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Methodology for developing a conceptual design of radar stations for prospective air defence weapon systems

https://doi.org/10.38013/2542-0542-2020-2-6-31

Abstract

This article discusses the task of developing a conceptual design of radar stations for various purposes in the process of updating the domestic military air defence system. The main structural and technical parameters characterizing radars at an early stage of their design are determined. The scientific task of developing a conceptual design of such systems is formulated. A system of design ratios was developed for a generalized analysis of the relationship of structural and technical parameters and radar functions. A procedure for determining a rational conceptual design of radar systems is proposed. An example of the conceptual design of a radar sector display for detecting ballistic targets is provided.

For citation:


Druzin S.V., Gorevich B.N. Methodology for developing a conceptual design of radar stations for prospective air defence weapon systems. Journal of «Almaz – Antey» Air and Space Defence Corporation. 2020;(2):6-31. https://doi.org/10.38013/2542-0542-2020-2-6-31

Introduction. Role and function of radar in a prospective combat air defence weapon system. Definition of the task of developing a conceptual design of radar

Currently, the Russian Federation combat air defence weapon system, being a complex of functionally interrelated fire units (surface-to-air missile complexes and systems), reconnaissance and target designation assets, automated control systems and other facilities, is undergoing the process of radical renovation. The work on developing a conceptual design of combat air defence weapon system has been initiated and is in good progress, it will be followed by a series of research and development of certain weaponry with further batch production thereof.

Article [1] explains the necessity of development of new weaponry, as well as principles and procedure of developing a conceptual design of combat air defence weapon system. The main underlying reason for weaponry renovation is the continuing development of aerospace attack weapons of an enemy and significant improvement of their air defence penetration capabilities, and the technical basis for renovation is formed by successful development of electronic components, microelectronics, as well as by the new developed technologies in different scientific and technological fields, including the radars.

Various-purpose radars remain the main sources of information in the developed combat air defence weapon system, however, they are developed based on the new hardware components and with the use of new technologies. The existing radars (Fig. 1) incorporate passive phased arrays (PhAr) and are constructed based on 1980s technologies, therefore failing to fully satisfy the requirements for the advanced weaponry in terms of both operational indicators and purpose indicators.

Fig. 1. Main modern combat air defence radars: 1 - Xband 9S19 Imbir radar; 2 - S-band 9S15 Obzor-3 radar; 3 - S-band 9S18M1 Kupol radar; 4 - VHF-band 1L13 Nebo-SV radar (four transport units - hardware cabin, rotary antenna device, diesel power station, trailer with interrogator antenna device)

 

The developed air defence facilities, including the radars, being part of air defence formations and units, will be deployed in wide-area dispositions, and they will operate against different ballistic and aerodynamic targets, including the new types outperforming modern attack weapons. In [1], the efficient nomenclature of developed radars is determined based on the analysis of performance and reflectance profile of targets and considering dispositions of troops. This includes reconnaissance and target designation radars of command posts of air defence formations and SAMS carrying out circular and sectoral scanning (CS-SS radar), sector scanning radars for detection of ballistic targets (BT) - SS radars of surface-to-air missile systems and BT radars of surface-to-air missile complexes, as well as low-altitude targets detection radars (LAT radar) of SAMC. Depending on their intended purpose and characteristics of detected targets, the listed radar types cover a wide wavelength band of active radar - from SHF to VHF waves (subbands X, C, S, L, UHF and VHF).

The possibilities of grouping the air defence weapons by target killing depend on the capabilities of developed target detection radars, accuracy of target coordinates estimation and capacity of the radars. Therefore, justification of a conceptual design of the listed types of developed radars is one of the most important tasks in developing a conceptual design of the entire combat air defence weapon system.

The considered task of radar conceptual design justification is addressed during early stages of engineering and includes development of radar structural design proposals and identification of the required values of critical structural and technical parameters. Subsequently, the developed conceptual design of an article is detailed in the course of research and development - being elaborated in detail and engineering design, and finally implemented in the form of a prototype.

The development of radar conceptual design is aimed at identification of the main structural features of the radar, preventing system errors, which subsequently, during research and development, may result in the necessity of redesigning an article.

The approach to development of radar conceptual design may be based on an essential requirement for the combat air defence weapons: importance of their high mobility. For prospective radars, this requirement is most critical due to the necessity of quick relocation in view of significant improvement of emitting sources detection capabilities of an enemy and prompt application of precision weapons (PW) against the emitting source.

Based on this requirement, all radar hardware and equipment, including means of independent power supply (MIPS), shall be located on high-mobility chassis (wheel- or track-mounted, depending on standard accessories - see [1]), ensuring movement of troops within dispositions on different types of terrain. At that, the time required for closing-down/deployment of a radar is limited by a few minutes.

For high-potential radars with large antenna systems, the time of closing-down/deployment may be extended to a few dozens of minutes due to their in-depth operation, well away from the battle contact line, and coverage from PW with layered defence.

Due to lifting capacity and mobility limitations, high-potential radar hardware and equipment may be located on several chassis intended for locating antenna post, power supply system and hardware with the combat crew, respectively; however, the time of coupling these facilities at a combat position shall not limit the required time of radar closing-down/deployment.

Thus, chassis is an element that determines the primary appearance of a radar in terms of its maximum possible weight, dimensions of deployed antenna system, as well as consumed (and consequently emitted) energy.

The characteristics of a radar are mainly based on the characteristics of its antenna system and high-frequency transceiver section (design features of antenna, shaping, emission, reception and preliminary signal processing facilities). With regard to hardware and equipment location, the chassis, by limiting the weight and dimensions of antenna system, as well as signal power, defines the limit angular resolution, the power of emitted signal, signal/noise ratio and other parameters critical for a radar.

On the other hand, with regard to the intended purpose, the characteristics of developed radars shall be in line with the characteristics of end user - fire units. The information obtained by the radars shall ensure full implementation of fire units firing capabilities consisting in target killing at a maximum operating range of surface-to-air missiles (SAM) and in depth of a kill zone during massive raids (attacks).

These characteristics of fire units provide the basis for determining the purpose indicators of developed radars - required limits (ranges) of information output, quality of information (resolution and accuracy of target profile estimation) and radar capacity.

A multitude of purpose indicators of certain type radar will be represented by YПН:

YПН = {Rобн, Ωδ, Тобз},

where Rобн is the range of a preset target type detection under certain conditions; Ωδ is multitude of indicators of resolution and accuracy of target profile estimation (angular coordinates, range and velocity); Тобз is time of scanning of the specified space sector (being the main indicator of radar capacity).

