Dependance of monopulse radar boresight error on incident E-field polarization

Boresight error (BSE), the angular difference between a target's actual and radar-indicated position, is influenced by protective radomes used on airborne platforms. Research results have demonstrated a reliable computer modeling technique for predicting the BSE of electrically large radar-radome systems. This technique, based on a ray-trace receive formulation using geometric optics (GO), was extended to investigate the dependance of radome-induced BSE on various combinations of aperture scan angle, element polarization, and incident wave polarization. The results obtained compare very well with available empirical, published, and measured data for the specific scan angles and polarization cases considered. Generally, the BSE exhibits less dependance on incident wave polarization when the aperture elements are linearly polarized and a higher degree of sensitivity when aperture elements are circularly polarized.


INTRODUCTION
Monopulse processing systems are capable of precisely and quickly locating sources of Radio Frequency (RF) energy. Because of their accuracy and speed, monopulse techniques are extensively used in modern military aircraft fire control radar and missile seekeriguidance systems [l]. The high speed nature of these platforms dictates environmental protection which is structurally sound and aerodynamically stable be provided for onboard sensors. For monopulse radar and seeker systems, this protection is provided by a radome.
An ideal radome would be "transparent" to the system's electromagnetic (EM) wave of interest, i.e., would introduce no amplitude, phase, or polarization variations on a wave passing through it. However, production constraints and available radome materials dictate compromises between EM transparency, structural integrity, and aerodynamics. The compromised radome design has a shape which is "less than ideal" from an EM wave propagation perspective. The radome introduces refractive and reflective distortions at the material boundaries, adversely affecting EM propagation characteristics.
Incident EM plane waves are no longer planar or uniformly polarized after propagating through curved radome surfaces. An arbitrarily polarized plane wave, incident on a radome may be divided into Transverse Electric (TE) and Transverse Magnetic (TM) components at all points of intersection with the radome surface. Since TE and TM transmission coefficients generally differ, the two components of the incident E-field become unequally weighted (different amplitudes andor phases) while passing through the radome. Upon recombination of the TJ3 and TM components on the transmission side of the radome, the resulting polarization differs from the incident polarization and radome-induced "depolarization" occurs. This effect varies with both incident wave initial polarization, and the relative orientation of the radome surface with respect to the incident wave propagation direction. As a result, the depolarization effect is nonuniform across the surface of a curved radome. These "nonplanar" and "depolarized" transmitted waves are a principal cause of the radome-induced BSE generated by monopulse processing systems. The magnitude of BSE is dependant on both the absolute amount of distortionldepolarization and the relative asymmetry of the distortion across the system aperture.
Recent research results have demonstrated a reliable computer modeling technique for predicting the BSE of electrically large radome-radar systems [2,3]. The modeling technique employed a GO ray-trace receive formulation to investigate the effects of multi-layer tapered radome designs on system BSE. The technique provides a high degree of flexibility and possesses characteristics important to the current analysisimodeling effort, including 1) an aperture model which allows arbitrary element quantities, locations, co-polarized (CP) and cross-Polarized (XP) field pattem responses, amplitudeiphase weightings, and polarizations, 2) accurate tracking of E-Field amplitudes, phases, and polarizations along wave propagation paths, and 3) arbitrarily polarized referenceiincident E-Fields. The current effort expands the earlier modeling technique by incorporating a shell program to automatically control the reference E-Field polarization and aperture scan angle.
Model results, generated on a MICROVAX processing system, using standard Fortran, are validated against a previously published modeling effort [4] and contractor fumished measured data on a production radar-radome system. Predicted BSE was within 1.0 mRad of published and measured data for all cases in which the model was applied to the respective system. The validated cases are extended by predicting BSE sensitivity effects under numerous polarization states, i.e., various linear/circular combinations of aperture element and reference E-Field polarizations. Analysis and modeling results clearly indicate that 1) given circularly polarized elements, radome-induced BSE is heavily dependant on both the aperture scan angle and reference E-Field polarization, 2) given linearly polarized elements, radomeinduced BSE is primarily dependant on aperture scan angle and less sensitive to changes in reference E-Field polarization, and 3) for sensitiveidependant BSE cases, the BSE exhibits "asymmetrical" characteristics for polarization states where one might intuitively expect symmetrical error.

