Computer-implemented methods for optimizing signal reception in communication networks suitable for quantum concept processors.

Abstract

This disclosure relates to a computer-implemented method for optimizing signal reception in a cellular communication network having multiple antennas for communicating with terminals. The method comprises the steps of: specifying a set S of candidate sites s and a set D of candidate antenna configurations CAC for the placement of one or more antennas at the candidate sites s; specifying a set P of pixels p, each pixel p corresponding to a geographical location within a service area where signal reception should be optimized; and specifying a set B of candidate best server CBS for each pixel p based on the expected radio signal strength for terminals at the geographical location corresponding to each pixel p. p At the stage of selection, each set B p The process includes: a step of including zero or more candidate servers corresponding to one of the candidate sites s and one of the CACs; and a step of determining a set of proposed servers. The determination includes at least: an optimized aggregated signal-to-noise ratio SNR calculated for all pixels p such that all of the proposed servers in the set are constructed with the corresponding CACs at the corresponding candidate sites s, and each set B of CBS. p This is based on a first restriction that requires at most one CBS to be included in the proposed set of servers. The disclosure further relates to quantum concept processors and computer programs.

Description

[Technical Field]

[0001] This disclosure relates to the field of computer-based planning and optimization of communication networks. In particular, it relates to computer-implemented methods, quantum concept processors, and computer programs for optimizing signal reception in communication networks having multiple radio cells. [Background technology]

[0002] The proper placement of base station antennas in a communications network is crucial to its quality of service in terms of total coverage and expected data rates for mobile terminals. For example, as disclosed in 3GPP TR36.942, base stations with three 3-sector antennas per site can be arranged on a hexagonal grid at a distance of 3*R, where R is the cell radius. However, such a regular arrangement is only possible if there are no obstacles and other constraints.

[0003] Finding a suitable location for a new base station site and the corresponding antenna configuration associated with it becomes more complex when location selection is limited, for example, due to land ownership or access issues, or when physical obstacles such as mountains or buildings affect radio signal propagation.

[0004] Furthermore, if a communication network, including some existing, already installed radio cells, is to be upgraded in terms of coverage and expected data rates by adding new radio cells, the location of the antennas corresponding to the existing radio cells must be taken into consideration.

[0005] Current optimization methods employ a terrain model that allows for the estimation of the expected signal strength of a signal transmitted by a base station antenna with a specific antenna orientation, located at a candidate site, and received by a terminal at a given location within the service area. In addition to signal strength, it is necessary to estimate signal disturbances caused by other base station antennas. To achieve reasonable coverage with an acceptable level of interference across the service area, these estimations must be repeated for many locations (referred to in this context as "pixels"), and for many or all possible subsets and possible antenna orientations of the candidate site. This leads to a large number of potential combinations to consider, making this approach computationally very expensive and thereby significantly limiting the number of candidate sites, antenna configurations, and / or pixels that can be considered. [Overview of the project] [Problems that the invention aims to solve]

[0006] From the above perspective, improved or alternative methods and systems are needed to optimize signal reception in cell-based communication networks. [Means for solving the problem]

[0007] According to the first aspect, a computer-implemented method is provided for optimizing signal reception in a cellular communication network having multiple antennas for communicating with terminals. The method includes the following steps: specifying a set S of candidate sites s and a set D of candidate antenna configurations CAC for the placement of one or more antennas at the candidate sites s; specifying a set P of pixels p, each pixel p corresponding to a geographical location within a service area where signal reception should be optimized; and specifying a set B of candidate best servers CBS for each pixel p, based on the expected radio signal strength for terminals at the geographical location corresponding to each pixel p.p At the stage of selection, each set B p The steps include: a step including zero or more candidate servers corresponding to one of the candidate sites s and one of the CACs; and a step of determining a set of proposed servers. The determination is at least an optimized aggregated signal-to-noise ratio SNR calculated for all pixels p such that all of the proposed servers in the set are constructed with the corresponding CAC at the corresponding candidate site s, and each set B of CBS. p Therefore, it is based on the first restriction that requires at most one CBS to be included in the proposed set of servers.

[0008] In particular, the inventors have found that the determination of a proposed or to be constructed server, for example, an antenna having a given configuration to be placed at a potential site for a new base station and to cover a corresponding new cell of a communications network, can be greatly simplified if, in a first step, a set of candidate best servers is selected for each pixel based on the expected radio signal strength, and in a second step, at most one candidate best server from each of such sets is included in the proposed set of servers.

[0009] The above pre-selection and additional constraints achieve good coverage and signal quality while simultaneously simplifying network optimization. In particular, this is based on the insight that only sites with good expected radio signal strength, such as nearby candidate sites, should be considered to achieve satisfactory coverage and signal quality for a given pixel. At the same time, while any such site may be sufficient to provide the desired coverage and signal quality, further servers in the same radio environment will add significant interference. Therefore, once a particular candidate best server is considered for a pixel, it can be safely assumed that no other candidate best servers should be selected for the same pixel, significantly reducing the number of potential configurations that need to be considered in the numerical optimization procedure.

[0010] This approach also has the advantage that the best server for each pixel p can already be determined by the selection of candidate best servers from the set B of candidate best servers, which simplifies the optimization because no further calculations and / or decision variables are required to determine the best server for each pixel within the selected set of candidate sites having the corresponding antenna configuration. p In at least one implementation, the communication network includes a set of existing antennas, each existing antenna being installed at a fixed site s and having a fixed antenna configuration. This method further includes identifying a best fixed antenna (BFA) for each pixel p, the BFA corresponding to the antenna of the set of existing antennas that provides the highest expected radio signal strength at the geographical location corresponding to each pixel p. The step of selecting the set B of CBSs for each pixel p includes selecting as CBSs candidate servers that meet a second coverage criterion predefined with respect to the BFA for the corresponding pixel p. In this way, existing antennas located in proximity to the pixel and thus having a high expected radio signal strength can be taken into account in the optimization procedure, while at the same time further limiting the number of candidate best servers in the set B of candidate best servers for pixel p.

[0011] In at least one implementation, only candidate servers that provide a better DLR than the BFA for the corresponding pixel p are selected as CBSs. Here, DLR indicates the downlink reference value for each candidate server. The said limitation enforces that only candidate sites for which the best server - antenna has a CAC that exceeds the highest expected radio signal strength of the BFA can be selected into the set B of CBSs. In particular, this ensures that existing fixed antennas are not favored over the selected CBSs from B. f p p p p

[0012] p p p p

[0013] The above characteristics are particularly useful when an existing network of wireless cells should be improved, for example, to improve coverage or data rate, by adding one or more additional cells to the existing network. In principle, this is a very demanding task, as any selection of a new site and its antenna configuration must take into account interference caused by existing wireless cells and the new proposed server.

[0014] In at least one implementation, the set D of CACs for candidate sites s is equal to the number of antennas N installed at candidate sites s. a Characterized by at least one of the following: the horizontal mounting angle d of at least one first antenna (A0) installed at candidate site s; the vertical mounting angle of at least one antenna installed at candidate site s; and / or the mounting height of at least one antenna installed at candidate site s. This allows for the representation of similar antenna configurations in an efficient manner in computer-implemented optimization procedures while retaining physical characteristics.

[0015] For example, the number of antennas N a This applies to all candidate sites s in the set S, in particular to N a The horizontal mounting angle d is fixed at =3, and the N is installed at candidate site s. a Orientation of individual equally spaced sector antennas d a Used to show, in particular, d a =360 / N a a+d, where a∈{0,…,N} a This means that a single reference angle d is sufficient for each candidate site s to determine the configuration of all possible antennas to be installed.

[0016] The inventors have also found several ways to map the task of optimizing signal reception in the network detailed above, with or without the above-mentioned pre-selection and constraints, to a quadratic unconstrained binary optimization (QUBO) function. By reformulating the above task as a QUBO, it becomes possible to perform it on a quantum conceptual computer, thereby very quickly evaluating a large number of possible system configurations. In a QUBO system, the binary decision variables can correspond to the best server for potential sites, antenna configurations, and / or pixels, which can be used to define a Hamiltonian containing polynomial terms representing the optimization goal and any desired constraints of the optimized system. In this way, the optimal or near-optimal configuration for a communication network can be found using a digital annealing method.