A multitude of main structural and technical parameters of a radar, determining conceptual design of the same, will be represented by XКТП.

The most critical structural and technical parameters, which allow to calculate radar purpose indicators at an early stage of conceptual design development, include the following: λ - radar wavelength; Рср - mean power of signal emitted by antenna; Sa - antenna aperture area; ρ - aperture efficiency; kш - receiver noise factor; kп - к signal loss factor (total signal emission, reception and processing losses); Δf - signal band.

The structural and technical parameters have a multidirectional impact on the purpose indicators. Thus, caeteris paribus, an increase of wavelength will lead to an increased radar capacity and at the same time to a decreased accuracy of coordinates estimation.

Considering the multidirectional impact factor, the task of developing a conceptual design of radar requires optimal solution, i. e., it is essential to find compromise (rational) values of structural and technical parameters ХКТП, ensuring the required level of purpose indicators YПН ensuring the required level of purpose indicators 7ПН within the framework of existing weight-and-dimension-al and power limitations imposed by the chassis type used at a minimum cost of developed radar version СРЛС:


where Rтр, Ωτρ, Tобз тр are purpose requirements (requirements to target detection range, resolution, accuracy of target profile estimation and time of scanning of the specified space sector, respectively); Мтр, РСАЭС, Sш  are limitations imposed by the chassis type used (limitations by radar weight, MIPS power, antenna aperture area, respectively); Рпотр  is power consumed by the radar.

The task of developing conceptual design of the radar may be expanded by considering other requirements and factors, not formalized in the statement of (1). In particular, current requirement for ensuring radar mean time between failures of hundreds of hours clearly determines the necessity of designing a radar based on solid-state PhAr. Besides improving the performance, application of active phased array antennas (APAA), and in particular digital APAA (DAPAA), offers a range of other opportunities (see [2][3]) and effectively addresses the challenge of targets detection and tracking in a complicated air and jamming environment of future scenarios.

Consequently, despite relative radar value appreciation, only options of radar design with APAA are further considered for the prospective weapon system.

The optimal task solution (1) requires mathematics to calculate purpose indicators Rобн, Ωδ, Тобз, аas well as indicators of design limitations imposed by the chassis type used - МРЛС, Рпотр, Sa, and radar cost indicator СРЛС depending on structural and technical parameters ХКТП. We further derive the following relations, using wavelength λ as a reference variable, on which all indicators used in (1) depend.

  1. Establishment of design basis and basic dependencies for developing a conceptual design of radar

1.1. APAA as the main structural element of radar, which is subject to limitations imposed by the chassis applications

The initial, non-formalized stage of developing the radar conceptual design, preceding optimal task solution (1), consists in establishment of radar architecture and design limitations Мтр, РСАЭС, Sш within the framework of which a concrete radar design version may be implemented.

Reverse engineering of prospective (most advanced existing or being under development) domestic and foreign various-purpose radars with APAA was carried out in order to establish possible architecture of combat air defence radars under development, over their entire projected operating wavelength, from SHF to VHF waves. Figure 2 shows the appearance of some of these radars.

Fig. 2. Prospective radars of different ranges: 1 - radar module (RM) of high-potential radar AN/TPY-2 ofX-band (USA) [4]; 2 - RM of high-potential domestic radar of X-band (design option) [8]; 3 - radar LTAMDS of С-band of prospective SAMC Patriot (USA) [4]; 4 - radar of type Yenisei [5]; 5 - RM of SHF band (RLM-S module) being part of radar complex 55ZH6M Nebo-M; 6 - RM of UHF band (RLM-D module) being part of radar complex Nebo-M; 7 - radar of VHF band 1L119 Nebo-SVU; 8 - RM of VHF band (RLM-M module) being part of radar complex Nebo-MM; 9 - RM of VHF band (RLM-M module) being part of radar complex Nebo-M

Besides, wheeled and tracked chassis were analysed satisfying the requirements for mobility applicable to advanced weaponry of combat air defence and suitable for locating various-purpose radar hardware and equipment. Figure 3 shows an example of typical mobility equipment with maximum lifting capacity, ensuring development of mobile radars of combat air defence.

Fig. 3. Mobility equipment with maximum lifting capacity for development of mobile combat air defence weapons (wheeled truck with cross-country capacity BAZ-6909 and modified self-propelled chassis of type Ob'yekt 830 [6])

The analysis revealed that APAA-based prospective mobile radars for combat air defence may structurally include three main components arranged on a single chassis - antenna post, hardware container and MIPS. The antenna post design is based on APAA and it ensures shaping and emission of signal, its reception and primary processing. The antenna post also accommodates other devices that are common for radars, e. g. devices ensuring target identification.

As a rule, the hardware container accommodates the hardware and computing facilities for secondary and subsequent signal processing, operator workstations hardware, including indicators, and other hardware ensuring control over the radar operation, communication and interaction as part of weapon system.

Due to enhanced weight-and-dimensional characteristics of antenna system, the elements of high-potential radar may be arranged on several mobile chassis and include several individual equipment units, respectively, e. g. radar module with APAA, radar combat control module (hardware container) and radar power supply module.

Considering digitization of radar hardware design, their specific features are almost completely determined by antenna post (radar module), especially by APAA design features. The design of hardware containers of different radars in a prospective combat air defence weapon system is unified by the configuration of hardware and performed functions to the maximum extent (for details refer to [1]).

Antenna post APAA largely determines both radar purpose indicators and possibility of satisfying the limitations imposed on the developed radar: the analysis revealed that 60-80 % of the radar cost is determined by APAA cost (in VHF band, due to reduced number of array elements - to a lesser extent, in SHF band - to a greater extent); APAA uses 70-80 % of all energy consumed by the radar; radar mobility significantly depends on antenna dimensions and its closing-down time.

Consequently, when searching for an optimization task (1) solution variable component in the radar design is APAA - its structural and technical parameters, weight, antenna aperture area and power consumption. Hardware container is a unified component having fixed characteristics for different radar design versions.

Design limitations for APAA required for task solution (1) will be determined based on the characteristics of prospective chassis.

In order to ensure high mobility (required closing-down/deployment time), the antenna post, hardware container, MIPS and other radar equipment shall be located on a single chassis. Based on the maximum weight of air defence mobile facilities, the prospective chassis can accommodate up to 20 t of payload. At that, considering the potential weight-and-dimensional characteristics of hardware container and other equipment unified for different radar design versions, as well as of antenna post hardware, APAA weight is limited by value mогр ≈ 8 т.

