Method, computer program, device and radio frequency system for estimating interference on a radio frequency system using a set of channels

Abstract

The present invention relates to a method for estimating interference on a set radio frequency system using a set of channels (CHi), the interference being caused by interference sources of an interference system using a set of transmission bands (TBi), each of the transmission bands extending over a plurality of consecutive channels of the set of channels. The method comprises: - determining a set of all possible configurations of occupancy or non-occupancy of the set of transmission bands defined as a set of possible vectors, - constructing a matrix based on the superposition of all possible vectors, - obtaining measurements of the occupancy of at least a part of the set of channels at corresponding instants, - calculating probabilities using a channel transfer function to determine an estimated activity rate for each transmission band based on the measurements, the estimated activity rate corresponding to the occupancy rate of the transmission band by the interference source within the given observation time window, and the probability calculation comprising an iterative solution of a non-linear optimization problem with constraints derived from Gibbs' inequality.

Description

Technical Field

[0001] The present invention relates to a system that can use a given radio frequency channel (e.g., frequency hopping in the ISM common band (ISM stands for "Industrial, Scientific and Medical radio frequency band")) and may thus be subject to interference from other devices (e.g., WiFi devices). Background Art

[0002] Examples of such systems that may be affected by interference sources can be, for example, the computer communication devices of autonomous vehicles, or, as another example, communication-based train control devices with radio technology communication devices.

[0003] The interference problem can cause serious problems in these autonomous vehicle applications.

[0004] Cognitive radio-based interference avoidance techniques can be further developed. For example, during each vehicle journey, measurements of adjacent interference can be fed back from the vehicle to the server together with the vehicle position. At the server, a database can be established with a statistical function to collect measurements belonging to clusters of positions and frequency channels (commonly used for regular vehicle routes). Examples of this type of implementation are described, for example, in documents WO-2017 / 122548 and WO-2017 / 122549.

[0005] This knowledge can thus be used to perform radio resource management and radio system monitoring. In the case of vehicle radio monitoring, identification methods can typically be implemented to decide whether a WiFi device is responsible for problems occurring at the radio level. However, a disadvantage of this method is that a large number of measurements need to be fed into the database. Signal analysis and identification are well-researched topics. Usually, devices are specifically designed to provide optimal detection performance, but in the context of the invention below, the communication system may be limited by its own radio design.

[0006] For an example of an implementation carried out by the applicant for a system for communication-based train control (CBTC), such a system uses the ISM frequency band to establish a connection between the train and the roadside. However, this (common) frequency band is also widely used by many other devices (WiFi, Bluetooth, etc.) that may interfere with the CBTC signal. In document EP-18305112, a method for identifying the activity rate of interference in each WiFi channel is proposed. This information is necessary in the feedback link to help the server collect sufficient knowledge to perform efficient resource management or radio condition monitoring.

[0007] More precisely, in the case of power less than that of the WiFi signal in the measurement frequency band, there is no known method other than the method proposed in document EP-18305112 for determining the statistical occupancy rate of one or several interference sources in some a priori unknown transmission frequency bands within the entire Wifi transmission frequency band. One difficulty is the identification of interference sources, as these interference sources may have an impact and be active in other transmission frequency bands as well.

[0008] Figure 5 shows the problem solved in document EP-18305112. The radio frequency system provides a set of channels (from 1 to 16 in the Figure 5 example shown). The index of the channel is labeled CHi. For example, each of these channels may have a bandwidth of 5 MHz.

[0009] The interfering radio frequency system (e.g., a Wifi system) may have one or several interference sources, each of which is liable to be active on a transmission frequency band composed of several consecutive channels. In the Figure 5 example, the interfering system may have 1 to 13 transmission frequency bands, and the transmission frequency bands have an index labeled "TBi" in the Figure 5 figure.

[0010] More specifically, in the Figure 5 example, the bandwidth of each transmission frequency band TBi is 20 MHz, and:

[0011] - TB1 extends over four consecutive channels 1 to 4,

[0012] - TB2 extends over four consecutive channels 2 to 5,

[0013] - TB3 extends over four consecutive channels 3 to 6,

[0014] - and so on

[0015] - TB13 extends over four consecutive channels 13, 14, 15, 16.

[0016] It is worth noting here that the index TBi has the same value as the first channel CHi of the consecutive channels. Therefore, in the following description, this index is simply labeled "i" and is assigned to the interference source index (from 1 to I, where I = 13 in the Figure 5 example).

