Method for adjusting the directional characteristics of phased multi-channel antennas and antenna beamforming device

Abstract

A method and an antenna beamforming device for adjusting the directional characteristics of phase-controlled multi-channel antennas by controlling the phases ( ϕ i ) for the signals of the individual antennas (A i ) to achieve a given antenna characteristic (G̃(ϑ)). The phases (ϕ i ) is determined using a quantum search algorithm by checking with a quantum oracle whether the antenna characteristic (G(ϑ)) for phases (ϕ i ) and antenna far fields (a i (ϑ)) satisfy the conditions for the desired, specified antenna characteristic (G̃(ϑ)). The antenna beamforming device is configured to execute a quantum search algorithm. The quantum search algorithm is used to determine the phases (ϕ i ) by checking the fulfillment of a quantum oracle, whether the antenna characteristic (G(ϑ)) for phases (ϕ i ) and antenna far fields (ai (ϑ)) of the individual antennas (A i ) meet the conditions for the desired specified antenna characteristic (G̃ (ϑ)).

Description

[0001] The invention relates to a method for adjusting the directional characteristics of phase-controlled multi-channel antennas by determining the phases ϕ i for the antenna far fields a i (ϑ) of the individual antennas to achieve a given antenna characteristic G̃(ϑ).

[0002] The invention further relates to an antenna beamforming device for this purpose.

[0003] Antennas play a central role in a wide range of applications involving the transmission and reception of electromagnetic signals. One example is communications technology, from mobile communications to satellite television. Another major application is radar technology. Modern antennas are equipped with multiple channels that are distributed in terms of signal amplitudes. i , as well as the signal phases ϕ i are controllable.

[0004] A challenging special case is multi-channel antennas that are operated for transmission in such a way that only the phases ϕ i controlled and the amplitudes g i be left constant (where g i = 1). The goal is now to select a set of phases such that the multi-channel antenna radiates with a specific, predefined target characteristic (also called the antenna pattern). In English-language publications, this type of pattern optimization is referred to as phase-only pattern synthesis.

[0005] Mathematically, the optimization problem can be described as follows: Starting from the definition of the antenna pattern, ie the attenuation or gain (G) in dB over the elevation angle ϑ GTx(ϑ)=1nc|∑i=1nceiϕiai(ϑ)|2 mathematical conditions can be defined for the above-mentioned requirements for the antenna pattern GTx(ϑl)≥G˜(ϑl), GTx(ϑm)≤G˜(ϑm), which must be fulfilled, where on the right side of the inequalities are the target antenna patterns G̃, which correspond to the diagonal dashed lines in the Fig. 2. Here, inequality (2) is the condition for the principal ray, and inequality (3) is the condition for the side lobes. The indices l and m indicate that these are discrete angles. This formulation is also called the feasibility problem.

[0006] Typically, all types of antenna optimization problems are solved using computer algebra systems as computer programs on classical digital computers. The optimization problem addressed here aims at calculating n c real-valued phases ϕ i , where n c is the number of antenna channels.

[0007] On a digital computer, real numbers are always approximated by their binary representation, meaning there is a finite set of numbers that a computer can represent. The problem space is therefore spanned, on the one hand, by the number of antenna channels and, on the other hand, by a set of discrete phase values ​​n. b in the interval between zero and 2π per channel. The search space therefore has the dimension n c · n b . In principle, one can pursue the approach of searching the entire problem space, i.e., inserting and evaluating every combination of phase values ​​into equations (1) to (3). However, such an approach is not useful for practically relevant problems, as the problem space is far too large. For example, if an antenna with 50 channels and 6-bit phase quantization is to be optimized in this way, 2 300 Phase combinations are evaluated.

[0008] On classical computers, algorithms for solving such problems are typically executed in floating-point arithmetic, meaning the real-valued phases are approximated in binary with a specific word length. This means that most methods treat this problem as a continuous optimization problem. Basically, all current algorithms for solving such antenna optimization problems are iterative methods, which are presented below.

[0009] Starting with parameter initialization, where, for example, a starting value is specified, the actual routine follows, in which the problem space is searched according to a specific rule. The algorithm terminates when a certain number of iterations have been completed or when another termination criterion is met.

[0010] Various optimization methods are known for synthesizing antenna patterns. However, the optimization can be limited to phases as optimization variables.

[0011] J. DeFord and O. Gandhi, “Phase-Only Synthesis of Minimum Peak Sidelobe Patterns for Linear and Planar Arrays,” IEEE Transactions on Antennas and Propagation, vol. 36, no. 2, pp. 191-201, Feb 1988 and A. Densmore and Y. Rahmat-Samii, “Particle Swarm Optimized Three-Parameter Aperture Distribution for Antenna Synthesis,” in IEEE Antennas and Propagation Society International Symposium, 2010, pp. 1-4 disclose algorithms for linear and planar array antennas with the goal of minimizing sidelobe levels to reduce interference.

[0012] F. Castella and J. Kuttler, "Optimized array antenna nulling with phase-only control," IEE Proceedings F (Radar and Signal Processing), vol. 138, pp. 241-246, Jun 1991, and F. Castella and D. Marable, "Optimized planar array antenna nulling with phase-only control," in 23rd European Microwave Conference, 1993, pp. 886-888 describe a vector Newton algorithm and an iterative gradient method for setting nulls.

[0013] S. Smith, "Optimum Phase-Only Adaptive Nulling," IEEE Transactions on Signal Processing, vol. 47, no. 7, pp. 1835-1843, Jul 1999, describes another gradient-based approach in the form of a 'conjugate gradient method'.

[0014] O. Bucci, G. D'Elia, and G. Romito, "Synthesis technique for scanning and / or reconfigurable beam reflector antennas with phase-only control," IEE Proceedings - Microwaves, Antennas and Propagation, vol. 143, pp. 402-412, Oct 1996 discloses an antenna pattern synthesis for array-fed reflectors with phase-only control, and O. Bucci and G. D'Elia, "Power synthesis of reconfigurable conformal arrays with phase-only control," IEE Proceedings - Microwaves, Antennas and Propagation, vol. 145, pp. 131-136, Feb 1998 disclose a corresponding synthesis for conformal arrays.