Considering weight-and-dimensional characteristics, single mobile chassis can accommodate MIPS with power of up to 400 kW. At that, considering power consumption of other types of radar hardware and equipment, APAA power consumption is limited by value Рогр ≈ 350 кВт.

The analysis of prospective radar antenna system structures allows to draw a conclusion that the maximum mobile radar antenna aperture area (in VHF band) is limited by value Sогр ≈ 130 м2.

1.2. Specific features of prospective radars APAA design

1.2.1. Basis of design and implementation examples of SHF band APAA

Outstanding domestic and foreign prospective radars with APAA are or were developed for addressing their specific tasks in different fields of application. Radar designs are developed based on compromise solutions related to the need to ensure the required values of purpose indicators and performance characteristics, as well as to simplify the process of design and meet the deadlines of the same (see, e. g. [2][3][7][8][9]). Consequently, APAA of prospective radars have a wide variety of implementation versions, in particular, for different wavelength bands (which is even reflected by their appearance). At the same time, APAA of prospective radars have the same design basis.

Let’s consider SHF band APAA as an example of common design basis of prospective radars APAA.

The most strict weight-and-dimension-al requirements are applied to APAA design in this waveband. Strict requirements result from the need to arrange antenna emitting elements at a distance not exceeding approximately 0.6 of wavelength from each other in order to exclude secondary emission directions. Thus, at small wavelength a very tight arrangement of receiving and transmitting channels (RTCh) of antenna array is required. (RTCh comprises an emitter and high-frequency elements of receiving and transmitting paths connected to it via a switch (circulator)).

Thus, at wavelength of 3 cm each APAA RTCh cross-sectionally occupies approximately 3 cm2 of antenna curtain (when elements are arranged hexagonally). This area accommodates the array emitter, and further, deeper in the antenna curtain, - RTCh elements connected to the same. Due to large number of RTCh arranged on the array curtain (tens of thousands) and relatively low efficiency factor (EFF) of solid state power amplifiers of transmitting channels (compared to electronic tubes of passive PhAr) caused by tight arrangement of curtain elements, one of the main difficulties in the design of closely spaced arrays constitutes in heat removal from the transmitting channel elements.

The issue of ensuring tight arrangement of antenna curtain of prospective APAA can be solved through RTCh miniaturization by way of developing the main elements of RTCh (transmitting channel power amplifiers (PA), receiving channel low noise amplifiers (LNA), phase shifters (PhS) and attenuators (ATN) of channels, receiving channel protection devices (PD), etc. - see Figure 4) with the use of monolithic microwave integrated circuits (MIC) of frameless type.

Fig. 4. Elementary functional diagram of RTCh and 4-channel RTM (power amplifier of transmitting channel is shown separately)

Gallium arsenide (GaAs) or a more promising material - gallium nitride (GaN), is typically used for manufacturing solid-state active elements of RTCh.

As a rule, a board with RTCh elements is made using LTCC-technology (Low Temperature Co-Fired Ceramic technology). At a relatively low cost of manufacture, this technology ensures high strength and good heat conductivity of the board together with the multi-layer design for arrangement of RTCh elements and creating passive elements.

Several RTCh designed based on frameless MIC are fitted into a single body as a multi-channel receive/transmit module (RTM). The same body accommodates power supply devices common for several RTCh (DC/DC voltage converters), circuits of synchronization, channels phase and amplitude digital control, and the metal base of the module accommodates the tubes of liquid cooling system for removal of emitted heat. Figure 4 shows an example of RTM including elements of four RTCh (except for emitters) and various common channel devices.

RTM is a primary replaceable structural element of APAA.

Several RTM are structurally and functionally combined in APAA subarray unit.

The subarray unit is a functionally complete APAA element (independent mi-ni-APAA) with own control, power supply (АC/DC) and cooling systems. DAPAA subarray unit can additionally perform digitization of the received signal.

The subarray unit can be used as a basic element for development of APAA with different dimensions and configurations for various-purpose radars (so called APAA scaling technology [4]).

Basically, the entire SHF APAA of prospective radar consists of a certain number of subarray units arranged on the main frame of antenna curtain, as well as a radiation pattern shaper (subarray signal multiplexer), subarray control and operation synchronization devices, power supply and array cooling devices.

With such type of arrangement, the characteristics of prospective APAA are ultimately determined by the characteristics and number of RTCh, basically, by power and EFF of transmitting channel power amplifier, noise factor of receiving channel LNA, weight-and-dimensional characteristics and cost of RTCh.

A representative example of A-band radar, where the described APAA design concepts are implemented, is mobile (towed) radar AN/TPY-2 with A-band APAA of the USA antimissile defence (AMD) system.

Radar AN/TPY-2 is a high-potential radar - its maximum range of target detection with 0.01 m2 RCS is estimated as 870 km (with signal duration of 0.1 s) [4]. This radar includes 4 main elements: antenna module with APAA, electronic module, cooling device for APAA (cooler) and 1300 kW, 4160 V (3x60 Hz) power source.

Antenna module is an APAA (Fig. 2, 5) with the area of 9.2 m2, made of 72 similar subarray units, making 25,344 channels in total. APAA mean emitting power is equal to 81 kW (mean emitting power of one transmitting channel is 3.2 W). APAA RTCh are implemented in a form of GaAs-based solid-state MIC.

The cost of antenna module is 140 mln dollars, the weight is 24 t.

Fig. 5. AN/TPY-2 APAA architecture. Subarray unit and one RTM are shown separately

The electronic module shapes control signals, processes received signals, sets APAA operating procedure during scanning and target tracking, shapes transmission signals, interacts with AMD control system. The cost of electronic module is 23 mln dollars, the weight is 16.4 t.

The cost of cooler and power source is 7.5 and 15.5 mln dollars, respectively, and the weight is 18.6 and 28.6 t.

Currently, a program of consistent modernisation of all 12 radars AN/TPY-2 operated by the US Army is implemented with the replacement of RTCh with new GaN-based ones. The approximate cost of modernization of one radar is 63.0 mln dollars. The modernization will allow to significantly (presumably by tens of percents) increase the emitting power without any changes in the level of radar power consumption.