[0017] It is also worth noting here that two interference sources may be active, for example, on two consecutive transmission frequency bands that overlap on three channels. In addition, the interference sources may be active from time to time rather than permanently.

[0018] Then, the problem solved in document EP-18305112 is to identify on which transmission frequency band an interfering source is ultimately active within a given time window frame, and generally to give the activity rate of the interfering source in the corresponding transmission frequency band within this time window.

[0019] To estimate the activity rate of interference in each WiFi channel, document EP-18305112 is based on knowledge of the interference structure generated by the CSMA / CA protocol when no contention occurs. Then, an expectation maximization algorithm is executed to solve the estimation problem. The maximization step of this algorithm includes calculating the solution of an underdetermined system. This problem is solved by using a simple approximation. However, in some cases, this approximation may lead to suboptimality.

[0020] Generally, improvements to the solution proposed in document EP-18305112 are sought to achieve faster convergence and higher accuracy in the estimation of the activity rate.

[0021] In addition, document EP-18305112 proposes to establish a set Ω of all N possible configurations of the occupancy or non-occupancy of transmission frequency bands that satisfy a non-overlap condition. This non-overlap condition corresponds to the fact that in a set of I possible interfering sources, only one interfering source i can be active at the same time k on each channel, and this channel, together with consecutive channels, forms a transmission frequency band i as Figure 5 shown.

[0022] The set Ω of all N possible configurations is as Figure 2 shown, and is further detailed below because it is still relevant to possible embodiments of the present invention.

[0023] This non-overlap condition is a constraint added to solve the problem in a simpler way using the method proposed in document EP-18305112.

[0024] However, in very rare but possible cases, overlap may occur in a CBTC type of system. In fact, in the case of a so-called "hidden node", such a node may be located between two interfering sources and thus "hear" two overlapping interfering sources. Summary of the Invention

[0025] The present invention aims to improve this situation.

[0026] To this end, the present invention proposes a method for estimating interference on a radio frequency system using a set of channels, said interference being caused by interfering sources of an interference system using a set of transmission frequency bands, each of said transmission frequency bands extending over a plurality of consecutive channels of said set of channels.

[0027] The method includes:

[0028] - Determine the set of all N possible configurations of occupied or unoccupied of the set of the transmission bands defined as the possible vector Z k = [Z 1,k , …, Z i,k , … Z I,k , the set Ω

[0029] - Construct the matrix A according to the stack of all possible vectors Z k

[0030] - Obtain the measurements X1, …, X k , …, X K of the occupancy of at least a part of the set of the channels at the corresponding moment k, 0 < k ≤ K, where K defines the given observation time window

[0031] - Calculate the probability defined as , where P(X|Z) defines the channel transition function, to determine the estimated activity rate τ for each transmission band based on the measurements X1, …, X k , …, X K , and the estimated activity rate τ corresponds to the occupancy rate of the interference source for the transmission band i within the given observation time window

[0032] More specifically, the probability calculation iteratively includes in each iteration t:

[0033] * Solve the non - linear optimization problem with the constraints defined as follows:

[0034] Maximize

[0035] Subject to

[0036] Aθ = τ (t)

[0037]

[0038] where the vector τ (t) is the column of the activity rate in the corresponding transmission band i estimated at the iteration index t, and the vector θ is the hidden variable

[0039] * Calculate the vector as the hidden variable, for example:

[0040]

[0041] * And update the vector of the activity rate at the next iteration index t + 1 to

[0042]

[0043] ​More specifically, the constraint (1) expressed above can be derived from the Gibbs inequality statement regarding the mathematical entropy of a discrete probability distribution (i.e., the information entropy is less than or equal to its cross-entropy with any other distribution, as applied in the following detailed description).

[0044] In a non-limiting example of an embodiment, the possible vectors Z of the set Ω k = [Z 1，k , …, Z i，k , … Z I，k satisfy the non-overlapping condition of the radio frequency system at time k, where the non-overlapping condition corresponds to the fact that in a set of I possible interference sources, only one interference source i can be active at the same time k on each channel in the set of channels, and the consecutive channels form a transmission band i.

[0045] In another example of an embodiment, the non-overlapping condition can be derived from the multiple access implementation scheme (CSMA / CA or CSMA / CD) performed by the radio frequency system, where the multiple access implementation scheme defines communication time slots and the measurement X k is acquired at each time slot k.