[0017] Therefore, in at least one implementation, the step of determining the set of servers proposed is: at least the first polynomial term H SNR and the second polynomial term H one_best_server The step of providing a quadratic unconstrained binary optimization (QUBO) function, in particular a Hamiltonian, which includes the first polynomial term H SNR This represents the objective function showing the aggregated SNR calculated for each pixel p, and the second polynomial term H one_best_server This involves a step representing a first constraint based on a first restriction, and optimizing the QUBO function using a quantum concept processor (QCP) to determine the proposed set of servers.

[0018] In at least one implementation, the QUBO function has a third polynomial term H that represents a second constraint requiring that for each candidate site s, only a single common antenna configuration is included in the proposed set of servers. allowed_degrees It also includes.

[0019] In at least one implementation, the QUBO function takes a predetermined number S num The fourth polynomial term H represents a third constraint that requires the site and / or server to be included in the proposed set of servers. number_sites It also includes.

[0020] In at least one implementation, the QUBO function has a limit S on the number of servers included in the proposed set of servers. max and lower limit S min It is optimized based on an inequality that requires it to be restricted by at least one of the following.

[0021] Such additional terms allow for further simplification and / or control of the optimization procedure by applying further constraints to the QUBO function.

[0022] In at least one implementation, QCP is configured to perform digital annealing using multiple binary decision variables, with binary decision variables y associated with each of the candidate sites s and CACs. s d This includes a first set of variables, which indicates whether at least one antenna is constructed at each CAC at the corresponding candidate site s. Such binary decision variables correspond to the desired optimized configuration of the communication network.

[0023] According to the second aspect, a quantum concept processor QCP, in particular a digital annealing processing unit or a quantum annealing processing unit, is provided. The QCP is configured to perform one or more steps of the method according to the first aspect or any implementation thereof, in particular the step of determining a proposed set of servers.

[0024] According to the third aspect, a computer program is provided. The computer program includes instructions that cause one or more processors to perform the first aspect or any implementation thereof when the program is executed by one or more processors.

[0025] Further aspects and implementation details of the disclosed methods, devices, and systems are disclosed in the attached claims and the detailed description provided below. [Brief explanation of the drawing]

[0026] [Figure 1] This shows potential sites for establishing new base stations. [Figure 2] This shows a subset of candidate sites and antenna configurations that are considered to be the best candidate servers for the pixels. [Figure 3] This indicates the expected field strength of the best server antenna in the area of ​​the pixels. [Figure 4] Figures 2 through 4 show the same candidate sites, each containing nine pixels to consider. [Figure 5] 5A and 5B show possible antenna configurations for each candidate site. [Figure 6] This flowchart shows a computer-implemented method for optimizing signal reception in a communication network. [Figure 7] 7A and 7B compare simulated annealing and digital annealing, respectively. [Figure 8] 8A to 11B show different optimization results for a given service area obtained using the prototype system. [Figure 9] 8A to 11B show different optimization results for a given service area obtained using the prototype system. [Figure 10] 8A to 11B show different optimization results for a given service area obtained using the prototype system. [Figure 11] 8A to 11B show different optimization results for a given service area obtained using the prototype system. [Modes for carrying out the invention]

[0027] First, several novel concepts for optimizing network coverage and performance are described and explained with reference to Figures 1 to 6. These concepts are applicable to various optimization approaches, including simulated annealing and digital annealing. Subsequently, specific solutions based on digital annealing are described at a mathematical level. Some of these solutions utilize the novel concepts, while others are more general. While the use of the novel concepts in the digital annealing approach yields very good results in a relatively short time, it should be noted that the two aspects of this disclosure may be used separately from each other.

[0028] Figure 1 shows several potential candidate sites (CS) for establishing a new base station. Each base station to be established may consist of a specific antenna configuration. The antenna configuration may be expressed as the preferred orientation or direction of signal radiation and reception, given by the number of antennas to be installed at each candidate site and their horizontal mounting angles, i.e., the angle relative to a given reference direction such as geographical north. Furthermore, there may be configuration parameters such as the vertical mounting angle of the antennas, i.e., the angle of inclination or tilt relative to the horizontal direction, and the mounting height. However, for better understanding, only the two parameters mentioned above, namely the number of antennas and their orientation, will be considered below.

[0029] Furthermore, because these are common types of antennas used in communication networks, only two types of antenna installations will be considered in specific examples: a set of two antennas pointed in opposite directions (a two-sector antenna) and a set of three antennas pointed in three different directions separated by 120° (a three-sector antenna). In such an installation, once the direction of the first antenna A0 is selected, the directions of the remaining antenna A1 or the remaining two antennas A1 and A2, which will be installed at the same candidate site CS, are also fixed.

[0030] In the example in Figure 1, a total of nine candidate sites CS are considered. Hereafter, this will be referred to as the set S of candidate sites s. At each candidate site CS, two different configurations of three-sector antennas A0, A1, and A2 are considered, namely, antennas oriented at 0, 120, and 240°, or 60, 180, and 300°. The potential angles of the first reference antenna A0 can be expressed as a set D of orientations or antenna configurations, i.e., D = {0, 60}. The orientations of the remaining two antennas A1 and A2 are implied. In actual implementations, further configurations may be considered, for example, the selection of two-sector or three-sector antenna installations oriented in 10° or 30° increments, e.g., D = {0, 30, 60, 90}.

[0031] The number of candidate sites CS and antenna configurations, for example, the size of sets S and D, may be relatively small, but the number of their potential combinations is quite large, leading to a high degree of complexity when an extended service area 200 is investigated, as will be detailed later. Therefore, as detailed in Figure 2, for each pixel p from the set of pixels P to be considered, a subset B of all candidate sites S and antenna configurations D is considered. p Only subset B is considered. p This also facilitates the selection of the best server for each pixel, i.e., for a specific site and corresponding antenna configuration, as will be explained in more detail later.

[0032] This initial pre-selection is based on the expected signal strength, which may be obtained from the terrain model of service area 200 and / or calculated distances. For example, as shown in Figure 2, only candidate sites CS adjacent to pixel p and antenna configurations including antennas A0, A1, or A2 roughly oriented at the location of pixel p are included in subset B. p It is included in.

[0033] Based on the above pre-selection, subset B pEach of the candidate site CSs and antenna configurations should provide good coverage for each pixel p. This is schematically shown in Figure 3, which shows the expected field strengths of each best server antenna BSA1-BSA5 in the area of ​​pixel p. Figure 3 further shows subset B. p If all of the candidate site CS and antenna configurations within the scope were actually constructed, pixel p would experience very high signal interference, severely limiting signal quality. To address this problem, a further selection criterion or heuristic is derived: at most one of the servicing antennas BSA1-BSA5 should be constructed. This criterion should result in a high signal-to-noise ratio for pixel p if any one of the servicing antennas BSA1-BSA5 is constructed, or no coverage at all or only very low coverage if none of the servicing antennas BSA1-BSA5 are constructed. The latter is mitigated by optimizing the aggregated coverage for all pixel p, as will be discussed later.

[0034] So far, only a single pixel p has been considered. Figure 4 shows the same set S of candidate sites CS, with nine pixels p1-p9 to be considered. Each pixel p has its own subset B of best candidate servers. p While there are various factors, attention must be paid to the fact that their interrelationships must be considered during network planning. For example, a single candidate site may serve or, in fact, interfere with several pixel p. This leads to a large number of combinations to consider. When planning cells, the impact of each possible candidate site and each possible antenna configuration on each pixel p being considered must be examined.

[0035] Figures 5A and 5B show possible configurations for only two candidate sites, each having three 3-sector antennas with possible modulo angles of 0, 30, 60, and 90 degrees, respectively. As will be discussed in more detail below, such configurations can be represented in a compact form as binary decision variables. As will be detailed later, each of the four possible configurations per candidate site CS can be identified using a corresponding single bit, i.e., four bits per candidate site.

[0036] Figure 6 schematically illustrates how the above considerations can be used in a computer-implemented method 300 for optimizing signal reception in a communication network having multiple radio cells. As described above, each radio cell includes at least one antenna configured to communicate with terminals located within the service area 200. The method includes steps 310 to 350, as detailed below.

[0037] Step 310: Provide a set S of candidate sites s for placing at least one additional antenna. This initial input to the optimization process can be provided by supplying the x, y, and optionally z coordinates of sites that are manually or automatically identified as candidate sites, such as the roof of a tall building, unused open space, or similarly promising locations.