[0015] O. Bucci, G. D'Etia, and G. Romito, "Optimal Synthesis of Reconfigurable Conformal Arrays with Phase-Only Control," in IEEE Antennas and Propagation Society International Symposium, 1996 Digest, vol. 2, 1996, pp. 810-813, presents the synthesis problem as an intersection finding problem, which is solved using a generalized projection algorithm.

[0016] A. Trastoy and F. Ares, “Phase-only synthesis of continuous linear aperture distribution patterns with asymmetric side lobes,” Electronics Letters, vol. 34, no. 20, pp. 1916-1917, Oct 1998 describes a generalization to linear aperture antenna patterns.

[0017] S.-M. Lin, Y.-Q. Wang, and P.-L. Shen, “Phase-only Synthesis of the Shaped Beam Patterns for the Satellite Planar Array Antenna,” in IEEE International Conference on Phased Array Systems and Technology, 2000, pp. 331-334 proposes a synthesis of antenna patterns based on Fourier domain methods using an iterative method with Fourier analysis for planar phased array antennas.

[0018] A. Capozzoli, C. Curcio, G. D'Elia, A. Liseno, D. Bresciani, and H. Legay, "Fast Phase-Only Synthesis of Faceted Reflectarrays," in 3rd European Conference on Antennas and Propagation, 2009, pp. 1329-1333, discloses a pure phase synthesis based on an advanced fast Fourier transform algorithm for reflect arrays. A further generalization based on Fourier calculus is the non-uniform fast Fourier transform (NUFFT), which has been used in the context of conformal reflect arrays and is described in A. Capozzoli, C. Curcio, G. D'Elia, and A. Liseno, "Fast phase-only synthesis of conformal reflectarrays," IET Microwaves, Antennas & Propagation, vol. 4, pp. 1989-2000, Dec 2010.

[0019] An important class of solvers are so-called global methods, i.e., algorithms that are, in principle, capable of finding a global optimum. A well-established algorithm in this context is the genetic algorithm, described in S. Katoch, S.S. Chauhan, and V. Kumar, "A review on genetic algorithms: past, present, and future," Multimedia Tools and Applications, vol. 80, pp. 8091-8126, Oct 2021, and belonging to the class of evolutionary algorithms. These types of algorithms are heuristic and constructed as iterative routines.

[0020] For example, genetic algorithms were investigated for phase-only nulling in R. Haupt, "Phase-only adaptive nulling with a genetic algorithm," IEEE Transactions on Antennas and Propagation, vol. 45, no. 6, pp. 1009-1015, Jun 1997. K. Sabet, D. Jones, J.-C. Cheng, L. Katehi, K. Sarabaudi, and J. Harvey, "Efficient printed antenna array synthesis including coupling effects using evolutionary genetic algorithms," in IEEE Antennas and Propagation Society International Symposium, vol. 3, 1999, pp. 2084-2087 discloses genetic algorithms for the synthesis of printed antenna arrays including coupling effects. In the field of wireless communications, genetic algorithms are presented by Y. Fan, R. Jin, B. Liu, and J. Geng, "Phase-only Pattern Synthesis of Antenna Arrays Based on A Modified Genetic Algorithm," in Proceedings of ISAP'04, Aug 2004. A. Capozzoli and G.D'Elia, "Global Optimization and Antenna Synthesis and Diagnosis, Part Two: Applications to Advanced Reflector Antennas Synthesis and Diagnosis Techniques," Progress In Electromagnetics Research (PIER), vol. 56, pp. 233-261, 2006 describes the synthesis of reflector surfaces and B. Kadri, M. Boussahla, and FT Bendimerad, "Phase-Only Planar Antenna Array Synthesis with Fuzzy Genetic Algorithms," IJCSI International Journal of Computer Science Issues, vol. 7, no. 2, pp. 72-77, Jan 2010 a phase-only pattern synthesis problem solved using genetic algorithms.

[0021] Another class of global optimization algorithms are simulated annealing approaches, described, for example, in D. Henderson, S.H. Jacobson, and A.W. Johnson, Handbook of Metaheuristics. Boston, MA: Springer US, 2003, ch. The Theory and Practice of Simulated Annealing, pp. 287–319. As a heuristic, simulated annealing mimics the behavior of physical systems, which includes the heating or cooling of materials. This concept was applied to phase-only pattern synthesis in A. Trastoy, F. Ares, and E. Moreno, "Phase-Only Control of Antenna Sum and Shaped Patterns Through Null Perturbation," IEEE Antennas and Propagation Magazine, vol. 43, no. 6, pp. 45-54, Dec 2001 and used for application to reflect arrays in A. Trastoy, F. Ares, and E. Moreno, “Phase-Only Synthesis of Non-φ-Symmetric Patterns for Reflectarray Antennas with Circular Boundary,” IEEE Antennas and Wireless Propagation Letters, vol. 3, pp. 246-248, 2004.

[0022] A third heuristic optimization method that has been investigated for pattern problems is particle swarm optimization (PSO), which is disclosed, for example, in AG Gad, "Particle Swarm Optimization Algorithm and Its Applications: A Systematic Review," Archives of Computational Methods in Engineering, vol. 29, pp. 2531-2561, Apr 2022. In J. Robinson, S. Sinton, and Y. Rahmat-Samii, "Particle Swarm, Genetic Algorithm, and their Hybrids: Optimization of a Profiled Corrugated Horn Antenna," in IEEE Antennas and Propagation Society International Symposium, vol. 1, 2002, pp. 314-317, particle swarm optimization and hybridization with a genetic algorithm were used for the design of profiled horn antennas. Another example where PSO was used to optimize array-fed reflector antennas can be found in S. Xu and Y.Rahmat-Samii, “Multi-objective Particle Swarm Optimization for High Performance Array and Reflector Antennas,” in IEEE Antennas and Propagation Society International Symposium, 2006, pp. 3293-3296 and with application to the synthesis of aperture distributions in A. Densmore and Y. Rahmat-Samii, “Particle Swarm Optimized Three-Parameter Aperture Distribution for Antenna Synthesis,” in IEEE Antennas and Propagation Society International Symposium, 2010, pp. 1-4.