[0046] However, in a general embodiment where the above non-overlapping condition may not apply, the set Ω of possible vectors can include up to 2 I elements (I is the total number of transmission bands considered), as detailed in the following description.

[0047] In an embodiment where the communication system implements frequency hopping on the channels, the steps of obtaining the measurements X1, …, X k , …, X K are performed according to the frequency hopping implementation scheme.

[0048] In a possible embodiment described in detail below as an example, the number of consecutive channels forming the transmission band is four, and the total number of channels in the set of channels is sixteen.

[0049] In this example of the embodiment, each of the channels is spread over 5 MHz, while each of the transmission bands is spread over 20 MHz using a spread spectrum technology implementation scheme.

[0050] This example of the embodiment generally corresponds to an implementation scheme where the radio frequency system corresponds to an ISM-type communication system while the interference system corresponds to a Wifi-type communication system.

[0051] The method may further include a step of selecting the communication of at least one channel in the set of channels, where the selected channel is within the transmission band with the lowest estimated activity rate τ.

[0052] The object of the present invention also lies in a computer program, which comprises instructions that, when run by a processor, are used to execute the above method. The following detailed description Figure 3 shows an example of the general algorithm of such a computer program.

[0053] The object of the present invention also lies in a device for estimating interference on a radio frequency system using a set of channels, the interference being caused by interference sources of an interference system using a set of transmission bands, each of the transmission bands extending over a plurality of consecutive channels of the set of channels. More specifically, the device comprises a processing circuit for executing the above method, as shown in the example Figure 4 below.

[0054] The object of the present invention also lies in a radio frequency communication system, which comprises a device for estimating interference liable to occur on channels to be used by the radio frequency communication system.

[0055] The present invention is shown by way of example and not limitation in the accompanying drawings other than the above Figure 5 ones. BRIEF DESCRIPTION OF THE DRAWINGS

[0056] Figure 1 Figure 1 Schematically shows the frequency hopping communication schemes DL, UL implemented by a radio frequency communication system according to the present invention compared to the noise scheme WINT due to interference sources in a subset of consecutive channels (here four channels), the subset being constant over time (over at least several consecutive time slots) and defining the transmission band of the interference system.

[0057] Figure 2 Figure 2 Shows all N possible configurations of the set Ω of occupied or unoccupied interference sources of channels in the entire set of channels.

[0058] Figure 3 Figure 3 Shows an example of the main steps of the method according to the present invention.

[0059] Figure 4 Figure 4 Schematically shows an example of the processing circuit of the device according to the present invention.

[0060] Figure 5 Figure 5 Schematically shows an example of a radio frequency system providing a set of channels in document EP - 18305112. DETAILED DESCRIPTION OF THE INVENTION

[0061] ​​​​​​​​​​The problem solved by the present invention is to classify interference (WiFi or non-WiFi) based on measurements performed by a radio system. In the example disclosed below, the radio frequency system involved has the following characteristics:

[0062] · Hopping frequency at a rate of approximately 4 ms on channels in the 5 MHz frequency band

[0063] · Packets of 1.5 ms

[0064] · In each time slot of 4 ms, CSMA / CA or CSMA / CD multiple access (two transmission attempts)

[0065] · Collecting measurements in each time slot

[0066] The characteristics of the WiFi system are

[0067] · Spread spectrum technology on a 20 MHz transmission frequency band

[0068] · WiFi PHY layer packets (including acknowledgment ACK) typically of 200 μs

[0069] · Transmission frame duration (transport layer packets) averaging approximately 100 ms

[0070] · CSMA / CA multiple access

[0071] Therefore, in this example of the implementation, it is assumed that each current transmission frequency band of the interfering system is considered with observations on the 5 MHz frequency band in 16 channels of the radio system. Each current transmission frequency band is spread over a total of 20 MHz according to the WiFi system characteristics, which here corresponds to four consecutive channels of the radio system. Of course, the numbers of 16 channels and 4 consecutive channels are examples given here and variations are allowed. In addition, the transmission frequency bands (hereinafter also referred to as "W channels") can overlap, resulting in a total of 13 transmission frequency bands. By indexing the 5 MHz wide channels from 1 to 16, the transmission frequency bands are defined by the aggregation of channels with the following indices:

[0072] [1 2 3 4], [2 3 4 5], …, [12 13 14 15], [13 14 15 16].

