The purpose of the study was to build a surveillance radar station (radar) with an axisymmetric (i.e. cylindrical, conical, etc.), multibeam receiving-transmitting active phased array (APAR) and investigate its characteristics. The radar station makes it possible to shorten the surveillance time, increase the rate of updating information, provide flexibility in changing operating modes, increase the reliability and service life of a radar station as compared to a radar station with mechanical rotation of antenna systems. The radar station is compared with electronic circular scanning based on cylindrical, three- and tetrahedral APAR

Предложено построение и исследованы характеристики радиолокационной станции (РЛС) кругового обзора с осесимметричной (цилиндрической, конической и др.) многолучевой приемо-передающей активной фазированной решеткой (АФАР). Такая РЛС позволяет сократить время обзора, увеличить темп обновления информации, обеспечить гибкость изменения режимов работы, повысить надежность и ресурс РЛС по сравнению с РЛС с механическим вращением антенных систем. Проведено сравнение РЛС с электронным круговым сканированием на основе цилиндрической, трех- и четырехгранной АФАР

With emergence of air attack weapons flying at high supersonic speeds, an issue arises of reducing the time required for their detection, lock-on, and tracking.

To improve the rate of information updating in surveillance radars with electromechanical rotation of antenna systems in azimuth, increased rotation speeds are applied: up to 10, 20, 30 or even 60 rpm [

In this respect, a relevant problem is that of building all-round radar surveillance facilities that would be free from the weaknesses inherent in radars with electromechanical rotation of antenna systems.

Also applied are radars with pyramidally arranged planar phased antenna arrays (PAA), ensuring electronic scanning in two planes and forming the number of beams corresponding to the number of faces [

It is known that axisymmetrical PAAs (cylindrical, conical, etc.) do not feature a dependence of their parameters (directivity factor (DF), beam width) on beam direction in azimuth. In this respect, it is of interest to compare the characteristics of radars with axisymmetrical and pyramidal PAAs. In this paper, such comparison is made for the case of active PAAs.

Normally, axisymmetrical PAAs have a single beam, formed by radiating elements located in a restricted excited sector of the antenna surface. In the course of scanning, it is necessary to ensure excited sector movement over the antenna surface. Such APAA will knowingly be inferior to a multibeam pyramidal APAA in terms of the total radiated power at an equal number and power of the modules, since in any given moment of time part of its modules are not involved in the radiation process. The surveillance rate of an axisymmetrical APAA will be less than that of a pyramidal APAA, whose number of beams is equal to the number of faces. Besides, it is necessary to provide for excited sector movement over the antenna surface, which leads to complication of the beam-forming arrangement of an axisymmetrical PAA.

These drawbacks can be eliminated by forming, in an axisymmetrical APAA, of a multilobe radiation pattern (RP) for transmission and respective number of beam groups for reception. In the all-round surveillance mode, the maxima of a multilobe RP, which has K (2–4) similar main lobes, are oriented relative to one another at an angle of 360°/K in azimuth (Fig. 1). For reception, a group of receiving RPs is formed in the direction of each lobe of the transmitting RP, intended for detection of targets and mono-pulse measurement of their angular coordinates. Scanning is performed by simultaneous coordinated movement of all RPs in azimuth and elevation. In the transmission mode, all APAA modules operate for radiation with equal power, which allows to ensure the maximum APAA potential (product of the directivity factor by the radiated power [

Implementation of a multilobe RP operating for transmission is illustrated by a three-lobe RP of a conical PAA, shown in Fig. 1 in the azimuthal plane. The RP calculation is made for uniform amplitude distribution of incident waves at the input of all radiators. Phase distribution within the limits of each 120-degree PAA sector is optimal for sharp beam formation [

Fig. 1. Three-lobe RP for transmission of a conical APAA with base diameter 2a = 20λ; angle between axis and cone generatrix α = 12°; number of elements on the circle - 120; on the generatrix - 20; φ - azimuth angle

The maximum effective cross-section of a multibeam PAA, when operating for reception, can be obtained in APAA only, since the presence of low-noise amplifiers makes it possible to eliminate beamformer dissipative losses and losses for the non-orthogonality of beams [

This paper draws a comparison between the characteristics of surveillance radars with all-round electronic scanning on the basis of pyramidal and axisymmetrical APAAs, with multilobe RP for transmission and multibeam RP for reception. The comparison is drawn as per such criteria as the minimum possible surveillance time in the all-round sector, potential and DF, beam width, potential measurement accuracy of angular coordinates, and APAA overall dimensions.

