WO2017084713A1

WO2017084713A1 - A computational efficient method to generate an rf coverage map taken into account uncertainty of drive test measurement data

Info

Publication number: WO2017084713A1
Application number: PCT/EP2015/077118
Authority: WO
Inventors: Symeon CHOUVARDAS; Mathieu Leconte; Moez DRAIEF; Stefan Valentin
Original assignee: Huawei Technologies Co., Ltd.
Priority date: 2015-11-19
Filing date: 2015-11-19
Publication date: 2017-05-26
Also published as: CN108293193A

Abstract

A controller for constructing a coverage map of a radio network, the controller comprising a computation unit configured to compute a coverage map based on one or more signal quality measurements of one or more measurement locations; a completion unit configured to complete the coverage map; an uncertainty unit configured to determine an uncertainty in the coverage map; and an identification unit configured to identify, based on the uncertainty in the coverage map, one or more test locations.

Description

A COMPUTATIONAL EFFICIENT METHOD TO GENERATE AN RF COVERAGE MAP TAKEN INTO ACCOUNT UNCERTAINTY OF DRIVE TEST MEASUREMENT DATA

TECHNICAL FIELD The present invention relates to a controller, a system and a method for constructing a coverage map of a radio network. The invention also relates to a computer-readable storage medium storing program code, the program code comprising instructions for carrying out a method for constructing a coverage map of a radio network. BACKGROUND

Reliable reconstruction of coverage maps, i.e., maps corresponding to certain areas, which contain measurements such as path- loss, Received Signal Strength, SINR, data rate, etc., is a matter of paramount importance for cellular networks. In particular, coverage maps are im- portant for: a) network planning: For the initial rollout and to identify coverage problems;

b) self-Optimizing Network functions such as: Dynamic tilting, optimization of handover, admission control and radio resource management (RRM) parameters;

c) new optimization approaches such as: anticipatory resource allocation and anticipatory handover.

All the aforementioned functions rely on an accurate estimation of coverage maps and path loss. However, the cost of obtaining accurate coverage maps can be very high.

A typical method to obtain a coverage map is a drive test. Typically, drive tests acquire measures of geographic position and received signal strength in cellular networks, which allow to construct path loss values for coverage maps and to fill gaps in existing maps. Nevertheless, drive tests are very costly, since they require substantial personnel, time and equip- ment to accurately cover an area of sufficient scale. Moreover, this cost poorly scales with the area size: It grows vastly, the larger the studied area becomes.

As a consequence, some methods were developed to reduce the cost by minimizing the number of necessary drive tests by providing more data. A relatively cost efficient way to do so is to exploit information from so-called crowdsourcing applications. With crowdsourcing, a user installs an application on an off-the-shelf smartphone and returns measurements to a database. The immediate drawbacks of this approach are:

1) increased signaling overhead, which reduces the user's data budget and the battery lifetime;

2) systematic measurement errors due to the wide fluctuation of hardware in the

Smartphones (HF radio frontend, different processing algorithms, GPS chipsets);

3) possible manipulation of the database by sending wrong measurements.

As a result, data coming from crowdsourcing can be unreliable and can lead to erroneous path loss values in coverage maps.

Accurately predicting path loss in wireless networks is an ongoing challenge. Over the past years, path loss models in various types of networks have been proposed and analyzed. Despite the fact that path loss modeling is useful in many applications, the deviation between the actual/measured path loss and the one given by the model can be large. Even the best models still produce significant errors when compared to actual measurements.

For that reason, learning-based construction of a path loss map, in the following also referred to as reconstruction, has been extensively studied since it can be tailored to the specific environment under consideration and give more accurate results. In a nutshell, in learning-based reconstruction, one has access to a number of input and output measurements, which in this case they correspond to location and channel gains, and one tries to estimate a function mapping the input to the output. Subsequently, the unknown path loss at a certain location is estimated using the computed function.

Such measurement-based learning approaches can be divided in two large subcategories:

Batch Algorithms assume the complete data to be available before performing the reconstruction algorithm;

Online Algorithms do not require the complete data set to be available in advance. They assume that the data is received sequentially, once per iteration step, and update the mapping function dynamically. The topic of minimization of drive tests has also been considered in the literature. For example, 3 GPP has standardized centralized reporting in UMTS and LTE [3 GPP TS 37.320] for the minimization of Drive Tests (MDT). SUMMARY OF THE INVENTION

The objective of the present invention is to provide a controller, a system and a method for constructing a coverage map of a radio network, wherein the controller, the system and the method overcome one or more of the above-mentioned problems. In particular, an objective of the present invention can include providing an efficient way of estimating an accurate coverage map of a radio network.

A first aspect of the invention provides a controller for constructing a coverage map of a radio network, the controller comprising: a computation unit configured to compute a coverage map based on one or more signal quality measurements of one or more measurement locations;

a completion unit configured to complete the coverage map;

an uncertainty unit configured to determine an uncertainty in the coverage map; and - an identification unit configured to identify, based on the uncertainty in the coverage map, one or more test locations.

The controller of the first aspect can reduce the cost of obtaining a coverage map, while still ensuring high accuracy. This is achieved because the identification unit can identify one or more test locations where further measurements maximize the accuracy of the construction of the coverage map. Furthermore, the controller can accurately construct coverage maps even from coarse and unreliable measurements, and estimate the best areas to acquire further data so as to reconstruct the maps in an optimal way. The computation unit can be configured to compute an initial coverage map based on one or more initially available signal quality measurements, e.g. signal quality measurements that are available from crowdsourcing or previous drive tests.

The radio network can be e.g. a UMTS, LTE or 5G cellular network. The uncertainty unit can be configured to quantify the uncertainty of one or more locations of the coverage map. For example, the uncertainty can be a measure of an error obtained when different map completion methods are compared. The uncertainty in the coverage map can be e.g. the uncertainty in one or more elements of a matrix representing the coverage map.