[0073] The system is able to detect adjacent interference sources and attempt another connection in case of collision detection. It is worth adding that these interference sources are generally not affected by the current radio systems that usually use directional antennas at the transmitter. The interference sources are not considered to be active according to the hopping frequency scheme, but are active on a fixed subset of several channels, as commented below Figure 1As shown. However, in the embodiments proposed thereafter (even if the present invention can be implemented without the so-called "non-overlap condition"), as a result of the CSMA / CA multiple access scheme, it is still considered that interfering sources generally comply with the non-overlap condition (according to which two interfering sources cannot overlap on the same channel simultaneously). These observations explain the following general wording:

[0074] - Each interfering source is prone to being active on a transmission frequency band formed by multiple consecutive channels of the entire channel set (especially at the corresponding moment k), and

[0075] - Only one interfering source can be active on each transmission frequency band at the same time k,

[0076] - And for example, when two transmission frequency bands (with a width of 20 MHz) overlap on one or several channels (from one channel to three channels, each channel with a width of 5 MHz), the additional condition is that only one interfering source can be active on each channel at the same time k.

[0077] In order to distinguish the transmission frequency band of an interference system (such as WiFi) from the channels of a communication system (such as ISM) hereinafter, the transmission frequency band is hereinafter referred to as the "W channel", while the "channel" remains the channel of the communication system.

[0078] Figure 1 A diagram showing the coexistence of radio system packets (uplink UL and downlink DL) and WiFi interference (WINT) is shown, where the frequency / time usage of the ISM band is shown. In the WiFi interference area, the time occupancy is segmented into small PHY WiFi packets using the collision avoidance mechanism. Approximately half of the frequency hopping is used for the downlink, while the other half is used for the uplink. Therefore, by configuring a given observation time window, the number of interference measurements on each channel may be different. Some channels may not even have any measurement opportunities within this time window.

[0079] Hereinafter, the following symbols are used:

[0080] · k is the moment, that is, one hop of the current radio system. More precisely, a time window of K moments is considered.

[0081] · X k is the interference observation on one channel at moment k in this example of the embodiment: 0 < k ≤ K. Each X k can correspond to the power measurement or signal-to-noise ratio measured in each channel, or correspond to the simulation according to a given scheme.

[0082] · f k is the index of the frequency channel measured at moment k.

[0083] ·Z i,k is a random variable that indicates whether interference is active on the i-th W-channel at time k (in I).

[0084] - In the embodiments presented here as non-limiting examples, as a result of the CSMA / CA multiple access scheme, two interfering sources cannot overlap simultaneously, which can be written mathematically as:

[0085]

[0086] - The random variables are independent over time, i.e.,

[0087]

[0088] where E[.] represents the mathematical expectation. When this expectation has to be performed over a finite set of values, the arithmetic mean is used to replace and approximate this expectation.

[0089] - Since the non-overlapping condition still applies hereafter, we first still consider the set of possible vectors Z defined as satisfying this non-overlapping condition at time k k = [Z 1,k …Z I,k of the set Ω.

[0090] Figure 2 The set Ω on 16 5-MHz channels in the 80-MHz ISM band is shown by the dot D1 (light gray). Then, one dot D1 shows the starting index i of the W-channel, and three dots D2 (black dots, above and below the dot D1, if possible) show the channel indices i+1, i+2, and i+3 of the WiFi interfering sources also assigned to the 20-MHz wide frequency band associated with the W-channel consisting of the four channels i, i+1, i+2, i+3.

[0091] For example, when using the channel index 9 with the dot D1 at the first third of the X-axis (representing one abscissa of a possible configuration of the vector Z in the set Ω), the W-channel 9 consists of channels 9, 10, 11, 12. The dot D1 represents that channel 9 is the index for identifying this 20-MHz wide W-channel. It can be observed that since two W-channels cannot overlap at the same time, only the W-channels starting from indices 13, 5, 4, 3, 2, 1 can coexist simultaneously with the W-channel starting from index 9. According to another example of Figure 2 corresponding to another possibility of the set Ω, a configuration can be achieved where four interfering sources with W-channels starting from indices 1, 5, 9, 13 are all active simultaneously, which is shown as the last configuration at the right end of Figure 2 .