In estimation of the minimum possible surveillance time, we assume that, despite the high speeds of targets, the time of target echo-signal integration is not that high so as to require accounting for the effects associated with target’s spatial movement over the integration time..

In this case, surveillance time T can be estimated using the known formula defining detection range during surveillance [

where Er min - received signal minimum energy, determined as per specified probabilities of detection and false alarm with the use of known relationships [

It is presumed that the values of parameters in formula (1) do not depend on direction in the surveillance sector.

We shall reckon that the losses associated with reflection of a portion of power at the radiating elements’ inputs do not depend on scanning direction and radiator position on the APAA surface. Since the case under consideration is that of simultaneous radiation of all APAA elements with the same power, radiation mean power P = P1N, where P1 – mean output power of the active module (per single radiating element); N – number of APAA elements.

Let us analyse the surveillance time at fixed values of RCS and range in the surveillance sector, taking into account that APAA effective cross-section for reception depends on the direction in space. Then formula (1) will be transformed to the view

The effective surface of a narrow-beam conformal antenna is easily obtained based on the expression for its DF [

where ka - aperture taper efficiency factor (TEF); under tapered amplitudes, to reduce the level of side lobes for reception ka

As a result, for the minimum surveillance time, from expressions (2), (3) we obtain

Using formula (4), it is possible to compare different radars with APAAs in terms of the space surveillance time.

Let us split the aperture of an axisymmetrical APAA into K sectors, corresponding to the number of RP main lobes for transmission. Each sector will be forming a single-beam RP, in accordance with polarisation and phase distribution which is optimal for obtaining the maximum DF [

To obtain the maximum potential, uniform APAA amplitude distribution for transmission is selected. In this case, from the relationships for DF of a conformal antenna under high-directivity radiation [

where Sk - sector area.

Potential Πk of the APAA is determined by the product of DF by radiation power, and in the considered case, Πk = P1NkDt(k) where Nk - number of elements in the k-th sector. For equal sectors

and APAA DF for transmission Dt = Π /P1N = Dt(k)/K.

Let us draw a comparison between different allround electronic surveillance systems. For simplicity, we shall consider a cylindrical multibeam APAA and tri- and tetrahedral APAA in the form of a prism (Fig. 2). We assume that the scanning sector in elevation is small, so that it could be possible to consider the characteristics of all APAA types similar and compare them in terms of scanning characteristics in the horizontal plane.

Fig. 2. Contours of cylindrical (a), tetrahedral (b) and trihedral (c) APAA in plan view; a – cylinder radius; L – face horizontal size

In drawing comparison, we shall assume that APAA module mean output power P1 and the number of elements N is similar for all APAA versions. Factors ka for reception are also assumed similar in all configurations.

In case of a cylindrical APAA, to obtain the maximum possible effective cross-section for formation of each receiving beam, we shall use the entire illuminated aperture half. For a polyhedral APAA, each receiving beam (or group of beams) is formed by one face only. This is explained by the presence of a gap between the faces, virtually unavoidable due to design considerations, which, when several faces are used jointly, leads to unacceptably high level of side lobes for reception [

where C – constant; H – cylinder height; φ' - azimuthal angle of point on the antenna cylindrical surface.

For a K-face prism, the minimum surveillance time will be

From the condition of the absence of diffraction lobes, circumferential spacing of cylindrical APAA elements must not exceed λ / 2. Hence, the minimum number of elements

where dz – vertical spacing.

From the condition of the absence of diffraction lobes, horizontal spacing d of the flat-face elements must not exceed d ≤ λ / (1 + sin (π / K)) [2, 4], and then the minimum number of elements

Equating the number of elements (10) and (11), we correlate cylindrical antenna radius and linear dimension of the face:

The values of surveillance time, potential, DF, and other parameters are normalised to respective values for a cylindrical APAA with single-lobe RP for transmission T0, D0 etc. In so doing, we shall assume that in a single-beam APAA, only a 180-degree sector of antenna cross-section is used both for reception and transmission.

