Upgrading Two Dimensional Search Radar to Three Dimensional Search Radar Based on SDR

This paper presents an exploitation of the existing two dimensional radars (2D) which have t wo identical antennas for reception to be upgraded to a three dimensional radar (3D) in order to measure the height as well as the slan t range and azimuth direct ion. The height measurement is important for pre liminary information for reducing the time required for acquisition. Software Defined Radio (SDR) is chosen for the implementation of height finder processor is given in this paper. Desig n parameters are selected for the proposed height finder processor in order to accommodate SDR requirement. This work i s also concerned with the analysis of the parameters which affect the accuracy of height finding. These parameters include the refraction index, smooth surface reflecti on, divergence and rough surface reflection. The results of the analysis show the feasibility of this proposal to upgrade the 2D to 3D rada rs.


Introduction
The principle of the radar operation is based on generating pulses of radio frequency energy and transmitting these pulses via a directional antenna, as shown in Fig. (1).When a pulse hits a target in its path, a small portion of the energy is reflected back to the antenna.The radar receives a reflected pulse if it is higher than a certain optimized threshold.The radar indicates the range to the target as a function of the time required of the pulse travelling to the target and returning [1,2].The radar indicates the direction of the target by the direction of the antenna at the time of the received reflected signal.
The basic requirement, to measure the range, bearing and other attributes of a target remains the same for all radar applications.The radar systems must obtain certain information from the radar signal.The kinds of radar information that can be extracted include range, azimuth angle, elevation angle(height finding), target size and target shape.To obtain various kinds of information, different techniques must be used to optimize the desired kind of information.
Developments trends in radar systems are the system design, the method and speed of processing the return radar signals, the amount of information which can be obtained, and the way that the information is displayed to the operator.The heart to modern radar systems is the digital computer and its data processing capability, which can extract avast amount of information from the raw radar, signals [2] This paper aims at exploiting the existing two dimensional (2D) radar (azimuth and range information that can be extracted from 2D radar) which have two separate antennas and upgraded to three dimensional(3D) radar to evaluate the height of the target as well as the azimuth direction and range which are given by two dimensional radar.This work includes an analysis and a simulation of the elevation error due to the surface reflections in addition to a proposed implementation technique of the height finding processor based on SDR.

Description of the proposed height finder radar
Target height found by ground radar is based on calculation rather than a direct measurement because the basic information from radar includes range and angular measurements.Height evaluation is carried out by computations, utilizing the range of the target and its elevation angle.3. The azimuth position of the two centers of the vertical and slant beam blips and their angular separation can be measured (the angle θ) by using synchro converter and synchro to digital converter (SDC).A synchro converter is a transducing instrument to measure shaft angle and positioning systems.The rotor winding of a synchro converter is excited by an AC voltage.The voltage induced in stator winding terminals (S 1 , S2, S3) will be proportional to the cosine of the angle between the rotor coil axis and stator coil axis.The induced voltages in terminals (S 1 , S2, S3) will be converted into digital format by SDC.The code for the digital output of SDC is binary and the word lengths range from 10 to 18 bits (12 bits is chosen for this proposed system which gives accuracy 0.088 o ).The signal of synchro to digital converter applied to SDR unit as shown in Fig. (3).

Target Height Elevation Analysis
The height of the target ( h), as shown in  However, the relationship between the radar range and propagation factor is given by: ….… (9) Where radar detection in free space.

All
Equation ( 9) shows that if , then an error is introduced in the value of the slant range ( ) but the height of the target depends on the value of ( ) according to equations (6,7b).Thus the error in the height finding radar is a function of the propagation factor.The magnitude of propagation factor can be obtained by substituting equation (10,11) in equation ( 8).Yield:

= . (12)
To improve the accuracy of height determination the following effects must be taken into consideration -Atmospheric reflection -Ground reflection

Atmospheric Refraction
In free space, radio waves travel in straight lines.However, in the presence of the earth atmosphere, they bend (refract).Refraction is a term used to describe the deviation of radar wave propagation from straight line caused by the variation of the index of refraction [4].The index of refraction is defined as the ratio of the electromagnetic wave in free space to the velocity of electromagnetic wave in the medium.
The general method of accounting for atmospheric refraction in radar height calculations is to replace the actual earth radius ( by an equivalent earth radius which is given by: = ..( 13) where = (factor by which the earth radius must be multiplied).Equation ( 13) is used to replace by in order to change the actual atmosphere by a homogenous atmosphere in which electromagnetic wave travels in straight lines rather than curved lines.This method is used only for approximating calculation in short range height finding, otherwise the factor is given by [8]:

=
.. ( 14) where is the rate of change of reflective index n with height.

Ground Reflection
The characteristics of the reflected radar waves from the earth's surface are changed in amplitude and phase.Three factors that contribute to these changes are the reflection coefficient for a smooth surface, the divergence factor due to earth curvature and the surface roughness [5].

Smooth Surface Reflection Coefficient
For parallel and perpendicular polarizations, the smooth reflection coefficients are given by[7]: Smooth surface reflection coefficient for perpendicular polarization.