[0038] Step 320: A set D of candidate antenna configurations is provided for each of the candidate sites s. These may be uniform for all sites, i.e., a 3-sector antenna arrangement spaced 120° apart from each other, or they may be site-specific, i.e., limited by the field of view, or a mixture of both, for example, a selection from several available types of configurations, for example, a selection to install 2-sector or 3-sector antennas at each candidate site s.

[0039] Stage 330: Provide a set P of pixels p, where each pixel p corresponds to a geographical location within the service area where signal reception should be optimized. Again, these input parameters may be provided automatically, for example, as a fixed grid of pixels at regular intervals, or they may be provided manually to cover specific points of interest, such as roads and railway lines within the service area 200.

[0040] Stage 340: For each pixel p, a set of candidate best server CBSs B is selected based on the expected radio signal strength for the terminal located at the geographical location corresponding to each pixel p. p Select each set B. p This includes zero or more CBS corresponding to one of the specified candidate sites s and one of the specified candidate antenna configurations. Typically, each set B p It should include at least one CBS. Set B p If the array is empty, the corresponding pixel p cannot be reliably served by any of the new candidate sites being considered. This can be, for example, a pixel p already covered by a nearby existing antenna, or a pixel p located at a great distance from any of the candidate sites. Pixels that cannot be served by any of the candidate sites or any of the existing antennas may be removed from the set of pixels P to simplify later optimization stages. This selection can be performed, for example, using a known topological model of the service area 200 and corresponding simulations for signal propagation based on the locations of candidate sites, antenna configurations, and pixel locations.

[0041] Step 350: Determine at least one server that is proposed to be built. For example, the set of proposed servers is the set of all CBS for all pixels p. p It can be selected from the union of the sets B. In particular, this selection is possible for each set B of the CBS. pTherefore, the selection is based on the constraint that at most a single CBS is selected as the proposed server. This constraint reduces interference and limits the number of solutions. The selection is further based at least in part on the optimization of the signal-to-noise ratio (SNR) calculated for all pixels p, given that the at least one proposed server is constructed at the corresponding candidate site s with the corresponding antenna configuration.

[0042] Of all possible configurations, the one with the best overall coverage and best signal quality, i.e., the highest SNR, should be identified in step 350 using optimization. One suitable approach for such a statistical optimization problem is simulated (thermal) annealing. Starting from an initial, typically random configuration or system state, the available decision variables are varied to find the global optimal. To limit the computational effort, an energy is associated with each system state. A state change is randomly selected from among the accepted candidate changes. Candidate changes that result in lower system energy are accepted. All other candidate changes are randomly accepted with decreasing probability with respect to the energy delta and the increase in time. With increasing time, the acceptance of candidate state changes that increase energy becomes increasingly unlikely to reach the final state in the form of a local or global minimum.

[0043] Simulated annealing can be applied to network planning and optimization problems. However, the large number of possible solution combinations and the significant effort required to calculate the expected signal strength at each pixel present several challenges. Each optimization run takes a long time or requires substantial computational resources. This implies that the size of the planning area, the number of candidate sites, the configurations considered, and / or the pixels considered must be limited.

[0044] Quantum annealing, or digital annealing, is another optimization process that uses quantum fluctuation-inspired processes to find a global minimum of a given objective function on a given set of candidate solutions or states. Quantum annealing is particularly useful for problems where the search space is discrete (combinatorial optimization problems) and there are many local minimums, such as finding the ground state of a spin glass. The inventors have found that quantum annealing can also be applied to network cell programming.

[0045] The solutions described herein utilize approaches inspired by quantum computing. The computation of optimized solutions to stress or QUBO functions for determining optimal coverage and signal quality can be performed by a so-called quantum conceptual processor. In the context of this disclosure, a processor is defined as a quantum conceptual processor that solves a so-called "Ising model" or equivalent quadratic unconstrained binary problem (QUBO). For example, this is a processor configured to solve the optimization problem by quantum annealing or quantum annealing emulation. Such processors are based, for example, on conventional hardware technologies, such as complementary metal oxide semiconductor (CMOS) technology. An example of such a quantum conceptual processor is Fujitsu's digital annealer. Alternatively, any other quantum processor can be used for the methods described herein, and in the future, technologies based on actual qubit technology may also be used. Further examples of such quantum conceptual processors include DWave's (e.g., 5000Q) quantum annealer, quantum gate computers (IBM, Rigetti, OpenSuperQ, IonQ, Honeywell) and their future successors, or alternative quantum computing designs that utilize quantum optimization algorithms such as Quantum Approximate Optimization Algorithms (QAOA) or Variational Quantum Eigensolvers (VQE). In other words, a quantum conceptual processor as defined herein is a processor that realizes the concept of minimizing a so-called quadratic unconstrained binary optimization (QUBO) function, whether it be a special processor based on classical techniques, a quantum gate computer, or a quantum annealer.

[0046] Digital annealing, based on quantum conceptual computing, offers many advantages over conventional optimization algorithms, including faster processing speeds. This is partly due to the fact that quantum annealing allows for the separation of the objective function (or main QUBO) from specific constraints or optimization targets. Thus, in contrast to simulated annealing, which requires reformulating and recalculating the entire cost function, subsequent calculations based on modified constraints or optimization targets in digital annealing become computationally more efficient.

[0047] Figures 7A and 7B compare simulated annealing and digital annealing, respectively. These show that in digital annealing, constraints and optimization goals are calculated based on QUBOs calculated based on partial values ​​of the cost function. Sequential iterations in the search space are always affected by these values ​​of the QUBO. In contrast, in simulated annealing, control over the search and cost function calculation is directly based on the original data. In other words, digital annealing allows for the use of large-scale trials based on the same original data. Therefore, the main QUBO can remain the same for all trials. However, each trial can offer its own conditions. For example, the first trial might determine between 1 and 3 candidate sites, while the second trial might determine between 1 and 10 candidate sites.

[0048] The arrows in Figure 7A and B visualize the entry points for each new test or scenario to be evaluated. As shown in Figure 7A, in simulated annealing, defining the cost function for a given test is relatively straightforward. Thus, each test starts anew by constructing a test-specific cost function. However, the computational cost lies in evaluating the test-specific cost function. Since each test requires its own test function, running multiple tests increases the computational cost. As shown in Figure 7B, in digital annealing, constructing the main QUBO is complex and requires more time. However, the main QUBO is the same for all tests. Each test can use the same main QUBO and modify it with additional constraints. This can be implemented and computed efficiently. Therefore, the QUBO-based approach becomes more efficient when many different tests are run, for example, for large values ​​of K.

[0049] In the described implementation based on Fujitsu's digital annealer, each term of the QUBO can be computed individually. These terms are then added together before performing digital annealing. However, individual pre-computation has the advantage of allowing individual parts of the QUBO to be reused for different optimizations.

[0050] However, before optimizing the problem with digital annealing, it needs to be formulated in an appropriate way, namely using a quadratic form for the objective function and associated constraints. Furthermore, the objective function and constraints or penalty terms must be expressed in terms of digital decision variables. Finally, the number of decision variables should be limited as much as possible, taking into account the number of decision bits available in the current hardware implementation and / or to allow scaling of the solution to a large set of candidate sites.

[0051] These challenges are discussed in more detail below with respect to several different QUBOs. Each QUBO described addresses one or more of the challenges above. For example, the first QUBO focuses on how the non-quadratic equation representation of the expected signal-to-noise ratio can be reformatted using a quadratic equation. The second QUBO focuses on how to reduce the number of binary decision variables required to represent a single standardized configuration of a candidate site. The third QUBO focuses on how to extend the optimization to also consider existing fixed antenna locations. The fourth QUBO focuses on how to reduce the number of binary decision variables required to represent existing fixed antenna locations and also introduces a further optimization goal to define the number of candidate sites selected. The fifth QUBO focuses on how to keep the number of binary decision variables small while simultaneously allowing for various standardized configurations of candidate sites (e.g., 2-antenna or 3-antenna configurations). The sixth QUBO, as mentioned earlier, focuses on how to further reduce the number of binary decision variables by assuming that, per pixel, at most one candidate is constructed from the set of best candidate servers. Although each QUBO is described individually, their respective contributions to the overall problem can be combined in many ways to achieve their respective advantages.

