “Analysis of a multibeam optical beamforming network based on Blass matrix architecture,” J. Lightw. Technol., vol.36, no.16, pp.3354–3372, 2018.

[0007] [5] J. Blass, “Multidirectional antenna-A new approach to stacked beams. IRE International Convention Record,” Vol.8, Mar 1960. vol.48, no.3, pp.402–402, 1960.

[0008] [6] Peizhao Li, Han Ren and Bayaner Arigong, “A Symmetric Beam-Phased Array Fed by a Nolen Matrix Using 180◦ Couplers,” IEEE Microwave and Wireless Component Letters, Vol. 30, No.4, April 2020, pp.387-390.

[0009] [7] Charles A. Guo and Y. Jay Guo, “A General Approach for Synthesizing Multibeam Antenna Arrays Employing Generalized Joined Coupler Matrix,” IEEE Transactions on Antennas and Propagation, Vol. 70, Issue 9, September 2022, pp. 7556-7564, DOI: 10.1109 / TAP.2022.3153037.

[0010] [8] Charles A. Guo, Y. Jay Guo, He Zhu, Wei Ni and Jinhong Yuan, “Optimization of Multibeam Antennas Employing Generalized Joined Coupler Matrix,” IEEE Transactions on Antennas and Propagation, Vol. 71, Issue 1, January 2023, pp. 215-224, DOI: 10.1109 / TAP.2022.3220976.

[0011] [9] H. Zhu, T. Zhang and Y. J. Guo, "Wideband Hybrid Couplers With Unequal Power Division / Arbitrary Output Phases and Applications to Miniaturized Nolen Matrices," in IEEE Transactions on Microwave Theory and Techniques, vol.70, no.6, pp.3040-3053, June 2022, doi: 10.1109 / TMTT.2022.3164673.

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[0010] Y. Jay Guo, J. Bunton and Val Dyadyuk and Xiaojing Huang, Hybrid Adaptive Antenna Array, US 8754810, 2009.

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[0011] X. Gao, L. Dai, S. Han, C.-L. I, and R. W. Heath, “Energy-efficient hybrid analog and digital precoding for mmwave mimo systems with large antenna arrays,” IEEE Journal on Selected Areas in Communications, vol.34, no.4, pp.998–1009, 2016.

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[0012] C. Han, L. Yan, and J. Yuan, “Hybrid beamforming for terahertz wireless communications: Challenges, architectures, and open problems,” IEEE Wireless Communications, vol.28, no.4, pp.198–204, 2022.

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[0013] W. R. Jones and E. C. DuFort, “On the design of optimum dual-series networks,” IEEE Transactions on Microwave Theory and Technology., vol. MTT-19, pp.151-158, May 1971.

[0016]

[0014] S. Mosca, F. Bilotti, A. Toscano and L. Vegni, “A Novel Design Method for Blass Matrix Beam-Forming Networks” IEEE Transactions on Antennas and Propagation, vol 50, pp.225- 232, Feb 2002.BACKGROUND OF THE INVENTION

[0017] Any discussion of the background art throughout the specification should in no way be considered as an admission that such art is widely known or forms part of common general knowledge in the field.

[0018] Antenna devices have increased utility when they provide some directionality preference for transmission and reception of signals.

[0019] For example, an antenna typically has at least one beam power pointed to a specified direction in order to support a communications link. The narrower the beam, the better the communications quality in terms of data rates, distance of transmission and immunity against potential interference and noise.

[0020] Multi-beam antennas are antennas that can produce more than one beam simultaneously. This is advantageous when it is required to support more than one communications link at any given time. For instance, a base station antenna in a cellular system needs to support a number of users most of the time, and using multibeam antennas generally yields greater communications quality between the base station and the users supported, and greater system capacity.

[0021] Future communications systems such as beyond 5G (B5G) and the six generation (6G) wireless communications systems are expected to support peer-to-peer networking, in which each user, being a person, a drone or a satellite, would need to be connected with a number of neighboring users at any given time. This would require the antennas of many users, if not the most, to have the multibeam capability. Consequently, multibeam antennas are regarded as one of the most critical technologies for future wireless communications networks [1] [2].

[0022] In comparison to digital beamforming techniques that form multibeams in the digital domain and have been widely used in 4G and 5G, analogue beamforming techniques are of much lower cost and energy consumption. Analogue multi-beams can be formed by using either circuit- type feed networks or quasi-optical approaches [1, 2]. Common circuit-type feed networks for feeding multi-beam antennas include the Butler matrix, the Blass matrix and the Nolen matrix [1, 3, 4, 5, 6]. A standard Butler matrix is a ^^ × ^^ square matrix using hybrid couplers and phase shifters to produce N orthogonal beams [3]. Although all the beams can be rotated together, their relative beam directions are fixed. Therefore, the Butler matrix is most suited for covering sectors in conventional base stations. Blass matrices and Nolen matrices employ directional couplers and phaseshifters to produce multi-beams [4, 5, 6]. A Blass matrix is an ^^ × ^^ rectangle matrix with matched loads at the end of each row to produce M beams, and it is regarded as being lossy. A Nolen matrix is an ^^ × ^^ diagonal matrix with all the energy into its diagonal nodes directed in the direction of the antennas to make it lossless and saves almost half of the network nodes / circuit components. In theory, Blass matrices and Nolen matrices can support multibeams in any directions, which is the reason these matrices have attracted increasing interest recently. However, the beams produced by these matrices are inter-dependent, that is, the direction change of one beam would necessarily change some of the other beams. Therefore, to support adaptive multibeam operations, most of the matrix elements of the Bulter matrix and the Nolen matrix need to be reconfigured on the fly. This makes the circuit design complicated and, as a result, all reported Blass matrices and Nolen matrices only support fixed multibeams. On the other hand, since the user directions / locations in a mobile communications system can change all the time, it is significant and important to have an advanced analogue multibeam technology that support individually controllable beams at low cost. SUMMARY OF THE INVENTION

[0023] It is an object of the invention, in its preferred form, to provide an improved form of beamforming circuit, referred to as the generalised joined coupler (GJC) matrix.

[0024] In accordance with a first aspect of the present invention, there is provided an antenna beam forming circuit of the transmission of directional electromagnetic radiation, the circuit including: a series of m input ports for input of transmission signals; a series of n output antennas; a series of directional couplers and phase shifters arranged in a matrix form to distribute m streams signals to n antennas in such a manner to form m directional beams..

[0025] In accordance with a further aspect of the present invention there is provided an antenna beam forming circuit of the reception of directional electromagnetic radiation, the circuit including: a series of m output ports for output of received signals; a series of n input antennas; a series of directional couplers and phase shifters arranged in a matrix form to guide m signals received by n antennas to m output ports.

[0026] In some embodiments, the phase shifters are partitioned into two, with a fixed phase shifter and a variable phase shifter. The fixed phase shifter can be integrated into the directional coupler. The directional coupler parameters and phase shift values can be determined by the desired initial beam directions and beam shapes;

[0027] In some embodiments, the tunable phase shifters are the same for each row to support uniformly distributed arrays; or a different to support non-uniformly distributed antenna arrays; The couplers can be formed into a Blass-like GJC matrix or a Nolen-like GJC matrix.

[0028] The switches can be placed at the input or output ports to accommodate variation of the directional beamforming circuits. In some embodiments, the beamforming circuit includes an analog beamformer combined with a digital beam former forming a hybrid array. BRIEF DESCRIPTION OF THE DRAWINGS

[0029] Embodiments of the invention will now be described, by way of example only, with reference to the accompanying drawings in which:

[0030] Fig.1 illustrates the functionality of a directional coupler.

[0031] Fig.2 illustrates the part of a GJC matrix for transmitting four beams.

[0032] Fig.3 illustrates the directional coupler and a phase shifter form a GJC matrix node.

[0033] Fig.4 illustrates the part of a general GJC matrix.

[0034] Fig.5 illustrates the Blass-like GJC matrix.

[0035] Fig. 6 illustrates the synthesized beam patterns using a Blass-like GJC matrix when M = 3 and N = 8.

[0036] Fig. 7 illustrates the synthesized beam patterns using a Blass-like GJC matrix when M = 3 and N = 12.

[0037] Fig. 8 illustrates the three beams produced by using 20 antenna elements and a Taylor distribution (M=3 and N =20).