Each of 72 subarrays (Transmit/Receive element assembly - T/REA) of AN/TPY-2 APAA consists of 11 RTM (Transmit/Receive (T/Rmodule). Each RTM consists of two submodule boards including 16 RTCh each. Two submodules, mounted on a common metal base in inversed manner, structurally form a single 32-channel RTM. Apart from 32 RTCh, RTM includes 8 DC/DC voltage converters, 4 integrated circuits of control system controller and 2 - of beam shaping.

The RTM base serves for submodules fastening and at the same time acts as a radiator for removal of emitted heat, for which purpose it accommodates tubes with liquid coolant.

The submodules are mounted on the base with a vertical shift relative to each other by 1/4 of the wavelength in order to form a hexagonal antenna array.

Apart from 11 32-channel RTM, each subarray unit (T/REA) includes a unit consisting of 352 emitters connected with the corresponding receiving and transmitting channels, 2 modules of subarray operation control (SAM) and 2 AC/DC voltage converters.

As a result, the subarray unit represents a tightly packed and functionally complete APAA element, being the main replaceable element during on-line repair.

Apart from 72 subarray units, APAA also includes subarray control and input voltage conversion units (4160/150 V).

The domestic X-band prospective mobile radar with APAA, described in articles [8][9][10][11] (possible appearance is shown in Figure 2), being under development, features the design similar to that of radar AN/TPY-2. Its APAA consists of 128 subarray units arranged on a curtain of 16 columns and 8 lines.

The subarray unit represents a 256-channel antenna system. It includes eight 32-channel RTM, emitters unit with a shelter, addition and division module, distribution module, amplification module, cables, electric and hydraulic connectors (Fig. 6).

Fig. 6. The structure of domestic prospective mobile radar APAA subarray unit: appearance of subarray unit; diagram of one RTM (3 OPA and 2 SPS are not shown to demonstrate the cooling tube); emitting element

Each RTM consists of two submodules located on a common metal base with channel shift (Al-Li alloy). A copper tube with circulating liquid coolant is laid inside the RTM base under the channels’ output power amplifiers (OPA) and secondary power sources (SPS), this tube ensures heat removal from both submodules. Liquid cooling tubes of separate RTM are hydraulically interconnected within the subarray unit structure. A submodule includes 16 RTCh, 4 SPS, phase shifters and attenuators control module and signal summing module.

The emitter of each RTCh is designed as a cylindrical ferrite rod braced with heter-opolar permanent magnets.

Total heat emitted by all APAA RTM amounts to hundreds of kilowatts. To remove such amount of heat and extract it to atmosphere, each APAA column (per every 8 subarray units) features special liquid cooling device (LCD) containing thermotechnical equipment (pump, heat exchangers, fans, etc.) and electronic units [12].

Apart from APAA and 16 LCD, the radar module includes units of space-time processing, control and commands, synchronization and monitoring, control computer and technological workstation [8][11].

1.2.2. Specific features of APAA of UHF and VHF wavebands

APAA of prospective radars of UHF and VHF wavebands, as well as APAA of SHF band, are designed based on RTM developed using MIC technology and GaAs or GaN materials.

Specific features of APAA of UHF and VHF wavebands consist in increased distances between emitting elements of APAA structure and consequently decreased number of RTCh being part of RTM. Thus, e. g., the developed S-band APAA of AN/SPY-6( V) prospective multi-functional radar of Aegis BMD AMD ship (USA) features 6-channel RTM being part of subarray unit (two 3-channel submodules in each RTM), the distance between channels is ~ 0.06 m (Fig. 7).

Fig. 7. Multi-functional radar AN/SPY-6(V): appearance of one side of multi-functional radar (four sides in total); APAA bearing framework for arrangement of subarray units; one subarray unit (24 RTM, one 6-channel RTM is extended)

As the wavelength increases, in prospective radars the number of RTCh being part of RTM decreases. APAA RTM are implemented in a single-channel version in a long-wave-length part of UHF band and in VHF waveband.

As the wavelength increases, the value of specific heat emission per APAA surface unit decreases, which allows to use forced air cooling of RTM instead of liquid cooling in a short-wavelength part of UHF band, and natural air cooling - in a long-wavelength part of UHF band and in VHF waveband.

Thus, VW-band APAA of VHF band radar module being part of “Nebo-M” radar complex have RTM and their power supply sources located near each emitting element, they feature natural air cooling and are integrated in a single structural element - column (Fig. 8).

Fig. 8. Structural elements of APAA of long wavelength: 4-channel RTM of L-band (forced air cooling); one-channel RTM of VHF-band (natural air cooling); radar complex Nebo-M RLM-M APAA column elements

Another specific feature of APAA of a long-wavelength part of UHF and VHF wavebands is a transition from hexagonal array arrangement of RTCh on antenna curtain to their arrangement on rectangular array. This is due to the lack of sufficiently reliable technologies of closing-down of oversized antennas with hexagonal array available nowadays.

The performed design analysis of prospective APAA of different wavebands allows to make a conclusion that specific features and characteristics of APAA of different wavebands mainly depend on the characteristics and number of RTCh. In turn, the characteristics and possible number of APAA RTCh depend on the used wavelength and chassis lifting capacity limitations. Let’s establish these dependencies.

1.3. Establishment of APAA characteristics dependence on the wavelength

The basic characteristics used in all further calculations for APAA of developed combat air defence radars are the following: Рк - сmean emitting power of one APAA channel, mк - reduced channel weight, Ск - discounted relative channel cost, η - APAA EFF.

For these characteristics, there are dependencies of Рк(λ), mк(λ), Ск(λ), η(λ) at a wavelength change in the range of 0.03-1 m. The listed dependencies are shown in Figure 9 in a form of mean values and variation range limit values (with 90 % probability).

 

Fig. 9. Dependencies Рк(λ), mк(λ), Ск(λ), η(λ), characterizing technical capabilities of developing APAA of combat air defence prospective radars

The dependencies are obtained based on the analysis of available design characteristics data of 12 domestic and foreign prospective radars of different wavebands. Besides, these dependencies were obtained considering the data of domestic hardware components, which are available (by cost and manufacture time) and may be used for development of combat air defence prospective radars APAA.

Mean channel emitting power Рк is defined by the characteristics of output power amplifier and its design features (e. g. application of LDMOS--technology [13]), characteristics and number of preamplifier stages, used material (GaAs, GaN).

The obtained dependency Рк(λ) is steadily increasing. Thus, in X-waveband hardware components, which are available for batch production of combat air defence prospective radars APAA RTCh, allow to develop APAA with one channel mean emitting power Рк2-9 W. As the wavelength increases, channel mean power Рк significantly rises. In VHF band, values Рк = 140-220 W and higher are ensured.

