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Military institute of telecommunications and informatization named after Heroes of Kruty, Kyiv, Ukraine VECTOR-SPACE APPROACH TO EVALUATION OF THE EFFICIENCY OF USE OF RADIOELECTRONIC CONTROLS

The intensive development of information and control technologies, as well as their integration into a single information space, leads to an increase in the role of such technologies in the processes of control of troops (forces) and weapons, including high-precision. At the same time, the electronic material basis of information infrastructure, created within the framework of the concept of a network-centric war, is potentially vulnerable to the devices of electronic warfare. However, the analysis of the experience of using electronic devices has shown that in practice there are cases where the level of effectiveness of the use of these devices is lower than necessary. Accordingly, the improvement of the effectiveness of electronic warfare devices is an important area of scientific research. The primary component of increasing the effectiveness of electronic warfare devices is the substantiation and development of indicators that provide an objective assessment of the effectiveness of the use of these tools, taking into account all the important factors and conditions (including inaccuracies or uncertainties about the parameters of suppressed objects). Accordingly, the article develops an approach to the selection of indicators for assessing the effectiveness of the use of electronic warfare devices. The basis of the proposed approach is that the potential ability of the devices of electronic warfare to perform the tasks set forth is sufficiently fully described by the corresponding vector space, each point of which is determined by the corresponding vector, which includes a certain number of indicators describing the properties of these devices. In the course of the research, the main provisions of the theory of electronic warfare, the method of analysis of hierarchies, as well as general scientific methods of analysis and synthesis were used. The proposed approach to the evaluation of the effectiveness of the use of electronic warfare devices allows us to use a combination of system-resource approach to calculate indicators on the basis of the multilevel description of the composition of the devices of electronic warfare, when the multi-dimensional structure of its integral index (level of functioning) is gradually filled with parametric content, which is the advantage of this methodological approach. Also, the developed approach to evaluation allows us to develop, on a quantitative basis, recommendations on the choice of rational indicators of the composition of electronic warfare in accordance with the tasks set, to determine the level of functioning of the devices of electronic warfare by converting their partial and aggregate indicators.


Introduction
The intensive development of information and other advanced technologies, as well as their integration into the information-control systems of the armed forces of the leading countries of the world, the continuation of the implementation of the principles of "network-centric concept" management of troops and weapons become the most important factor determining the course and outcome of modern armed struggle. At the same time, the electronic material basis of the information infrastructure of the "network-centric concept" for conducting a modern armed struggle is potentially vulnerable to the impact of radiocommunication facilities and, accordingly, is the direct object of such influence [1][2][3].
Nowadays, significant progress has been made in the leading countries of the world in the development of radiocommunication facilities, which has increased the capabilities of the latter [4,5]. However, in practice, there are cases where there is a contradiction between the achieved and necessary levels of effectiveness of radiocommunication facilities. In the presence of this contradiction in terms of efficiency, there is a problem of finding ways to increase it.
One of the primary components of increasing the efficiency of technical devices (including radiocommunication devices) is the substantiation of objective indicators for evaluating their effectiveness, taking into account the influence of all significant factors and conditions (including inaccuracies or uncertainties about suppressing objects).
At the same time, the efficiency indicators should be rational, that is, those in which the devices of radiocommunication meet the requirements that they are put forward to the maximum, and the cost of resources for their improvement does not exceed the specified objective restrictions.
The possibility of a comprehensive practical confirmation of the rationality of the indicators of the effectiveness of radiocommunication facilities is somewhat limited. Therefore, the role and importance of methodological support for the development of adequate managerial decisions regarding the use of radiocommunication facilities, as well as their further development, is enhanced.
The purpose of this article is to develop an approach to assess the effectiveness of the use of radioactive contamination.

