Phased Array System toolbox: An implementation of Radar System

Phased Array System toolbox: An implementation of Radar System A qualitative study of plane geometry and bearing estimation Adam Johansson Faculty of Health, Science and Technology Engineering Physics 3 hp (ECTS) Supervisors: Thijs J Holleboom, Stefan Eriksson Examiner: Lars Johansson Date 218-4-6 Serial number

P R O τ 3 θ 3

Antenna Transmitted signal Transmitter Plane target Receiver Echo signal Range to target

Waveform - generator Transmitter Duplexer Antenna Transmitted signal Received signal Low-noise - RF amplifier Display Local - oscillator Mixer Data - processor Signal - processor IF - amplifier H(Ω) S(Ω) t 1 t 2 t = t 2 t 1 R R = c t 2, c 1/2

P z θ ϕ P = (R, θ, ϕ) y x P R O R

Target R Antenna θ ϕ P P P = 4πR1 2. 2 G = P G 4πR1 2.

P = ( R 1)Gσ 4πR1 2, σ P = 4πR2 2, R 2 A = AK A K P P = P AK 4πR2 2. P = P Gσ 4πR 2 1 4πR 2 2 AK, P = P GσAK (4π) 2 R1 2. R2 2 R 1 R 2 R 1 = R 2 = R λ G = 4πAK λ 2 A = Gλ2 4πK P = P GσK (4π) 2 R 4 Gλ 2 4πK = P G 2 λ 2 σ (4π) 3 R 4. L P = P G 2 λ 2 σ (4π) 3 R 4 L.

R R = ( G 2 λ 2 σ (4π) 3 L P P ). τ Power Pulse width PRI t τ = c 2. R = cτ/2 R R R t τ t

Pulse envelope Radar τ R R = cτ/2 Power Received signal Echo from target at R = 2R /c R Echo from target at R = 2R /c t t cτ/2 R = cτ 2. 3 CR = 2R ( ) θ3, 2

Point reflectors Radar 2Rsin ( ) θ 3 2 Rθ3 Rθ 3 R 3 θ 3 V θ 3 ϕ 3 V = π ( R θ 3 2 ) ( ) R ϕ 3 R = π 2 4 R2 θ 3 ϕ 3 R. θ d (θ)

Target Plane wave approximation in far-field where R λ. R θ dsinθ θ d Azimuth Cut (elevation angle =. ) Non-taper Taper -1 Normalized Power (db) -2-3 -4-5 -6-2 -15-1 -5 5 1 15 2 Azimuth Angle (degrees)

A τ ( ) πβ x(t) = τ t2, t τ β x(t) = e jπβt2 /τ F i (t) = 1 dθ(t) = β t. 2π dt τ

i 1. LFM waveform, B product = 5.8.6.4 Amplitude.2 -.2 -.4 -.6 -.8-1..1.2.3.4.5.6.7.8.9 1. Normalized time t/ 5 Instantaneous frequency of an LFM pulse 45 4 35 3 F (t) [Hz] 25 2 15 1 5.1.2.3.4.5.6.7.8.9 1. Time t [s] β β

I = A (ω 1 t + ϕ ), Q = A (ω 1 t + ϕ ) I + iq Range sample L 1 N 1 Receiver channel Fast time Pulse M 1 Slow time τ τ t i t f τ t

R = ct /2 1/β Receiver channel n N-1 Pulse m M-1 Range sample l L-1

H(Ω) Y (Ω) = H(Ω)X(Ω) X(Ω) t M y(t M ) 2 = 1 2π 2 X(Ω)H(Ω)e iωt M dω. H(Ω) = αx (Ω)e iωt M h(t) = αx (t M t) X x Input signal FFT Multiplier Inv. FFT Matched filter output FFT of stored replica R 2 R 3 R 4 X Y

N Y i = X ij, j=1 Y i = N X ij 2. j=1 f b = f a c v b c v a, f a f b S a S b v a v b c v = v b v a v b = v v a = v f b = f a 1 + v/c. f f = 2v c f a. F (ω) = f(t)e iωt dω

f f + f d f d = 2v/λ v 3 Simulated received noise 2.5 2 Power [W] 1.5 1.5 1 2 3 4 5 6 7 8 9 1 Range bin H H 1

M N M N

σ Y Y = 4πσ λ 2 X, X X [ ] E () H E () = V [ 4π λ 2 E ( ) H E ( ) V ]. ( ) 2 4πR L =. λ P = P G 2 λ 2 σ (4π) 3 R 4 L, L L = L + L + L + L.