[0023] US 8,988,279 B2 discloses a method for reducing sidelobe interference in a radar or communications system. The method comprises selecting a desired amplitude weight to be applied to radar or communications antenna elements and determining phase weights for the radar or communications system elements such that each pair of adjacent phase-weighted elements, when summed, provides the desired amplitude weight.

[0024] US 10,788,578 B2 describes an antenna pattern synthesizer that synthesizes an antenna pattern by applying the QPSO (Quantum-Behaved Particle Swarm Optimization) algorithm to a satellite synthetic aperture radar (SAR). The SAR system includes an antenna array in which multiple antennas are arranged in a multidimensional structure, and a generator configured to calculate a signal amplitude and a signal phase for the antenna array to generate a first antenna pattern using QPSO. The first antenna pattern is generated in the designed mask template based on the calculated signal amplitude and the calculated signal phase.

[0025] US 9,553,363 B2 discloses an apparatus for optimizing the transmission and reception of radiation by elements in a phased array antenna based on a predicted future health state for elements in the phased array antenna. The apparatus has a phased array antenna optimizer configured to identify various time periods during which elements of a phased array antenna are expected to be used, to identify predicted future health states for the elements in the phased array antenna for the identified time periods, and to identify various configurations for the elements for the identified predicted future health states to generate a radiation pattern based on the predicted future health states for the elements.This takes into account the potential degradation of a group of elements. When identifying the configurations for the elements, the phased array optimizer is configured to optimize the configuration of the elements to use the radiation pattern based on the predicted future health states for the elements, taking into account the potential degradation of the group of elements. When optimizing the configurations of the elements, the phased array optimizer is configured to consider a combination of potential degradations of the group of elements.

[0026] US 10,334,454 B2 discloses a communication device comprising an antenna array and a beamforming controller configured to determine a set of beamforming weights for the antenna array based on a target radiation pattern having a plurality of main fingers (main lobes). The beamforming controller is configured to identify, in each of a plurality of iterations, a search space of beamforming weights for a plurality of elements of the antenna array and, based on the contribution of one or more of the plurality of elements to a plurality of the plurality of main fingers, determine an updated set of beamforming weights in the search space to reduce a difference between an actual radiation pattern and the target radiation pattern. The antenna array is configured to transmit or receive radio signals based on the updated set of beamforming weights.

[0027] US 10,656,234 B2 describes a method for determining a normalized far-field pattern for each radiating element of a plurality of antenna elements on an individual element-by-element basis. The plurality of antenna elements are associated with a phased array antenna. An overall electromagnetic far-field pattern for the phased array antenna is determined based on individual normalized element far-field patterns and beamforming parameters associated with a location of interest. The overall electromagnetic far-field pattern can be used to determine the signal strength of a signal transmitted by the phased array antenna at the location of interest.

[0028] US 7,728,769 B2 describes an adaptive processing method and system for interference suppression in a phased array beam pattern. The amplitude distribution of the transmit elements of a two-dimensional phased array is determined. A desired pattern with low sidelobes for a linear array is synthesized. The amplitude distribution of the transmit elements of the two-dimensional phased array is compared with the synthesized pattern. Selected elements of the two-dimensional array are deactivated to best match the determined amplitude distribution of the transmit elements of the two-dimensional phased array to the synthesized beam pattern. A phase-only pattern synthesis is performed to generate a desired two-dimensional beam pattern with low sidelobes to minimize any best-fit errors.

[0029] The technical problem for the task of finding a suitable set of phase values ​​ϕ i The key to calculating the desired antenna pattern lies in the way these phase values ​​are found and optimized. Typically, numerical methods are used, i.e., mathematical algorithms that run on conventional digital computers and automatically calculate these phases.

[0030] Tosi, L., Anselmi, N., Polo, A., Rocca, P.: Array Antenna Power Pattern Analysis Through Quantum Computing. In: 16th European Conference on Antennas and Propagation (EuCAP), 2022, pp. 1-3. - ISBN 978-1-6654-1604-7 discloses an analysis of the power pattern generated by a uniform linear array using a quantum computer. The analysis method is based on the quantum Fourier transform algorithm and the values ​​observable at the output of the quantum computation. Antenna coefficients are optimized for amplitude and phase.

[0031] The disadvantages of known methods for solving the antenna optimization problem include, firstly, potentially very long computation times. For example, if the optimization algorithm is not specified with a fixed number of iterations, but rather with a different termination criterion, the algorithm may either take a very long time to compute or converge to an unusable solution.

[0032] Gradient methods typically suffer from the problem that they can get stuck in local optima and thus calculate a suboptimal solution. Global methods can, in principle, come very close to the global optimum. In practice, however, this depends heavily on the problem size, the choice of boundary conditions (the target pattern G̃ and the angle ϑ j ) and the starting point, as well as on the problem topology itself.

[0033] The object of the present invention is to provide an improved method and an antenna beamforming device.

[0034] The object is achieved by the method having the features of claim 1 and by the antenna beamforming device having the features of claim 10. Advantageous embodiments are described in the subclaims.

[0035] It is proposed that the phases ϕ i be determined with a quantum search algorithm by checking with a quantum oracle whether the antenna characteristic (G(ϑ)) for phases (ϕ i ) and antenna far fields (a i (ϑ)) meet the conditions for the desired, specified antenna characteristic (G̃(ϑ)).

[0036] The fulfillment of a Boolean function can be checked whether the antenna characteristic G(ϑ) for phases ϕ i and antenna far fields a i(ϑ) fulfill the conditions for the desired, given antenna characteristic G(ϑ).

[0037] By implementing the optimization algorithm for determining the antenna parameters suitable for a given antenna characteristic in a quantum search algorithm, a significant acceleration of the computation and a reduction in computational runtime are achieved. This allows larger antenna optimization problems to be solved in a similar amount of time as much smaller problems that can just barely be solved on classical computers. The problem size here refers to the number of free parameters, i.e., the number of phase values. With the help of the quantum search algorithm, it is possible to find higher-quality solutions.

[0038] The method is designed to be executed on gate-based quantum computers and is based on a process that involves transferring the function underlying the antenna optimization problem to an oracle that can be subjected to a quantum-mechanical Boolean true-false test.