[0092] It can be observed that N = 95 allocations with at least one interference source and satisfying the CSMA / CA non-overlap characteristic between interference sources are possible (the abscissa along the X-axis is 95).

[0093] Due to the non-overlap condition, this set Ω with a finite number of N possible configurations in the present embodiment generally can simply have multiple elements corresponding to N = 2 I where I is the number of transmission frequency bands, and for example in Figure 1 and Figure 5 I = 13. This generalization enables the consideration of overlapping situations such as hidden nodes between two interference sources. Due to the fast convergence of the method described below, the algorithm of the present invention enables this generalization.

[0094] Hereinafter, when referring to Figure 2 the symbol Ω can be for the set given above, or in general, can be for a set with 2 I possible vectors.

[0095] Another symbol also used below is:

[0096] ·τ i which is the activity rate of the i-th interference source, i.e., τ i = E k [Z i,k

[0097] where E k [.] represents the mathematical expectation at different times. When this expectation must be performed on a finite set of values (i.e., when considering a finite time window), the arithmetic mean is used to replace and approximate this expectation.

[0098] The problem to be solved is to calculate the set τ from the observation vector X = [X1,..., X K .

[0099] The maximum a posteriori can be transformed into a maximum likelihood problem by considering that all variables τ are a priori equally probable .

[0100] This involves that before receiving any observations, there is no information indicating that one activity rate in τ i representing the i-th W channel is higher than another.

[0101] Furthermore, the latent variable Z is also a priori equally probable, such that:

[0102]

[0103] This gives a new optimization problem to be solved. ​

[0104] Problem It is difficult to handle due to the high dimensionality of τ and the set of possible vectors Z (∈ Ω). Therefore, the expectation-maximization method that iteratively approximates the maximum likelihood solution is used in the literature EP-18305112.

[0105] The object of the present invention remains to estimate the expectation of the random vector Z based on the observations {X k} at the output of a channel defined by its transition probability P(X|Z), where the realizations {Z k} of Z belong to a known finite set Ω (which can be represented by the matrix A below when stacking all its elements row by row).

[0106] Referring Figure 3 , in a possible implementation, the present invention may include the following steps:

[0107] - Step S1: Determine the set Ω of possible configurations (possibly 2 I ), and more specifically:

[0108] * Obtain the matrix A of possible configurations of the stacked random vector Z,

[0109] * Define the channel transfer function P(X|Z) introduced above.

[0110] - Step S2: Initialize τ with zero values (1) and set t to t = 1; where t represents the iteration index in the following iterative process;

[0111] - Step S3: Acquire the measurements X1,..., X K ;

[0112] - Step S4: Calculate the probability:

[0113] - Step S5: Solve the inequality-constrained nonlinear optimization problem (ICNLOP), for example:

[0114] Maximize

[0115] Subject to

[0116] Aθ = τ (t)

[0117]

[0118] - Step S6: Calculate the vector as:

[0119]

[0120] - Step S7: Update

[0121] Iteratively repeat Steps S5, S6, and S7 until a stopping condition is met. In each new iteration, increment the index (t) (Step S8) until convergence is achieved.

[0122] Specifically, Step S5 involves intermediate results of functions that are not the initial objective of the optimization problem. Thus, an improper choice of intermediate results will slow down the convergence of the algorithm and thereby reduce its accuracy within a finite computation time. Here, it is proposed to transform the constraint on τ (t+1) into the maximization of a hidden variable that constrains θ to Aθ = τ (t) which is much easier and allows the derivation of closed - form expressions for some parts of the optimization. This improves the convergence of the algorithm.

[0123] At the output of a channel characterized by a transition probability p(X|Z) as given in Step S1 above Figure 3 observe the random variable X of the random process Z. The set of discrete values taken by Z is Ω and the cardinality is N = |Ω|. The parameter τ does not depend on the channel, i.e., p(X|Z,τ) = p(X|Z) and p(Z,X|τ) = p(X|Z)p(Z|τ).

[0124] In other words: τ → Z → X is a Markov chain. The goal is to estimate the vector parameter τ which is a linear combination of the probabilities P(Z = z j |τ) for all |Ω| possible values z j in the set Ω.