The identification unit can be configured to identify the one or more test locations based on a given budget for performing measurements at one or more test locations. Test locations can be locations in which further measurements should be collected, e.g. locations which are identified in measurement requests that are sent to one or more user terminals.

In a first implementation of the controller according to the first aspect, the completion unit is configured to represent the coverage map as a matrix with one or more missing entries.

The matrix representation with missing entries allows for computational efficient processing of the coverage map.

In a second implementation of the controller according to the first aspect as such or according to the first implementation form of the first aspect: the computation unit is configured to compute the coverage map based on one or more trusted signal quality measurements and one or more untrusted signal quality measurements; and

- the completion unit is configured to complete the coverage map by assigning a higher importance to the trusted signal quality measurements than to the untrusted signal quality measurements.

The controller of the second implementation has the advantage that measurements from dif- ferent sources can be used for the computation of the coverage map, while still making sure that less reliable measurements (e.g. untrusted signal quality measurements from crowdsourc- ing) do not overwrite accurate measurements from trusted measurements. In a third implementation of the controller according to the first aspect as such or according to any of the preceding implementation forms of the first aspect: the completion unit is configured to obtain a plurality of completed coverage maps using a plurality of map completion algorithms; and

the uncertainty unit is configured to determine the uncertainty in the coverage map by comparing the plurality of coverage maps.

If different map completion algorithms yield different results for a certain map area, this is a clear indication that there is uncertainty about this area. Thus, the controller of the third implementation provides an efficient way of determining areas of high uncertainty.

The plurality of map completion algorithms can include k-nearest neighbours and/or expectation maximization and/or kernel-based methods.

In an example embodiment, the uncertainty unit can be configured to determine an uncertainty measure for an i,j-element of a matrix representing the coverage map, based on a comparison of an i,j-element of a coverage map out of a plurality of alternative coverage maps. In a fourth implementation of the controller according to the first aspect as such or according any of the preceding implementation forms of the first aspect, the uncertainty unit is to determine an uncertainty measure d_t j for an zj-element of the coverage map as:

wherein h is an zj-element of an a-th coverage map and is an zj-element of a b-th coverage map of the plurality of coverage maps.

This represents an efficient way of comparing the outcomes of different map completion algo- rithms.

In a fifth implementation of the controller according to the first aspect as such or according to any of the preceding implementation forms of the first aspect, the identification unit is con- figured to compute one or more test locations as locations corresponding to one or more areas of largest uncertainty in the coverage map.

In a sixth implementation of the controller according to the first aspect as such or according to any of the preceding implementation forms of the first aspect, the completion unit is configured to complete the coverage map based on one or more trusted signal quality measurements by solving a trusted optimization problem which minimizes a rank of a matrix representing the completed coverage map and/or by solving a relaxation of the trusted optimization problem, which minimizes a nuclear norm of the matrix representing the completed coverage map, wherein it is ensured that entries in the matrix representing the completed coverage map that correspond to the one or more trusted signal quality measurements have same values as the one or more trusted signal quality measurements.

Determining a completed coverage map matrix by minimizing a rank of a matrix that comprises the non-missing entries has the advantage that accurate estimates for the missing entries can be obtained. However, solving a rank minimization is an NP-hard problem and thus has high computational requirements. Therefore, it can be preferable to solve a relaxation of the rank minimization problem.

In a preferred embodiment of the sixth implementation, the completion unit can be configured to complete the coverage map based on one or more trusted signal quality measurements by solving a trusted optimization problem which is representable as: min rank(A)

A

s. t. Aij = Py, V 6 Ω and/or the completion unit is configured to complete the coverage map by solving a relaxation of the trusted optimization problem, wherein in particular the relaxation of the trusted optimization problem is representable as: minlMI .

A

s. t. Aij = Pij, V ( j) e Ω where ||Α ||_* stands for a nuclear norm which comprises a sum of absolute values of one or singular values of matrix A, A is a matrix of the completed coverage map, P is a matrix of an incomplete coverage map and Ω is a set of entries corresponding to the one or more trusted signal quality measurements.

In an example embodiment, the completion unit is configured to solve the relaxation of the trusted optimization problem using an algorithm to complete the matrix that represents the coverage map with noiseless entries. In a seventh implementation of the controller according to the first aspect as such or according to any of the preceding implementation forms of the first aspect, the completion unit is configured to solve the relaxation of the trusted optimization problem using Singular Value Thresholding, in particular by iteratively computing:

Y = shrinkiX*-¹ ,τ)

Xⁿ = X"-¹ + S_kP_a{P - Y) wherein shrink{X,x) is a nonlinear function which applies a thresholding rule at a level τ to singular values of an input matrix X, and forces a smallest singular value of the input matrix X to zero; Ρ_Ω is an orthogonal projector onto a span of matrices vanishing outside of Ω, so that zj-element of Ρς (Χ) is equal to if £ Ω and zero otherwise; and {¾} is a sequence of scalar step sizes.

This represents a particularly efficient way of solving the relaxation of the trusted optimiza- tion problem.

In an eighth implementation of the controller according to the first aspect as such or according to any of the preceding implementation forms of the first aspect, the completion unit is configured to complete the coverage map based on the untrusted signal quality measurements by solving an untrusted optimization problem which minimizes a rank of a matrix representing completed coverage map and/or by solving a relaxation of the untrusted optimization problem which minimizes a nuclear norm of the matrix representing the completed coverage map, wherein it is ensured that entries in the matrix representing the completed coverage map that correspond to the one or more trusted signal quality measurements have same or similar as the one or more untrusted signal quality measurements.