Indicators mK and Ск are APAA full weight and cost values, reduced/discounted (proportionally) to one channel. They were defined with consideration of APAA hardware only (including cooling system hardware). Radar module hardware, not included in APAA, is considered unified for different wavelengths (see [1]) to the maximum extent for the developed combat air defence weapons, and weight and cost of this hardware (within the task of developing radar preliminary conceptual design) are considered independent of waveband.

Thus, reduced channel weight mк represents APAA weight corresponding to one RTCh. At that, consideration is given to the weight of one RTM itself, as well as the weight of common channel modules of a subarray unit and its framework, the weight of subarray signal multiplexing hardware, power voltage converters, cooling system and other common hardware of APAA, corresponding to one RTM.

The obtained dependency mк(λ) is steadily increasing with two jumps of reduction by ~15 and ~5 % in L and UΗF-wavebands, due to change of cooling system type - transition from liquid cooling to forced air cooling type, and then to the natural air cooling, respectively. To ensure the accuracy of further calculations, it is assumed that jumps of function mк(λ) occur at wavelengths of 0.23 and 0.7 m, respectively. (Wavelength values of possible transition from one cooling system type to another may differ, depending on availability of the corresponding technologies.) Mean value of function mк(λ) varies from 0.6 to 13 kg.

At a stage of conceptual design development, the cost is an indicator of the developed radar which is most difficult to determine. Absolute cost values depend on both technology factors of radar development as such, and industrial and other external factors. E. g. the cost of radar AN/TPY-2 in different years of production varied by up to 20 % (depending on the price of accessories, technology assimilation and available investment in production development) [4].

The task of developing a conceptual design of radar (1) defined in a form of cost minimization problem allows to exclude the necessity of estimating the cost absolute values and to consider only APAA cost variation (at λ variation) resulting from technology factors, relative to some basic level. The cost of APAA of 3-centimetre band is accepted as a reference point for estimating the cost of different waveband APAA options. Design features of this class of APAA are described above in detail.

Expenditures for liquid cooling and forced air cooling systems of APAA RTCh are the factors increasing the cost of RTCh in SHF and short-wavelength part of UHF band. At the same time, the analysis revealed that discounted relative RTCh cost tends to rise as the wavelength increases, which is caused by appreciation of MIC amplifiers, secondary power sources, as well as ADC integration into RTM [14].

APAA EFF η, defined as the ratio between mean emitted and mean consumed power of APAA, depends on the EFF and number of power amplification stages of transmitting channel, EFF of power sources (voltage converters) of RTM, subarray unit and entire APAA and substantially less significantly - on EFF of transmission channel passive elements (attenuators and phase shifters), as well as other APAA hardware power consumption level. Due to long power conversion circuit and relatively low EFF of solid-state emitting hardware components (as compared to vacuum-tube components), EFF of solid-state APAA is low, in particular at small wavelengths. Thus, EFF of radar AN/TPY-2 APAA developed in early 2000s is about 8 %.

For solid-state hardware components available for developing APAA of combat air defence prospective radars, EFF of power amplifiers is characterized by the values from 25-40 % in SHF band up to 50-65 % in VHF waveband, at that, the highest EFF values are reachable when using GaN-materials (see e. g. patents [15][16][17]). Accordingly, APAA EFF steadily rises in λ parameter from 11-20 % in А-band to 30-50 % in UHF, VHF wavebands.

If new data becomes available, the obtained dependencies Рк(λ), mк(λ), Ск(λ), η(λ) may be adjusted with respect to their absolute values. However, the revealed common trends based on the analysis of prospective APAA structural features will remain unchanged - i. e. the outstripping rise of one channel emitting power as wavelength X increases at simultaneous rise of APAA EFF versus less significant increase of channel reduced weight and discounted cost. These trends allow to make a conclusion about potential preference of a long-wavelength band of prospective radars with respect to the emitting power indicator.

The limiting number of RTCh nк being part of APAA considering APAA weight limitations mогр equals to

nк = mогр/mк

The dependence of RTCh limiting number nк(λ), calculated based on previously obtained value of prospective radar APAA weight limitation mогр = 8 t, is shown in Figure 10.

Fig. 10. The limiting number of RTCh being part of APAA at mогр = 8 t

Antenna aperture area depends on the elements arrangement pattern.

When the elements are arranged in the square or equiangular triangle angles (square or hexagonal array lattice), the area corresponding to one emitting element is calculated (see [18]) using the following formulas, respectively

where θмах is limit angle of beam deviation from the normal in vertical (horizontal) plane, determined by the condition of beam uniqueness.

Hexagonal lattice is preferable with regard to minimizing the number of elements per area unit to ensure the required value θмах. However, this lattice is inconvenient when developing folding (closing-down) antenna arrays.

The diagram of dependence of APAA area corresponding to one channel on the wavelength is shown in Figure 11. When plotting the diagram it is assumed that in wavelength band λ < 0.5 m hexagonal array lattice is used, and in λ ≥ 0.5 m – square array lattice, θмах = 45°. 

Fig. 11. APAA area corresponding to one channel

Antenna aperture area is defined as the product of the number of RTCh nк and area corresponding to one channel Sк. Considering antenna aperture limitation Sorp, the maximum antenna aperture area Sa is defined as the smallest of two values:

Sа = min{nкSк; Sогр},

where Sк assumes a value Sтр, or Sкв в depending on the array lattice.

Figure 12 shows the dependency diagram of APAA maximum aperture area Sа(λ), calculated considering weight limitations (mогр = 8 t) and based on the maximum antenna area (Sогр = 130 m2), arranged on a mobile chassis.

Fig. 12. Maximum antenna aperture area

Jumps of function Sa(λ) shown in Figure 10 in points λ = 0.23 and 0.7 m result from a change of RTCh cooling type, and in point λ = 0.5 m -from a change of the array lattice.

In order to use dependence nк(λ) in further calculations, it shall be recalculated considering the impact of antenna size limitations Sorp on the number of RTCh:

nк(λ) = Sа(λ)/Sк(λ).

Maximum mean emitting power of APAA Pa is defined as the product of the number of RTCh nK and one channel mean power Рк considering power consumption limitation:

Ра = min{nкРк; Рогрη}.

Figure 13 shows the diagram of change of APAA maximum emitting power considering limitation Рогр = 350 kW by power of MIPS used on a mobile chassis.