[0052] It is important to note that reducing the number of binary decision variables in QUBO is crucial for the technical feasibility of this approach and for its application to real-world scenarios. On the one hand, quantum processors and quantum-inspired processors can only handle a limited number of such variables, and in real-world scenarios, a naive QUBO formulation can easily exceed this number. On the other hand, a QUBO formulation with a reduced number of variables must reflect all relevant physical features in order to provide a meaningful solution.

[0053] Below, we will express and convert the cell programming problem detailed above into a mathematical form suitable for quantum-concept computers such as Fujitsu's Digital Annealer.

[0054] Formal problem description and formulation of the first QUBO Let S be the number of candidate sites or cells. For each site s∈S, three antennas can be constructed. Therefore, for each site, we count the antenna options as a∈A={0,1,2}. Assuming the use of a 3-sector antenna, the antenna options for each site are separated by 120 degrees. Furthermore, for each candidate site, all antenna positions within a 360-degree radius should be represented in steps of 30 degrees. Since the antennas are interchangeable, we only need to consider four different configurations. More precisely, for candidate cell s, as detailed above with respect to A and B in Figure 5, the antenna frequencies for antenna a=0 can be 0, 30, 60, and 90. Thus, the antenna frequencies for antenna a=1 are 120, 150, 180, and 210, and for antenna a=2 are 240, 270, 300, and 330.

[0055] We define the set of directions D = {0, 30, 60, 90} modulo 120 degrees. Then, for any d ∈ D, the angle of the antenna is d a d is defined as =120a+d. a Regarding =120a+d, d a Note that modulo 120 = d.

[0056] N d : The number of directions for the antenna. In our case, N d =4 N a : The number of antennas for any given cell. In our case, N a =3 Define the first set of binary decision variables.

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[0057] Constraint 1: Each antenna has at most one frequency. For all antennas, there is at most one frequency, and the same frequency is used. a Please note that this is the number of antennas for any given site. In our case, N a = 3. Each antenna a at any site s can have at most one direction. An antenna does not need to have a direction; this means it is not considered in the solution. Furthermore, the modulo 120 degrees of all antennas at a site must be the same; that is, the antennas must be separated by 120 degrees. This can be expressed as shown in equation (1) below.

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[0058] Alternatively, the same constraint may be expressed as shown in equation (2) below. In the implementation in which the annealer is used, equation (2) can be evaluated more efficiently and is therefore used below. Nevertheless, in other implementations, the same constraint may be expressed as shown in equation (1) above, or in any other equivalent way.

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[0059] Constraint 2: For any given pixel, at most one best server. Apart from the sites and antennas, there are traffic pixels p∈P. The optimization problem consists of finding the antenna positions for each site so that as many pixels as possible are covered in the best possible way.

[0060] First, let's describe the parameters that need to be calculated to obtain the optimized solution. For fixed downlink and uplink thresholds DLTh and ULTh, a pixel p is covered by an antenna a∈A of site s∈S where d∈D is:

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[0061] In the above, DLR and ULR indicate signal strength. In the described implementation, DLR specifically indicates the downlink reference value (dB), and ULR indicates the uplink reference value (dB). These values ​​are based on the site index s and direction d a Based on the antenna position indicated by, as well as the provided model of the service area 200 under investigation, signal propagation modeling, etc., calculations can be performed for each pixel p. Appropriate thresholds DLTh and ULTh can be determined experimentally to obtain acceptable coverage at pixel p. In the above formula, for corresponding d and a, d a Please note that this is equal to 120a + d.

[0062] For each pixel, assuming that the pixel is covered, we need to find the best server site, antenna, and its frequency (best server or best server antenna BSA). In this regard, for each pixel p∈P, we define a set of binary decision variables that indicate whether cell antennas a∈A, s∈S, and d∈D are the best servers. As a result, the binary decision variables used in optimization can also be used to identify the best server for each pixel. More precisely, we define the set of binary decision variables as follows:

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[0063] If either inequality (3) or (4) is violated, the corresponding antenna a in that configuration cannot be the best server. Therefore, those b p,s,a d We correct this to 0. Therefore, in a more general way, the decision variable b p,s,a d This can be expressed as follows:

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[0064] For each pixel, at most one antenna can be the best server antenna. In particular, if a pixel is not covered, we do not allow a best server antenna. This constraint can be enforced by:

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[0065] Furthermore, a cell antenna a with frequency d can only be a candidate for the best server if the antenna is present in its configuration. Therefore, the following must be enforced:

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[0066] In particular, the last two conditions can be enforced by the QUBO constraint.

[0067] H one_best_server =0 and H x_over_b If = 0 is satisfied, then for each pixel p, the correct bit b p,s,a d This forces the selection of . This can be done by minimizing the following expression.

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[0068] Formulation of the objective function: SNR optimization The optimization target is to maximize coverage under the aforementioned constraints. Physically, this corresponds to maximizing the aggregated signal-to-noise ratio summed across all pixels. This can be expressed by the following objective function:

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[0069] Item 1 is the downlink reference intensity DLR in decibels (dB). p,s,a d It depends on the decision variable b p,s,a d This represents the signal contribution of the best serving antenna selected by [the system]. The second term depends on the downlink reference strength DLR_W in watts (W), and the decision variable x s',a' d' This represents the noise contribution or interference of all other antennas.

[0070] Conversion: Decibels to Watts It should be noted that, in general, decibel values ​​of signal strength, such as downlink or uplink reference values, path loss, and the aforementioned gain, can be converted to watts, and vice versa, as follows:

[0071] Given a value in decibels, Val_W can be obtained by the following conversion.

number

[0072] Given a value in watts, Val_W, the corresponding value in decibels, Val, can be obtained using the following conversion.

number

[0073] The optimization parameter load in equation (11) above indicates the extent to which interference is considered. In the implementation described, this is set to a value of 0.5. This may be varied within a range of, for example, 0.3 to 0.8 to give more or less weight to interference caused by other antennas. This may depend, for example, on the specific signal transmission technology and coding.

[0074] Unfortunately, this (nonlinear) form of the objective function does not allow for a QUBO formulation. In other words, this objective function cannot be directly optimized by a digital annealer. However, the function log 10 Our attention is drawn to the fact that (x) is monotonic. Therefore, the condition SNR(p)≧SNRTh (12) Instead, equivalent conditions 10 -SNR(p) / 10 ≤10 -SNRTh / 10 (13) This can be formalized.

[0075] For a valid decision bit vector b, p,s*,a* d* Let's assume that this is a single bit with the value 1, and all other bits have the value 0. Then we can perform the following conversion.

number

[0076] This function (14) is not identical to the original objective function (which has logarithmic form) defined above in (10) and (11), but it can be computed directly by the digital annealer unit. Furthermore, although it does not function with the same values ​​as the original objective function defined above in (10) and (11), due to the monotonicity of the exponential function applied in (14), it should result in a set of optimized decision variables similar to that of the original objective function.

[0077] Therefore, using digital annealing, the following equivalent objective function can be minimized.

number

[0078] Note that when minimized under the constraints discussed above, the equivalent objective function (15) prioritizes configurations with low inter-antenna interference and high signal strength for pixels (the first part of the terms in the sum) while simultaneously optimizing pixel coverage by the best server, i.e., the number of pixels where the parentheses are negative.

[0079] Furthermore, taking into account all the constraints discussed above, we obtain the following QUBO that needs to be optimized. HQ=w A ·H allowed_degrees + w B ·H one_best_server + w C ·H x_over_b + w D ·H SNR w A , w B , w C and w D is the respective QUBO penalty weight. In the embodiments described, the penalty weight w A , w B , w C These are selected to implement each QUBO term as a hard constraint.

[0080] The constraint condition (9) discussed earlier is the objective function HSNR Attention is drawn to the fact that it is often automatically satisfied by minimizing. Thus, in a practical implementation, in the final QUBO, the term H one_best_server may be omitted.

[0081] In practice, when a large number of pixels, candidate sites, and antenna configurations should be considered, the set of binary decision variables can become very large and may exceed the number of decision variables available in existing quantum concept processors. Thus, some additional optimizations that are useful for reducing the number of binary decision variables are considered below.

[0082] Second QUBO Formulation In a second formulation, to simplify the first QUBO and allow its implementation for more pixels and / or candidate sites, an additional auxiliary constraint is assumed that each newly constructed site contains all of its antennas. There is a practical reason for this constraint. This limitation may reduce the maximum possible coverage, but opens up the possibility of different QUBO formulations with fewer required bit variables.