In a preferred embodiment of the eighth implementation, the completion unit is configured to complete the coverage map based on the untrusted signal quality measurements by solving an untrusted optimization problem which is representable as: mm rank(A)

A

s. t. II Aij— Pij and/or the completion unit is configured to complete the coverage map by solving a relaxation of the untrusted optimization problem, wherein in particular the relaxation of the untrusted optimization problem is representable as: minlMI.

A

s. 1. Au - P ≤ ε, V (i ) 6 Ω where ||-4 ||_* stands for a nuclear norm which comprises a sum of absolute values of one or singular values of matrix A, A is a matrix of the completed coverage map, P is a matrix of an incomplete coverage map, Ω is a set of entries corresponding to the one or more untrusted signal quality measurements, and e is a predetermined parameter.

A second aspect of the invention refers to a system, comprising: a map completion node comprising a controller according to the first aspect or one of its implementations, configured to determine one or more candidate test locations; arpdanning node comprising a measurement planning unit, configured to determine from the one or more candidate test locations a reduced set of test locations.

A third aspect of the invention refers to a method for constructing a coverage map of a radio network, the method comprising: computing a coverage map based on one or more signal quality measurements of one or more measurement locations; completing the coverage map using a matrix completion algorithm;

determining an uncertainty of the coverage map; and

identifying, based on the uncertainty in the coverage map, one or more test locations. The methods according to the third aspect of the invention can be performed by the controller according to the first aspect of the invention. Further features or implementations of the method according to the third aspect of the invention can perform the functionality of the controller according to the first aspect of the invention and its different implementation forms. The method of the third aspect is preferably based on a batch computation of the coverage map.

In a first implementation of the method of the third aspect, the steps are carried out repeatedly until a budget for signal quality measurements is used up. This has the advantage that the method can integrate into a system where only a limited budget for signal quality measurements is available. The budget may correspond to a fixed number of signal quality measurements or the budget may limit a total cost for measurements, where e.g. measurements at different locations may be assigned different costs. In a second implementation of the method of the third aspect as such or according to the first implementation form of the third aspect, the method further comprises: completing the coverage map using one or more further matrix completion algorithms to obtain a plurality of completed coverage maps; and

- determining the uncertainty in the coverage map by comparing the plurality of coverage maps.

In a third implementation of the method of the third aspect as such or according to any of the preceding implementation forms of the third aspect, the method further comprises: determining one or more points of highest uncertainty in the coverage map; and identifying among the points of highest uncertainty one or more trusted test locations for trusted signal quality measurements and one or more untrusted test locations for untrusted signal quality measurements, wherein a number of the one or more trusted test locations and/or a number of the one or more untrusted test locations are based on a predetermined budget of signal quality measurements, wherein preferably the coverage map is computed based on a set of initial signal quality measurements, and wherein a set of further signal quality measurements correspond to the one or more points of highest uncertainty.

The method may also comprise determining one or more indices which correspond to the one or more points of highest uncertainty in the coverage map. In an example embodiment, the coverage map is computed based on an initial set of (B + signal quality measurements, the number of points of highest uncertainty in the coverage map (1 — ) (B + B'), the number of trusted test locations is (1 — a)B and/or the number of untrusted test locations is (1 — α)Β' , wherein B is a budget for trusted signal quality measurements, B ' is a budget for untrusted signal quality measurements, and 0 < a < 1.

This has the advantage that optimal use can be made of an available budget for different kinds of signal quality measurements.

In embodiments of the invention, the method of the third aspect can also include a step of deciding which users to activate for reporting signal quality measurements, based on a current user position and previously collected measurement data.

A fourth aspect of the invention refers to a computer-readable storage medium storing program code, the program code comprising instructions for carrying out the method of the fourth aspect or one of the implementations of the fourth aspect.

BRIEF DESCRIPTION OF THE DRAWINGS

To illustrate the technical features of embodiments of the present invention more clearly, the accompanying drawings provided for describing the embodiments are introduced briefly in the following. The accompanying drawings in the following description merely show some embodiments of the present invention. Modifications of these embodiments are possible without departing from the scope of the present invention as defined in the claims. FIG. 1 is a block diagram illustrating a controller in accordance with an embodiment of the present invention;

FIG. 2 is a block diagram illustrating a system in accordance with a further embodiment of the present invention;

FIG. 3 is a flow chart of a method for constructing a coverage map in accordance with an embodiment of the present invention;

FIG. 4 is a flow diagram of a method for constructing a coverage map of a radio network in accordance with an embodiment of the present invention;

FIG. 5 shows a performance comparison between a kernel-based approach for computing a coverage map and a matrix completion approach in accordance with an embodiment of the present invention;

FIG. 6 is a flow chart of a method for identifying areas of uncertainty in a coverage map in accordance with a further embodiment of the present invention; FIG. 7 is a block diagram of a system for constructing a coverage map of a radio network in accordance with a further embodiment of the present invention;

FIG. 8 is a block diagram of a matrix completion unit in accordance with a further embodiment of the present invention; and

FIG. 9 is a block diagram of an architecture for integrating a controller for constructing a coverage map in accordance with a further embodiment of the present invention into a standardized Minimization of Drive Test architecture. DETAILED DESCRIPTION OF THE EMBODIMENTS

FIG. 1 shows a controller 100 for constructing a coverage map of a radio network, wherein the controller 100 comprises a computation unit 110, a completion unit 120, an uncertainty unit 130 and an identification unit 140. The computation unit 110 is configured to compute a coverage map based on one or more signal quality measurements of one or more measurement locations. For example, the computation unit 110 can be configured to compute an initial coverage map based on the signal quality measurements that are initially available.

The completion unit 120 is configured to complete the coverage map. For example, the completion unit 120 can be configured to use matrix completion methods to obtain a completed coverage map. The uncertainty unit 130 is configured to determine an uncertainty in the coverage map. For example, the uncertainty unit 130 can be configured to determine the uncertainty by comparing results of different matrix completion algorithms or by comparing results of completed coverage maps that have been completed using different sets of measurement data. The identification unit 140 is configured to identify, based on the uncertainty in the coverage map, one or more test locations. For example, the test locations can correspond to areas of highest uncertainty, as identified by the uncertainty unit 130.