Presentation of the main material
The article gives an approach to the choice of the indicated rational indicators for assessing the effectiveness of radiocommunication facilities on the basis of the assumption that their potential ability to perform the tasks can be described by the corresponding vector space, each point of which is determined by a vector, which includes certain quantitative indicators that reflect the corresponding properties of radiocommunication facilities .
The integral index of the state of a given set of radiocommunication devices can be calculated by convolution of partial indicators, which reflect: quantitative and qualitative composition; structure of the radiocommunication system; equipment radiocommunication devices; tactical and technical characteristics of radiocommunication equipment; possibilities for restoring radiocommunication facilities; the state of the infrastructure facilities that provide a radiocommunication system, etc. [6][7][8][9][10][11][12].
Adhering to the principles of system analysis in the interest of choosing an adequate system of indicators, it is advisable to provide a set of radiocommunication facilities in the form of the systems hierarchy. This approach is used in the practice of research of hierarchical multi-level military systems [6][7][8][9][10][11][12].
The system of radio-contradiction includes a set of common purpose shared functions of its functional subsystems and can be described by a vector of indicators characterizing the contribution of the latter to the level of functioning of the system of radiocontradiction: where LM n Е is the level of functioning of the n-th of the functional subsystem; N is the number of functional subsystems.
Under the functional subsystems of the system of radio-contradictions of membership levels are understood subsystems: radio electronic opposition (REO), control, radio-electronic information and technical support (RIS, TS).
The REO subsystem includes organizational forms that are used to disrupt management. The subsystem of control of the radiocommunication system includes: the control bodies; control points; communication and data communication system. Then, each functional subsystem can be described by a vector of indicators that characterize the contribution of its elements in the membership level of the functional subsystem: where FS k Е is the level of affiliation of the k -th element of a functional subsystem; K is the number of elements in the functional subsystem.
Indicators of the effectiveness of radiocontradiction, both qualitative and quantitative, in aggregate reflect the state, divided into integral, generalized and partial [4]. The integral index of the system of radioactivity of the corresponding level of membership, which characterizes the level of functioning of the system, is the convolution of the generalized indexes of its functional subsystems, whose elements, in turn, are characterized by sums of partial indicators.
In the formalized form, the integral index of the radio-collision system of the corresponding level of affiliation can be described as follows: where LM E is the the level of functioning of the radiocontradiction level of affiliation at the time t (on the ℓth stage) of the period T , t T  ;       , , R t U t Q t is the generalized indicators (operating levels) of subsystems of the radiocontradiction system;   Y t is the conditions of development of radiocommunication facilities.
Level of functioning of the radiocommunication subsystem in conditions   Y t is defined by the expression [6][7][8][9][10][11][12]: where , are levels of operation of the control elements of the radiocommunication subsystem, systems and devices of automation and communication.
Thus, partial indicators that quantitatively characterize the system of radio-contradiction, taking into account the classes of radio-electronic devices (RED), can be described in the form as shown in the table.1.