[0083] Similar to the first QUBO formulation, for each pixel, if that pixel is covered, it is necessary to find the best server site as well as the antennas and frequencies. Thus, for each pixel p ∈ P, s ∈ S and d ∈ D, the binary variable is

Number

[0084] Note that, in contrast to the first QUBO formulation, the index a ∈ A for the antennas has been omitted.

[0085] Constraint 1: Allowed frequency for antennas on a site As before, each cell can only be constructed with one configuration. Therefore, the modulo degree of the site must match for all pixels. This can be enforced by the following constraint:

number

[0086] Constraint 2: At most one best server for any given pixel. Furthermore, for each pixel, there can be at most one best server site, and this means

number

[0087] For each pixel, we want to assign a site and configuration that includes the best server antenna for that pixel. This can be achieved by minimizing the following equation:

number

[0088] As detailed above regarding the first QUBO, this section may be omitted in some implementations.

[0089] Constraint 3: Determine whether a candidate site has been selected. To represent the SNR value for a pixel, we first need to introduce a second set of binary variables. For s∈S and d∈D, we define the following:

number

[0090] To force these binary variables to behave as expected, that is, to force the decision variables to be forced to 1 only if the corresponding site and its configuration are the best server for at least one pixel, we require the following:

Number

[0091] Also note that this second set of binary variables that replaces the first set of binary decision variables of the first QUBO is used to determine whether all three antennas of the site are constructed or no antenna is constructed.

[0092] Formulation of the objective function: SNR optimization With this constraint condition, the SNR value of pixel p ∈ P for some fixed threshold SNRTh can be defined as follows.

Number

[0093] Since the above formulation is not yet in QUBO form, adapt it in the same way as the first QUBO formulation. The following optimization targets are obtained for the second QUBO.

Number

[0094] The above formulation of the objective function significantly reduces the number of binary decision bits required because generally only one decision bit is required for each candidate site and antenna degree, rather than one for each candidate site, antenna degree, and number of antennas.

[0095] Also, considering all the constraint conditions discussed above, the following QUBO that needs to be optimized is obtained. HQ = w A ·H allowed_degrees + w B ·H one_best_server + w C ·H chosen + w D ·H SNR

[0096] Third Formulation of QUBO This formulation maintains the second additional auxiliary constraint of QUBO, that each new site constructed contains all of its antennas.

[0097] Furthermore, the concept of existing antennas that are assumed to remain unchanged within the network is also incorporated. That is, already established (fixed) sites within the network are modeled, and the coverage, signal, and interference they provide are taken into consideration.

[0098] It should be noted that the methods disclosed can also be used to optimize existing networks. This could involve, for example, removing or re-orienting existing antennas that cause significant interference to other existing or newly planned antennas. However, in this case, the existing antennas under investigation should be modeled as candidate sites, not as fixed antennas.

[0099] Each fixed site consists of one, two, or three antennas arranged at a predetermined angle (degrees). f ∈S f Let S represent a fixed site. Here, f These are all static sites. Furthermore, d f ∈D f sf is a fixed site s f Let D be the angle of all the antennas above. f sf It includes two or more angles, and each angle is site s f It corresponds to the specific antenna shown above. D f sf is a fixed site s f This is sometimes called the antenna configuration.

[0100] These fixed sites not only act as the best servers for the required pixels, but they can also cause interference. To consider both cases, we introduce a new bit variable z as follows: p,sf Define.

number

[0101] The condition for fixed bits is defined as b above. p,s d Note that this is similar to a constant bit condition for bits. The constant bits are specifically defined as follows:

[0102] For all antennas at site s in configuration d, if the DLR value for pixel p is less than DLTh, or the ULR value is less than the threshold ULTh, then all bits b p,s d Let = 0. Fixed sites f For all antennas, if the DLR value for pixel p is less than DLTh, or the ULR value is less than the threshold ULTh, then all bits z p,sf Let = 0.

[0103] Constraint 1: Allowable frequency for antennas on the site As before, any site can only be built in one configuration. This can be enforced by constraint (16) above.

[0104] Constraint 2: For any given pixel, at most one best server. Similarly, any pixel can have at most one best server. Note that the pixel can choose its best server from either candidate sites or fixed sites. This condition is met by the following penalty QUBO clause.

number

[0105] Constraint 3: Determine whether a candidate site has been selected. To facilitate the calculation of the SNR value, it is first necessary to determine whether a given candidate site s with a specific modulo frequency d has been selected. This is achieved by the same penalty term (19) as before.

[0106] Formulation of the objective function: SNR optimization Here, we define the maximum DLR value at pixel p from either the candidate site or the fixed site, along with the corresponding best angle.

number

[0107] Here, a* p,s,d This shows the strongest antenna for a given candidate site and configuration for a given pixel, and DLR* p,s,d This shows the DLR value of the strongest antenna for a given candidate site and configuration for a given pixel, and d* p,sf This indicates the direction of the strongest antenna at a given fixed site for a given pixel, and DFR_F* p,sf This indicates the DLR value of the strongest antenna among the fixed site antennas for a given pixel. DLR_F (p,sf,df) DLR is used to indicate that it refers to a fixed site. df (p,sf) It is used for this purpose. The same notation is also used for DLR_W_F to indicate its value in watts.

[0108] SNR item when a candidate site is selected: Using the above definitions, we can formulate the total SNR value for any given pixel p when pixel p selects a candidate site as its best server with some modulo frequency d.

number

[0109] Here, DLR_W_F (p,sf,df) This is the antenna direction d for a given pixel. f Fixed sites with f This represents the downlink reference value of the antenna in watts. Item d is used to determine the antenna orientation for each newly considered site. a In contrast to the parameters DLR* and DLR_W, which are parameterized by =120a+d, the corresponding parameters DLR_F* and DLR_W_F determine the fixed antenna orientation, based on the fixed antenna direction d f It is parameterized by [the specified method].

[0110] SNR item when a fixed site is selected: Similarly, if pixel p selects a fixed site as its best server, the total SNR value at any given pixel p is

number

[0111] Using the same considerations as for the first QUBO, we can find a QUBO formulation with a similar minimum.

[0112] The objective QUBO term for this problem can be written as follows:

number

[0113] Taking into account all the constraints discussed above, we obtain the following QUBO that needs to be optimized. HQ=w A ·H allowed_degrees + w B ·H one_best_server + w C ·H chosen + w D ·H SNR

[0114] Formulation of the fourth QUBO This formulation maintains the additional auxiliary constraint (8) of the second and third QUBOs, that each new site being constructed includes all of its antennas. Furthermore, as with the third QUBO, it also considers already constructed (fixed) antennas, however, in a different way, leading to a reduction in the number of binary decision variables. In addition, the fourth QUBO includes further restrictions on the number of candidate sites selected.

[0115] All fixed sites already exist in the network with predefined antennas and angles. DLR_F* p Assuming that is the best DLR value provided to pixel p from all fixed sites, f* p However, let's assume that pixel p is the best static site. Therefore, let's assume that pixel p is the best server for static site s f All that's needed is to decide whether or not to have it.

number

[0116] Equation (31) shows that for each pixel p, all fixed sites S that achieve the best signal level f and antenna direction D f sf Best fixed site from f* p and antenna d* fp Define.

[0117] Based on the above, a new bit variable z is created as follows: p Define.

number

[0118] For all antennas at site s in configuration d, if the DLR value for pixel p is less than DLTh, or the ULR value is less than the threshold ULTh, then all bits b p,s d Let = 0.

[0119] If a new cell is constructed at candidate site s in modulo frequency d, then for each pixel p, the maximum DLR value DLR* provided by this (s,d) pair is given by this pair. p,s,d DLR_F* can be calculated. p This is defined as above by the best DLR value provided to pixel p from all fixed sites, and f* p Let's assume this is the best fixed site for pixel p. DLR* p,s,d <DLR_F* p Therefore, for pixel p, the best server antenna cannot be at modulo degree d in candidate site s, and fixed site f* p It can be asserted with certainty that it is located at b. p,s This means that d can be set to the constant 0.

[0120] In this process, attention must be paid to the thresholds DLTh and ULTh for DLR and ULR, respectively.

[0121] The complete description of b bits (b-bits) can be formally written as follows:

number

[0122] When combined, b p,s d and z p This represents the complete problem formulation as a QUBO.

[0123] Constraint 1: Allowable frequency for antennas at the site As before, any site can only be built in one configuration. This can be enforced by constraint (16) above.