The computation unit 110, completion unit 120, uncertainty unit 130 and identification unit 140 can be realized in the same physical unit, e.g. in the same processor.

The controller 100 can be configured to control other components of the radio network. For example, the controller 100 can be configured to send instructions to other nodes of the network, e.g. instruction these nodes to perform drive tests to acquire signal quality measure- ments for one or more test locations identified by the controller 100. In other embodiments, the controller 100 does not send instructions to other nodes, but merely determines the test locations. These test locations may be retrieved by other nodes of the radio network.

FIG 2 shows a system 200, comprising a map completion node 210 and a planning node 220. The controller 100, which may be e.g. the controller 100 shown in FIG. 1, is configured to determine one or more candidate test locations. The planning node 220 comprises a measurement planning unit 222, configured to determine from the one or more candidate test locations a reduced set of test locations. The completion node 210 and the planning node 220 may be connected by a radio link and/or by a wired connection. They may be located at different layers of the radio network.

The planning node 220 can be configured to connect via radio links 225a, 225b to a first mo- bile terminal 230a and a second mobile terminal 230b. The planning node 220 can be configured to send instructions to the mobile terminals 230a, 230b about drive tests that should be carried out at one or more drive test locations specified by the planning node 220. These drive test locations can be a subset of the test locations that the map completion node 210 has determined and provided to the planning node 220. For example, the planning node 220 can be configured to group the test locations such that a drive effort for the mobile terminals 230a, 230b is reduced. As an illustrative example, the planning node 220 can instruct the first mobile terminal 230a to acquire signal quality measurements at a first set of drive test locations that are located in a first area and the second mobile terminal 230b to acquire signal quality measurements at a second set of drive test locations that are located in a second area. Thus, a cost of the signal quality measurements may be reduced compared to randomly assigning the drive test locations to the mobile terminals 230a, 230b.

FIG. 3 is a flow chart of a method 300 for constructing a coverage map of a radio network. The method comprises a first step 310 of computing 310 a coverage map based on one or more signal quality measurements of one or more measurement locations.

In a second step 320, the coverage map is completed using a matrix completion algorithm. In a third step 330, an uncertainty of the coverage map is determined.

In a fourth step 340, based on the uncertainty in the coverage map, one or more test locations are identified. The method may comprise a further step (not shown in FIG. 3) of instructing one or more mobile terminals of the test locations.

FIG. 4 is a flow diagram of a method 400 for constructing a coverage map of a radio network. In a first step 410, signal quality measurements obtained from drive tests and/or crowdsourc- ing are obtained. Examples of such measurements may include at least one of the following: signal intensity, signal quality, interference, anomalous events, quality of service information, etc. The operator has access to a number of data. The measurements may be from random locations. Preferably, only a subset of the available measurements are used.

In a second step 420, the coverage map is represented as a matrix, comprising the measurements obtained at step 410. This matrix also contains missing entries. The matrix may comprise data from one or more signal quality measurements as obtained in steps 460, 470, as described below.

In a third step 430, the coverage map, e.g. a path loss map, is completed using the available measurements, as stored e.g. in the matrix with missing entries obtained in step 420. For the coverage map completion, methods from the family of the matrix completion techniques can be employed. In a nutshell, the coverage map is represented as a matrix comprising a subset of observed entries and a subset of unobserved ones. Then, matrix completion techniques are employed for the estimation of the unobserved entries, which leads to the reconstruction of the coverage map. Preferably, the data, which is obtained by drive tests, is considered to be reliable, whereas crowdsourced data is assumed to contain some kind of error. To exploit this information and in order to avoid the crowdsourced data degrading the performance of the coverage map reconstruction, we reformulate our reconstruction problem appropriately. To be more specific, instead of requiring that our path loss prediction will be strictly equal to the crowdsourced measurements, we seek for estimates which are "close enough" to the unreliable measurements.

After the (initial) reconstruction of the coverage map, the focus turns in a fourth step 440 to the estimation of the informative areas. Note that some areas, especially in cities can be of highly non-smooth nature. This is the consequence of the existence of large buildings, obsta- cles, tunnels that further attenuate the propagating radio wave. Due to these, e.g. the path loss in such areas exhibits low spatial correlation and this can lead to poor reconstruction effects. Consequently, such areas require targeted drive tests, as discussed above. In order to identify the regions that require additional measurements the following method is employed: After the reconstruction of the coverage map using an initial subset of the available measurements, we reconstruct the path loss using further techniques and algorithms. Specific techniques and algorithms will be discussed below. Next, we compare the outcome of the reconstruction techniques and find areas, which are represented as entries of the matrix, with the largest "disagreement". After the identification of these areas data is collected from the identified areas using drive tests and crowdsourced data. To summarize, in step 470 we make use of adaptive sampling methods to identify uncertain areas and to plan new tests. In a fifth step 450, it is determined if there is sufficient budget available for further drive tests. If so, further drive tests are performed in a sixth step 460 in the areas found in step 440. In particular, in step 460, new drive tests are planned according to identified areas and input measurements, e.g. signal quality measurements, are obtained from the drive tests. If there is no sufficient budget available, in a seventh step 470 input measurements from crowdsourced data are obtained. To this end, minimization of drive test reporting can be activated at User Entities in these areas and/or data can be requested from crowdsourcing applications to learn these entries. After step 460 and/or step 470, the method continues at step 420.

By employing the above-described method, the cost of drive tests for path loss reconstruction can be reduced significantly without performance degradation. In order to quantify the potential benefits we compare the performance of the proposed reconstruction algorithm against a state of the art algorithm, which is concerned with the same problem.