[0125] Thus, the constraint on τ is a fixed - point problem:

[0126] τ = f(τ) = A [p(Z = z1|τ),…,p(Z = z N |τ)] T (3)

[0127] where A is an I×N matrix, I is the length of τ (i.e., the assumed number of interference sources I which can a priori correspond to the number of channels, i.e., in the above Figure 5 example I = 13). The j - th column of A is z j and assuming I < N, this implies that A is non - invertible, which constitutes the main difficulty of the problem. Thus, the variable τ should always be a fixed - point of the function f(.), which does not have to be unique.

[0128] Through the likelihood p(X|τ) = E zMaximizing [p(Z,X|τ)] to optimally estimate τ is generally intractable because the cardinality of Ω is high and X is a sequence of many observations of the channel. To reduce the computational complexity, an iterative algorithm can be used. At each iteration t+1, the estimate of τ is refined based on the knowledge of the output τ (t) at iteration t (t+1) . In one iteration, generally the expectation maximization step is used, which involves

[0129] · Using the knowledge of τ (t) to compute the probabilities p(Z = z j ∈Ω) for all possible z j |X,τ (t) ).

[0130] · Refining the estimate of τ

[0131]

[0132] according to the set of probabilities p(Z = z j |X,τ (t) ) using the following formula (t+1) .

[0133] In the context, p(Z,X|τ) = p(X|Z)p(Z|τ), where p(X|Z) is known from the channel, but due to A being non-invertible, p(Z = z j |τ) cannot be uniquely known from τ. Thus, several vectors [p(Z = z1|τ), …, p(Z = z N |τ)] T satisfy the constraint (3). However, in the optimization problem (4), two different versions of f(.) do not lead to the same result.

[0134] In the literature EP - 18305112, the vector [p(Z = z1|τ), …, p(Z = z N |τ)] T is selected according to a heuristic function, i.e., it is not selected to improve (4).

[0135] Therefore, to provide the best convergence of the algorithm, it would be interesting to optimize [p(Z = z1|τ), …, p(Z = z N |τ)] T together with τ to obtain the best τ (t+1) . To make this optimization possible, it is proposed here to add an additional term in the optimization problem (4), which still guarantees convergence but also drives the coupling of the variables τ and [p(Z = z1|τ), …, p(Z = z N |τ)] T towards the most effective choice of τ (t+1) .

[0136] Return reference Figure 2 , the set Ω is shown by the light gray dots D1 generated by the allocations on 16 channels. The set Ω can be transformed into an interference configuration matrix A. In fact, the set Ω is rewritten in matrix form A to use linear algebra tools to solve the optimization problem. Thus, the matrix A depicts in its columns the combinations of the active states of all interference sources in the considered frequency band at the same time. The value of each entry is 1 or 0, which indicates whether there is interference on that channel. The cardinality of Ω is the number of columns of A. The construction of A must comply with the protocol used by the interference sources (hereinafter, for example, CSMA / CA).

[0137] τ i is the active rate of interference in the i-th WiFi channel, i.e., τ i = E k [Z i,k .

[0138] The goal is to estimate the active rate vector τ = [τ1,..., τ K based on the measured observations X = [X1,..., X I .

[0139] A general expectation-maximization algorithm can be implemented, more specifically, an iterative algorithm that improves the log-likelihood logP(X|τ) in each iteration, called "expectation-maximization", and is reproduced in the following equation.

[0140] By introducing the latent variable Z, we can obtain:

[0141] logP(X|τ) = logP(X,Z|τ) - logP(Z|X,τ (t) ) (5)

[0142] By multiplying both sides by marginalizing over Z, we get:

[0143]

[0144] where H(τ|τ (t) ) is the conditional entropy of the random variable τ given τ (t) , and Q(τ|τ (t) ) is the expected value of the likelihood function of τ with respect to the current conditional distribution of Z given X and the current estimate of the parameter τ (t) , such that:

[0145]

[0146] Equation (6) holds for τ (t)

[0147] logP(X|τ (t)) = Q(τ (t) |τ (t) ) + H(τ (t) |τ (t) )

[0148] To maximize logP(X|τ), an iterative method can be implemented that maximizes an incremental logP(X|τ) - logP(X|τ (t) ) at each step of the algorithm, resulting in

[0149] logP(X|τ) - logP(X|τ (t) ) (7)

[0150] = Q(τ|τ (t) ) - Q(τ (t) |τ (t) ) + H(τ|τ (t) )

[0151] - H(τ (t) |τ (t) )