ANALYSIS APPROACH
This effort builds on previous research efforts [2,4,5,61 which characterized monopulse BSE for tangent ogive radomes. Generally, past efforts focused on the scan angle dependance of system BSE for a limited number of polarization cases and identified scan regions inherently possessing greater BSE degradation as shown in Fig 1. This effort extends these results by performing an analysis driven by polarization sensitivity effects. A modeling technique developed and validated by [2] served as the basis for the current work; the following development closely parallels the previous effort and is introduced with permission. Incident E-Fields are established using a GO ray-trace receive technique for rays in a bundle, each of which experiences amplitude, phase, and polarization distortion upon propagating through the radome. At each ray-radome intersection point a local "plane of incidence" is established and complex TE and TM transmission coefficients calculated.
Aperture element voltages are calculated from incident E-Fields which have propagated via GO through the radome structure. Element voltages are combined to generate a monopulse error signal which is compared with known scan angle information to establish radome-induced BSE. The E-Field incident on the m" array element, due to a direct ray may be determined per Eq (1).
For a reference E-Field Er=Erbr, incident on the outside of the radome, E@) incident on an aperture element is clearly dependant on the coyplex reference field strength E,, initial reference polarization pr, and wave propagation direction with respect to the radome surface orientation.
Eq (2) defines parallel and perpendicular unit vectors for establishing the local "plane of incidence" used for E-Field decomposition. These definitions were developed by Munk [7]. Superscripts i and t in Eq (1) differentiate between the incidence and transmission sides of the radome.
Element polarization vector fie represents the E-Field polarization of a "typical" array element, neglecting polarization differences due to an element's location within the array. For a planar ;may constructed of "typical" elements, the orthogonal H-Field polarization vector bh is defined as bh = AA x b, where AA is the apxture plane (i.e., plane containing array ekments) surface normal vector. Polarization vectors p, and ph are used to decompose ET(m) into CP and X P components as shown in Eq (3). ET(m) is the total E-Field incident on the m* array element, and may include reflected as well as direct rays. Although the model has the capability to include reflected rays, they were not ConsideTFd for this analysis. For this direct-ray-only analysis, ET(m)=E,(m).
The total voltage response V, of a typical aperture element is given by Eq (4) where E&(m) and E&(m) are calculated per Eq (3). The A, and om terms in Eq (4) represent amplitude and phase weights used in controlling pattem shape and main beam pointing direction. Assuming mutual coupling effects are identical for all elements within the array, the CP element pattem fp(e,@>, X P element pattem fy(e,@), and element polarization directions belbh are identical. Independent CP and XP element pattems allow for varying polarization responses to be analyzed depending on the specific element type being used.
A "simple" method is employed to analyze tracking performance. The radar aperture is divided into symmetrical quadrants. Complex element voltages, calculated per Eq (4), are summed within each aperture quadrant to produce quadrant sum voltages. These are then combined to form monopulse sum and difference voltages, V, , , and V, , , respectively 111. The monopulse error signal E,(fi,Y,Y) is formed from the complex monopul se voltage ratio V, , , /V, , , using an "exact" monopulse processor implemented as in Eq (5). E,,(b,y,Y) is defined over an angular range of y for a fi polarized incident wave at a frequency of Y. 'fie sensitivity K is determined by the slope of the normalized difference pattem with units of (v/v)/Rad [81.
The monopulse error signal E,,(;,y,Y) is used to establish and characterize "system" BSE sensitivity under varying 6 polarization conditions. In this context, "system" BSE is defied as the angle indicated by Eq (5) when the aperture has no pointing error, i.e., the aperture scan direction equals the true source location. This is equivalent to fixing the aperture scan direction while repositioning the source until Eq ( 5 ) equals zero. The angular difference between the scan direction and source location is the system BSE. For a given aperture scanh direction, system BSE may be expressed as in Eq (6) where, n, is a unit vector in the aperture scan direction and unit vector nmp represents the direction of the source location such that Emp(;,Y,V) = 0.