[0038] Fig. 9 illustrates the five beams produced by using 20 antenna elements and a Taylor distribution (M=5 and N =20).

[0039] Fig.10 illustrates the multiple beam scanning by changing phase shifts only (solid line, - s), and optimizing the GJC matrix (circles, -o) with M=3 and N =12.

[0040] Fig.11 illustrates a 4 × 8 Nolen-like GJC matrix.

[0041] Fig. 12 illustrates a comparison of four beams produced by a Blass-like GJC matrix (circles, -b) and a Nolen-like GJC matrix (solid line, -n) using eight antenna elements (M = 4 and N = 8).

[0042] Fig.13 illustrates an extended conventional Nolen Matrix.

[0043] Fig.14 illustrates a Nolen-like GJC matrix.

[0044] Fig.15 illustrates details of the GJC matrix node consisting of a directional coupler and a phase shifter.

[0045] Fig.16 illustrates a Blass-like GJC matrix implementation.

[0046] Fig.17 illustrates a Nolen-like GJC matrix implementation.

[0047] Fig.18 illustrates a switchable Blass-like GJC matrix supporting varying beam numbers.

[0048] Fig.19 illustrates a switchable Nolen-like GJC matrix supporting varying beam numbers.

[0049] Fig.20 illustrates a hybrid array for reception.

[0050] Fig.21 illustrates a hybrid array for transmission.

[0051] Fig.22 illustrates a plan view of a 3 × 10 Nolen-like GJC matrix circuit. DETAILED DESCRIPTION

[0052] The embodiments provide for a system and method which allows for the formation of an improved beam forming device, known as the generalised joined coupler (GJC) matrix.

[0053] Despite the rapidly increasing interest in analog multibeam antennas, there has been a lack of systematic theoretical approaches to synthesizing circuit-type multiple beamforming networks, such as the Blass matrix and the Nolen matrix.

[0054] Initially, there is defined a generalized joined coupler (GJC) matrix, which encapsulates both the Blass matrix and the Nolen matrix, as well as their variants, and presents a novel theoretical framework for generating individually and independently controllable multiple beams using the GJC matrix.

[0055] A GJC matrix has N columns to feed N antenna elements and M rows to feed M beams, and the direction of each individual beam can be controlled by tuning the phase shifters in the associated row of the GJC matrix. The GJC matrix can be analysed, synthesized and optimised to produce optimal multibeams using a set of matrix based equations. Specifically, the preferred GJC matrix has at least two matrix variants for practical applications, the Blass-like matrix and the Nolen- like matrix.

[0056] Multibeam antennas are regarded as a critical technology for 5G and beyond 5G (B5G) wireless communications networks. In comparison to digital beamforming techniques, analog beamforming techniques are of low cost and low energy consumption. Analog multibeams can be formed by using either circuit-type feed networks or quasi-optical approaches. Widely known circuit- type feed networks for feeding multibeam antennas include the Butler matrix, the Blass matrix, and the Nolen matrix [1], [4]. The standard Butler matrix is an N x N square matrix using hybrid couplers to produce N orthogonal beams. Although all the beams can be rotated together, their relative directions are fixed. Therefore, the Butler matrix is most suited for covering sectors in conventional base stations. Unlike Butler matrices, Blass matrices and Nolen matrices employ directional couplers and phase shifters without crossovers to produce flexible multibeams, which can be designed to point in desired directions [4], [6]. A Blass matrix is an M x N (M <=N) rectangular matrix with matched loads at the end of each row and column to produce M beam ×s, thus making it lossy. A Nolen matrix is an N x N diagonal matrix with the nodes lying along the diagonal constructed to direct all ingoing energy (for transmission) to the row above, hence making it lossless and also saving almost half of the matrix nodes.

[0057] Beamforming networks, such as Blass and Nolen matrices, have two functions. The first function is to route different input signals to the antenna elements to realize desired signal magnitude distributions across the antenna array. The second function is to produce different phase distributions to realize desired beam directions for different input signals. The major building blocks of these matrices are couplers and phase shifters A chief task in synthesizing Blass and Nolen matrices is to determine the parameters of the joined couplers.

[0058] To treat all these matrices in a universal manner, therefore, we introduce a new concept, the generalized joined coupler (GJC) matrix, which encompasses the Blass matrix, the Nolen matrix, and other variants. One interesting new variant of the GJC matrix is introduced, in which the phase shifter associated with each matrix node is placed to the right of the directional coupler instead of above it as is the case in conventional matrices. This makes it possible to realize independent individual beam scanning. A further feature of GJC matrices is that they can be used to produce up to N number of beams flexibly by adjusting the number of matrix nodes required, the coupling coefficients, the associated phase shifter of each node, and the termination of the matrix.

[0059] One of the primary difficulties in employing Blass matrices or Nolen matrices and GJC matrices, in general, is the complexity of synthesizing the matrix.

[0060] This is in contrast to the Butler matrix; the methods for designing it have been well developed [1]. Some design procedures for special Blass matrices and Nolen matrices have been reported in the literature. In

[0013] , a method was proposed for a matrix with a maximum of two rows, and the procedure shown in

[0014] is not an accurate solution and it is not suited for optimization. Due to the lack of systematic theoretical work on the topic, there have been scant publications investigating the synthesis of multiple beams and their individual control in spite of the increasing interest from the antenna and microwave communities.

[0061] What is described is a novel systematic approach for synthesizing flexible multibeams employing GJC matrices. In particular, a matrix form expression linking the GJC matrix outputs, i.e., the antenna excitation coefficients, with the array input ports or beam ports is given for the first time. This not only provides a mathematical framework for multibeam synthesis but also reveals various characteristics of the Blass matrix and the Nolen matrix for the first time.

[0062] Next below a computationally efficient optimization method to synthesize a GJC matrix in order to generate desired multibeams is described. Then some examples of synthesizing multiple beams using Blass-like and Nolen-like GJC matrices, and reveal some features of these systems, including beam scanning and the realization of low sidelobe beam patterns.

[0063] Theoretical Framework

[0064] To feed a single beam antenna array, one needs a number of power dividers and phase shifters to produce the desired array excitation coefficients. For convenience, we shall refer to a set of such coefficients as an array excitation vector. In order to produce flexible multibeams, one wouldneed a GJC matrix. The directional couplers in the GJC matrix are used for directing the signal flow and distribution, and the phase shifters are needed to produce beams in different directions.

[0065] In general, the function of a directional coupler can be illustrated 1 in Fig. 1. The ports are indexed clockwise. The signal transfer among the four ports is described by an S matrix given by:

[0066] Where j = √-1. As shown in Fig.2, a GJC matrix 2 consists of directional couplers e.g 3 and phase shifters e.g. 4. A directional coupler and a phase shifter comprise a matrix node 5, as shown in Fig.3. For a GJC matrix, we use m to represent the mth row corresponding to the mthinput signal and n to represent the order of the nth column corresponding to the nth antenna element. We denote θmn as the parameter for determining the signal flow within a directional coupler in the node positioned in the mthrow and the nth column of a GJC matrix, and ϕmn as the phase shifter value of this same node. It should be noted that, in Fig.2, the phase shifter in each matrix node is connected to port 3 of its corresponding directional coupler, whereas, in traditional Blass matrices and Nolen = matrices, each phase shifter is connected to port 2 of its corresponding directional coupler. This important difference makes it possible to realize independent individual beam scanning.

[0067] In Fig. 2, there are four antenna input ports with input xm, m = 1, 2, 3, 4, and the array excitation vector is given by yn, n = 1, 2, ... , N , with N representing the number of antenna elements. In what follows, the signal inputs xm are collectively referred to as the array input vector.

[0068] Due to the use of directional couplers, for transmission, the signal flowing through any antenna port or beam port to the inside of the GJC matrix only travels upward and to the right, as shown in Fig.1, with its S matrix in (1). The lower the antenna input port, the more paths the signal flow takes. This makes the handling of GJC matrices with more than two rows highly complex. In the following, we take a matrix approach to derive their relationship in a closed-form formula.