[0124] Constraint 2: At most one best server for any pixel As before, any pixel can have at most one best server. Note that the pixel can choose its best server from either a candidate site or a fixed site. This condition is satisfied by the following simplified penalty QUBO term based on the new bit variable z p [Number]

[0125] Constraint 3: Determine whether a candidate site is selected To facilitate the calculation of the SNR value, it is first necessary to determine whether a given candidate site with a specific modulo degree d is selected. This is achieved by the same penalty term (19) as before.

[0126] Constraint 4: Restrictions on selected candidate sites As a result of the optimization, recall that sites containing a specific number of antennas (at a specific angle) are constructed at each selected candidate site. It is economically beneficial to limit the total number of sites constructed throughout the network as long as the pixels can provide high DLR / SNR values. Therefore, it makes sense to control the number of selected candidate sites.

[0127] Constraint 4a: Specified range of candidate sites As an example, the number of sites selected can be restricted within a minimum and maximum value range. Let the desired minimum number of selected sites be S min and the desired maximum number of candidate sites be S max . Then, by invoking a bilateral inequality containing y s d binary decision bits, this requirement can be realized. Formally, this can be written as follows. [Number]​

[0128] Although the above is not a QUBO term, in version 3 of the Fujitsu Digital Annealer, such a simple inequality constraint condition for binary decision variables can be automatically converted into a corresponding QUBO constraint condition. For older versions or other systems, such inequalities can be expressed by additional QUBO penalty terms based on additional decision variables.

[0129] Constraint 4b: Exact number of candidate sites Also, there may be cases where it is desirable to select a predefined number of candidate sites. For example, if the desired number of candidate sites is S num then this requirement can be enforced using the following QUBO terms.

Number

[0130] In the described implementation, it is necessary to select either Constraint 4a or Constraint 4b.

[0131] Formulation of the objective function: SNR optimization The expressions (23) to (27) given above for the SNR terms regarding candidate sites and fixed sites remain the same. In the definition of each SNR term for the fixed sites in the above expression (28), the new bit variable z p is used.

Number

[0132] Based on the same considerations as above, using logarithmic operations, SNR_fixed(p) can be written in QUBO form.

[0133] The objective QUBO terms for this problem can be described as follows.

Number

[0134] Complete QUBO Case 1: No restriction on the number of candidate sites

Number

Number

Number

[0135] w A , w B , w C , w D and w E are the respective QUBO penalty weights. In the described embodiment, the penalty weights w A , w B , w C and w E are selected to implement the respective QUBO terms as hard constraint conditions.

[0136] The fifth formulation of QUBO In this formulation, each newly constructed site is assumed to include two or three equally spaced antennas, i.e., three antennas spaced 12° apart, or two antennas spaced 180° apart. This can be combined with any of the aforementioned approaches. More generally, any number of antennas per site, e.g., four or more antennas per candidate site, can be treated in a similar manner.

[0137] Similar to previous QUBO formulations, if pixels are covered, we need to find the best server site, antenna, and its frequency for each pixel. Therefore, we have a binary variable b for each pixel p∈P, s∈S, and modulo frequency d∈D. p,s,2 d and b p,s,3 d Let us define it again as follows:

number

[0138] The constant bits are specifically defined as follows: For all antennas at site s, for pixel p, if the modulo degree d and all DLR values ​​for site s with two antennas are less than DLTh, or if each ULR value is less than the threshold ULTh, then all bits b p,s,2 d Let = 0. Similarly, for pixel p, if all DLR values ​​of site s with modulo degree d and three antennas are less than the downlink threshold DLTh, or if each ULR value is less than the uplink threshold ULTh, then all bits b p,s,3 d Let = 0.

[0139] As mentioned above, all fixed sites already exist in the network with predefined antennas and angles. Furthermore, for the option of having two and three antennas, and for each pixel p, the maximum DLR value DLR* provided by this (s,d) pair when a cell is constructed at candidate site s in modulo degree d is given. p,s,d2 and DLR* p,s,d,3 DLR_F* can be calculated. p However, assuming that this is the best DLR value provided to pixel p from all fixed sites, f* p However, this is the best fixed site for pixel p. However, DLR* p,s,d,2 <DLR_F*p and DLR* p,s,d,3 <DLR_F* p In that case, for pixel p, the best server cannot be at candidate site s in modulo frequency d, but rather at fixed site f* p It can be asserted with certainty that it is located in d p,s,2 d and b p,s,3 d This implies that it can be set to the constant 0.

[0140] In this process, attention must be paid to the thresholds DLTh and ULTh for DLR and ULR, respectively.

[0141] A complete description of b bits can be formally written as follows:

number

[0142] Based on equations (30) and (31), the bit variable z p It is defined as described above.

[0143] Constraint 1: Allowable frequency for antennas on the site As mentioned earlier, any site can only be constructed in one configuration. Therefore, the modulo degree of a site must be consistent for all pixels. This can be enforced by the following constraint:

number

[0144] Constraint 2: For any given pixel, at most one best server. As before, any pixel can have at most one best server. This condition is met by the following penalty QUBO term.

number

[0145] As before, in order to represent the SNR value for a pixel, we first need to introduce a second set of binary variables. For s∈S and d∈D, we define the following:

number

[0146] In addition, b p,s,2 d , b p,s,3 d , y s d and z p This represents the complete problem formulation as a QUBO.

[0147] Constraint 3a: Determine whether the candidate site is constructed with 0, 2, or 3 antennas. For each candidate site, we need to decide whether it will be built at all, and if so, whether it will be built with two or three antennas. This mutually exclusive choice can be enforced as follows:

number

[0148] Constraint 3b: Determine whether a candidate site has been selected. To facilitate the calculation of the SNR value, it is first necessary to determine whether a given candidate site s with a specific modulo frequency d has been selected. This is achieved by the following penalty term.

number

[0149] Constraint 4: Restrictions on selected candidate sites As mentioned earlier, it is economically beneficial to limit the total number of servers built across the network, as long as they can provide good DLR / SNR values ​​to the required pixels. Therefore, it makes sense to limit the number of candidate sites to be selected.

[0150] Constraint 4a: Specified range of candidate sites For example, the number of sites selected can be limited to a range between a minimum and a maximum value. The desired minimum number of sites to select is S min The maximum number of desired candidate sites is S max If that is the case, then y s,2 d and y s,3 d By using binary bits, this requirement can be implemented using an inequality. Formally, this can be written as follows:

number

[0151] As described above, such simple inequality constraints on binary decision variables can be automatically converted into corresponding QUBO constraints.

[0152] Constraint 4b: The exact number of candidate sites In addition, it may be desirable to select a predefined number of candidate sites. For example, if the desired number of candidate sites is S num If so, this requirement can be enforced using the following QUBO clause.

number

[0153] The implementation described requires selecting either constraint 4a or constraint 4b.

[0154] Formulation of the objective function: SNR optimization Similarly, here we define the maximum DLR value per pixel from the (candidate or fixed) site, along with the corresponding best angle. The maximum DLR value from the fixed site has already been defined in (25) and (26) above.

[0155] For the candidate sites, set A2={0,1} and A3={0,1,2}, and further define the following.

number

[0156] SNR item when a candidate site is selected: As described above, by using the above definition, we can formulate a total SNR value at any given pixel p such that pixel p selects a candidate site at some modulo frequency d as its best server.

number

[0157] SNR item when a fixed site is selected: Similarly, the total SNR value at any given pixel p such that pixel p selects a fixed site as its best server is as follows:

number

[0158] Based on the same considerations as above, SNR_fixed(p) can be written in QUBO format using logarithmic operations.

[0159] The objective QUBO clause for the problem can be written as follows:

number

[0160] Complete QUBO Case 1: No limit on the number of candidate sites

number

number

number

[0161] w A , w B , w C , w D , w E and w F is the respective QUBO penalty weight. In the embodiments described, the penalty weight w A , w B , w C , w E and w F These are selected to implement each QUBO term as a hard constraint.

[0162] Formulation of the sixth QUBO The sixth QUBO is constructed in a manner generally familiar to quantum concept processors, particularly digital annealers, building upon some of the previous approaches to formulating the objective function and associated constraints. It combines these approaches with the initial observation that at most one site should be constructed from a set of best server candidates. This allows for a particularly compact representation of the QUBO, with a reduced number of binary decision variables. As a result, the sixth QUBO is particularly useful for optimizing reception based on more candidate sites and pixels.