The function of RTCh limiting number nK(λ) allows to estimate the change of APAA maximum cost depending on the wavelength. APAA relative maximum cost (relative to the cost of basic APAA with wavelength λб = 0.03 m) equals to

The diagram of APAA relative maximum cost is shown in Figure 14.

Fig. 14. Relative maximum cost of APAA

The diagram Са(λ) shows that as wavelength λ increases, despite an increase of channel relative cost Ск, the outstripping decrease in the number of RTCh contributes to significant reduction of APAA cost. The generally steady nature of function Са(λ) decline allows to make a conclusion that optimal task solution (1) in case of several options satisfying the preset requirements is in higher wavelength values.

The reviewed characteristics are sufficient for calculating the purpose indicators used in definition of the task of developing the radar (1) conceptual design. Other characteristics and APAA (e. g. noise factor kш) do not significantly depend on wavelength λ, which is significant within the framework of solution of the task of preliminary development of the radar conceptual design.

Further, the procedure of task solution (1) is based on calculating radar purpose indicators depending on the wavelength and comparing the obtained results with the required ones. For clarity, the procedure of actions shall be considered simultaneously with performing numeric calculations in connection with solution of the task of developing a conceptual design of SS radar located on the command post of long range SAMS (see [1]), at the same time pointing out the calculation distinctions for other radar types.

  1. Calculation of radar purpose indicators considering structural and technical parameters characterizing its conceptual design

2.1. Estimation of radar operating range

The operating range of different types of radars is defined as the product of

RРЛС = R0 Кп.атм Кинт,                                      (2)

where R0 is radar operating range in free space (not considering the ground effect and signal attenuation in the atmosphere); Кп.атм, Кинт are signal energy loss factor with atmospheric propagation and ground interference multiplier, respectively.

Radar operating range in free space against a target with effective scattering area (ESA) σц with matched signal processing is determined by the formula  

where Gпер = ρ(4πSа2) - is antenna transmit-ampli-fication gain; τс is signal duration (single or burst of coherent pulses); 0 is product of Boltzmann’s constant and antenna noise temperature; kш is receiver noise factor; kр is discriminating factor (preset signal/noise ratio); kп is factor of radar total signal loss during emission and reception; p is aperture efficiency.

Indicators РаSa, Gnep are wavelength λ functions. Limit values Ра(λ), Sa(λ), calculated considering chassis limitations, are defined above. Indicator Gnep is calculated by the formula

Gпер = ρ(4πSа2)

Parameters kТ0, kш, kп for developed SS radar, based on its design features, shall be taken equal to: kТ0 = 4×10-21 (Втхс), kш = 2,5 дБ; kп = 8 dB.

Discriminating factor is connected with the probability of false alarm F and correct detection D:

Values F, D are selected, inter alia, considering radar capacity analysis (see information below). For developed SS radar, it is assumed that kр = 13 dB, which corresponds to signal extraction from noise with false alarm probability F = 10-6 and correct detection probability D ≈ 0,52.

Formula (3) allows to determine radar slant operating range against a target observed at an angle θ relative to the normal to PhAr curtain. Depending on this angle value, factor ρ is calculated by the formula:

ρ = ρ0cosθ,

where ρ0 is antenna aperture efficiency when operating against the normal.

For SS radar, it is assumed that ρ0 = 0.7, limit value θ equals to 45°.

Indicators τс, σц depend on the radar purpose. For clarity, it is assumed that the main purpose of SS radar is ballistic targets detection to a range Rтр = 300 km and more. The targets are represented by short-range ballistic missiles and medium-range missile warheads. Generally, the targets ESA is a wavelength function. For BT of considered class, dependency оц(λ) shown in Figure 15 [4] shall be used.

Fig. 15. Effective scattering area of BT

For detection of small targets like BT at long ranges, it is necessary to increase signal energy, at the same time increasing its duration. However, the increase of signal duration is limited by the possibilities of its coherent processing, as well as by allowable time of beam fixing in one angular position for ensuring high radar capacity. Considering the above, for developed SS radar it is assumed that тс = 1 ms.

The results of SS radar operating range R0 calculation depending on the wavelength with preselected structural and technical parameters are shown in Figure 16.

Signal energy loss factor with atmospheric propagation Кп.атм is determined by the known ratio [19][20][21][22]:

Кп.атм = ехр{–0,115βзат2Rп},                                   (4)

where βзат is factor characterizing specific attenuation (in decibels per kilometre) at propagation of radio waves in the atmosphere in one direction; Rп is length of radio waves path at atmosphere propagation in one direction (path duplication corresponds to radio wave propagation in forward and backward directions).

Attenuation factor βзат as wavelength function is a known value. In wavelength bands from SHF to UHF, factor βзат reduces steadily, and at λ ≥ 0.5 m it is assumed equal to zero.

The length of radio waves path in the atmosphere can be calculated having been given a depth of the atmosphere Натм and knowing target elevation angle s.

It can be shown that for a spherical model of the Earth with radius R3 covered with an even atmospheric layer with depth Натм, the path length in one direction is expressed by the formula

The troposphere contains more than 80 of the total atmospheric air mass. The troposphere depth varies with latitude. It is 10-12 km in middle latitudes. Considering this fact, the depth of the atmosphere in middle latitudes is assumed equal to Натм ~ 12 km.

The diagrams of dependencies of the path length on the target elevation angle and wavelength loss factor for certain target elevation angles calculated by formulas (5) and (4), respectively, for middle latitudes are shown in Figure 17.

Radar operating range considering signal energy loss with atmospheric propagation shall be defined as the product of

R0п.атм = R0Кп.атм.

For considered SS radar, diagrams of operating range R0п.атм(λ) in the direction of APAA normal (9 = 0°) for different elevation angles of the normal are shown in Figure 18.

SS radar is characterized by operation with high elevation angles of APAA normal (not less than 20°). At that, Figure 18 demonstrates that signal atmospheric propagation energy loss has minor impact on radar operating range.

At low elevation angles of APAA normal (few degrees), by which LAT radars are characterized, the impact of signal attenuation in the atmosphere is significant for the operating range, in particular in X, C, S-wavebands.

Besides atmospheric impact, at low elevation angles comparable to beam width, the interference of a direct wave and a wave reflected from the Earth surface has impact on radar operating range. This impact can be considered using ground interference multiplier Кинт, calculated by formula [19][20][21][22]

where Нант is height of antenna array phase centre; e is target elevation angle; р is wave reflection factor,  р ∈ [0, 1]; φ is phase change of wave reflected from the Earth surface, φ ∈ [0, π].