[0152] Gibbs' inequality states that the information entropy is less than or equal to its cross-entropy with any other distribution (i.e., H(τ|τ (t) ) ≥ H(τ (t) |τ (t) ). Thus, it can be written as

[0153] logP(X|τ) - logP(X|τ (t) ) ≥ Q(τ|τ (t) ) - Q(τ (t) |τ (t) ) (8)

[0154] From (8), the expectation-maximization algorithm can be derived. This algorithm enhances the log-likelihood at each iteration by ensuring that the right-hand side of (8) is always positive. To this end, the expectation is computed as Q(τ|τ (t) ), and then the maximization problem is solved as

[0155] τ (t+1) = argmax τ Q(τ|τ (t) ). As a result, the log-likelihood is iteratively improved.

[0156] More specifically, the special properties of the problem solved in the present invention are utilized below, which constitute an improvement over the usual prior art of the expectation-maximization algorithm.

[0157] As previously mentioned, in the usual expectation-maximization algorithm, the maximization step assumes that τ (t) is known from the output of the previous iteration, which involves substantially Q(τ|τ(t) ) should be maximized and greater than a fixed Q(τ (t) |τ (t) ).

[0158] In this method, it is considered that Q(τ|τ (t) ) - Q(τ (t) |τ (t) ) can be expressed as a function of τ, and τ is constrained to be a fixed point of f(.). Then the problem becomes

[0159]

[0160] This is a further constraint added to the expectation - maximization problem, which ultimately leads to two optimization problems that can be solved below.

[0161] Optimization is difficult under the fixed - point constraint. By considering the j - th entry θ j = p(Z = z j |τ) and the hidden variable θ where τ = Aθ; and the j - th entry θ j (t) = p(z = z j |τ (t) ) and τ (t) = Aθ (t) of the hidden variable θ (t) to solve this problem. Note that since A is a projection (rectangular matrix), τ (which is the output of the process) can be determined from θ, but θ (t) cannot be uniquely determined from τ (t) . This means that the optimization of τ can be replaced by the optimization of θ, and an additional optimization of θ (t) is required, but it allows for the expression of a simpler optimization algorithm than the optimization algorithm using the fixed - point constraint.

[0162] In fact, by using

[0163] · the temporal independence of the observations X X over time,

[0164] · Bayes' rule,

[0165] · marginalization over the possible set Z,

[0166] one can obtain:[[]]

[0167]

[0168] By representing θ j = p(Z = z j |τ) and θ j (t) = p(Z = z j|τ (t) ) to obtain the equivalent function

[0169]

[0170] Therefore, the optimization problem becomes

[0171]

[0172] Since this method maximizes the improvement in each iteration, it helps to accelerate the convergence of the log-likelihood.

[0173] Note that in a typical Expectation-Maximization algorithm, only the τ value is actually optimized (the second term Q(τ (t) |τ (t) ) has no effect in the optimization). In the method of the present invention, the second term is retained, which helps to optimize θ (t) , which in turn allows θ to be found and then return to τ (t+1) . This is one of the advantages of the present invention.

[0174] The joint optimization can be carried out as follows. First, consider a fixed θ (t) . Optimizing argmax θ D(θ, θ (t) ) leads to a closed-form solution

[0175]

[0176] Substituting this into the maximization problem of θ (t) , we can obtain:[[]]

[0177]

[0178] Taking into account all the constraints, the optimization problem becomes:[[]]

[0179] Calculate

[0180] Subject to

[0181] Aθ (t) = τ (t)

[0182]

[0183] The optimization problem defined in these latest equations can be solved by any numerical optimization toolbox. Alternatively, by randomly generating several values of θ (t) , select the ones that satisfy (or nearly satisfy) the constraints Aθ (t) = τ (t) and value and calculate the value Then retain the θ that provides the highest value (t) random selection of to solve the optimization problem

[0184] The criterion of "nearly satisfied" constraint can correspond to, for example, applying a threshold to the constraint such that

[0185]

[0186] Then, from the optimized θ (t) , can be derived by using derive θ (t+1) , which allows obtaining τ (t+1) = Aθ (t+1) .