[0163] For simplicity, in this formulation, we assume once again that each site is constructed with three antennas, as previously described for the second through fourth QUBOs. Formulations where a site has two or three antennas can be formulated in the same way as described for the fifth QUBO.

[0164] As with previous QUBO formulations, if pixels are covered, for each pixel, it is necessary to determine which site is the best server site and antenna, along with its frequency. In previous approaches, this assignment is done using a binary variable b for each pixel p∈P, s∈S, d∈D. p,s d This was achieved by [the method / method].

[0165] To keep the problem size small and allow for optimization of larger data sets, we conserve these bits in this formulation. For each candidate site s∈S and modulo frequency d∈D, we define the following binary decision variable:

number

[0166] Binary decision variable y s d Attention is drawn to the fact that each candidate site is associated with a binary decision variable y. s d The number increases linearly with the number of new sites to consider, rather than with the number of pixels p considered.

[0167] Definition of maximum DLR value: Similar to equations (23) and (24), for each pixel p∈P, s∈S, d∈D, we define the following:

number

[0168] Definition of the best server candidate set: For a user-specific threshold t∈(0,1) and pixel p∈P, the following set of best server candidate B p Define.

number

[0169] The threshold t is the DLR value of the selected server candidate that exceeds the threshold DLTh. (p,s) d The margin is the best possible DLR value.

number

[0170] For the sixth QUBO, each best server candidate set B p We assume that at most one site should be constructed from these. As detailed at the beginning of this specification, the heuristic behind this is that if two sites with high DLR values ​​for pixels are constructed simultaneously, the one with the (slightly) lower DLR value will interfere more strongly with the other, thus significantly reducing the SNR value for pixels.

[0171] As before, the network also needs to incorporate already established (fixed) sites. Each fixed site consists of one, two, or three antennas at several predetermined angles (degrees). f∈S f Let S represent a fixed site. Here, S f These are all static sites. Furthermore, d f ∈D f Let D be the angle of all antennas on fixed site f. f It includes two or more angles, each corresponding to a specific antenna on fixed site f.

[0172] These fixed sites not only act as the best servers for the required pixels, but they can also cause interference.

[0173] Therefore, for each pixel p∈P, we define the best DLR value provided to pixel p from all fixed sites, and define the corresponding fixed site along with the antenna frequency that gives that best DLR value.

number

[0174] Furthermore, like the fourth QUBO, it defines the best server bits for fixed sites.

number

[0175] Binary decision variable z p Attention is drawn to the fact that each pixel is associated with a binary decision variable z. p The number of pixels increases linearly with the number of pixels being considered.

[0176] Constraint 1: At most one modulo degree for the site. As before, any site can only be constructed in one configuration. Therefore, only one modulo frequency can be selected for each site. The binary decision variable y s d Using a new set, this can be enforced by the following constraint:

number

[0177] Constraint 2: For any given pixel, at most one best server. As before, any pixel can have at most one best server. Note that the pixel can select its best server from either candidate sites or fixed sites. The binary decision variable y s d Using the new set, this condition can be enforced by the following penalty QUBO term.

number

[0178] Note that the above conditions reduce the need for constraints 3a and 3b of the fifth QUBO.

[0179] Constraint 3: Restrictions on selected candidate sites As detailed previously, it is economically beneficial to limit the total number of servers built across the network, as long as good DLR / SNR values ​​can be achieved for all / most pixels. Therefore, it makes sense to regulate the number of candidate sites selected.

[0180] Constraint 3a: Specified range of candidate sites For example, the number of sites selected can be limited to a range between a minimum and a maximum value. The desired minimum number of selected sites is S. min The maximum number of desired candidate sites is S max Let's assume that this is the case. Then, y s d This requirement can be implemented by using a two-sided inequality involving binary bits. Formally, this can be written as defined previously in equation (33), which is reproduced below.

number

[0181] Constraint 3b: The exact number of candidate sites In addition, it may be desirable to select a predefined number of candidate sites. For example, the desired number of candidate sites may be S num This requirement can be enforced using the QUBO term defined earlier in equation (34), which is reproduced below.

number

[0182] The implementation described requires selecting either constraint 3a or constraint 3b.

[0183] Formulation of the objective function: SNR optimization The target of minimizing the SNR value of all pixels is achieved by minimizing the QUBO, similar to previous approaches. The difference is that the best server for pixel p∈P is bit b p,s d It is not determined by s∈S and d∈D, but rather by (s,d)∈B p The bit y is 1. s d This means that it will be determined by y. Furthermore, interference from candidate sites will be y s' d' Candidate sites where = 1

number

number

[0184] Based on the same considerations as above, the logarithmically manipulated optimization target is as follows:

number

[0185] From a physical standpoint, the first two terms in the first set of parentheses represent interference affecting the selected candidate site with respect to signal reception strength, originating from other selected candidate sites and fixed antennas, respectively. The first two terms in the second set of parentheses represent interference affecting the fixed site selected as the best server antenna with respect to signal reception strength, originating from the selected candidate site and other fixed antennas, respectively. Remaining terms in each equation -10 -SNRTh / 10The parentheses are fixed and enforce that a site with the configuration is selected as the best server site for that pixel only if the threshold SNRth is exceeded for that pixel. In the latter case, the parentheses achieve a value less than 0, which is valuable for H_SNR. If the SNR value for the pixel is less than SNRth, the parentheses achieve a value greater than 0, which implies a penalty if the variable before the parentheses is 1. Note that for each pixel p, at most one of the two parentheses contributes to the overall Hamiltonian.

[0186] If there is no existing fixed antenna, i.e., S f Note that when =φ, the second term of the first set of parentheses and the entire second set of parentheses become 0 and can be omitted. Therefore, in this simplified case applicable to greenfield design, the objective function is as follows:

number

[0187] Complete QUBO Case 1: No limit on the number of candidate sites

number

number

number

[0188] w A , w B , w C and w D is the respective QUBO penalty weight. In the embodiments described, the penalty weight w A , w B, w C These are selected to implement each QUBO term as a hard constraint.

[0189] Optimization results Figures 8A to 11B show the optimized results for a given service area 200, obtained using a prototype system based on the sixth formulation of QUBO and adapted for a more flexible antenna configuration, as described above with respect to the fifth QUBO. The prototype system was configured, for example, to return a predefined number of the best results obtained using different random starting conditions. Furthermore, the results obtained can be influenced by using slightly different QUBO penalties and weights and / or threshold parameters, as described above.

[0190] Providing multiple best solutions is useful for several reasons. In particular, further decision criteria beyond optimized system performance may be considered, such as required building permits, costs, and environmental considerations. Such further decision criteria can also be included in the QUBO if they can be expressed as corresponding constraints using available binary decision variables.

[0191] In each case, a specific task or test is presented before the dash, for example, identifying just one site, and then specifying the acceptable antenna configuration. The text in the diagram indicates how well the optimization target has been achieved.

[0192] For the results shown in Figures 8A and 8B, the sixth QUBO is extended along the fifth QUBO to allow the selection of either two or three antennas per candidate site. Furthermore, as a boundary condition, the system was configured to select exactly one candidate site. Figure 8A shows a solution using a single site with two antennas that provides a very high overall SNR value for all covered pixels. In contrast, Figure 8B shows a solution using a single site with three antennas that provides a slightly lower overall SNR value but better coverage (corresponding to the number or percentage of pixels exceeding the defined receive and / or transmit strength thresholds).

[0193] The results shown in Figures 9A and 9B are obtained in the same way as the results shown in Figures 8A and 8B, except that the system was configured to select between 1 and 10 candidate sites. Figure 9A shows a solution that provides a very high SNR using two sites, each with two antennas. In contrast, Figure 9B shows a solution that provides very high coverage using two sites, each with three antennas.

[0194] The results shown in Figures 10A and 10B are obtained in the same way as the results shown in Figures 8A and 10B, except that the system was configured to select just three candidate sites. Figure 10A shows a solution that provides medium to high SNR and high coverage using three sites, each with two antennas. In contrast, Figure 10B shows a solution that provides high coverage using a single site with three antennas and two additional sites, each with two antennas.

[0195] The results shown in Figures 11A and 11B are obtained in the same way as the results shown in Figures 9A and 11B, except that the system was configured to select only two-sector antennas for each candidate site. Figure 11A shows a solution that provides high coverage using five sites, each with two antennas. In contrast, Figure 11B shows a solution that provides high SNR and high coverage using only two sites, each with two antennas.