[0069] Given that the matrix shown 2 in Fig.2 is a cascade of a number of similar vertical units, or columns, each consisting of four directional couplers and four phase shifters, or conjunction of four nodes, for the nth column, one can express the relationship between their inputs and horizontal outputs as (2a)–(2d), shown below:^^3 ^^= cos ^^3 ^^^^− ^^ ^^3 ^^^^3( ^^−1)+ ^^2sin ^^3 ^^sin ^^4 ^^^^− ^^ ^^3 ^^^^4( ^^−1), (2c) ^^4 ^^= cos ^^4 ^^^^− ^^ ^^4 ^^^^4( ^^−1). (2d)

[0070] Without loss of generality, N is chosen as 4 first. In (2a), (2b), (2c), and (2d), the first subscripts, e.g., 1 and 2 in in u1n and u2n, are aligned with the order of the nodes (see Fig.2).

[0071] The second subscript, such as n in u1n and u2n, represents the position of the column. As indicated by the number of terms in each equation, (2d), (2c), (2b), and (2a) show that only one signal travels through the bottom node, and progressively, more signals go through the upper nodes.

[0072] Define the signal transformation matrix of the nth column as (3):

[0073] The signals entering horizontally into the first column of the GJC matrix are transformed to the output as:

[0074] and the signal transformation taking place at the nth column of the GJC matrix is described as

[0075] With 2<= n <= 4.

[0076] More specifically, one has:

[0077] A signal passing through a directional coupler can continue horizontally or can be directed upward, as shown in Fig. 1. The transformation of the signals in the first column of a GJC matrix that is directed toward the first antenna is represented as:

[0078] Where:

[0079] The transformation of signals in the nth column of the GJC matrix that is directed toward the nth antenna is represented as:

[0080] Where:

[0081] Consequently, we have the following expression of the array excitation vector in terms of the array input vector:

[0082] Where:

[0083] The above derivation is for a full GJC matrix with four antenna input ports and four antenna elements, and the antenna excitation vector is [y1, y2, y3, y4]T.

[0084] A general full GJC matrix with M signal input ports and N antenna elements to feed is shown in Fig.4. All the major matrices for the general case are derived following the above procedure and are given in the following.

[0085] We define the general signal transformation matrix for the nth column of a GJC matrix as (6) below:

[0086] where the superscript of A(n)M×Mdescribes the nth column of the GJC matrix transformation. The signals passing horizontally through the first column of joined couplers are transformed as:

[0087] and that through the nth column of joined couplers as

[0088] Defining

[0089] the transformation of the signals in the first column of the GJC matrix that is directed toward the first antenna is represented as:

[0090] and that directed by the nth column of the GJC matrix to the nth antenna is:

[0091] Combining (6)–(11) yields

[0092] Where:

[0093] To quantify the losses occurring in the matched loads, we define the transmission efficiency of the GJC matrix as:

[0094] It should be noted that the transmission efficiency of the GJC matrix defined in (14) is for all of the beams, but it can also be used to calculate the transmission efficiency of individual beams. It is a representation of how much ohmic loss occurs in the matrix. In the case of the Blass matrix, the losses will occur in the matched loads at the end of each row and column. In the case of the Nolen matrix, the transmission efficiency is theoretically 100% if all of the matrix nodes are lossless. In the case of a general GJC matrix where some nodes are connected to a matched load and some may be treated in the same way as in the Nolen matrix, (14) can be easily modified to calculate the transmission efficiency.

[0095] With the above equations, one can obtain the antenna excitation vector of any antenna beam by considering only one beam input at a time. In practice, we would be faced with the problem of synthesizing multibeams by synthesizing the GJC matrix. This will be discussed below.

[0096] Design of GJC Matrices for Multiple Beams

[0097] The synthesis of single beam arrays is usually treated as a problem of optimizing the antenna weights or the array excitation vector. Similarly, the synthesis of multiple beams can be treated as a problem of optimizing the parameters of a GJC matrix to produce M predefined beams.

[0098] Taking the case of single antenna pattern synthesis, one method is to calculate the radiation pattern in an angular range of interest in each optimization step and use a cost function toguide the iteration process in order to obtain the optimal array excitation vector to achieve the desired beam pattern. This can be computationally time-consuming for producing multibeams, especially when the dimensions of the GJC matrix are large.

[0099] In the following, a method is proposed to synthesize GJC matrices by optimizing the array excitation vector for each beam directly. This is much more computationally efficient as one can use a classical array distribution function, such as the uniform, Taylor, or Chebyshev distributions as the targeted array excitation vectors; no beam pattern calculation is required. Due to the employment of the phase shifters in each row of the GJC matrix, no optimization of the phase distribution is required in the proposed strategy.

[0100] Single Beam Synthesis

[0101] We first start with the synthesis of a single beam. This is equivalent to synthesizing a series-fed linear antenna array or a leaky wave antenna. This special case is pertinent because it can be used as the first step in synthesizing multibeams. We choose to optimize the GJC matrix to produce a uniform array excitation to produce the sharpest antenna beam with maximum aperture efficiency. Intuitively, the power “leakage” should be [ 1 / N, 1 / (N − 1), 1 / (N − 2), ... , 1], where N is the number of antenna elements. The coupler parameter θ1n (n = 1, 2,..., N) is, thus, given by

[0102] which results in a uniform array excitation. A constant phase shift ϕ1can be assigned to produce a beam in the following direction:

[0103] where k is the wavenumber and d is the antenna element spacing; a uniformly distanced array has been assumed. It should be noted that, if we use the above approach, the feed network is lossless, as all the input energy is radiated. This is important as (15) can be used to design series fed liner antenna arrays and leaky wave antennas. An alternative approach is to synthesize beam 1 in the same way as other beams.

[0104] B. Multibeam Synthesis

[0105] Next, we show how to synthesize multiple beams. We can keep the directional coupler and phase shifter design for beam 1 the same as in (15) and (16) above and then synthesize the couplers in the other rows of the GJC matrix (see Fig.2). Intuitively, we can keep all the phase shifts the same as ϕ2 to obtain the second beam in the direction of γ2 as follows:

[0106] This is where the complexity of the problem arises. Since the signal flow from the second row to the first row of the GJC matrix and then to the antennas takes place via many different multipaths, we no longer know how to set the coupler parameters optimally to obtain the desired beam pattern as for the first beam. Furthermore, we typically need to keep the transmission efficiency high. Therefore, we need to resort to an optimization strategy.

[0107] From beam 2 onward, we define the targeted magnitude distribution of the array excitation vector elements for the mthbeam as ^^^(^^^), ^^ = 1, 2, ⋯ , ^^. ^^^^( ^^), ^^ = 1, 2, ⋯ , ^^ can be chosen from a classic distribution, such as the uniform distribution or the Taylor distribution. Then, the cost function for the optimization of the couplers in the mthrow of the GJC matrix is given by:

[0108] where ^^^(^^^), ^^ = 1, 2, ⋯ , ^^, are the antenna excitations generated by the GJC matrix for the mthbeam based on (11). In practice, we can make the magnitude distribution of all the targeted array excitation vectors the same. It should be noted that, in (18), we have chosen to optimize the magnitudes of the array excitation vector elements. This is because the phases of these elements are primarily determined in a first order approximation by the phase shifter values given by (19). When implementing the uniform excitation, Y(m)ncan be calculated as:

[0109] The strategy is to optimize the coupler parameters θ(m)n, n = 1, 2, ... , N , in order to minimize the cost function f(m). It is noted that the L1 norm is employed in (18) though other norms can also be used. The successful synthesis of the desired beam is achieved in practice when the cost function reaches a minimum.

[0110] Thus, an algorithm for synthesizing multiple beams is given as follows:

[0111] Multibeam Synthesis Algorithm

[0112] 1. Select the magnitude distribution of the antenna coefficients for the M beams;

[0113] 2. Select the directions of M beams and set the phase shifter values using (19);

[0114] 3. Define a cost function for optimization, such as the one given in (18);

[0115] 4. Optimize the directional couplers in the first row of the GJC matrix using an optimization algorithm;

[0116] 5. Use the above directional coupler values for the first row in the GJC matrix and then optimize the directional couplers in the second row of the GJC matrix;

[0117] 6. Repeat step 5 until M beams have been synthesized.

[0118] Due to the complexity of this form of objective functions, it has become a common practice to use a genetic algorithm or particle swarm optimization (PSO) algorithm for array synthesis

[0023] . In this embodiment, therefore, the PSO algorithm is employed.