As an example, we consider a path loss map of Berlin, originating from the data of the MOMENTUM project [http://momentum.zib.de/]. To be more specific we reconstruct the path loss within an area of 7500 m x 7500 m. As we have already mentioned, we represent the area as a matrix with partially observed entries and we resort to matrix completion techniques to estimate the missing values. In this example, we consider that the size of each pixel, i.e., entry of the matrix, equals to 50 m and, consequently, the size of the matrix we want to recon- struct to be 150 x 150. The total number of base stations equals to 187 and we take into consideration the base stations with the strongest signal to fill the observed entries of the matrix.

FIG. 5 illustrates the performance of two reconstruction algorithms, a kernel-based reconstruction and a matrix completion approach as outlined above. The horizontal axis to the number of available measurements out of the total, which is 22500 measurements. The vertical axis corresponds to the normalized mean square error, NMSE, which has the definition:

NMSEi := E \H - H \\²

WW where H stands for the path loss matrix comprising all the coefficients andH is the predicted matrix resulting from the reconstruction algorithms. It is worth pointing out that the used in both algorithms are optimized so that they achieve their optimal performance.

From FIG. 5, it becomes clear that the presented reconstruction technique using matrix completion can significantly outperform the reconstruction using the kernel based algorithm. Note that with our method the benefit is approximately 4.5 dB in the 7500 measurement case. On top of that, apart from the NMSE performance plots, the reconstruction technique used in our invention is computationally efficient, as the operation time for the 5000 measurement scenario is to 4 s approximately, whereas for the state of the art technique the operation time was approximately 30 s.

The reasoning behind this improved performance compared to the kernel based reconstruction algorithm, can be summarized as follows: The latter method attempts to fit a nonlinear function between the geographical location and the power gain. A drawback of this approach is that it can lead to overfitting, i.e., producing an excessively complex function which may describe random errors or noise instead of the underlying relationship. On the contrary, the matrix reconstruction approach can exploit spatial correlation and smooth patterns. As can be seen by the results of FIG. 5, this leads to lower NMSE values. This is achieved by combining erroneous measurements with more reliable ones and by estimating the best areas to acquire further data so as to reconstruct the maps in an optimal way.

In the following, we consider a setup in which the goal is the path loss reconstruction of a given area, e.g., a large metropolitan area. The area is represented as a matrix, the entries of which correspond to the path loss or a similar measure (such as RSSI, SNR, SINR). We further assume that measurements come from drive tests and are considered reliable. The goal is the estimation of the unobserved measures in order to complete the matrix. The problem of estimating the unobserved entries of the matrix, i.e., the path loss measurements corresponding to areas in which a drive test has not taken place can be described as follows: Compute a matrix A such that Ay = Py and which will be as close as possible to the original matrix, where with Py we denote the observed path loss entries. A way to do so is to solve the following problem: min rank(A)

A

s. t. Aij = Py, V i,j 6 Ω₁

where Ω denotes the set of observed entries. The physical reasoning of the above optimization can be summarized as follows. Due to the regular propagation of a radio wave in un- environments, path loss maps in such areas exhibit spatial correlation and smooth patterns. Here, the above minimization produces low rank matrices and, thus, provides a good estimate of the missing entries.

The rank minimization problem described previously cannot be solved efficiently, since it is NP-hard. However, in the context of the matrix completion task, this problem can be relaxed and solved via convex optimization. To be more specific, here we solve the convex relaxation of the initial problem: minlMI .

A

s. t. Aij = Pij, \ i,j 6 Ω where ||-4 ||_* stands for the nuclear norm, that is the sum of the absolute values of the singular values of the matrix.

Several techniques have been proposed to solve the aforementioned optimization. A fast and computational efficient technique is the Singular Value Thresholding. This algorithm is iterative and solves the above convex relaxation of the initial problem using the following iterative procedure, for an arbitrary initial matrix:

Y = shrinkiX⁷¹-¹ , τ)

where the function shrinkQ is a nonlinear function which applies a thresholding rule at level τ to the singular values of the input matrix, and forces to zero the smallest of them. The thresholding procedure keeps unaffected the singular values with absolute values larger than r, whereas forces the rest to zero. In that sense, it produces a matrix of low rank. Tuning the parameter τ depends on several factors and one can resort to cross-validation techniques to find the value of τ which leads to the best results. Intuitively, the smaller the τ, the larger the number of singular values that are be set to zero and, consequently, the lower the final rank of the matrix will be.

In the following, we focus on the scenario where apart from the reliable measurements coming from drive tests, we have at our disposal data collected by crowdsourcing in order to increase the number of available data. As it has been already mentioned, these measurements are noisy and should be treated in a different fashion so as not to harm the quality and the reliability of the reconstructed coverage map.

The reasoning will remain the same as in the previous example, in which we employed the drive test data, albeit here we slightly reformulate the problem. In fact, we formulate the new problem as follows: mm rank(A)

A

s. t. II Aij— Pij

Notice that, instead of requiring strict equality of our path loss prediction to the crowdsourced measurement, we aim at finding an estimate that is "close enough", which is determined by the parameter ε, to the unreliable measurements. Similarly to the optimization shown above for the drive test data, this is an NP-hard problem, and in order to solve it efficiently we can resort to the following relaxation: min l l^ l

A

s. 1. Au - Pij \\≤ ε, ν i,j 6 Ω

This optimization can be solved by using a technique referred to as Stable Matrix Completion. In particular, the aforementioned problem is solved using Semi Definite Programming Techniques, and can be solved efficiently in terms of computational complexity. The threshold parameter ε has been employed in the Stable Matrix Completion algorithm, which discusses the noisy matrix completion problem. The approach followed the idea that larger uncertainty regarding the measurements should lead to a larger value of this parameter. Since the measurements come from multiple sources with different certainty, a larger ε would be typically chosen for crowdsourcing data than for data from 3 GPP standardized feedback, while the smallest ε (which can be even equal to zero) would be applied to data from professional drive tests. A possible way of choosing the precise value of ε is via cross-validation. Another way to choose this parameter is with the aid of our proposed signaling protocol. Each user transmits information to the controller about the uncertainty of the measurement.