[0039] This exploits the functionality of quantum computers, which is based on the quantum mechanical principles of superposition and entanglement. This makes it possible to execute certain algorithms in significantly less time than with classical computers. It exploits the ability of quantum computers to represent the problem space in a superposition, which is not possible classically. Furthermore, the search for solutions is accelerated by a factor of N possible, compared to a classical search, in which every element of the problem space is evaluated. A quantum search algorithm also has the ability to find solutions, if they exist, guaranteed, which is not the case with classical methods.

[0040] The task is solved using a quantum search algorithm.

[0041] The so-called Grover algorithm, first described by Grover in LK Grover, "A Fast Quantum Mechanical Algorithm for Database Search," in Proceedings of the Twenty-Eighth Annual ACM Symposium on Theory of Computing, ser. STOC '96. New York, NY, USA: Association for Computing Machinery, 1996, pp. 212-219, is advantageous in this case. A so-called oracle quantum circuit has been developed for this algorithm and is, in principle, available.

[0042] This oracle quantum circuit can be configured specifically for the optimization task of solving equations (1) to (3). The Grover algorithm is capable of solving combinatorial optimization problems in a runtime O(N) where N is the number of all possible combinations / solutions, while a classical method would have to evaluate each combination and therefore would require 0(N) operations. The Grover algorithm therefore has a factor N Reduced runtime. This speed advantage is based on the quantum mechanical principles of superposition and entanglement, and thus the ability to represent the entire problem space simultaneously. By repeatedly applying the Grover operator, the probability amplitudes for solutions are successively amplified and the amplitudes for non-solutions are suppressed. Furthermore, the Grover algorithm is guaranteed to find solutions, provided they exist.

[0043] The determination of the phases ϕ i with the quantum search algorithm, summing up the events in which the fulfillment of the quantum oracle with a Boolean function was detected, comparing the sum of the events with the number of Boolean functions and detecting a solution when the sum of the events is equal to the number of quantum oracles to be checked, where the phases ϕ i from a sum function of the detected solutions evaluated with the Boolean value one (1), where the antenna characteristic G(ϑ) for phases ϕ i and antenna far fields a i (ϑ) which satisfies the conditions for the desired, given antenna characteristic G̃(ϑ) can be calculated.

[0044] The results can be written into registers in a quantum circuit and transported through the processing stages.

[0045] The quantum search algorithm can be initialized with a Hadamard gate into a superposition state. Subsequently, a Grover operator can be applied multiple times in succession to solve the Boolean function implemented in the oracle circuit using an oracle quantum circuit of the Grover operator. Solutions can be separated from non-solutions by rotations in Hilbert space, and an initial state |ψ(ϕ)〉 containing the solutions can be obtained.

[0046] The desired phases ϕ i can be stored in binary variables x ik about the connection ϕi=2π2nb∑k=0nb−12kxik, be coded, where n b is the number of antenna channels. This allows the oracle quantum circuit to determine the phases ϕ i as the only variable sought using a summation function for binary variables x ik take place.

[0047] The given antenna pattern functions can be determined by given phases ϕ i and specified amplitudes of the antenna far fields ā i for given elevation angles ϑ j be encoded as a parameter in the oracle quantum circuit.

[0048] It is possible to add given phases ϕ i the antenna far fields a i , which is dependent on a given elevation angle ϑ j depend on the determined desired phases ϕ i with a modulo-2π adder.

[0049] A quantum Fourier transformation is advantageous, to which the desired phases ϕ i containing register, a fixed coding of the given phases ϕ to be added i using phase gates (P(λ)) and applying an inverse quantum Fourier transform to obtain the summation result.

[0050] The quantum oracle can comprise several sequentially evaluated Clausens. Thus, for each elevation angle ϑ j There must be a clause that is checked. For each clause, a Boolean function can be checked using a Clausen quantum circuit. The return values ​​of the Clausen quantum circuits, for which for the respective elevation angles ϑ j the antenna characteristic G(ϑ j ) for phases ϕ i and antenna far fields a i (ϑ j ) the conditions for the desired antenna characteristic (G̃(ϑ j )) are summed up and a solution is recognized if the sum is equal to the number of Clausens, where the phases ϕ i serve as a solution for adjusting the directional characteristics of phased multi-channel antennas. These phases ϕ ican be read out from the quantum circuit and fed to phase control units of the individual channels or antennas of the multi-channel antenna for phase control.

[0051] The quantum search algorithm can be used to quantize the real part and the imaginary part of the addition results of a determined desired phase ϕ i and the corresponding, for a given elevation angle ϑ j given phase ϕ i This means that when solving the complex exponential function of a function implemented in the oracle quantum circuit f(ϑj):=|∑i=1nca¯iei(ϕi+ϕ¯i)|2° nc⋅G˜(ϑj), °∈{≤,≥} separate, parallel circuits are used for the real and imaginary parts.

[0052] The results can be cascaded, with separate real and imaginary components. Cascading allows the circuit to be easily adapted to the required number of antenna channels.

[0053] An antenna beamforming device for adjusting the directional characteristics of phased multi-channel antennas by controlling the phases ϕ i for the signals of the individual antennas A i , in order to achieve a given elevation angle ϑ, is configured to execute a quantum search algorithm. The quantum search algorithm or the quantum gate circuit configured to execute it is configured to determine the phases ϕ used for control. i by checking the fulfillment of a quantum oracle, whether the antenna characteristic G̃(ϑ) for phases ϕ i and the far fields a i (ϑ) of the individual antennas A iis an element of a desired predetermined antenna characteristic G̃(ϑ).

[0054] The quantum search algorithm can preferably be implemented as a Grover algorithm for solving a function implemented in an oracle quantum circuit f(ϑj):=|∑i=1nca¯iei(ϕi+ϕ¯i)|2° nc⋅G˜(ϑj), °∈{≤,≥} with the number of channels n c , which is determined by pairs of antenna far-field functions ā given for an elevation angle ϑ i and phase ϕ i represented antenna pattern functions and the desired target antenna pattern G̃(ϑ j ). Thus, the antenna optimization problem is embedded in an oracle of a quantum circuit.