[0119] Numerical Examples

[0120] To verify the methodology developed above and the GJC matrix synthesis strategy proposed above, a number of results are presented revealing some characteristics of GJC matrices.

[0121] As stated in the introduction, GJC matrices have a number of variants. In what follows, focuses on those variants in which the phase shifters are placed to the right of the associated directional couplers. Specifically, we examine two important variants, namely, the Blass-like GJC matrix and the Nolen-like GJC matrix.

[0122] Multiple Beamforming and Sidelobe Control

[0123] We first demonstrate the effectiveness of the prop −osed approach in synthesizing Blass- like GJC matrices for generating multiple beams. The illustration of such a matrix is given 50 in Fig. 5. Fig. 6 shows three beam patterns 60 of an eight-element array fed by a Blass-like GJC matrix with uniform distribution as the targeted magnitude distribution of the array excitation vector. The beams numbered as b1, b2, and b3 are pointed at ( 30◦, 0◦, 30◦) as intended in the matrix synthesis, with side lobes less than 12dB. We can see that the proposed optimization strategy does result in desired results. The magnitude of the antenna excitation coefficients and the antenna efficiency are shown in Table I below. To compare, Fig.7 shows three beam patterns 70 of a 12-element array fed by a Blass-like GJC matrix. The simulated beams are again pointed at ( 30◦, 0◦, 30◦) as intended in the synthesis. In this case, the transmission efficiency is increased from 95.8% to 97%. The magnitude of the antenna excitation coefficients and the GJC matrix transmission efficiency are shown in Table II. From these two examples, we observe that, despite the conventional perception that Blass matrices are generally lossy and, therefore, would be undeserving of implementation, their transmission efficiency can actually be made high. TABLE I MAGNITUDES OF ARRAY EXCITATION VECTOR ELEMENTS FOR N = 8 AND M = 3. ACHIEVED ηt = 95.8%TABLE II MAGNITUDES OF ARRAY EXCITATION VECTOR ELEMENTS FOR N = 12 AND M = 3. ACHIEVED ηt= 97.0%

[0124] The beam patterns in Figs. 6 and 7 are obtained with uniform antenna excitation coefficients for all the beams. The leftmost beams are created by the first row of the GJC matrix, and as such, they exhibit classical linear array beam patterns. Because of the multipath effects, however, it is seen that the sidelobe levels of other beams, corresponding to beam ports that are lower in theGJC matrix, deteriorate. In practice, low sidelobe levels may be required for some or all of the beams. To achieve this, we can use tapered antenna excitations as the objective for optimization, such as the Taylor distribution or the Chebyshev distribution. Fig.8 shows three beams 80 created by using 20 antenna elements with a Taylor distribution exhibiting 20 dB sidelobe levels. It is seen that, counting from the left, although the sidelobe levels of the second and third beams increase from that of the first, they are still close to 20 dB. Fig. 9 shows the results of synthesizing five beams 90 using the same amplitude taper, and it is seen that the sidelobe levels of the third to fifth beams have increased to 15 dB. This demonstrates that the multipath effect does become stronger as the beam number increases.

[0125] Beam Scanning

[0126] The GJC matrix can be used to produce a scanning beam by simply changing the phase shift values and optimizing the directional coupler parameters to obtain the desired antenna excitation coefficients. For single beam, it is effectively a series-fed phased array. For multiple beams, beam scanning can also be achieved by optimizing the coupling parameters once and then fixing them while changing the phase shift values. To demonstrate this, we chose to divide a scanning range of [ 60◦, 60◦] into three regions [ -60◦, -20◦], [ -20◦, 20◦], and [20◦, 60◦], and produce three scanning beams in the three regions.

[0127] To investigate the optimality of the above strategy, we first optimize the Blass-like GJC matrix to produce three beams pointing at ( 30◦, 0◦, and 30◦). Then, we scan the three beams by simply changing the phase shifter values according to (19). The results are shown 100 in Fig.10. It is seen that the beam patterns are well maintained. This is significant as it means that Blass-like GJC matrices can be used for multibeam phased arrays. To further confirm this, Fig.10 also compares the beams pointing at ( -40◦, -20◦, 50◦) produced by direct optimization of the directional couplers and by just changing the phase shift values, respectively. It is observed that the two sets of results are highly similar. It should be noted that the sidelobe levels of the second and third beams from the left have higher sidelobes than the first. To prevent beams associated with the lower beam ports from deteriorating, in practice, the number of antenna elements N would need to be sufficiently high compared with the number of beams M.

[0128] Nolen-Like GJC Matrix

[0129] For clarity, we have investigated only Blass-like matrices with N columns and M rows so far. A generalized joined coupler (GJC) matrix does not need to be a full rectangular matrix.Depending on the specific performance and cost requirements, some elements can be removed. The GJC can be terminated by match loads, or similar to the Nolen matrix, one can truncate some rows and direct the signal flow in the last nodes upward. This results in a lossless Nolen-like GJC transmitting matrix 110 shown in Fig.11.

[0130] A Nolen matrix is realized by setting the parameters of the diagonal directional couplers as θm(N−m+1) = π / 2, m = 1, 2, ... , M, thus preventing the signal flow from passing from left-to-right through the directional couplers positioned along the diagonal of the Nolen matrix. Since all the input energy to an ideal Nolen matrix is directed to the antenna elements, Nolen matrices are understood to be lossless and, thus, have been recently favored for implementation. The synthesis of Nolen matrices can be realized using the methodology developed above; one simply needs to have the parameters of the diagonal couplers fixed to π / 2. The parameters of matrix nodes below the diagonal ones can be set to any value as they do not affect the calculations and would effectively not exist in the physical implementation of this matrix.

[0131] Although the Nolen matrix is theoretically lossless and requires almost only half of th −e elements of the Blass matrix for large N, it does exhibit critical drawbacks; to produce N beams with a Nolen matrix, we have N - 1 variables to optimize Beam 1, N - 2 variables to produce Beam 2, and so on. We do not have any variable to optimize beam N. Effectively, beam N is determined by the N-1 beams. The quality of the higher order beams can, thus, deteriorate significantly. To show this, we chose a Nolen-like GJC matrix with N = 8 and M = 4, and set the parameters of the last four diagonal elements as θm(N−m+1)= π / 2, m = 1, 2, 3, 4. We call it a Nolen-like GJC matrix as it is not diagonal, and its configuration is shown 110 in Fig. 11. Some numerical results of the Nolen-like GJC matrix are provided 120 in Fig.12. The matched loads at the bottom of the matrix 110 (Fig.11) are for receiving only, and they do not consume any transmission power. It is seen from Fig.12 that, compared with the Blass-like GJC matrix counterparts, the third and fourth beams produced by the Nolen-like GJC matrix have more prominent sidelobes in addition to broadened main lobes as a result of reduced matrix nodes.

[0132] Analog multiple beamforming serves as a low-cost and energy-efficient way to produce multiple beams. The Blass matrix is usually regarded as too lossy, and therefore, recent research activities have been focused on the Nolen matrix. To address the issue of lacking general theory and synthesis approaches, we have developed an initial methodology for synthesizing multiple beams with individual beam direction and sidelobe control using the generalized joined coupler (GJC) matrix and have shown how the proposed approach can be employed through numerical examples. The demonstrated loss of a Blass-like GJC matrix can be made relatively small, and therefore, itwould deserve more attention as a candidate for feeding multibeam antenna arrays. The Nolen matrix and the Nolen-like GJC matrices can lead to faster beam quality degradation than in the Blass-like GJC matrix case if many beams are needed. The embodiments show that low sidelobe multibeam phased arrays can be produced by using appropriate distribution functions as the optimization target and using tunable phase shifters to control the beam directions.

[0133] The feed network of a traditional analogue phased array consists of power dividers and phase shifters. The power distribution among the array antenna elements, which is reflected in the array excitation vector, determines the beam performance that typically includes the half-power beamwidth and the sidelobe level. The phase shifter values, which typically changes in a progressive manner for equally distributed linear arrays, determines the direction of the beam. In order to produce multibeams, one requires a two dimensional feed network such as the Butler matrix, the Blass matrix and the Nolen matrix. The generalised joined coupler (GJC) matrix is adapted to produce individually steerable multibeams. The couplers in the GJC matrix are used for directing the signal flow and thus determining the power distribution, and multiple rows of phase shifters are used to produce multibeams in different directions. This provides a practical means for steering multibeams independently.