The impact of wave interference is most significant for LAT radars, which operate at low elevation angles, and in particular - at long wavelength. For SS radars, such impact depends on the BT trajectory type.

To estimate the features of SS radar operation against BT with different trajectories, operational areas of two SS radars (operating at wavelengths λ = 0.77 and 0.03 m, respectively) and two BT trajectories (MRBM with flight range Ln = 1000 and 3500 km, respectively) were shaped in the vertical plane passing through the radar normal (Fig. 19).

Fig. 19. Cross-sections of operational areas of two SS radar versions (with λ = 0.03 and 0.77 m) and trajectories of two targets of MRBM class

Operational areas are calculated by formula (2) in elevation sector of 0.3-75° at normal elevation angle of 45°; ground interference multiplier is assumed equal to р = 1, φ = п.

The target trajectories are shaped for the case of optimal program flight (to the maximum range). Models given in [4] were used for calculations.

A radar operating at wavelength of 0.77 m has the maximum operating range of ~400 km. For a 3-centimetre radar, the operating range is significantly lower (not more than ~190 km), besides, signal loss is possible at low elevation angles (however, it will be shown below that high targets resolution is achieved).

Figure 19 shows that at MRBM optimal program flight the angles of targets entry to SS radar operational areas are within 45-60°. Considering the above, antennas normals elevation angles are assumed equal to 45°.

In the lower part of the area, the operating range is lower due to signal energy loss and antenna aperture efficiency reduction. At λ = 0.77 m, the beam width in the lower part of the area is ~10°, at that, within the beam directed along the Earth surface, there are significant interference lobes. Interference lobes allow to detect short-range BT (at a range up to 500-700 km) on the ascent part of trajectory (in the barrier area) with subsequent continuation of their movement.

For further calculation of developed radar capacity, the velocity of targets entry to radar operational area is estimated. At a range of 300 km, they were equal to ~2.4 km/s for BT with Lп = 1000 km and ~5 km/s for BT with Lп = 3500 km.

The calculations are supported by three-dimensional representation of SS radar operational areas and targets trajectories, acting from different azimuth directions (Fig. 20). Radar operational areas are shaped by the formulas and based on initial data specified above. The width of azimuth sector of each SS radar is assumed equal to 90°. Target trajectories are shaped using models [4].

Fig. 20. Three-dimensional representation of two SS radars operational areas against two targets of MRBM class

Generally, the given formulas and sequence of their application allow to estimate the correspondence of possible radar versions operating at different wavelengths to the operating range requirements.

With respect to considered SS radar, at required operating range Rтр = 300 km task solution (1) will be in wavelength band from λ = 0.25-1 m, with a preference (by minimum cost criteria) to longer waves.

Radar version may be finally selected based on the results of radar resolution, accuracy and capacity estimation.

2.2. Calculation of resolution and accuracy of target profile estimation

Radar resolution is estimated by the following formulas [19]:

  • by angle coordinates (elevation angle ε and azimuth β, generally – by angle Θ) when using antenna for transmission and reception [19, p. 283]:

where Lа is linear dimension of antenna aperture in the plane of angle concerned; Θ is angular deviation of signal reception direction from the normal;

  • by range:

ΔR = с/(2 · Δf)

where c is light speed; Δf is signal band;

  • by radial velocity:

ΔV = λ/(2 · τс).

To refer the indicator of radar resolution in range to the wavelength, it shall be written over as follows

ΔR = λ/(2 · kf),

where  kf = Δf/fс - is ratio between receiver pass band and signal carrier frequency. For prospective radars, factor kf is within the range  kf = 0,05-0,1.

The accuracy of target parameter measurement (root-mean-square deviation) is directly proportional to radar resolution with respect to this parameter and inversely proportional to the root of the signal/noise ratio (q), at which the measurements are carried out, with certain factor of proportionality depending on signal processing particularities. To estimate potential accuracy of target angular coordinate, range and radial velocity measurement, formulas [19, p. 328, 331] may be used, respectively:

Signal/noise ratio, considering signal loss in the atmosphere, may be defined by formulas (2), (3):

q = q0 · Кп.атм4,

where is signal/noise ratio, not considering atmospheric impact.

For the considered SS radar, diagrams of dependency of maximum possible value q on wavelength λ in the direction of APAA normal at range Rтр for different elevation angles of the normal are shown in Figure 21.

The calculation results for indicators of resolution and accuracy of target profile estimation are shown in Figure 22.

The indicators of SS radar resolution by angle coordinates and accuracy of angle coordinates estimation are calculated in the direction of normal (angle Θ = 0°). Dimensions of antenna aperture are defined based on its area: La = Sa1/2. SS radar resolution by range is estimated based on factor kf = 0.05.

Weak dependence of accuracy of target profile estimation on the wavelength should be noted (when developing APAA with maximum weight, which is limited by chassis lifting capacity, and fixed signal parameters). Such behaviour of accuracy indicators is caused by a rise of signal/noise ratio as the wavelength increases due to previously revealed tendency of “RTCh mean power/RTCh weight” ratio rise.

It should be noted that calculated indicators of resolution and accuracy of target profile estimation are maximum achievable. In practice, worse values should be expected, however, the tendency of indicators dependency on the wavelength will remain.

2.3. Estimation of radar capacity

Radar capacity depends on the time of scanning of the specified space sector. The size of the scanned sector is equal to the product of elevation and azimuth centre angle ΔE×ΔB. The number of beam angular positions in the scanning sector with beams overlapping factor Кпер.л may be estimated by the formula 

Nл = ΔE · ΔB/(Δε · Δβ · Кпер.л2),

where Δε, Δβ is radar resolution by elevation angle and azimuth, respectively (determined by formula (6)).

Net sector scanning time (in the absence of scanning delay for targets route initiation, their tracking and false alarm follow up) is equal to

Тч.обз = ТлNл,

where Тл is time of beam fixing in one angular position.

Value Тл may be determined based on the necessity of target detection at a preset range Rтр:

Тл = 2Rтр/C,

at that, it shall not be less than signal duration τс.

During scanning, the range is estimated, and in some cases - also by the velocity of detected targets. The number of range and velocity cells is determined by the formulas, respectively

Nяч.R = (Rтр – Rн)/ΔR, Nяч.V = (Vтр – Vн)/(ΔV · Кпер.V),

where Rн, Ун are initial values of slant range distance and radial velocity ranges, respectively; Vтр is preset value of maximum radial velocity of detected targets (for the above SS radar we get Vтр ~ 5 km/s); Кпер.V is velocity filter overlapping factor.