A specific example strategy for tuning ε using this information is summarized in the following. The controller receives the measurements of the users. Depending on the level of accuracy, which is reported by the users at a global level, the (noisy) optimization problem is solved by applying one of three different values of ε: a) 8Mgh, which will be large if the uncertainty of the measurements is large;

b) 8normai, which will be smaller than 8high and will be employed if the accuracy is normal; and

c) 8iow which will take a small value if the accuracy is high.

The exact values of the thresholds can be determined for example via cross validation.

FIG. 6 is a flow chart diagram which illustrates the identification of areas of uncertainty, e.g. high noise areas. We describe an example on how informative areas are identified via adap- tive sampling, in which further measurements should be collected. We have an initial budget of B points of the map from drive tests and B' points of the map from crowdsourcing data.

The steps can be summarized as follows: In a first step 610, we reconstruct the path loss map using α*(Β+Β'), 0<α<1 measurements. This implies that we perform an initial reconstruction using a subset of our data. The reconstruction can take place for example using the matrix completion techniques described previously. We reconstruct the path loss using the same measurements as in the previous step, by employing further techniques. Examples of such techniques include: K-Nearest Neighbors Expectation Maximization.

In a second step 620, the outcome of the reconstruction techniques (obtained in step 610) is compared and in a third step 630, the k points, wherein e.g. k=(l-a) *(B+B'), with the largest "disagreement" are found. Let us describe an example technique of computing this disagreement. Assume that we use three algorithms and the estimated entries are denoted by:

where the subscript indices denote the matrix entry and the superscript corresponds to each algorithm. We compute for each entry the disagreement metric as follows:

Afterwards, we stack these entries in a vector and we sort them in a descending order. The indices which correspond to the first (1-a) *(B+B') have the largest disagreement. In a fourth step 640, it is determined if there is available budget. If so, in step 650 we acquire further points, e.g. (l-a)*B points, which correspond to our available budget, from the identified areas using drive tests and we obtain (1-α)*Β' points from crowdsourced data. Step 650 can involve activating MDT reporting at UEs in these areas. Subsequently, the method continues with step 610.

If in step 640 it is determined that there is no available budget for drive tests, the method ends in step 660.

Finally, the matrix reconstruction procedure is performed again. This can be repeated until the budget for drive test is used up or until measurements have been obtained for all entries of the coverage map matrix.

Regarding the choice of parameters for this procedure: the parameters B and B' denote the available budget one has for drive tests and for crowdsourcing measurements, respectively. The first parameter, thus, depends on the available budget of the operator and the second on the cost of feedback (overhead, energy spent) and the number of users providing it;

- regarding the parameter a. Assume that (Β+Β') data points are available. A possible strategy is to use all of them for the matrix reconstruction. However, in order to identify the areas with the largest disagreement (as it will be discussed later on) a fraction of them will be used to that direction. This is the role of the parameter a. A specific choice of this parameter depends on several factors, such as the initial budget, the quality of crowdsourcing data and the area itself. So, cross validation techniques provide a good strategy to find the value of this parameter.

FIG. 7 is a block diagram of a system 700 for constructing a coverage map of a radio network. The system 700 comprises database for radio data 710, a map completion node 720, a plan- ning and measurement node 730, and a user equipment (UE) 740.

The map completion node 720 comprises a matrix representation 722 of incomplete data. This matrix representation 722 stores radio data from the database of radio data 710. The matrix representation of incomplete data is provided as input P to a matrix completion unit 724. Fur- ther inputs of the matrix completion unit 724 may include a data type and a parameter. The matrix completion node 724 is configured to provide a matrix estimate A^A to an area identification unit 726. The area identification unit 726 determines a set of locations of interest (LOI) which it provides to the planning and measurement node 730. The planning and measurement node 730 comprises a drive test planning unit 732 and a data collection unit 734. The drive test planning unit 732 receives as input the set of locations of interest, which may comprise drive test locations, and a budget /?. From this, it determines a subset of locations of interest which it provides to the data collection unit 734. The data collection unit 734 generates one or more measurement requests which it sends to the user equipment 740.

The user equipment 740 comprises a user equipment application 742, a wireless modem 744, and a location source 746. The wireless modem 744 provides one or more radio signal quality measurements to the UE application 742. The location source 746 provides a current position the UE application 742.

In the following, the operation of the units of the system 700 shall be described in more detail. Assuming that the system is embodied at the application layer, the process starts based on radio data available from previous measurements, stored in the database 710. This data is used as an input to the Map Completion Node 720, which can be a dedicated server or software program running on an already existing server in the operator's core network. Initially, a matrix representation function, in the matrix representation unit 722, converts the incomplete data into a matrix, the components of which are entries of the previous database 710.

This matrix is used as an input to the matrix completion unit 724 which also takes as an input the specific type of data (reliable/unreliable), which will be processed, and the parameter ε. Its detailed functionality is illustrated in FIG. 8 below. According to the problem specification (reliable data/unreliable data), proper solvers are chosen and the matrix is reconstructed in the matrix completion unit 724. The output of this block is a number of completed matrices A^A, which are inserted to the area identification function. The output of the latter is a set of locations of interest (LOI). These are the input of the drive test planning unit 732 together with the available budget β. The output is a subset of LOIs, which in turn are employed in the Data Collection entity 734. This interacts with the UE 740, giving measurement request and receiving a measurement report.