[0134] For most applications such as wireless communications, or joint communications and sensing which is an emerging technology for 6G, it is normally required that the multiple beams should cause minimum interference to each other. This can be achieved by having low sidelobes as well as by forming nulls in the directions of other beams. It is very hard to achieve nulling by approximating the array excitation vectors to known distributions, but it can be easily done by directly optimizing the beam patterns.

[0135] A Beam-by-Beam Optimization

[0136] The characteristics of the ^^ matrix of the couplers dictate that, for transmission, the signal inputs to the upper beam ports do not travel downwards. Therefore, to simplify the optimization process, the beams can be optimized one by one by optimizing the couplers in each row of the GJC matrix downwards, one row at a time. These would lead to the following objective functions.

[0137] Define:where Pat( ^^)(. ) represents the radiation pattern of an N element linear array for the mthbeam, ^^ and ^^^^denote the observation angle and the beam direction of the mthbeam, respectively, and θ( ^^)comprises all the θmn, n = 1, 2, … , N, values of the mthrow couplers to be optimized.

[0138] Pat( ^^)(. ) is given bywhere ynis given by (12) and ^^^^( ^^) represents the embedded radiation pattern of the nthantenna element, which includes the coupling effect between antenna elements, and ^^^^is the same as that in (12).

[0139] The objective function for beam 1 is given bywhere ^^ ^^, ^^ ^^ ^^ ^^1and ^^ ^^ ^^ refer to the desired sidelobe level, the half-power beamwidth, and the maximum interference level, or the depth of the null, respectively. The objective functions for beam ^^, ^^ = 2, 3, ⋯ , ^^, the ( ^^ − 1) beams, are given by: subject to:0 ≤ ^^^(^^^)≤ ^^ 2 , ^^ = 1, … , ^^, (24d)

[0140] Based on the strategy described above, an algorithm for optimizing ^^ beams is given in the multibeam optimization algorithm below.

[0141] MultiBeam Optimization Algorithm Step 1) Choose the directions of the multibeams; Step 2) Choose the desired sidelobe level SL and the maximum interference level MIL, and estimate the half-power beam width HPBW for each beam; Step 3) Beginning from Beam 1, for each chosen beam ^^, use (12), (19) and (22) to calculate the radiation pattern with given θ( ^^). Step 4) Employ (23a) to (24d) to optimize beam ^^. Step 5) Repeat steps 3 and 4 until ^^ beams have been optimized and all the coupler parameters are determined.

[0142] Joint Optimization

[0143] As shown above, the multibeams beam-by-beam can be optimized by optimising the GJC matrix row-by-row. This strategy is computationally efficient and is well suited for implementations where the computational complexity is of critical importance. To obtain optimal results, however, one can employ a joint optimization method, where all the couplers and phase shifters in the GJC matrix are optimized jointly. This issue arises naturally as one can easily see from Fig.11 that, in the conventional Nolen matrix case of M=N, there would be no coupler to optimize in the last row of the GJC matrix 110 and there would be only one coupler to optimize in the second to the last row, and so on. If a joint optimization method is used, all the coupling coefficients can be optimized together for all beams to obtain similar performance. In the first instance, one can optimise all the couplers together.

[0144] To achieve joint optimization, a new objective function can be used as follows:

[0145] The constraint conditions for (25) are the same as those used for beam-by-beam optimizations. Instead of optimizing the couplers in the GJC matrix row by row, however, (25) requires all the couplers to be optimized at the same time, thus achieving improved performance at the expense of increased the computational complexity.

[0146] A number of methods can be used in the optimization process. In particular, one can employ the PSO algorithm.

[0147] Now we compare the two optimization strategies. To this end, Nolen-like GJC matrices with M=4 and increasing N was chosen. For the beam-by-beam optimization strategy, the beams in the directions of 45°, -40°, 25° and -15° are optimized sequentially. When using the beam-by-beam optimization strategy, the last beam has a much higher sidelobe level than the other beams. In contrast, the joint optimization strategy results in more consistent beam patterns, thus serving as a much preferred method for synthesizing full (N=M) Nolen-like matrices. The full Nolen-like matrix has high sidelobe levels, which may not be acceptable for many practical applications. To reduce the sidelobe levels, one can employ Nolen-like GJC matrices with N>M. When N is increased to 6, a difference in the multibeam performance can be obtained using the two different optimization strategies. When N is increased to 7, the two sets of multibeams obtained have similar performance. When the dimensions of the GJC matrix are such that the two optimization strategies result in similar performance, the sidelobe levels of individual beams become similar even when using the beam-by- beam optimization strategy.

[0148] As shown in the Further Refinements below, one can split each phase shifter into a fixed phase shifter and a tuneable phase shifter. In this case, the optimization process presented above can include the optimization of both the parameters of the couplers and the fixed phase shifters.

[0149] The optimization of both the parameters of the couplers and the fixed phase shifters can be done in an alternative manner. This means that the process can have many iterative steps and, in each step, one can optimise all the directional couplers first and then optimise the fixed phase shifters. Such steps are repeated until satisfactory results are obtained.

[0150] Other methods, such as closed-form solutions and hybrid optimizations, can also be employed to achieve the same objective as using the above optimization methods.

[0151] Multibeam Performance

[0152] In this section, the algorithm developed is employed to achieve a number of beam optimization objectives and investigate the performance of the multiple beams. Only the directional couplers are optimized. Two different approaches, both employing the multibeam optimization algorithm presented above, are covered as follows. The first one is to employ sidelobe control to mitigate the mutual interference among multiple beams. The effectiveness of scanning the beams by only changing the phase shifter values can be observed. The second approach is to enforce “nulling” to suppress mutual interference between different beams. The multibeam qualities is dependence on the dimensions of the GJC matrix. Without loss of generality, the antenna element pattern is assumedto be cos^^^^,, where p is chosen to achieve a 140° beamwidth. The wide antenna element beam pattern chosen is necessary for achieving wide-angle scanning without suffering from significant scanning losses. A half wavelength inter-element spacing is adopted.

[0153] Interference Mitigation Using Only Sidelobe Control

[0154] Since suppressing the sidelobe level of all beams would result in low interference between all beams and immunity against unknown interference signals in directions outside of the main beams. The multibeams produced by a 4 × 16 Blass-like GJC matrix may have four beam ports and 16 outputs to feed 16 directional antenna elements. It is assumed that the multibeams are in the following directions: −45°, −25°, 10°, and −5°. The targeted sidelobe level is −28dB. The radiation patterns of the four beams can achieve low sidelobe levels of less than −28dB.

[0155] Tuning the Phase Shifters for Steering Multibeams

[0156] For multiple beams created using the GJC matrix, beam steering can be achieved by optimizing the coupling parameters once and then fixing them while changing the phase shifter values. In practical applications, one can divide the angular range of interest into several sub-regions, and then scan each beam in the corresponding sub-region as required. To show the effectiveness of this approach, we employ the 4×16 Blass-like GJC matrix and scan the multibeams by simply tuning the phase shifters to two new set of directions (-35°, -15°, 5°, and 30°) and (-50° -25°, -5°, and 40°), respectively. The beam patterns of this embodiment are well maintained. It is noted that all the sidelobe levels have been increased slightly. This is attributed to the multipath effects as the notion of "phased multibeams" is based on a first order approximation, neglecting the multipaths taken in the signal flow. In practice, this means that the sidelobe levels of the "initial beams" must be set lower than the desired sidelobe levels of the scanned beams. It should be pointed out that realising beam scanning by changing phase shifter values is of great importance in practical systems. This is because, for many applications, having only M voltages to drive M rows of phase shifters to achieve the scanning of M beams, instead of reconfiguring all the couplers and phase shifters to change the beams, makes the system much simpler.

[0157] Using Both Sidelobes and Interference Controls

[0158] Another effective approach to mitigate the interference between multibeams is to control the sidelobe levels of all beams as well as enforce a certain degree of nulling in the directions of other beam centres. It is known that nulling can actually lead to certain undesirable behaviors for abeam, such as increasing the sidelobe level and changing the beam pointing direction. Therefore, a practical approach is to adopt (23a) - (24d) to balance the minimization of sidelobe levels and the nulling effect. As an illustration, we use a 4×16 Blass-like GJC matrix to produce four beams at - 50°, -30°, -5° and 30°, respectively. The sidelobe level is set at -17 dB and the maximum interference level MIL, or the depth of the nulls, is set at -30 dB. The sidelobe levels of all beams can be controlled under -17 dB and nulls at or below -30 dB have been produced in the directions of other beams.