Grazing Angle
Relative Dielectric constant

Divergence
When an electromagnetic wave is incident on a round earth surface, the reflected wave diverges, because of the earth's curvature and energy is defocused.The divergence factor ( D) is given by [7]: ….(16a) where = Sectors length between the projection of the radar and targets, respectively, over round earth and earth center.

… (16b)
However, the divergence factor can be extracted from curves presented by Blake [8].

Rough Surface Reflection
Surface roughness strongly influences the strength of radar returns.Surface roughness (S r ) is given by[9]: where is the rms surface height irregularity.
The total reflection coefficient can be expressed by combining the above three factors as follows [5]: ... (18) where is the surface reflection coefficient for horizontal or vertical polarization.
is used instead of in equation ( 11) to introduce the effect of ground reflection.The parameters are calculated for small grazing angle by using equations (13a, 14a, 15) as follows: 1.The value of is approximately -1.

The value of D is approximately 1 (since )
3. The average value of is approximately 0.97 for = Thus the value of is approximately ( ). Fig ( 6) shows the flow chart which is used for analysis and calculation.

Software Defined Radio (SDR)
SDR is a collection of hardware and software technologies that enable reconfigurable system architectures for wireless networks and user terminals to reduce the amount of signal processing in radio application [10,11] The ideal SDR architecture consists of a digital subsystem and a simple analog subsystem.The analog functions are restricted to those that cannot be performed digitally.The architecture pushes the analog conversion stage right up as close as possible to the antenna, in this case prior to power amplifier in the transmitter and after the low noise amplifier in the receiver [13].SDR technique is used to implement height finder processor, as shown in Fig ( 3) according the steps in article (2).

Results
Fig ( 7) shows the variation of as function of elevation angle according to the equation ( 11).The difference in the amplitude of is the results of the vector summation of the signals through direct path and reflected path.Fig ( 7) also shows the effects of divergence and surface roughness according to equation ( 18) by substituting instead of in equation (11).Fig (8) shows the relationship between the height of the target and elevation angle for different slant ranges for both cases of flat and spherical ground according to equations (6,7b).Fig( 8), also shows the effects of divergence and surface roughness according to equations ( 18) by substituting instead of in equations (6, 7b).Fig ( 9) shows the variation of propagation factor as a function of elevation angle according equation ( 12).This variation is due to the reflected received signal which is a function of the incident angle of the returned echo.Fig ( 9), also shows the small effects of divergence and surface roughness on the propagation factor, by substituting by using equation (18).Fig (10) shows the effect of the propagation factor upon the value of the height of the target for both flat and spherical cases ( )according to equations (6, 7b) after multiplying the value of R by factor for each value of elevation angle according to equations (8 and 9).

Conclusions
Upgrading the existing 2D radar to 3D based on SDR is proposed.This proposal can be also used to replace the main processing hardware units by using a software based on SDR to increase capability and reduce both size and cost.Theoretical analysis shows that the error in the height measurement is within acceptable error for normal 3D radar.
used in civilian and military air surveillance operations utilizing the V-beam principles [4].V-beam principle employs two antenna beams with 45 o seperation between them, radiated from a common rotating antenna structure as shown in Fig(2).The Vbeam technique is used because of the compatibility and simplicity to upgrade the available two dimensional radars in service.Fig (3) shows the block diagram of the proposed height finder.The steps of upgrading process can be summarized as follows: 1. Rotating one of these two antennas by 45 o with respect to the other antenna in order to form two V-beams PDF created with pdfFactory Pro trial version www.pdffactory.comand slant beam).The two beams are energized by either two or single transmitter.2. Converting the received two signals to an intermediate frequency and then applied to analog to digital converter (ADC).These two signals applied to SDR unit as shown in Fig. (3).
Fig (2), is given by [4]: ……….(1) where D = Ground range from radar to the target θ = Angle between centers of the vertical and slant beam blips is measured when the antenna rotates, the vertical beam intersects the target first and then after that, by angle , the slant beam intersects the target.But .... (2) where R = slant range of the target Substitute eq (2) by (1) …….(3) Equation (3) describes the height of target which is determined by radar in term slant range and angle .However, the target height is determined as function of elevation angle .The relationship between angle and elevation angle can be found as follows.The target height ( ) for the flat earth case, as shown in Fig (4), is given by: ...... 7a) expressed the height of the target as a function of the angle .The effect of the radar antenna height is neglected since the height of the radar antenna is small if compared with target height and to simplify the analysis[4].
height finding techniques accuracy are based on the accuracy of elevation angle measurements.The main source of the error is the surface reflection and atmospheric reflection.Surface reflections combine vectorially with direct path signals by antenna, produce an error in the elevation angle measurement due to the variation in the amplitude and phase of the received signals.Propagation factor ( F ) is used to express the relationship between the direct and indirect signals.The propagation factor, also accounts for the radar antenna pattern effects, is given by Assume the two beams (A and B) of the antenna are identical and have the same propagation factor.Fig (5)   shows the geometry for analysis of elevation errors due to ground reflections.The relative received field strength of either beam A or B arriving along the direct path at elevation angle ( ) is given by [4field strength at the feed point of each antenna direct and indirect fields are given by [4]:PDF created with pdfFactory Pro trial version www.pdffactory.com