[0055] One of the number of Clausen n dA corresponding sequence of Clausen quantum circuits can be connected in series with a subsequent summing network and inverse oracle quantum circuit. At the end of the summing networks, an operator circuit designed to generate a query qubit through a conditional XOR operation can be arranged.

[0056] The antenna beamforming device can be connected to phase control units of antennas of a multi-channel antenna and configured to phase control the signals of the antennas. This allows the phases ϕ determined for controlling the multi-channel antenna to be i To achieve a desired predefined antenna characteristic G(ϑ), not only can a parameter set be predefined and stored in a stored form for control purposes without the need for re-determination. Rather, it is also possible to determine the parameters during operation and use them for control purposes.

[0057] The invention can be implemented using a quantum computer or quantum processor that is already available today. Any interference caused by quantum noise and uncertainty can be addressed using known methods of quantum error correction. Fault-tolerant quantum logic can be used for this purpose. However, multiple executions on the same or different processors, along with error detection and, if necessary, error correction using diversity methods, are also conceivable. This problem is explained in detail in M. Nielsen, I. Chuang: Quantum Computation and Quantum Information, 10th ed., Cambridge.

[0058] The invention is explained in more detail below using an exemplary embodiment with the accompanying drawings. They show: Fig. 1 - Sketch of a so-called array or group antenna controlled by an antenna beamforming device; Fig. 2 - Diagram of typical transmitting antenna patterns; Fig. 3 - Quantum circuit for the large-scale test algorithm; Fig. 4 - Quantum circuit for the quantum counting algorithm; Fig. 5 - Quantum circuit for the Grove operator; Fig. 6 - Quantum circuit for the phase-only pattern synthesis oracle; Fig. 7 - Quantum circuit for the Clausen f(ϑ j ); Fig. 8 - Quantum circuit for a modulo-2π adder in the Draper implementation; Fig. 9 - Cascaded addition network for n c = 8 antenna channels; Fig. 10- Initial state of the Grover initial state for an exemplary optimization problem.

[0059] Fig. 1 shows a sketch of a so-called array or group antenna with n c = 8 channels in the form of a transmitting antenna, which is fed with a signal via a power divider 1. The functions a i(ϑ) symbolize the co-polar far fields of the individual antennas A i or radiator as a function of an angle ϑ. In a receiving antenna, signals are received from the antennas A i with a specific directional characteristic and combined via signal amplifier 2 and a power coupler 1 to form the received signal S. The exemplary explanations for the transmitting antenna therefore apply equally to a receiving antenna.

[0060] The signal amplifiers 2 amplify or attenuate the respective antenna signal to signal amplitudes g i , which are kept constant during pure phase control.

[0061] The elevation angle ϑ is determined with an antenna beamforming device A by adjusting the phases ϕ i of the individual phased antennas A i or channels are controlled by phase control units 3 in order to achieve a predetermined antenna beam pattern (antenna pattern).

[0062] Fig. Figure 2 shows a diagram of typical transmitting antenna patterns G Tx ("Transmitting antenna pattern") for two polarizations h and v for a satellite-based remote sensing mission over the elevation angle ϑ. The same principle also applies to receiving antennas and the typical receiving antenna patterns.

[0063] The main beam within the dashed vertical lines would illuminate the strip on the ground. The goal is to optimize the main beam so that it lies near or above a limit, as indicated by the diagonal dashed line between the two vertical dashed lines. Outside this range are the so-called side lobes. Often, it is required that the side lobes remain below or as close as possible to a certain level. This is indicated by the diagonal dashed lines, each separated by a vertical dashed line of decreasing attenuation G.Tx [dB].

[0064] Fig. Figure 3 shows a block diagram of a quantum circuit for the Grover search algorithm. This is an iterative procedure that allows finding solutions with a number r r=NINT(π4 arcsinM / N−12)

[0065] Calling the Grove operator G. Here, NINT denotes the rounding operation to the nearest integer and M the number of solutions. N = 2 n , n = n c · n b , is the total number of possible combinations, where n c is the number of antenna channels and n b the number of bits per phase.

[0066] The register of word length n is initialized from the initialization state |0) using the Hadamard gates H=12(111−1) into a superposition state. The register of word length n' is a so-called working register, whose size depends on the optimization problem. After applying the Grover operator r times, the initial state |ψ(ϕ)〉, which contains the solutions, can be read out.

[0067] Fig. Figure 4 shows a quantum circuit for the quantum counting algorithm.

[0068] Since the number of possible solutions M is usually unknown a priori, it can be determined using a counting routine, which is described, for example, in MA Nielsen and IL Chuang, Quantum Computation and Quantum Information: 10th Anniversary Edition. Cambridge University Press, 2010. The Fig. The quantum circuit shown in Figure 4 uses a register of word length t to store this number.

[0069] Fig. Figure 5 shows a quantum circuit for the Grove operator G.

[0070] The core element of the Grove operator G is the so-called oracle circuit 0, which was developed specifically for the phase-only pattern synthesis problem and is described below. In terms of its operation, the Grove operator G separates solutions from non-solutions through rotations in Hilbert space, i.e., the probability amplitudes of solutions are amplified while the probability amplitudes of non-solutions are dampened. This operating principle and its geometric interpretation are described in detail in M.A. Nielsen and I.L. Chuang, "Quantum Computation and Quantum Information: 10th Anniversary Edition," Cambridge University Press, 2010.

[0071] The design of the oracle quantum circuit is based on the fact that the optimization problem of equations (1) to (3) can be solved using the substitution ai(ϑj)=a¯i(ϑj)eiϕ¯i(ϑj) for the antenna pattern functions of the individual channels in the following form: f(ϑj):=GTx(ϑj)∘G˜(ϑj), ∘∈{≤,≥}.

[0072] The function f is a Boolean function, called a clause in the following, which returns the value ONE ('1') if it is fulfilled and the value NULL ('0') if it is not fulfilled.