[0159] It is worth noting that, with the proposed method, nulling is achieved in the specified directions; this is in contrast to low sidelobe realization which is achieved in all directions outside of the main beams. When the phase shifter values are changed to steer the beams to different directions, the nulling effect may become irrelevant. In other words, whilst the joint sidelobe control and nulling method is powerful for fixed beams, it is not as flexible as the method of controlling the sidelobes only.

[0160] The Effect of the GJC Matrix Dimensions M and N

[0161] When employing a GJC matrix to create multiple beams, one needs to decide on the two basic parameters, i.e., the number of beams M and the number of antenna elements N. The number of antenna elements is normally determined by the beam gain or the half-power beamwidth, whereas the number of beams is typically determined by other system requirements, such as the number of users to be supported for wireless communications or the number of communications and sensing beams needed in joint communications and sensing systems. Although the maximum number of beams which a GJC matrix can produce is the same as the number of antenna elements in theory, having M smaller than N would increase the degree of freedom in achieving desired beam performance. The smaller M relative to N, the lower the sidelobe levels of all beams can be achieved, and the better the scanning performance. The sidelobe performance of the multibeams may be degraded when M is increased relative to a fixed N.

[0162] With an M×N Nolen-like GJC matrix with M=2 and N=7, the two beams are pointed at - 30° and 30°, respectively, aiming to cover “two sectors” in a (-60°, 60°) angular range via beam steering. The targeted sidelobe level is set at -22dB. A sidelobe level of -22 dB can be realised in this embodiment. To demonstrate the beam scanning performance, the figures show the beam patterns. It can be seen that the sidelobe levels of the scanned beams are slightly increased to about -19dB when the two beams are steered to 45° and 45°, and -15° and - 15°, respectively.

[0163] In one embodiment, an M×N Nolen-like GJC matrix with M=3 and N=7 is configured with three beams pointed at -40°, 0° and 40°, respectively, aiming to cover “three sectors” in a (-60°, 60°) angular range via beam scanning. With three beams and the 3×7 Nolen-like GJC matrix, it is very hard to achieve -22dB sidelobe level so the targeted sidelobe level is now at -17dB. With the three beams pointed at the centres of “three sectors”, it is seen that a sidelobe level of -17dB has indeed been realised. When the three beams are steered to -45°, -10° and 30°, and -25°, 15° and 45°, respectively, the sidelobe levels of the scanned beams can be observed to be slightly increased to about -16dB.

[0164] In another embodiment, an M×N Nolen-like GJC matrix with M=4 and N=7 is configured with four beams pointed at -45°, -15°, 15° and 45°, respectively, aiming to cover “four sectors” in a (-60°, 60°) angular range via beam scanning. With four beams, the achievable sidelobe level is around -12.5dB.

[0165] From a practical point of view, any pattern with sidelobe levels higher than −12 dB would be of very limited use. With seven antenna elements, the maximum number of beams a Nolen-like GJC matrix can support in most practical applications would be around four. Admittedly, the above simulations are based on certain parameter settings such as the beamwidth of the element pattern. Nevertheless, it has been shown that, increasing ^^ relative to ^^ would result in unavoidable degradation of beam patterns, such as increased sidelobe levels. Therefore, in practice, the system designer needs to balance the needs of the number of beams to be supported and the quality of all the beams. Intuitively, this is explainable as the greater the number of beams, the more multipaths the signals from the lower ports would need to go through, and the less degrees of freedom available for manipulating the beams, thus leading to greater sidelobe levels.

[0166] The design here aims to achieve low sidelobes using a 3×10 Nolen-like GJC matrix. In order to achieve low sidelobes, it is necessary that N is much larger than M. The objective is to achieve less than -23dB sidelobe levels for all the three beams.

[0167] In a practical GJC matrix, the coupling coefficients of the couplers would be limited to a range smaller than (0, 1), and the range is largely dependent on the type of couplers used. Although this can be easily handled by the proposed optimization method, the limitation would make the realizable sidelobe levels higher than using ideal couplers. Owing to their simplicity, microstrip based branch line couplers is adopted in one embodiment. If only one-section branch line couplers are used, the coupling coefficients are found to be in the general range of 0.33< cos θ <0.82. For two- section branch line couplers, the range changes to 0.48< cos θ <0.95. To realise a good couplingrange, therefore, we adopted a mix of both one-section and two-section microstrip branch line couplers in the design. The range of coupling coefficients therefore becomes 0.33< cos θ <0.95.

[0168] In one embodiment, the reflection coefficient in the adopted topology, s11, is controlled to be under -30dB, and those for other ports are controlled to be under -25dB, which proved to be a successful and easy to implement strategy. For the linear antenna array employed, the antenna element is chosen as microstrip antennas with a half-power beamwidth of 100°. The inter-element spacing is chosen as 0.55λ. The embedded antenna element patterns can be obtained by employing EM simulator Ansys HFSS and used in the optimization process. The details of the system design will be reported in a separate paper, focusing on various engineering aspects of the GJC matrix circuit.

[0169] Fig.22 shows the plan view for fabrication of a 3×10 Nolen-like GJC matrix designed at 5GHz. All the circuit elements, i.e., the couplers and phase shifters, are designed according the results of the beam optimization method. The fabricated 3 × 10 Nolen-like GJC matrix circuit in this embodiment comprises antenna ports A1-A10, beam ports B1–B3, and ports L1–L7 for matched loads. We note that, similar to the Blass matrix, the Nolen-like GJC matrix has some matched loads. This would result in extra losses in addition to dielectric, conductor and radiation losses in the circuit. For this design, the total loss of the circuit is about 22%. The connections between the GJC matrix and the linear antenna array are realized by using coaxial cables. In one embodiment, the designed and measured antenna beam patterns comprise three beams pointed at 35°, -30° and 5°, respectively. It is observed that, despite a large number of components used in the GJC matrix, the experimental results are quite close to the theoretical ones, achieving a sidelobe level of lower than -22.6dB.

[0170] Generating multibeams using analogue feed networks is an important technique for future wireless communications and sensing networks such as 6G. It has the great potential of saving hardware cost and energy consumption. A new optimization method for producing individually controllable multibeams employing the generalized joined coupler (GJC) matrix is presented here. It has been demonstrated that by optimizing the multibeams directly, multibeams with low sidelobes and nulls can be generated. These two features are critically important in reducing the mutual interference among different beams as well as increasing the immunity against other interference such as jamming signals. Numerical results verified the effectiveness of the proposed method. Some inherent features of the GJC matrix such as the effect of its dimensions on the multibeam qualities are disclosed above. Experimental results of a 3 × 10 Nolen-like GJC matrix verified the proposed method.

[0171] As described above, in comparison to the Blass matrix and the Nolen matrix, the GJC matrix places the phase shifters to the right of the couplers instead of on the top. This leads to two new beamforming circuits for multibeams, the Blass-like GJC matrix and the Nolen-like GJC matrix. A salient feature of the GJC matrix is that it can support individually steerable beams by simply changing the tuneable phase shifters associated with the beam of interest. Further, for ease of implementation, such a change can be made by changing the corresponding voltage applied to those phase shifters.

[0172] To illustrate the difference between the GJC matrix and the existing Nolen matrix, Fig. 13 shows an extended Nolen matrix 130, where the matrix is extended from being diagonal to partially diagonal, and Fig. 14 shows the corresponding Nolen-like GJC matrix 140. It is seen that the phase shifters in the GJC matrix is placed to the right of the directional coupler instead of on the top as in the conventional Blass matrices and Nolen matrices. This is further illustrated in Fig. 15, where it is seen that the directional coupler 150 is determined by one parameter, ѳmn and the phase shifter 151 is determined by another parameter, φmn. Owing to the change of the positions of the phase shifters in the GJC matrix, the phase shifters can be tuned independently such that the beams can be steered individually. A further advantage of the GJC matrix is that, for a simple implementation, all the phase shifters in a given row can be the same. This makes the design and operation of multibeams much simpler, as only one phase shifter needs to be designed for each row, and only one control signal, such as a voltage, is needed to drive the change of each row of phase shifters and the corresponding beam.