The name of a set of indicators Name of indicators
-the proportion of satellite-based RED that are effectively suppressed -the proportion of short-wave short-wave RED that are effectively suppressed -the proportion of ultra short-wave RED frequency rejection that is effectively suppressed -the proportion of RED tropospheric communication that is effectively suppressed -the proportion of RED that are effectively suppressed -the proportion of RED of effectively transmitting information systems -the proportion of homing heads that are effectively suppressed -the share of REs for land and air users of navigation systems ("Navstar", "Glonass", "Beidou", etc.) that are effectively suppressed is the level of implementation of the networkcentric management method; con u is the level of compliance of the organizational structure of the control system by the devices of radio resistance to the management norms.
Partial Indicators   is the level of equipment management information-modeling complexes.
Level of functioning of subsystems of radioelectronic and technical maintenance of control units in the conditions   Y t is defined by the expression [6][7][8][9][10][11][12]: t are the partial indicators that reflect the effectiveness of spacious-spaced radio intelligence systems that are used in the interests of the radioresistance system; is the level of correspondence of the real width of the intelligence band of radio-electronic objects by the devices of radio-resistance to the necessary; rangin q is the level of correspondence of the real range of intelligence of radio-electronic objects by the devices of radio-resistance to the necessary; is the level of correspondence of the achieved time of receipt and bringing to the management bodies of the results of an integrated assessment of the state of protection of objects and organizational-staff structures from the technical devices of intelligence (operational control); fulcon q is the proportion of its objects that is covered by the control (completeness of coverage by the control). is the proportion of new methods and tools for the collection, processing, presentation and use of radio electronic data to increase the level of adaptation of automated systems and devices of the radioactivity control to its change; coop q is the level of information interaction with the joint execution of tasks. is the level of compliance of the equipment of the radiocommunication equipment, other material resources in the places of their storage to the requirements that are put forward to them; tr q is level of staffing with modern training equipment.
Taking into account (3) is the set of tasks assigned to the system of radiocontradiction, in j -th variant of its development, z Z  ; , , , I N Z J is a set of indicators, development measures, variants of the list of tasks assigned to systems of radio-contradiction, and variants of its development.
For the quantitative assessment of the impact of the development measures on the indicators of the radiocommunication system, the latter can be described as follows [6][7][8][9][10][11][12]: The following restrictions apply to the indicators of the system of radiocommunication: Definition of quantitative values of indicators of the system of radio-contradiction is carried out in the process of calculating the potential of j-th variants of the plan for the development of the radio-contradiction system by analyzing the effectiveness of the development of the system of radio-contradiction and the importance of the components of the radioresistance system using the method of analysis of hierarchies.
In accordance with the structure of the system of indicators (Table 1), the proposed vector-spatial approach to the evaluation of the effectiveness of the radio-protection system includes the following steps: The 1-st stage is an assessment of the effectiveness of the implementation of the first option of the development plan. Each measure is subject to a comprehensive assessment regarding: degree of influence on partial parameters of elements of functional subsystems of radio-contradiction, conformity of the concept of development of radio-resistance means to the tendencies of development of information management systems of the leading countries of the world, resource intensiveness and possibilities of realization in the given perspective. Taking into account the influence of factors, including financial, economic, military-technical, technical and technological, organizational in the manner indicated in [5].
2-nd stage is the evaluation of the levels of functioning of the elements of the functional subsystems of the radio-contradiction by the formula: 3-rd stage is the evaluation of the levels of functioning of the functional subsystems of the radiocontradiction system by the formula: -th stage is the assessment of the level of functioning of the radiocommunication system as a whole by the formula: where , , ij kj nj    is the importance of the i-th indicator of the k-th element of the n-th functional subsystem of the system of radioactivity at j-th variant of development, respectively. The coefficients of the significance of components of the system of radio-contradiction and their partial indicators can be calculated by the method of pair comparisons using the universal scale T. Saati [6][7][8][9][10][11][12].
Increase is the staffing of the radiocommunication unit with modern models of radio equipment technology. It is known that the staffing of the radiocommunication subsystem of the radiocommunication subsystem with modern models of radio equipment technology before the beginning of the program period is 60%. The deployment during the program period of an additional radiocommunication unit in this subsystem, equipped with radio-technology of the same class, allows precisely to determine the , which is grouped by the , r t u t q t , are considered rational for the implementation of a set of tasks Z, assigned to it in a given program period. It is also necessary to take into account that the conduct of each measure may lead to changes in the values of several indicators.
For example, the deployment of a new radiocommunication unit will change the quantitative ratio of new and old technology, its staffing of various categories, etc.

The conclusion from the article
Thus, the proposed vector-spatial approach to the evaluation of the effectiveness of the use of electronic countermeasures allows: the use of a combination of system-resource approach to the calculation of indicators on the principle of multi-level description of the radio-contradiction system, when the multidimensional structure of its integral index (level of functioning) is gradually supplemented by parametric content; on a quantitative basis, to make recommendations on the choice of rational indicators of the radiocommunication system in accordance with its tasks in the planned period; to determine the level of functioning of the system of radio-contradiction by converting partial and aggregate indicators with an attachment to the tasks assigned to them; to comprehensively take into account the influence of the development of the components of the system of radio-resistance on the change of their indicators, to analyze intermediate results and to identify patterns on this basis, which explain the reasons behind the development of some components of the system of radio-contradiction from others; to identify a rational set of measures to improve the system of radio-contradiction, which will allow them to end the program period from the initial state to the assignment, in which it will most fully meet the requirements imposed by the allocated resources; in advance to create in the regulatory bodies of radio control regulatory and calculation basis for planning the development of components of the system of radio-resistance in a given perspective.