The minimum surveillance time for a cylindrical APAA, with account of (7)

and for a polyhedral APAA, with account of (9), (12)

Then the transmission potential of a cylindrical APAA, with the use of (5), (6)

Here, integral is expressed through elliptic integrals, and can be calculated numerically too. For K equal to 2, 3, 4, values of γκ are, respectively, 1.198; 0.948, and 0.744.

For a polyhedral APAA, with account of (11)

where θ - angle of beam deflection from normal.

Let us write a mean value of the polyhedral APAA relative potential for the scanning sector in azimuth:

The effective cross-section for reception of a cylindrical APAA (same as the beam width) does not depend on the number of beams Ar/ Ar 0 = 1.Relative effective cross-section for reception of a polyhedral APAA

Then a mean value of the relative effective cross-section of a polyhedral APAA in the scanning sector

Relative beam width of a polyhedral APAA for horizontal reception is determined by the ratio of the lengths of equivalent apertures

mean value of relative width in the scanning sector as per the formula

The parameters of radar with a cylindrical APAA, with a different number of RP lobes for transmission, as well as with a tri- and tetrahedral APAA, calculated as per relationships (13)–(21), are given in Table 1.

As follows from the results given in Table 1, a radar with cylindrical APAA has the minimum possible surveillance time less by 12…22 % and the APAA potential higher than that of tri- and tetrahedral APAAs at the scanning sector edge, as well as less average beam width for reception and smaller overall dimensions.

Table 1

Parameters of active phased antenna arrays (APAA)

Parameters | Cylindrical APAA | Polyhedral APAA | |||
---|---|---|---|---|---|

Number of RP maxima for transmission, K | 2 | 3 | 4 | 3 | 4 |

Minimum surveillance time, T/T0 | 0,5 | 0,500 | 0,500 | 0,560 | 0,610 |

Potential for transmission, Π/Π0: • maximum; • average in azimuth; • minimum | 1 | 0,626 | 0,386 | 0,819 | 0,503 |

1 | 0,626 | 0,386 | 0,677 | 0,453 | |

1 | 0,626 | 0,386 | 0,409 | 0,356 | |

Effective cross-section for reception, Ar / Ar0: • maximum; • average in azimuth; • minimum | 1 | 1 | 1 | 1,122 | 0,920 |

1 | 1 | 1 | 0,928 | 0,828 | |

1 | 1 | 1 | 0,561 | 0,651 | |

Beam width for reception, Δθ / Δθ0: • maximum; • average in azimuth; • minimum | 1 | 1 | 1 | 1,782 | 1,537 |

1 | 1 | 1 | 1,120 | 1,220 | |

1 | 1 | 1 | 0,891 | 1,087 | |

Diameter of circumscribed circle | 1 | 1 | 1 | 2,250 | 1,300 |

It stands to mention that the comparison was drawn under excitation of a polyhedral APAA by distribution which is optimal with regard to the potential maximum criterion, whereas for a cylindrical APAA, distribution is only optimal for independent excitation of the cross-section area sectors. Given an optimal excitation of a cylindrical APAA, some additional increase in potential can be expected.

Remarkably, the minimum surveillance time for a radar with cylindrical APAA does not depend on the number of beams for transmission (2, 3, or 4), as with a greater number of beams more time is required for detection of target in each spatial direction, with the probabilities of detection and false alarm remaining the same.

Let us compare the systems under consideration for potential measurement accuracy of target angular coordinates, which is defined by noise RMSE [

where c – a certain constant; W – S/N ratio at receiver input.

The S/N ratio for the APAAs being compared differs, due to the differences in potential and effective cross-section for reception, in such a way that the relative error of angular coordinates measurement

Given in Table 2 are the calculation results of relative noise error of azimuth measurements as per APAA parameters (see Table 1).