[0173] Further Refinements

[0174] The discussion below presents two new techniques, one being a more advanced version of the GJC matrix and the other being the applications of the GJC matrix to large systems such as base stations for 6G.

[0175] There are two further refinements discussed below. The first one is improved implementation methods for the GJC matrix. The second one is to integrate the GJC matrix into hybrid arrays which may be required in large systems, such as base station for beyond 5G and 6G.

[0176] First Further Refinement

[0177] The GJC matrix implementation as discussed above is characterised in that the values of all the phase shifters in a row are kept in the same limits the capability of the GJC matrix, or thequality of the beams. If every individual phase shifter in each row can be allowed to be different, the beam patterns produced by the GJC matrix can be significantly improved in terms of sidelobe levels, supporting orthogonal beams and beam steering. This is due to the GJC matrix implementation method discussed above is based on a first order approximation, meaning that all the signals going into each row the GJC matrix only has two paths; at the directional coupler, they either go all the way up to the antenna or go to the right to the next coupler. In some cases, starting from the second row, there are a number of multiple paths for any signal coming from the right into the GJC matrix, noted as xi, and going into any antenna noted as yi, as shown in Fig.13. Making all the phase shifter values variable provides a new degree of freedom that can be used to compensate for the multipath effect. However, if one allows all the tuneable phase shifters in each row to be different, each individual phase shifter has to be tuned individually. This is likely to complicate the circuit design significantly. The further refinement discloses a cost effective and easy to implement method to solve the problem as discussed below.

[0178] Fig. 16 and Fig. 17 illustrate the proposed new implementations of the Blass-like GJC matrix 160 and the Nolen-like GJC matrix 170. It is seen that each phase shifter to the right of the coupler as shown in Fig.17 has now been split into two parts. The first part has a fixed value, noted as φmn, and it can be easily integrated into the directional coupler as shown in [9]. The second part is tuneable, noted as Фi, and it is the same for each row. This way, we can use both ѳmn and φmn to create M optimised beams in M given directions. The basic framework for optimising ѳmnand φmnis given above. In the meantime, we can also use the tuneable phase shifters Фi, which are the same for any given row, to steer the beam to other directions. In other words, ѳmn, which determines the signal split, and φmnare determined by optimising M beams in fixed directions. The phase shifters Фiare tuned in situ in operations. Now we have an improved GJC matrix implementation method that has superior performance and is easy to steer individual beams independently.

[0179] This forms the structure of the first further refinement.

[0180] The refined structure of the GJC matrices can also be optimized using the methods described earlier. In particular, one can use joint optimization methods, closed-form solution methods or the combination of the two that is known as hybrid methods.

[0181] In the closed-solution method, the antenna excitation vectors are obtained first through optimization or using known distributions such as the uniform distribution and the Taylor distribution with progressive phase distributions. Then, the parameters of the directional couplers and the fixedphase shifter values are obtained by solving a set of equations that are variations to the GJC matrix equations presented earlier.

[0182] In addition to support individually steerable multibeams, another application of the GJC matrix is to produce fixed orthogonal beams, where the peak of any given beam is aligned in the directions of the nulls / troughs of other beams. In particular, the Nolen-like GJC matrix can be used to replace existing Butler matrices with half the circuit complexity as the former is a diagonal matrix instead of a full one. This would offer significant cost advantage. Furthermore, significantly different from the Butler matrix, the GJC matrix can produce any number of orthogonal beams; the number of beams a Butler matrix can support must be an integer power of 2, i. e., 2n, whereas the GJC matrix has no such constraint. This makes the GJC matrix much more powerful to support different number of communications users and user distributions. Such special GJC matrices can be designed using the optimization methods, the closed form solution methods or the hybrid methods.

[0183] To make the system flexible, one can connect each GJC matrix with M switches to switch on or off each beam port. When a beam port is in the “off” state, the corresponding beam is switched off otherwise it is in the “on” state. This way, the system can accommodate the variation of the number of beams required in real-time.

[0184] This is illustrated in Fig.18 (180) and Fig.19 (190).

[0185] Second Further Refinement

[0186] The second further refinement is to employ the GJC matrix in hybrid antenna arrays, which is a common technology for 5G millimetre-wave antennas.

[0187] As shown in

[0010] , one can integrate an analogue beamforming circuit with a digital beamformer to create a hybrid array. A hybrid antenna array is a trade-off between system performance and energy efficiency and cost, and it is one of the most important technologies for 5G. The hybrid array proposed in

[0010] focuses on the single user case. By using the GJC matrix, however, the system can support multiuser communications. This further refinement makes the implementation of phase shifter network, and the hybrid array in general, much simpler.

[0188] Fig. 20 and Fig. 21 illustrate simple implementations 200, 210 of the new hybrid transmission array and reception array, respectively. In such arrays, the antennas are grouped into L subarrays of N elements. Each subarray is connected with a MxN GJC matrix. All the subarrays haveM beams, and different subarrays support M beams in the same directions. For reception, the outputs of L GJC matrices are combined in the digital beamformer to produce M output signals for M beams. One purpose of the digital beamfomer is to increase the signal quality, typically the signal to noise ratio, or the signal to noise and interference ratio. The second purpose is to determine the directions of the M beams automatically to control the tuneable phase shifters in the GJC matrices. For transmission, the purpose of the digital beamformer is to process the M input signals and distribute them into L GJC matrices. One preferred way to set the parameters in the GJC matrices in the transmission hybrid array is to use the same parameters as in the reception array. This is particularly effective in time division duplex (TDD) systems in which the two-way wireless communications channels are the same.

[0189] In the further refined beamforming circuit, referred to as the generalized joined coupler (GJC) matrix for forming independently steerable multiple beams is described further below. The GJC matrix has N columns of joined couplers and M rows of phase shifters as shown in Fig.15. The GJC matrix supports N antennas and M beams corresponding to M uses for transmission or reception. Each beam can be independently controlled.

[0190] The GJC matrix can take two forms, the Blass-like GJC matrix and the Nolen-like GJC matrix. The Blass-like GJC matrix is a full M by N matrix whereas the Nolen-like GJC matrix is partially diagonal (when M<N) or fully diagonal (when M=N).

[0191] The GJC matrix is comprised of a number of nodes; each node is composed of a directional coupler and a tuneable phase shifter. The directional coupler has an integrated phase shifter, and the tuneable phase shifter is placed to the right of the directional coupler.

[0192] The values of the integrated phase shifters in the couplers are determined by the directions of the initial beams. That is, given the initial beam direction settings, one can determine these phase shift values. The algorithm used to determine the parameters and the directional couplers and integrated phase shifters can be based on but not limited to the optimization algorithms discussed above.

[0193] The tunable phase shifter placed to the right of the directional coupler is the same for all the nodes in each row. They generally differ in different rows to support beams in different directions. They are tuned together to steer the beam corresponding to the row. If the antenna array is uniform with equal distance between antenna elements, the phase shifter value for the i’th beam, φi, can be determined via the following equation:

[0194] where γi representing the beam direction in radians, k = 2π / λ with λ as the wavelength and d as the distance between adjacent antennas.

[0195] The tunable phase shifter placed to the right of the directional coupler can vary if the antennas are not placed with equal distance.

[0196] Similar to the well known Butler matrix, the GJC matrix can produce orthogonal beams. This means that the maximum radiation direction of any given beam coincides with the nulls of all other beams. In particular, the Nolen-like GJC matrix can be used to replace existing Butler matrices with half the circuit complexity as the former is a diagonal matrix instead of a full one. Significantly different from the Butler matrix, the GJC matrix can produce any number of orthogonal beams; the number of beams a Butler matrix can support must be an integer power of 2, i. e., 2n, whereas the GJC matrix has no such constraint.

[0197] The GJC matrix can be employed in a hybrid beamformer. In such a system, a number of GJC matrices of small to moderate dimensions are used. In such a hybrid systems, one can use L MxN GJC matrices to support M communications users. In a more general case, the L GJC matrices may have different dimensions.