[0196] The results depend on various parameters affecting the topology and optimization of service area 200, but it can be observed that generally, better coverage is obtained with a larger number of antennas and / or sites. However, when fewer antennas are spaced further apart, less interference and better overall SNR values ​​are often obtained. Furthermore, as seen in Figures 8A to 10B, the antennas are typically not pointed toward each other. All of these results are consistent with conventional planning criteria and confirm the validity and accuracy of the assumptions underlying the developed prototype system. [Explanation of Symbols]

[0197] List of reference signs and formula symbols 200 service areas 300 ways 310-350 Methodology Stages A0, A1, A2 antennas BSA1, ..., BSA5 Best Server Antenna CS candidate sites B p A collection of the best candidate servers d Modulo degree D Antenna configuration set N a Number of antennas p, p1, ..., p9 pixels P: A collection of pixels s Candidate sites S: A collection of candidate sites

Claims

1. A computer-implemented method for optimizing signal reception in a cell communication network having multiple antennas for communicating with a terminal, the method comprising the following steps: - A step of specifying a set S of candidate sites s and a set D of candidate antenna configurations CAC for the placement of one or more antennas at candidate sites s; - A step of specifying a set P of pixels p, where each pixel p corresponds to a geographical location within a service area (200) where signal reception should be optimized; Based on the expected radio signal strength for the terminal at the geographical location corresponding to each pixel p, a set of candidate best server CBSs B for each pixel p. p At the stage of selection, each set B p This includes a stage that includes zero or more candidate servers corresponding to one of the candidate sites s and one of the CACs; - The step of determining the proposed set of servers, the determination of which includes at least: - The optimized aggregated signal-to-noise ratio (SNR) calculated for all pixels p when all of the proposed servers in the set are built with the corresponding CAC at the corresponding candidate site s, • Each set B of CBS p Therefore, the first restriction requires that at most one CBS is included in the aforementioned set of servers proposed. A method based on this.

2. Set B of CBS for each pixel p p The preceding step of selecting is: - Select candidate servers as CBS that meet a predefined first coverage criterion for the corresponding pixel p, specifically DLR ≥ DLTh and / or ULR ≥ ULTh, where DLR represents the downlink reference value for each candidate server, DLTh represents the downlink threshold, ULR represents the uplink reference value for each candidate server, and ULTh represents the uplink threshold; - Exclude candidate servers that exceed a predefined interference criterion for at least one other pixel p from the CBS set Bp; and - Selecting at most a limited number of predefined candidate servers as the CBS for each pixel p. The method according to claim 1, comprising at least one of the following.

3. The aforementioned communication network includes a collection of existing antennas, each existing antenna being located at a fixed site s f It is installed and has a fixed antenna configuration; The method further includes identifying the best fixed antenna BFA for each pixel p, the BFA corresponding to an antenna from the existing set of antennas that provides the highest expected radio signal strength at the geographic location corresponding to each pixel p; - A set of CBS for each pixel p B p The aforementioned step of selection includes: selecting a candidate server as the CBS that meets a predefined second coverage criterion with respect to the BFA for the corresponding pixel p, The method according to claim 1 or 2.

4. The method according to claim 3, wherein only candidate servers that provide a better DLR than the BFA for the corresponding pixel p are selected as CBS, in particular DLR ≥ DLTh and / or ULR ≥ ULTh, where DLR represents the downlink reference value for each candidate server, DLR_F represents the downlink reference value of the BFA, ULR represents the uplink reference value for each candidate server, and ULR_F represents the uplink reference value of the BFA.

5. - A step in which at most one best server is selected for each pixel p of a set of pixels P, wherein at most one best server is selected for each set of CBS that meets the BFA or the second coverage criterion. p One candidate server is selected from the following, The method according to claim 3 or 4, further comprising:

6. The set D of CACs for candidate sites s is: • Number of antennas installed at candidate site s: N a ; ・At least one first antenna (A 0 ) to be installed at the candidate site s, the horizontal mounting angle d; - The vertical mounting angle of at least one antenna to be installed at candidate site s; and / or - Mounting height of at least one antenna to be installed at candidate site s The method according to any one of claims 1 to 5, characterized by at least one of the above.

7. Number of antennas N a This is fixed for all candidate sites s in the set S, and in particular N a = 3, and the horizontal mounting angle d is N installed at candidate site s. a Orientation d of the equally spaced sector antennas a Used to show, in particular, d a = 360 / N a a + d, where a ∈ {0, ..., N} a The method according to claim 6, wherein the value is -1.

8. The step in determining the proposed set of servers is: - At least the first polynomial term H SNR and the second polynomial term H one_best_server A step of providing a quadratic unconstrained binary optimization (QUBO) function, in particular a Hamiltonian, which includes the first polynomial term H SNR This represents the objective function showing the aggregated SNR calculated for each pixel p, and the second polynomial term H one_best_server This represents a first constraint condition based on the first restriction, and is a stage; - A step of optimizing the QUBO function using the quantum concept processor QCP to determine the proposed set of servers. The method according to any one of claims 1 to 7, including

9. The QUBO function has a third polynomial term H that represents a second constraint requiring that for each candidate site s, only a single common antenna configuration is included in the proposed set of servers. allowed_degrees Further includes; The QUBO function is defined by a predetermined number S. num A fourth polynomial term H represents a third constraint requiring that the site and / or server be included in the proposed set of servers. number_sites This further includes; and / or - The QUBO function has an upper limit S for the number of servers included in the proposed set of servers. max and lower limit S min This method optimizes based on an inequality that requires it to be restricted by at least one of the following: The method according to claim 8.

10. The QCP is configured to perform digital annealing using a plurality of binary decision variables, the plurality of binary decision variables being: - A binary decision variable y associated with each of the candidate sites s and CAC. s d The first set of includes y s d This indicates whether at least one antenna is constructed at each CAC in the corresponding candidate site s. The method according to claim 8 or 9.

11. For each candidate site s, only the first class of the predefined CAC is considered, and a fixed number N is considered for all candidate sites s. a There are antennas, and in particular, three-sector antennas (A) that are spaced at equal intervals. 0 , A 1 , A 3 ) and a binary decision variable y s d The aforementioned first set of all N in the corresponding candidate site s a Indicates whether individual antennas will be constructed; or, For each candidate site s, one of several different classes of CAC is considered, and each of the several different classes is a different subset of the first set of the first binary decision variable, in particular the first subset y corresponding to sites having two sector antennas. s,2 d and a second subset y corresponding to sites with 3-sector antennas s,3 d Corresponding to, The method according to claim 10.

12. The communication network includes several existing antennas as described in claim 3; - The plurality of binary decision variables are associated with each of the pixels p, and a binary decision variable z indicates whether the corresponding pixel p is served by one of the existing antennas, which is identified to represent the best fixed antenna BFA for each pixel. p Further including the second set, The method according to claim 10 or 11.

13. The first polynomial term is, [Math 1] Here, d is one of several pre-configured horizontal mounting angles for the candidate server's antenna, in particular, the first antenna of the multi-sector antenna (A 0 ) represents the horizontal mounting angle, y s d This represents the first set of binary decision variables that indicate whether any of the antennas will be constructed at the corresponding candidate site s with an installation angle d, [Math 2] is B p A represents the complement of A, where A represents the set of antenna numbers for each candidate site, and a* (p,s,d) d represents the antenna number of the antenna at candidate site s with mounting angle d that provides the highest signal to the pixel, load represents the degree to which interference caused by other antennas is considered, DLR_W represents the downlink reference strength in watts, DLR* represents the downlink reference value of the antenna at candidate site s with mounting angle d that provides the highest signal to the pixel, d f ∈D f represents the horizontal orientation of the existing fixed antenna f, DLR_W_F represents the downlink reference value of the fixed antenna in watts, SNRTh represents the fixed SNR threshold, and z p This represents a second set of binary decision variables associated with each pixel p, indicating whether the corresponding pixel p is served by one of the existing antennas. The method according to any one of claims 8 to 12.

14. A quantum concept processor QCP, in particular a digital annealing processing unit or quantum annealing processing unit, configured to perform one or more steps of the method according to any one of claims 1 to 13, in particular the step of determining a proposed set of servers.

15. A computer program that, when executed by one or more processors, includes instructions causing one or more processors to perform the method described in any one of claims 1 to 13.

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