[0073] If equation (1) is inserted into (6) with the above substitution and the expression is multiplied by the number of channels n c , the optimization problem is as follows: f(ϑj):=|∑i=1nca¯iei(ϕi+ϕ¯i)|2∘nc⋅G˜(ϑi), ∘∈{≤,≥}

[0074] The design of the oracle quantum circuit is therefore parameterized in that the antenna pattern functions, which are defined by the number pairs (ā i , ϕ i ) are firmly encoded in the oracle quantum circuit. The desired phases ϕ i are in the binary variables x ik about the connection ϕi=2π2nb∑k=0nb−12kxik, encoded. This means that the large-scale experiments operate on these variables and the measured result is transformed back into phase values ​​between zero and 2π using equation (8).

[0075] Fig. Figure 6 shows a quantum circuit for the phase-only pattern synthesis oracle.

[0076] The task of the oracle quantum circuit is to distinguish solutions from non-solutions, i.e. to return the value ONE ('1') if a variable combination satisfies inequalities (2) and (3) and the value ZERO ('0') if it is not a solution. Mathematically, this corresponds to the effect |q〉→|q'〉=|q⊕[f(ϑ1)∧f(ϑ2)∧…∧f(ϑnd)]〉 to the so-called query qubit |q〉, where ⊕ denotes the Boolean XOR operation.

[0077] The oracle quantum circuit then has the Fig. 6 shown structure, which is shown using the example of n d= 2 Clausen. For j further Clausen, the quantum circuit would be correspondingly filled with the additional Clausen f(ϑ j ) the inverse application of the respective clause and the intermediate summation circuit.

[0078] The register |n d 〉 contains the binary representation of the Clausen (in the circuit shown here, |n d 〉 = |10)). ⌈Id(nd+1)⌉ qubits are required. The next register initialized with |0〉 is a counting register of the same word length ⌈Id(nd+1)⌉. In the lower part of the quantum circuit in Fig. are the quantum circuits for the individual Clausen f(ϑ j). The operating principle of the oracle quantum circuit is as follows: If a clause j is fulfilled, the j-th summing network Σ adds the number ONE ('1') to the counting register. If a clause is not fulfilled, the value ZERO ('0') is added. At the end of the circuit, the number in the counting register is multiplied by the number of clauses in the register |n d 〉 Only if this number is equal to the value n d the oracle circuit returns the value ONE ('1') for a solution x ik back.

[0079] The circuits marked with the dagger symbol f†(ϑj) denote the inverse application of the Clausen circuits, which is necessary to ensure the unitarity of the oracle operatos. The circuit † The one on the far right inverts the entire circuit part before the conditional XOR operation.

[0080] Fig. Figure 7 shows a quantum circuit for the Clausen f(ϑ j). Task of the quantum circuits for the individual Clausen f(ϑ j ) is to evaluate the Boolean expression according to equation (7). The design of this quantum circuit is shown as an example for two channels with two-bit phase quantization.

[0081] The j-th query qubit |q j 〉 contains the value of the Boolean expression |qj〉→|qj⊗f(ϑj)〉 and returns the value ONE (,1') if the clause f(ϑ j ) is met and the value NULL ('0') if this is not the case. On the left side in Fig. 7 are followed, alternating with working registers for the complex exponential functions, by the input registers which contain the phase values ​​ϕ i for the i-th antenna channel in binary representation.

[0082] Fig. Figure 8 shows a quantum circuit for a modulo-2π adder in the Draper implementation.

[0083] These phase values ​​ϕ iAccording to equation (7) the fixed phase values ​​ϕ i the antenna pattern functions a i , each of which depends on the angle ϑ j depend, with the help of the modulo-2π adder Σ im This is done with the Fig. 8, which is based on a description by Draper in TG Draper, Addition on a Quantum Computer, 2000 (https: / / arxiv.org / pdf / quant-ph / 0008033.pdf).

[0084] The operating principle is to apply a quantum Fourier transform to the first register (first part of the circuit up to the dashed line). The second register, which contains the phase values ϕ¯i=2π2nb∑k=0nb−12kx¯ik, for the antenna pattern functions, generates conditional rotations in the Fourier basis (middle circuit section), and after applying the inverse quantum Fourier transform (last circuit section), the summation result is obtained in the upper right register of the circuit diagram. In addition to Hadamard gates, the circuit contains so-called phase gates. P(λ)=(100eiλ).

[0085] This circuit has been modified so that the numerical values ​​for the antenna pattern phase values ​​ϕ i are permanently encoded in the circuit. Here, the value |x1 x0〉 = 101), which according to equation (11) corresponds to the decimal phase value 90°, was encoded. This allows the number of qubits required for phase summation to be halved. Other phase values ​​could also be encoded into the circuit in a similar manner.

[0086] The addition of the phases is followed by the evaluation of the complex exponential function according to equation (7), which is expressed with the amount ā i the antenna pattern function. For this purpose, the parameterized unitary operator Ei=∑{ϕ'}|ai exp(iϕ')〉〈ϕ'| implemented. On the input side, the first register contains the addition result ϕ' = ϕ i + ϕ i In addition, a number of working qubits is required, which depends on the output quantization for the real and imaginary parts.

[0087] In Fig. Figure 7 shows a 2-bit quantization, where the first bit is a sign bit (symbolized by +). To calculate the unitary operator, a quantization of the real and imaginary parts is first performed. Re=αi cos(iϕ')Im=αi sin(iϕ') according to a'(−1)xo2ne−1−1∑i=1no−12lxl Here, a' is a normalization constant that can be used to scale the quantization range. n o is the number of qubits for the real and imaginary parts, respectively. The quantized output values ​​are then calculated using nearest-neighbor interpolation. The number of working qubits depends on the number of identical output function values ​​and the selected number of bits n. o the output quantization. The number of qubits required for the complex exponential function is: ne=2no, if no>nb−1.