[0198] In another implementation, one can use different part of the hybrid array to support different users, this supporting more than M users. In this case, not all the GJC matrices need to have the same dimensions.

[0199] Summary of Second Further Refinement

[0200] It can be seen that the second further refinement provides a number of advantages.

[0201] These include a beamforming circuit known as the generalised joined coupler matrix comprising: directional couplers to direct the signal flows and energy distribution; phase shifters to determine the radiation directions of different beams (These are placed to the right of the directional couplers); M ports to feed M transmitting signals or receive M received signals; and N ports to connect N antennas.

[0202] In some embodiments, the phase shifters in the generalised joined coupler matrix are partitioned into two, a fixed phase shifter and tuneable phase shifter. The fixed phase shifter is preferably integrated into the directional coupler; The coupler parameters and the fixed phase shift values can be determined by the initial beam directions; The tuneable phase shifters can be the same for each row to support uniformly distributed arrays; The tuneable phase shifters in different rows can be different to support beams in different directions; The multibeams can be steered to different directions by applying a different a voltage to different rows of phase shifters.

[0203] In some embodiments, the GJC matrix can take two different forms, the Blass-like GJC matrix and the Nolen-like GJC matrix. The former is a full matrix and the latter is a diagonal or partially diagonal matrix. The former has more flexibility in forming desired beam patterns whereas the latter has lower losses.

[0204] Switches can be placed at the input (for transmission) or output (for reception) beam ports. These switches can be used to accommodate the variation of beams to be supported in the system.

[0205] The GJC matrix can be combined with digital beamformers to produce hybrid arrays.

[0206] For reception, the outputs of different GJC matrices can be combined in the digital beamformer to produce M output signals for M users. One purpose of the digital beamfomer is to increase the signal quality, typically the signal to noise ratio, or the signal to noise and interference ratio. The second purpose is to determine the directions of the M beams to control the tuneable phase shifters in the GJC matrices.

[0207] For transmission, the digital beamformer can process the M input signals and distribute them into different GJC matrices. One preferred way to set the parameters in the GJC matrices in the transmission hybrid array is to use the same parameters as in the reception array. Interpretation

[0208] Reference throughout this specification to “one embodiment”, “some embodiments” or “an embodiment” means that a particular feature, structure or characteristic described in connection with the embodiment is included in at least one embodiment of the present invention. Thus, appearances of the phrases “in one embodiment”, “in some embodiments” or “in an embodiment” in various places throughout this specification are not necessarily all referring to the same embodiment, but may. Furthermore, the particular features, structures or characteristics may be combined in anysuitable manner, as would be apparent to one of ordinary skill in the art from this disclosure, in one or more embodiments.

[0209] As used herein, unless otherwise specified the use of the ordinal adjectives "first", "second", "third", etc., to describe a common object, merely indicate that different instances of like objects are being referred to, and are not intended to imply that the objects so described must be in a given sequence, either temporally, spatially, in ranking, or in any other manner.

[0210] In the claims below and the description herein, any one of the terms comprising, comprised of or which comprises is an open term that means including at least the elements / features that follow, but not excluding others. Thus, the term comprising, when used in the claims, should not be interpreted as being limitative to the means or elements or steps listed thereafter. For example, the scope of the expression a device comprising A and B should not be limited to devices consisting only of elements A and B. Any one of the terms including or which includes or that includes as used herein is also an open term that also means including at least the elements / features that follow the term, but not excluding others. Thus, including is synonymous with and means comprising.

[0211] As used herein, the term “exemplary” is used in the sense of providing examples, as opposed to indicating quality. That is, an “exemplary embodiment” is an embodiment provided as an example, as opposed to necessarily being an embodiment of exemplary quality.

[0212] It should be appreciated that in the above description of exemplary embodiments of the invention, various features of the invention are sometimes grouped together in a single embodiment, figure, or description thereof for the purpose of streamlining the disclosure and aiding in the understanding of one or more of the various inventive aspects. This method of disclosure, however, is not to be interpreted as reflecting an intention that the claimed invention requires more features than are expressly recited in each claim. Rather, as the following claims reflect, inventive aspects lie in less than all features of a single foregoing disclosed embodiment. Thus, the claims following the Detailed Description are hereby expressly incorporated into this Detailed Description, with each claim standing on its own as a separate embodiment of this invention.

[0213] Furthermore, while some embodiments described herein include some but not other features included in other embodiments, combinations of features of different embodiments are meant to be within the scope of the invention, and form different embodiments, as would be understood by those skilled in the art. For example, in the following claims, any of the claimed embodiments can be used in any combination.

[0214] Furthermore, some of the embodiments are described herein as a method or combination of elements of a method that can be implemented by a processor of a computer system or by other means of carrying out the function. Thus, a processor with the necessary instructions for carrying out such a method or element of a method forms a means for carrying out the method or element of a method. Furthermore, an element described herein of an apparatus embodiment is an example of a means for carrying out the function performed by the element for the purpose of carrying out the invention.

[0215] In the description provided herein, numerous specific details are set forth. However, it is understood that embodiments of the invention may be practiced without these specific details. In other instances, well-known methods, structures and techniques have not been shown in detail in order not to obscure an understanding of this description.

[0216] Similarly, it is to be noticed that the term coupled, when used in the claims, should not be interpreted as being limited to direct connections only. The terms "coupled" and "connected," along with their derivatives, may be used. It should be understood that these terms are not intended as synonyms for each other. Thus, the scope of the expression a device A coupled to a device B should not be limited to devices or systems wherein an output of device A is directly connected to an input of device B. It means that there exists a path between an output of A and an input of B which may be a path including other devices or means. "Coupled" may mean that two or more elements are either in direct physical or electrical contact, or that two or more elements are not in direct contact with each other but yet still co-operate or interact with each other.

[0217] Thus, while there has been described what are believed to be the preferred embodiments of the invention, those skilled in the art will recognize that other and further modifications may be made thereto without departing from the spirit of the invention, and it is intended to claim all such changes and modifications as falling within the scope of the invention. For example, any formulas given above are merely representative of procedures that may be used. Functionality may be added or deleted from the block diagrams and operations may be interchanged among functional blocks. Steps may be added or deleted to methods described within the scope of the present invention.

Claims

CLAIMS:

1. An antenna beam forming circuit of the transmission of directional electromagnetic radiation, the circuit including: a series of m input ports for input of transmission signals; a series of n output antennas; a series of directional couplers and phase shifters arranged in a matrix form to guide the m input signals to n antennas in order to form m beams.

2. An antenna beam forming circuit of the reception of directional electromagnetic radiation, the circuit including: a series of m output ports for output of received signals; a series of n input antennas; a series of directional couplers and phase shifters arranged in a matrix form to guide the m input signals received by n antennas to m output ports.

3. A beamforming circuit as claimed in any previous claim wherein the phase shifters are partitioned into two, with a fixed phase shifter and a variable phase shifter.

4. A beamforming circuit as claimed in claim 3 wherein the fixed phase shifter is integrated into the directional coupler.

5. A beamforming circuit as claimed in any previous claim wherein the directional coupler parameters and phase shift values are determined by the desired initial beam directions and beam shapes.

6. A beamforming circuit as claimed in any previous claim wherein the tuneable phase shifters are the same for each row to support uniformly distributed arrays.

7. A beamforming circuit as claimed in any previous claim wherein the tuneable phase shifters in different rows are different to support non-uniformly distributed arrays.

8. A beamforming circuit as claimed in any previous claim wherein the directional couplers are formed into a Blass-like GJC matrix or a the Nolen-like GJC matrix.

9. A beamforming circuit as claimed in any previous claim further including switches placed at the input or outputs to accommodate variation of the directional beamforming circuits.

10. A beamforming circuit as claimed in any previous claim, wherein said beamforming circuit includes an analog beamformer combined with a digital beam former forming a hybrid array.

11. A beamforming circuit as claimed in any previous claim wherein the phase shifters interact after a corresponding directional coupler.

12. A beamforming circuit as claimed in any previous claim wherein the phase shifters are placed after the directional couplers.

13. A beamforming circuit as claimed in claim 8 wherein the Blass-like GJC matrix is a full rectangular matrix and a Nolen-like GJC matrix is a partially diagonal matrix.

14. A method of forming a beamforming circuit substantially as hereinbefore described with reference to any of claims 1 to 14.

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