The total number of range and velocity cells tested for target presence amounts to

Nяч = Nл Nяч.RNяч.V

Space scanning is carried out through cells testing for exceeding the detection threshold. The detection threshold may be exceeded with probability F due to noise spike (“false alarm” event). The total number of cells, in which “false alarm” will occur during space scanning, amounts to

Nяч.лт = NячF.

False alarm follow up takes certain time, which slows down scanning. Total time spent for checking all falsely activated cells amounts to

Тлт.сум = NячТлт,

where Тлт is time required for one false alarm follow up.

Time Тлт is determined by the used route initiation criteria. It can be shown that for the most commonly used route initiation criteria (“two out of two”, “three out of four with mandatory second”), false alarm follow up time may be assumed equal to beam fixing time:

Тлт = Тл

The time of scanning of the specified space sector, considering possible delays for false alarm follow up, amounts to

Тобз.лт = Тч.обз + Тлт.сум

The time of scanning of the specified sector is also increased by the time spent for tracking of previously detected targets.

An increase in time for tracking of targets is calculated recursively. It can be shown that total time of scanning of the specified sector, considering time spent for target tracking Nсц, at that equals to

Тобз = Тобз.лт /(1 – Kсц),

where factor Kсц = Nсцτсцсц; Тсц is period when radar addresses the tracked target; тсц is time of tracking of one target in one angular position of the beam.

The calculation results for the scanning time of SS radar are shown in Figure 23. The calculations were performed for the sector size of 75×90 deg.2 in the range of 20-300 km. It is assumed that for route initiation “two out of two” criterion was used, probability of false alarm F = 10-6; simultaneously with scanning, tracking of 10 targets was performed with target addressing period Тсц = 1 s and time for target tracking at each addressing to the same тсц = 1 ms.

  1. Procedure for determining rational conceptual design of radar systems

All analytical relations obtained for calculating the main radar purpose indicators represent functions of one common independent variable, i. e. wavelength, which allows to find an optimal graphical solution for developing conceptual design of radar (1). For task solution (1), it is necessary to plot the diagrams of purpose indicators calculated using certain values of considered variables characterising the radar and display the limitations imposed on purpose indicators. Due to the previously revealed steadily reducing dependency of APAA cost on the wavelength (Fig. 14), task solution (1) resulted in the highest wavelength values within the allowable values of purpose indicators and the corresponding quantitative values of considered radar structural and technical parameters.

Thus, for considered SS radar, the main purpose of which consists in space scanning within the specified sector sized 75x90 deg.2 during the time not exceeding 2 s, detection of ballistic targets at line Rтр = 300 km and estimation of their parameters with preset requirements for resolution and accuracy, the calculated diagrams of purpose indicators are shown in Figure 24.

Fig. 24. Main purpose indicators of SS radar and their limitations

With respect to the requirements preset for certain indicators shown in the diagrams, the solution lies in the wavelength band of ~0.65-0.8 m. By the minimum cost criteria, the best solution would be to develop SS radar with wavelength of 0.8 m. This SS radar version is characterized by the following main structural and technical parameters: mean power of one RTM of ~150 W, reduced weight of RTM of ~11.2 kg, number of RTM being part of APAA of 592, antenna aperture area of 130 m2, relative cost of APAA (relative to APAA with X = 0.03 m) of ~0.08, mean emitting power of ~89 kW, signal band of ~20 MHz, radar power consumption of ~400 kW. Assurance of the specified RTM mean power at expected level of APAA EFF η = 35-40 % and air cooling of array elements involves usage of GaN-mate-rials in RTM.

If the requirements imposed on purpose indicators can not be met, the possibility of adjusting the requirements should be considered. For example, for SS radar narrowing of scanning sector allows to reduce the scanning time almost with the same ratio in a long-wave-length part of considered waveband.

Besides, it is possible to adopt different unformalized design solutions. For example, unsatisfactory resolution of acquisition SS radar operating in VHF waveband may be compensated by firing multi-functional radar operating in SHF band, supplementing SS radar operational area, as shown in Figure 17.

Thus created version of radar conceptual design should be considered primary and requiring further detail development.

The detail development tasks include clarification of structural and technical parameters through application of different design solutions. For example, an increase of the number of reception channels at simultaneous reduction of the number of reception/transmission channels (which are more expensive than reception channels) allows to reduce APAA cost within the framework of achieved purpose indicators, at a certain increase of reception aperture.

The most important issue that requires further detail development within the framework of the developed radar conceptual design consists in ensuring interference immunity of radar under the specified operating conditions.

Conclusion

he proposed procedure of developing a conceptual design of various-purpose radar stations for created combat air defence weapon system represents a complex of interconnected analytical relations allowing to estimate the impact of the main structural and external factors on radar purpose indicators and select a solution satisfying the specified requirements at minimum implementation costs.

A distinctive feature of this procedure is connection of all considered indicators to one common independent variable, i. e. radar wavelength, which allows to graphically compare the options and gives clarity for selecting the best solution.

The procedure is based on the dependency of APAA RTM basic indicators on the wavelength, obtained from the analysis of design features of prospective radars with APAA and compilation of well-known data on different RTM. Based on the obtained dependencies and considering weight-and-dimensional limitations imposed on combat air defence mobile prospective radars, the relations are proposed for calculating radar basic purpose indicators.

The proposed procedure allows to develop the primary version of radar conceptual design which is subject to further detail development for clarification of the applied design solutions and adding factors not considered in the procedure.

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About the Authors

S. V. Druzin
“Almaz – Antey” Air and Space Defence Corporation, JSC
Russian Federation

Druzin Sergey Valentinovich – Cand. Sci. (Engineering), Deputy General Director for Scientific and Technical Development, First Deputy General Designer

Research interests: system analysis, radar systems.



B. N. Gorevich
“Almaz – Antey” Air and Space Defence Corporation, JSC
Russian Federation

Gorevich Boris Nikolaevich – Dr. Sci. (Engineering), Prof., Project Manager

Research interests: system analysis, radar systems.



For citation:


Druzin S.V., Gorevich B.N. Methodology for developing a conceptual design of radar stations for prospective air defence weapon systems. Journal of «Almaz – Antey» Air and Space Defence Corporation. 2020;(2):6-31. https://doi.org/10.38013/2542-0542-2020-2-6-31

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