RESULTS
Initial validation of analysis and modeling results is accomplished using a production radome, radar, and monopulse processing system. The production system is a mechanically scanned, 1368-element aperture, approximately 28-wavelengths in diameter with linearly polarized slotted waveguide elements. A modified cosinelcosine"2 amplitude taper is applied across the aperture yielding a half-power beamwidth (WBW) of approximately 2.488" and a first side-lobe level (FSSL) of approximately -30 dB. The production radome is a solid tapered wall design empirically "tuned" to provide minimum BSE. It is modeled using a reference ogive surface with a length of 90.26h, a base diameter of 36.136h, and constructed of material with a nominal dielectric constant of E, = 4.8 and a loss-tangent of 0.014. For analysis purposes, the reference E-Field and aperture element polarization vectors are separated by an angle defined as the polarization tilt angle. The polarization tilt angle is measured relative to the aperture element polarization with a plus (+) sign indicating counterclockwise rotation and a minus (-) indicating clockwise rotation as viewed facing the aperture. Hence, for a tilt angle of 0" the reference E-Field and element polarization vectors are equal. The polarization tilt angle is varied between k 60" while the aperture scan angle is varied between 0" and 40". The polarization tilt limits of t 60" are to ensure that the linearly polarized aperture receives enough energy for reliable processing. The resultant BSE for the production system is shown in Fig 2. This figure shows the BSE of Lefmight monopulse processing with the aperture scanned in azimuth only.    In Fig 4, the aperture is scanned diagonally, i.e., in both azimuth and elevation. The polarization dependance is due to the asymmetry of the radome depolarization effect. In the azimuth scan case of Fig 2, the depolarization had a form of symmetry above and below the azimuth scan plane; since an ogive is a figure of revolution, the top and bottom portions of the radome are reflected about the azimuth plane. However, there is no symmetry about a diagonal scan plane, so polarization dependance is evident.
The dependance of radome-induced BSE on incident E-Field polarization was previously identified for tangent ogive radomes [4,6]. These published results form a basis for validating the current modeling technique which extends previous results by identifying and substantiating the existence of an "asymmetric" BSE dependance on incident polarization. For comparison with published results, data is generated using a constant thickness (t = 0.31665 tangent ogive radome. The radome is a single layer design with a length of 30.0h, a base diameter of lO.Oh, and constructed of material with a dielectric constant of E, = 3.2 and a loss-tangent of 0.008. The system is a mechanically scanned, 208-element aperture, approximately 8-wavelengths in diameter with right-hand circularly (RHC) polarized elements. The aperture is gimballed 2.0h from the radome base and weighted with a uniform amplitude taper.
Predicted BSE results are generated for non-reflective in-plane and cross-plane BSE scanning cases. To ensure the asymmetrical and dual-dependance behavior of the radome-induced BSE is not an isolated phenomena for this particular radome-radar system, model results are generated using the production radome-radar system with RHC elements replacing the original linearly polarized elements. Figs 9 and IO are production BSE results using RHC elements for azimuth and diagonal (45.0' azimuth-elevation plane) aperture scans. Diagonal scan BSE data is generated by scanning the aperture in the diagonal plane while calculating azimuth BSE. In both cases, the BSE exhibits the same asymmetry and polarization dependance characteristics previously identified. Additionally, comparison of the two figures indicates a scan plane dependance as well.
The dependance of BSE on both aperture scan angle and incident polarization could greatly complicate the simplest table look-up scheme for BSE calibration or even have a major impact on the overall monopulse system design. Although aperture scan angle information is generally available, from either electrical or mechanical positioning components, monopulse systems do not typically "measure" or estimate incident wave polarization.
Since a circularly polarized transmitted radar wave may be retumed with a predominant linear component (dependant on target geometry), systems with circularly polarized elements may be incapable of correctly calibrating out or correcting radome-induced BSE. Even systems with linearly polarized apertures may receive energy in a polarization state different than transmitted (different than expected). In such a case, a look-up table may provide an incorrect BSE calibration factor.     A polarization dependant GO propagation technique is extended to analyze and model electrically large radar-radome monopulse processing systems. Extended model results are validated against empirical, published experimental, and measured BSE data for a production radare-radome system. Radomeinduced BSE is characterized under varying polarization conditions, i.e., reference E-Field vs. element polarization and scan angle, and found to exhibit a considerable amount of dependance/sensitivity for specific cases considered. Generally, BSE exhlbits less dependance on incident wave polarization when aperture elements are linearly polarized and a higher degree of sensitivity when aperture elements are circularly polarized.