Table 2

Noise error in azimuth measurement

APAA | Relative noise angular error in all-round surveillance sector, σθ / σθ0 | |
---|---|---|

average | maximum | |

Cylindrical: • two-beam; • three-beam; • four-beam | 1,00 | 1,00 |

1,26 | 1,26 | |

1,61 | 1,61 | |

Trihedral | 1,41 | 3,72 |

Tetrahedral | 1,99 | 3,19 |

The overall dimensions of a cylindrical APAA are smaller than those of a polyhedral one. With radiating elements of the neighbouring faces being adjacent, prism diameter (see Fig. 2) turns out to be larger than the diameter of a cylindrical APAA. According to the assemblability conditions of a polyhedral APAA, considering its thickness, its dimensions have to be larger still.

The shape of PAA axisymmetric surface generatrix can be different. Among the known designs are cylindrical, conical, spherical PAAs and PAAs on the surface of paraboloid of revolution [5, 11]. Let us consider the dependence of the maximum DF of a cylindrical, conical, and paraboloid antenna vs. scanning angle (RP) in the elevation plane at the same antenna height h and equivalent flat aperture area under radiation in the direction of horizon (Fig. 3).

Fig. 3. Vertical cross-section of axisymmetric cylindrical (a), conical (b), and paraboloid (c) PAAs

It is presumed that the radiating elements are arranged only on the side surface of the cylinder and cone.

Based on the formula (2.21) [

where a2 – base radius (see Fig. 3), ε - elevation angle from the horizon;

Expressions for the maximum DF of a cylindrical and conical antennas are given in [

By selecting surface shape, it is possible to ensure a required law of DF variation depending on elevation angle ε (see Fig. 3). A cylindrical PAA is suitable for scanning in a limited sector of elevation angles. At a change of elevation angle, DF of a conical PAA, with angle between axis and generatrix α=15°, changes insignificantly.

The given dependencies of DF vs. scanning angle relate to a PAA with controllable polarisation of radiators. Under fixed polarisation of radiators, DF can decrease much faster with the increase of the elevation angle. However, for a cylindrical and conical PAA with radiators in the form of slots or vibrators, whose axes are arranged along PAA surface generators, the losses associated with non-optimal polarisation of radiators are small at cone angles α ≤ 30° [

In the proposed configuration of an all-round surveillance radar with a multibeam axisymmetrical APAA for transmission, a multilobe radiation pattern is formed. The maximum radiation power and energy potential in each beam are provided due to equal radiation power of all APAA elements. In the receiving mode, respective number of receiving beams is used, with the maximum effective cross-section ensured due to digital beamforming in an APAA with intersecting apertures corresponding to different beams. Such radar makes it possible to reduce the time required for space surveillance. In so doing, the minimum surveillance time does not depend on the number of beams (2 or more), which can be selected, for example, with account for the duration of a coherent burst of radio pulses necessary for moving target selection.

It is shown that with equal power of the modules and equal number of elements, an axisymmetrical APAA has the minimum surveillance time less by 12…22 % and a higher potential as compared with the minimum potential of a polyhedral APAAs in the scanning sector, as well as less average beam width for reception, up to 2–3 times lower target azimuth measurement error, and smaller overall dimensions.

Due to selection of axisymmetrical PAA generatrix shape, it is possible to ensure a required form of DF and surveillance zone dependence on the scanning angle in the elevation plane. Use of a cylindrical PAA is relevant when the scanning sector is up to 60° in elevation. A conical PAA with cone angle of 15° makes it possible to ensure a virtually constant gain factor when scanning in elevation. Application of radiators in the form of slots or vibrators, whose axes are directed along PAA surface generators, allows to do without control of a conical and cylindrical PAA during scanning, with small losses in DF.

Potential of an arbitrary APAA [

where an - amplitude of incident wave at the n-th radiator input; fn (θ0, φ0) - value of element’s partial pattern in the direction of radiation pattern maximum.

Here, partial RP is understood as an RP with one element excited by an incident wave with the unit power, at matched loads at the inputs of all other elements, and with common phase origin point for all elements.

Power of an individual transmitting module of the APAA is limited by its technical capabilities, therefore it can be considered that the amplitudes of incident waves shall satisfy the inequalities

In this way, an optimal distribution, such that delivers the maximum of APAA potential, is defined by (A.5) and corresponds to equal (maximum) output power of all transmitting modules of the APAA.

The authors declare that there are no conflicts of interest present.