[0088] In the drawing in Fig. 7 is n o = n b = 2. In Table 1, the unitary operator according to equation (13) is shown as an example, as in Fig. 7 marked, listed. Table 1: Unitary operator for the exponential function according to equation (13), where ai = 1 was chosen. ϕ' a i exp(iϕ') ϕ' a i exp(iϕ') 0, 0, 0, 0 0, 1, 0, 0 1, 0, 0, 0 0, 1, 1, 0 0, 0, 0, 1 0, 0, 0, 1 1, 0, 0, 1 0, 1, 1, 1 0, 0, 1,0 1, 1, 1, 0 1,0, 1,0 1, 0, 0, 0 0, 0, 1, 1 1, 0, 1, 1 1, 0, 1, 1 1, 0, 0, 1 0, 1, 0, 0 0, 0, 0, 0 1, 1, 0, 0 1, 0, 1,0 0, 1, 0, 1 0, 0, 1, 0 1, 1, 0, 1 1, 1, 0, 0 0, 1, 1,0 0, 0, 1, 1 1, 1, 1, 0 1, 1, 0, 1 0, 1, 1, 1 0, 1, 0, 1 1, 1, 1, 1 1, 1, 1, 1

[0089] Fig. 9 shows a cascaded addition network for n c = 8 antenna channels.

[0090] After calculating the parameterized complex exponential functions for the individual antenna channels, adding networks for the real part Re j and imaginary part in j . These addition operators implemented here require 2n o + 2 qubits, where n o are the register widths for the two integers to be added and correspond to the number of output qubits for the real and imaginary parts of the complex exponential function. The addition network can be easily extended to any number of antenna channels by cascading, as shown in Fig. 9 for n c = 8 antenna channels. If the number of antenna channels is a power of two, then the number of working qubits for the adding network is 2n c - 1 each for the real and imaginary parts.

[0091] In the penultimate step, the Boolean operation according to equation (10) is still required. The unitary operator implemented for this purpose first performs the squaring and summation of the real and imaginary parts and then forms the logical operation according to equations (7) and (10). As in Fig. 7, the sign bits of the adding network are not required. This operator is shown as an example in Table 2 for a 2-bit quantization of the real and imaginary parts (as in Fig. 7). Table 2: Unitary operator that performs the Boolean evaluation according to equations (7) and (10). Re, Im, q j King, Im, q j ⊕ f(ϑ j ) Re, Im, q Re, Im, q j ⊕f(ϑ j ) 0,0,0,0,0 0, 0, 0, 0, 0 1, 0, 0, 0, 0 1, 0, 0, 0, 1 0, 0, 0, 0, 1 0, 0, 0, 0, 1 1, 0, 0, 0, 1 1, 0, 0, 0, 0 0, 0, 0, 1,0 0, 0, 0, 1, 0 1, 0, 0, 1, 0 1, 0, 0, 1, 1 0, 0, 0, 1, 1 0, 0, 0, 1, 1 1, 0, 0, 1, 1 1, 0, 0, 1, 0 0, 0, 1, 0, 0 0, 0, 1, 0, 1 1, 0, 1, 0, 0 1, 0, 1, 0, 1 0, 0, 1, 0, 1 0, 0, 1, 0, 0 1, 0, 1, 0, 1 1, 0, 1, 0, 0 0, 0, 1, 1, 0 0, 0, 1, 1, 1 1, 0, 1, 1, 0 1, 0, 1, 1, 1 0, 0, 1, 1, 1 0, 0, 1, 1, 0 1, 0, 1, 1, 1 1, 0, 1, 1, 0 0, 1, 0, 0, 0 0, 1,0,0,0 1, 1, 0, 0, 0 1, 1, 0, 0, 1 0, 1, 0, 0, 1 0, 1, 0, 0, 1 1, 1, 0, 0, 1 1, 1, 0, 0, 0 0, 1, 0, 1,0 0, 1, 0, 1, 0 1, 1, 0, 1,0 1, 1, 0, 1, 1 0, 1, 0, 1, 1 0, 1, 0, 1, 1 1, 1, 0, 1, 1 1, 1, 0, 1, 0 0, 1, 1, 0, 0 0, 1, 1, 0, 1 1 , 1, 1,0,0 1, 1, 1, 0, 1 0, 1, 1, 0, 1 0, 1, 1, 0, 0 1, 1, 1, 0, 1 1, 1, 1, 0, 0 0, 1, 1, 1,0 0, 1, 1, 1, 1 1, 1, 1, 1,0 1, 1, 1, 1, 1 0, 1, 1, 1, 1 0, 1, 1, 1,0 1, 1, 1, 1, 1 1, 1, 1, 1, 0

[0092] In the last step of the quantum circuit for the Clausen f(ϑ j ) in Fig. 7 all registers except the register |q j〉 is set to the initial state. This is symbolized by the †-operator and corresponds to the inverse application of the entire circuit before the operation q j ⊕ f(ϑ j ). This completely characterizes the entire oracle quantum circuit for the phase-only pattern synthesis problem according to equations (1) to (3).

[0093] The total number of qubits can be estimated as follows: n+n'=nf+2⌈Id(nd+1)⌉+1nf=4(nc−1)+2ncno+1

[0094] In the example in the Fig. 6 and Fig. 7 was n d = 2, n c = 2 and n o = n b = 2. This results in n f = 13 qubits for the Clausen quantum circuits and n + n' = 18 qubits for the entire oracle quantum circuit. It is n = n c · n b . n' is the number of qubits for the working registers.

[0095] In the following, a demonstration example is given, which was implemented as a numerical simulation of the governor algorithm for the phase-only pattern synthesis problem. For this purpose, an antenna with n c = 2 channels and n b = 2 bit phase quantization for a clause n d = 1. The antenna parameters are ā1 = a2 = 1, as well as ϕ1 = 90° and ϕ2 = 180°. The value 3 / 2 was chosen for the target pattern G̃. The expression to be optimized according to equation (7) then has the form: f:=|ei(ϕ1+ϕ¯1)+ei(ϕ2+ϕ¯2)|2≥nc⋅G˜.

[0096] Fig. Figure 10 shows a diagram of the initial state of the Grover optimization problem. It shows the probability distribution (discrete wavefunction) for the result register of the initial state after the Grover simulation. Due to the 2π phase ambiguity, as expected, there are four solutions using the 2-bit phase quantization.