[0187] The convergence ratio is faster than that in the literature EP - 18305112, and the result is more accurate

[0188] Of course Figure 3 All algorithms represented by the flowchart of are actually executed by a computer running an appropriate computer program, and this computer program has an algorithm corresponding to one of the algorithms represented by Figure 3 As shown in Figure 4 , such a computer includes

[0189] - Input interface InP, which is used to receive the measurement X k ,

[0190] - Memory MEM, which is used to store at least the instructions of the above computer program

[0191] - Processor PROC, which is used to read the instructions and then run the corresponding program, and

[0192] - Output interface OUT, which is used to transmit the signal SIG, and this signal SIG includes at least data related to the activity rate of the transmission band of the interference source and possibly recommended channel identifiers to avoid these interference sources

Claims

1. A method implemented by a computer device for estimating interference on a radio frequency system using a set of channels, the interference being caused by interference sources of an interference system using a set of I transmission bands, each of the transmission bands extending over a plurality of consecutive channels of the set of channels, wherein, The method includes the following steps: - Determine the set of all N possible configurations of occupied or unoccupied of the set of transmission bands defined as the possible vectors Z k = [Z 1,k , …, Z i,k , … Z I,k , the set Ω -Construct matrix A according to the stacking of all possible vectors Z k and - Obtain measurements X1, …, X of the occupancy of at least a portion of the set of channels at respective instants k k , …, X K , 0 < k ≤ K, where K defines a given observation time window - The calculation is defined as P(X k |Z k = z j ), where P(X|Z) defines the channel transfer function to determine, based on the measurements X1, …, X k , …, X K For each transmission frequency band, determine the estimated activity rate τ, where the estimated activity rate τ corresponds to the occupancy rate of the transmission frequency band i by the interfering source within the given observation time window. And wherein, the calculation of the probability iteratively includes in each iteration t: * Solving a non-linear optimization problem with constraints defined as follows: Maximize Subject to Aθ = τ (t) where the vector τ (t) is the column of the active rate in the corresponding transmission band i estimated at the iteration index t, and the vector θ is a hidden variable, *Computing vector As a hidden variable, such that: * And updating the vector of the activity rate at the next iteration index t + 1 to where \(1\leq j\leq N\), \(1\leq l\leq N\), \(z\) j and \(z\) l are the \(j\)-th column and the \(l\)-th column of the matrix \(A\) respectively, and \(\theta\) j and \(\theta\) l are the \(j\)-th entry and the \(l\)-th entry of the hidden variable \(\theta\) respectively.

2. The method according to claim 1, wherein, The possible vector Z k = [Z 1,k , …, Z i,k , … Z I,k of the set Ω satisfies the non - overlapping condition of the radio frequency system at time k, and the non - overlapping condition corresponds to the fact that on each channel in the set of channels, among the set of I possible interference sources, only one interference source i can be active at the same time k, and consecutive channels form a transmission band i.

3. The method according to claim 2, wherein, Derive the non-overlapping condition from the CSMA / CA multiple access implementation scheme performed by the radio frequency system, where the CSMA / CA multiple access defines communication time slots and the measurement X is collected in each time slot k k .

4. The method according to claim 1, wherein, The set Ω of possible vectors includes 2 I elements.

5. The method according to any one of claims 1 to 4, wherein, The communication system implements frequency hopping on the channel and obtains the measurements X1, …, X k , …, X K The steps are performed according to the frequency hopping implementation scheme.

6. The method according to any one of claims 1 to 4, wherein, The number of the continuous channels forming the transmission band is four, and the total number of channels in the set of channels is sixteen.

7. The method according to claim 6, wherein, Each of the channels is extended over 5 MHz, while each of the transmission bands is extended over 20 MHz using a spread-spectrum technology implementation.

8. The method according to any one of claims 1 to 4, wherein, The radio frequency system implements ISM-type communication, while the interference system implements Wifi-type communication.

9. The method according to any one of claims 1 to 4, the method further comprising the following steps: Select the communication of at least one channel in the set of channels, and the selected channel is within the transmission band with the lowest estimated activity rate τ.

10. A computer program product comprising instructions for implementing the steps of the method according to any one of claims 1 to 9 when executed by a processor.

11. An apparatus for estimating interference on a radio frequency system using a set of channels, the interference being caused by interference sources of an interference system using a set of transmission bands, each of the transmission bands extending over a plurality of consecutive channels of the set of channels, the apparatus comprising processing circuitry for performing the method according to any one of claims 1 to 9.

12. A radio frequency communication system, the radio frequency communication system comprising the apparatus according to claim 11, the apparatus being for estimating interference liable to occur on channels to be used by the radio frequency communication system.

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