A comparison between different types of weighting function used for radar antennas

Transcription

1 AARMS Vol. 3, o. 3 ( TECHOLOGY A comparison between different types of weighting function used for radar antennas GHEORGHE IUBU, IOA ICOLAESCU, DORU IOSIF, ADRIA STOICA Military Technical Academy, Bucharest, Romania Located at the interface between the free space and the radar system the antenna is an important part of any radar system. The latest technological achievements allow using more and more antenna arrays for different types of equipment. The individual elements that make up an array can be fed in different ways and, obviously, the parameters of the array depend on the way the elementary antennas are fed. The radar antennas have to meet two conflicting requirements. One the one hand, the beam width has to be as narrow as possible to achieve a good accuracy, and, on the other hand, the side lobes level has to be as low as possible to decrease the jamming probability. In order to study the influence of the amplitude distribution to the parameters of the antenna, an array made up of 7 elements is considered. The antenna elements are uniformly located at a half wavelength separation. The analysis has been made for a frequency of GHz and for several weighting function: Hamming, Hann, Blackmann and Taylor. Received: April, 4 Address for correspondence: GHEORGHE IUBU Military Technical Academy 8-83 George Cosbuc Avenue Bucharest, Romania iubuh@mta.ro Introduction The antenna is the element, which is located at the interface between free space and the radar equipment. The performance of the radar systems relies on antenna performance. During the time antenna systems have became more and more intricate. Due to the technological evolution a lot of equipment are using arrays. These can be fed in different ways and obviously their pattern properties depend on the way they are fed. Other elements, which determine radiation pattern of an array, are the type of individual antenna from which the array consists of, the number of antennas elements and the shape of the array. The radar antenna systems have to meet two contradictory conditions. One the one hand the beam width has to be as small as possible to achieve a good accuracy in target co-ordinates measurements and, on the other hand the sidelobes level has to be as low as possible to decrease jamming probability. In order to analyse the influence of the amlitude distribution to the parameters of the antenna an array made of 7 elements is considered. The antenna elements are uniformly located at a half wavelength distance. The analysis has been made for a frequency of GHz, that is

2 3 cm wavelength, and for three weighting function: cosines with pedestal, Blackmann and Taylor. The following notations have been made: discrete phase of weighting function k =,... k β(k : = π phase shift of two signals received by two adjacent elements of antenna (α is the angle between the direction to source and perpendicular line to antenna aperture: d π ψ( α : = π sin λ 8 α complex function which characterizes the spatial signal received by an antenna element (k =,... F(α,k:=e j.k. ψ(α p:=... I:=... unit matrix X I p,i := I p,p := vector function of spatial signal (a characterizes the amplitude of the signal: S(a,α = (a(f(α,,f(α,,f(α,,f(α,3,f(α,4,f(α,5,f(α,6, F(α,7,F(α,8,F(α,9,F(α,,F(α,,F(α,, F(α,3,F(α,4,F(α,5,F(α,6 T Cosines with pedestal weighting function The expression of generalized weighting function is given by: M j I β (k P = p (k : CM I e I= (M where M = is the number of terms, and p is a coefficient which value can be: for uniform weighting;.8 for Hamming weighting;.5 for Hann weighting. 46 AARMS 3(3 (4

3 m:= (M... M The coefficients of this function, for p =.8, are:.3 C m+m := C m+m =.54.3 p 4 p p 4 weighting matrix is: Pp n,n := P p (n vector function of spatial weighted signal is: S p ( := Pp. S(, the expression of directivity coefficient of the array is: Dp : (Pp (Pp k,k k,k, D p (db:=. log(dp, Dp =.947, D p (db =.545. db and worsening coefficient of the antenna gain is: p : Ppk,k, p(db:=. log( p, p =.53, p(db = db AARMS 3(3 (4 47

4 In Figures and the pattern of the array for p =.8 given by: are represented. Fp ( α, αs : = ( S ( α p T S(, αs ρp Figure. The pattern of 7 elements array with Hamming weighting Figure. The sidelobes of the pattern of 7 elements array with Hamming weighting 48 AARMS 3(3 (4

5 Blackmann weighting function In this case the similar variables like for cosines weighting function are: M:= 3 m:= (M... M M i I (k PB (k : CM I e I (M PB n,n := P B (n S B ( := PB. S(, C m+m := DB : (PB (PB k,k k,k D B (db:=. log(db DB = 9.6 D B (db = dB B PB k,k : B(dB:=. log( B B =.4 B(dB = db AARMS 3(3 (4 49

6 The patterns of the array given by: FB ( α, αs : = (( S ( α are represented in Figures 3 and 4. B T S(, αs ρb Figure 3. The patterns of 7 elements array with Blackmann weighting Figure 4. The sidelobes of the pattern of 7 elements array with Blackmann weighting 4 AARMS 3(3 (4

7 Taylor weighting function The number of Taylor s series given by: u:= 8 m:=... u and sidelobes level: α db := 8 A:= π acish αdb A=3.5 Taylor s function parameters are: σ : = A u + u σ= 983 Taylor s coefficients are: = u ((u! m F m : F (u + m!(u m! p + = := M:= u A p and the others parameters needed for Taylor weighting function: C M m := F m AARMS 3(3 (4 4

8 C M m = M i I (k P T (k : CM I e PT n,n := P T (n I (M (PTk,k S T ( := PT. S(. k DT : D T (db:=. log(dt (PTk,k DT = 9.9 D T (db = db T : PT (k T =.94 T(dB:=. log( T T(dB=.5. db FT (, s : T ST ( S(, T s 4 AARMS 3(3 (4

9 The patterns are showed in Figures 5 and 6. Figure 5. The patterns of 7 elements array with Taylor weighting Figure 6. The sidelobes of the pattern of 7 elements array with Taylor weighting AARMS 3(3 (4 43

10 Comparison between different types of weighting function In order to show the influences of different weighting function to parameters of the pattern, especially to beam width and sidelobes level, the patterns analyzed above have been represented on the same picture. On this picture is drawn also the pattern corresponding to unweighted array given by: F( α, α s : = (( S(, α T S(, αs Figure 7. The influence of weighting function to beam width (F(α,α s -unweighted array, F P (α,α s -Hamming weighting, F B (α,α s -Blackmann weighting, F T (α,α s -Taylor weighting Figure 8. The influence of weighting function to sidelobes level (F(α,α s -unweighted array, F P (α,α s - Hamming weighting, F B (α,α s -Blackmann weighting, F T (α,α s -Taylor weighting 44 AARMS 3(3 (4

11 Conclusions. The parameters of antenna array patterns are determined by the phase and amplitude distribution of the electromagnetic field on antenna aperture. In order to improve the characteristic of radiation pattern some weighting functions have been used. These change the distribution of amplitude and phase of signal received such as the beam width and the sidelobes level to be minimized. Usually decreasing of beam width is accompanied by increasing of sidelobes level.. The beam directivity is highest for an unweighted array (6 -beam width, followed by the array with Hamming weighting (9 -beam width, then Blackmann (.6 -beam width, and Taylor weighting ( -beam width. 3. The highest level of sidelobes corresponds to unweighted array (.3, followed by the array with Hamming weighting (., Blackmann (.3 and Taylor weighting ( Low beam width and low level of sidelobes are two contradictory requests for any antenna array. If one decreases the other decreases so a balance between the two has to be made for each specific application. References. GASPARE, G., Advanced Radar Techniques and Systems, Peter Peregrinus, UK, KRAUS, D. J., Antennas, McGraw-Hill, USA, SKOLIK, M. I., Radar Handbook, McGraw-Hill, USA, 97. AARMS 3(3 (4 45