[0097] The results are summarized in Table 3 below, where the phases ϕ1 and ϕ2 are given in binary and decimal encoding. The last column contains the antenna gain G Tx which satisfies inequality (18). Table 3: Results of the unitary simulation for the phase-only pattern synthesis problem according to equation (18). Zustand (binär) Zustand (dezimal) ϕ1 ϕ2 G Tx 0, 0, 1, 1 3 0° 270° 2 0, 1, 0, 0 4 90° 0° 2 1, 0, 0, 1 9 180° 90° 2 1, 1, 1, 0 14 270° 180° 2

[0098] The optimization of phased array antennas plays an important role in various fields of communications, navigation, and remote sensing. For example, in satellite communications, the exchange of information signals takes place via such phased array antennas with dynamic directional characteristic adjustment. This is necessary when the alignment between transmitter and receiver changes, for example, because the communications satellite is in a low Earth orbit and therefore moves rapidly relative to a user.

[0099] In radar remote sensing with synthetic aperture radars, active phased array antennas are used to optimally illuminate a strip of ground and suppress interference, such as range ambiguities, wherever possible. Typically, only the phases of the array antenna are optimized to maximize the available transmit power while simultaneously operating the transmit amplifiers in saturation.

[0100] Amplitude modulation broadcast satellites use phased array antennas to broadcast their programs in specific regions while minimizing interference with other areas.

[0101] The application of such antenna systems and the associated optimization extends to deep-space missions such as Messenger, which used a phased array antenna with circularly polarized slotted waveguides.

Claims

[1] Method for adjusting the directional characteristics of phase-controlled multi-channel antennas by controlling the phases (ϕ i ) for the signals of the individual antennas (A i ) to achieve a given antenna characteristic G̃(ϑ), characterized by that the phases (ϕ i ) can be determined using a quantum search algorithm by checking with a quantum oracle whether the antenna characteristic (G(ϑ)) for phases (ϕ i ) and antenna far fields (a i (ϑ)) meet the conditions for the desired, specified antenna characteristic (G̃(ϑ)). [2] Method according to claim 1, characterized bySumming up the events in which the fulfillment of the quantum oracle with a Boolean function was detected, comparing the sum of the events with the number of clauses to be checked for the multi-channel antenna, which represents the Boolean function to be checked, and detecting a solution if the sum of the events is equal to the number of clauses to be checked, where the phases (ϕ i ) from a sum function of the detected solutions evaluated with the Boolean value one (1), where the antenna characteristic (G(ϑ)) for phases (ϕ i ) and antenna far fields (a i (ϑ)) satisfy the conditions for the desired antenna characteristic (G̃(ϑ)). [3] Method according to claim 1 or 2, characterized byInitialization of the quantum search algorithm with a Hadamard gate into a superposition state, multiple consecutive applications of a Grover operator to solve the Boolean function implemented in the oracle quantum circuit using an oracle quantum circuit of the Grover operator and to separate solutions from non-solutions by rotations in the Hilbert space and to obtain an initial state containing the solutions (|ψ(ϕ)〉). [4] Method according to one of claims 1 to 3, characterized by that the desired phases ϕ i in binary variables x ik about the connection ϕi=2π2nb∑k=0nb−12kxik, ϕ i are coded, where n b is the number of bits per phase. [5] Method according to claim 4, characterized by adding respectively predetermined phases (ϕ i ) of the antenna far fields (a i ), which is determined from a given elevation angle (ϑ j) depend on the determined desired phases (ϕ i ) with a modulo-2π adder. [6] Method according to claim 5, characterized by Quantum Fourier transformation of one of the desired phases (ϕ i ) containing register, whereby an addition of predetermined phases (ϕ i ) by fixed coding using phase gates (P(λ)) and applying an inverse quantum Fourier transform to obtain the summation result. [7] Method according to one of the preceding claims, characterized by that the quantum oracle comprises several sequentially evaluated Clauses, where for each Clause a Boolean function is checked by means of a Clausen quantum circuit and the return values ​​of the Clausen quantum circuits, where for the respective elevation angles (ϑ j ) the antenna characteristic (G(ϑ j )) for phases ( ϕ i ) and antenna signal fields (a i (ϑ j)) the conditions for the desired antenna characteristic ((G̃(ϑ j )) are summed up and a solution is recognized when the sum is equal to the number of Clausens, where the phases (ϕ i ) serve as a solution for adjusting the directional characteristics of phased multi-channel antennas. [8] Method according to one of the preceding claims, characterized by Quantization of the real part and the imaginary part of the addition results of a determined desired phase (ϕ i ) and the corresponding angle of elevation (ϑ j ) given phase (ϕ i ). [9] Method according to claim 8, characterized by cascaded addition of the addition results separately for the real part and the imaginary part. [10] Antenna beamforming device for adjusting the directional characteristics of phase-controlled multi-channel antennas by controlling the phases (ϕ i) for the signals of the individual antennas (A i ) to achieve a given elevation angle (ϑ), characterized by that the antenna beamforming device is arranged to execute a quantum search algorithm, wherein the quantum search algorithm is used to determine the phases (ϕ i ) by checking the fulfillment of a quantum oracle, whether the antenna characteristic (G (ϑ)) for phases (ϕ i ) and antenna signal fields (a i (ϑ)) of the individual antennas (A i ) is an element of a desired predetermined antenna characteristic (G̃(ϑ)). [11] Antenna beamforming device according to claim 10, characterized by that the quantum search algorithm can be used as a Grover algorithm for solving a function implemented in an oracle quantum circuit f(ϑj):=|∑i=1nca¯iei(ϕi+ϕ¯i)|2∘nc⋅G˜(ϑi), ∘∈{≤,≥} with the number of channels n c, which is determined by for an elevation angle ϑ j each given pair of antenna far-field function ā i and phase ϕ i represented antenna pattern functions and the desired target antenna pattern G̃(ϑ j ). [12] Antenna beamforming device according to claim 11, characterized by that one of the number of Clausen (n d ) corresponding sequence of Clausen quantum circuits are each connected in series with a subsequent summing network and inverse oracle quantum circuit and at the end of the summing networks an operator circuit designed to generate a query qubit by an XOR operation is arranged. [13] Antenna beamforming device according to one of claims 10 to 12, characterized by that the antenna beamforming device is provided with phase control units (3) of antennas (A i ) of a multi-channel antenna and used to phase control the signals of the antennas (A i) is connected.

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