To be more specific, the wireless modem 744 provides the Radio Measurement to a software application running at the UE 740 and the Location Source 746 provides the current position to that application 742. The UE application 742 sends this data to the data collection function that can be part of the Planning and Measurement Node 730 or run on a dedicated server. After being collected, the data collection unit sends the new set of data to the data set.

FIG. 8 is a detailed block diagram of a matrix completion unit 800. The matrix completion 800 comprises a problem specification unit 810, a solver selection unit 820 and a set of 830, 832, 834. The solvers include semi-definite programming 830 and singular value decomposition 834. The solver selection unit 820 is configured to select a solver based on the problem specification specified in the problem specification unit 810. The problem specification unit 810 can receive as input P a matrix representation of incomplete data and/or a budget specification β. The problem specification can include e.g. an objective, constraints (such as the specified budget), and information about the data (e.g. where they originate, whether they are reliable or not). FIG. 9 is a block diagram of an architecture 900 for integrating a controller for constructing a coverage map into the Minimization of Drive Test (MDT) architecture according to 3 GPP TS 36.331.

The architecture 900 comprises an operation and maintenance center 910, a core network 920 and a radio access network 930.

The operation and maintenance center 910 comprises a database of radio data 912 and a map completion node, MCN, 914. The MCN 914 operates close to the database 912 while a planning and measurement node 922 should be added to the core network 920. The core network 920 further comprises an MDT server 924 which operates according to TS 36.331. The MDT server can also be configured to comprise the planning and measurement node functionality without violating the standard.

Since the MDT server 924 essentially specifies the RAN signaling, the previously described operation in the operation and maintenance center 910 and core network 920 still applies. The radio data are inserted as an input to the map completion node 914, as described previously, e.g. with reference to FIG. 7. Its output, comprising the locations of interest, is the input of the planning and measurement node 922, which produces a subset of them. The MDT server 924 is configured to use these locations of interest, which comprise test drive locations, to define its configuration parameters that are sent to a respective base station 932 in the radio access network 930. While this follows the standardized signaling procedure, our invention can heavily optimize and reduce the chosen locations of interest, which highly reduces measurement effort or (with a given budget) improves measurement quality.

Upon reception of these MDT configuration parameters, the base station 932 activates the functionality in a user equipment, UE, 934 by sending the MDT configuration parameters to UE 934. After the UE 934 performs relevant measurements, the UE 934 sends an MDT Acknowledgment to the base station 932 and reports the measurement results directly to the server 924. Finally, the MDT server 924 sends the radio measurements and locations to the database of radio data 912.

A preferred implementation of a system for coverage map construction employs a number of communication signals that are exchanged between the controller, the base stations, and the user equipment. The exchange of such data involves communication between the users and the central controller gathering the measurements and performing the reconstruction.

In particular, signals can be exchanged between three entities, (1) the controller, (2) the Base Stations (BSs), and (3) the User Equipments (UEs).

The signals can serve three main purposes: the Controller sends message to BSs of areas where drive tests should be conducted; the BSs send control messages to user indicated by the controller;

the UEs respond to the BSs which transmit the information back to the controller.

Embodiments of the exchange signals and messages can include: 1. One or more Information Request Control Messages, which can include: a) a location at which we want measurements;

b) a precision of requested measurements (do not report if user did not stay long enough to acquire good enough measurements, lower RSSI threshold, etc);

c) user ids of users that should or should not report; and/or

d) an expiration timer.

2 One or more Information Transfer Control Messages which can include: a) a user id, e.g., IMSI or phone number;

b) a device type, e.g., IMEI, model number, or an index in a given model table;

c) a user location, e.g., typically latitude, longitude, altitude in WGS84;

d) signal quality, e.g., RSSI in dBm or ASU;

e) a velocity and direction of motion; and/or f) an associated uncertainties, e.g., confidence levels and similar error notions.

Furthermore, signaling steps of a method may include: 1. the controller sends messages to BSs of areas where drive tests should be conducted, e.g., by HTTP GET requests;

2. the BSs send control messages to users indicated by the controller in the area, e.g., by HTTP responses. The proposed signaling differs from classic crowdsourcing. The presented controller and method aim at reducing signaling overhead, therefore the central controller demands for information only from specific areas. Furthermore, the presented controller requests the measurement from the UE, whereas in classic crowdsourcing the UE pushes the measurement. The presented method can leverage both drive tests measurements and crowdsourced data. The algorithm can adaptively select the area to complete within a radio map that is only partially given. As a consequence, the presented method provides an efficient reconstruction method for radio maps, from only a few measurements that may have diverse levels of accuracy.

To summarize, embodiments of the present invention relate to an adaptive method for planning where to conduct additional drive tests to complete an initial coverage map from incomplete and unreliable data from multiple sources. Embodiments can assume that we have access to an initial number of measurements. Based on this initial data we perform reconstruc- tion of the coverage map as well as identification of areas where an uncertainty is high and thus further measurements would be most informative. The term informative denotes the areas, from which, if we had access to data, then we could reconstruct the path loss matrix more efficiently. In the sequel and after the identification of the informative areas, embodiments of the invention may require further data (coming from drive tests and/or crowdsourcing) targeted from them. It is worth pointing out that in the first step of reconstructing the path loss map, preferably not the entire available budget is used, i.e., the total number of available measurements, as we want to save some of it to perform the drive tests in the "informative areas". Further embodiments of the invention relate to a method of integrating unreliable data (e.g., obtained from crowdsourcing) into the reconstruction process of a coverage map. Employing blindly the data coming from crowdsourcing may lead to degradation of the reconstruction performance, as this data may be inaccurate to some extent. Embodiments of the invention treat the crowdsourced data in a different fashion so as not to harm the quality and the reliability of the reconstructed coverage map.

Steps of the presented method for construction of a coverage map may include: a) representation of the coverage map as matrix with missing entries;

b) use of matrix reconstruction techniques for estimating the missing entries;

c) exploitation of the data coming from crowdsourcing taking into consideration that some of them can be unreliable;

d) use of adaptive sampling methods to identify informative areas and plan new tests.

The foregoing descriptions are only implementation manners of the present invention, the scope of the present invention is not limited to this. Any variations or replacements can be easily made through person skilled in the art. Therefore, the protection scope of the present invention should be subject to the protection scope of the attached claims.

Claims

A controller (100; 210, 220; 720, 730) for constructing a coverage map of a radio network, the controller comprising:

a computation unit (110; 722) configured to compute a coverage map based on one or more signal quality measurements of one or more measurement locations;

a completion unit (120; 724) configured to complete the coverage map;

an uncertainty unit (130; 726) configured to determine an uncertainty in the coverage map; and

an identification unit (140; 732) configured to identify, based on the uncertainty in the coverage map, one or more test locations.

The controller (100; 210, 220; 720, 730) of claim 1, wherein the completion unit (120; 724) is configured to represent the coverage map as a matrix with one or more missing entries.

The controller (100; 210, 220; 720, 730) of one of the previous claims, wherein

the computation unit (110; 722) is configured to compute the coverage map based on one or more trusted signal quality measurements and one or more un- trusted signal quality measurements; and

the completion unit (120; 724) is configured to complete the coverage map by assigning a higher importance to the trusted signal quality measurements than to the untrusted signal quality measurements.

The controller (100; 210, 220; 720, 730) of one of the previous claims, wherein

the completion unit (120; 724) is configured to obtain a plurality of completed coverage maps using a plurality of map completion algorithms; and

the uncertainty unit (130; 726) is configured to determine the uncertainty in the coverage map by comparing the plurality of coverage maps.

The controller (100; 210, 220; 720, 730) of claim 4, wherein the uncertainty unit (130; 726) is configured to determine an uncertainty measure for an zj-element of the coverage map as: d_i = Y o - h Y

a<b wherein h is an zj-element of an a-th coverage map and is an zj-element of a b- b-th coverage map of the plurality of coverage maps.

The controller (100; 210, 220; 720, 730) of one of the previous claims, wherein the identification unit (140) is configured to compute one or more test locations as locations corresponding to one or more areas of largest uncertainty in the coverage map.

The controller (100; 210, 220; 720, 730) of one of the previous claims, wherein the completion unit (120; 724) is configured to complete the coverage map based on one or more trusted signal quality measurements by solving a trusted optimization problem which minimizes a rank of a matrix representing the completed coverage map and/or by solving relaxation of the trusted optimization problem, which minimizes a nuclear norm of the matrix representing the completed coverage map,

wherein it is ensured that entries in the matrix representing the completed coverage map that correspond to the one or more trusted signal quality measurements have same values as the one or more trusted signal quality measurements.

The controller (100; 210, 220; 720, 730) of claim 7, wherein the completion unit (120; 724) is configured to solve the relaxation of the trusted optimization problem using Singular Value Thresholding, in particular by iteratively computing:

Y = shrinkiX*-¹ , τ)

Xⁿ = X¹¹-¹ + S_kPn(P - Y) wherein shrink{X,x) is a nonlinear function which applies a thresholding rule at a level to singular values of an input matrix X, and forces a smallest singular value of the matrix X to zero; Ρ_Ω is an orthogonal projector onto a span of matrices vanishing outside of Ω, so that an zj-element of P_Q, (X) is equal to Xij if £ Ω and zero and {¾} is a sequence of scalar step sizes.

9. The controller (100; 210, 220; 720, 730) of one of the previous claims, wherein the completion unit (120; 724) is configured to complete the coverage map based on the untrusted signal quality measurements by solving an untrusted optimization problem which minimizes a rank of a matrix representing the completed coverage map and/or by solving a relaxation of the untrusted optimization problem which minimizes a nuclear norm of the matrix representing the completed coverage map,

wherein it is ensured that entries in the matrix representing the completed coverage map that correspond to the one or more trusted signal quality measurements have same or similar values as the one or more untrusted signal quality measurements.

10. A system (200), comprising:

a map completion node (210) comprising a controller (100; 210, 220; 720, 730) according to one of the previous claims, configured to determine one or more candidate test locations; and

a planning node (220) comprising a measurement planning unit (222), configured to determine from the one or more candidate test locations a reduced set of test locations.

11. A method (300; 400) for constructing a coverage map of a radio network, the method comprising:

computing (310; 420) a coverage map based on one or more signal quality measurements of one or more measurement locations;

completing (320; 430) the coverage map using a matrix completion algorithm; determining (330; 440) an uncertainty of the coverage map; and identifying (340; 440), based on the uncertainty in the coverage map, one or more test locations.

12. The method (300; 400) of claim 11, wherein the steps are carried out repeatedly until a budget for signal quality measurements is used up.

13. The method (300; 400) of claim 11 or 12, and wherein the method further comprises:

completing the coverage map using one or more further matrix completion algorithms to obtain a plurality of completed coverage maps; and determining the uncertainty in the coverage map by comparing the plurality of coverage maps.

14. The method (300; 400) of one of claims 11 to 13, wherein the method further comprises:

determining one or more points of highest uncertainty in the coverage map; and identifying among the points of highest uncertainty one or more trusted test locations for trusted signal quality measurements and one or more untrusted test locations for untrusted signal quality measurements,

wherein a number of the one or more trusted test locations and/or a number of the one or more untrusted test locations are based on a predetermined budget of signal quality measurements,

wherein preferably the coverage map is computed based on a set of initial signal quality measurements, and wherein a set of further signal quality measurements correspond to the one or more points of highest uncertainty.

15. A computer-readable storage medium, storing program code, the program code comprising instructions for carrying out the method of one of claims 11 to 14.