db = 1 ( W ), W = 1 ( W /1), V s,r = fλ f = V s,r λ, f V s,r λ

Plane length Engine Front Plane width Back Wing apex

X(k) A Interpolated peak Measured values k 1 k k k +1 k k k = k + 1 2 X(k + 1) X(k 1) X(k 1) 2 X(k ) + X(k + 1). Measured position True position Range bin Bearing angle

γ = 1 N N (x i µ) 2, i=1 µ = 1 N N x i. i=1

1. Linear FM pulse waveform:real part, pulse 1.8.6.4 Amplitude.2 -.2 -.4 -.6 -.8-1. 1 2 3 4 5 6 7 Time [ s]

1. Pulse train of five pulses.8.6.4 Amplitude.2 -.2 -.4 -.6 -.8-1. 2 4 6 8 1 12 14 Time [ s] 1. Enlargement of rectangular envelope for pulse.8.6 Amplitude.4.2 -.2 -.4 -.6 -.8-1. 5 1 15 2 25 Time [ s]

3.1. PHASED ARRAY SYSTEM TOOLBOX CHAPTER 3. RESULTS 3D Response Pattern -5 z Az El 9-15 -2 el x Az az El -25 y Az 9 El -3-35 Normalized Power (db) -1-4 -45-5 Figure 3.4: Radiation pattern of an isotropic antenna. Hence, the radiation pattern is a half sphere as expected. Combining multiple antenna elements aligned in a URA changes the radiation pattern in Figure 3.4 to the one presented in Figure 3.5. 3D Response Pattern -5-15 -2 y Az 9 El el x Az El az -25-3 -35 Normalized Power (db) -1 z Az El 9-4 -45-5 Figure 3.5: Radiation pattern for URA. 29

Azimuth cut (elevation angle =. ) 9 12 3 6 2 15 1 3 Directivity [dbi] 18-1 -15-3 -12-9 -6 Directivity [dbi], Broadside at. Azimuth cut (elevation angle =. ) 9 12 3 6 2 15 1 3 Directivity [dbi] 18-1 -15-3 -12-6 -9 Directivity [dbi], Broadside at.

Elevation cut (azimuth angle =. ) 9 12 3 6 2 15 1 3 Directivity [dbi] 18-1 -15-3 -12-6 -9 Directivity [dbi], Broadside at. Elevation cut (azimuth angle =. ) 9 12 3 6 2 15 1 3 Directivity [dbi] 18-1 -15-3 -12-9 -6 Directivity [dbi], Broadside at.

3.1. PHASED ARRAY SYSTEM TOOLBOX CHAPTER 3. RESULTS 3D directivity pattern in u-v space 4 2 1-1 -2-3 -4-5 -6 1. -2-3.8 Directivity [dbi] Directivity [dbi] 3 4 3 2 1-1 -4.6.4.2 V -.2 -.4 -.6 -.8-1. -1. -.8 -.6 -.4 -.2.2.4.6.8 1. U -5-6 (a) Without tapering. 3D directivity pattern in u-v space 4 4 3 2 1-1 -2-3 -4-5 -6 1..8 2 1-1 Directivity [dbi] Directivity [dbi] 3-2 -3-4.6.4.2 V -.2 -.4 -.2 -.6 -.6 -.4 -.8 -.8-1. -1. 1..6.8.4.2-5 -6 U (b) With tapering. Figure 3.8: The three dimensional radiation pattern for the radar system. One can see the same tendencies over the complete 3D space as for the cut at zero degrees (Figure 3.6 and 3.7). The side lobes are suppressed compared to the main lobe and are at about the same level. There are, however, different levels of the U and V directions, but it depends on the appearance of the tapering matrix. It is easier to estimate the difference in strength for the side lobes and to see that they are about the same size when viewed from the side. The side 33

CHAPTER 3. RESULTS 3.1. PHASED ARRAY SYSTEM TOOLBOX views are presented in Figure 3.9 and 3.1. 4 3 3 2 2 1 1-1 -1-2 -2-3 -3-4 -4-5 -5-6 -6-1. -.8 -.6 -.4 -.2.2.4.6.8 Directivity [dbi] Directivity [dbi] 3D directivity pattern in u-v space 4 1. U (a) Without tapering. 4 3 3 2 2 1 1-1 -1-2 -2-3 -3-4 -4-5 -5-6 -6-1. -.8 -.6 -.4 -.2.2.4.6.8 Directivity [dbi] Directivity [dbi] 3D directivity pattern in u-v space 4 1. U (b) With tapering. Figure 3.9: The directivity in UV-space. It is shown in Figure 3.9 how the side lobes are reduced compared to the main lobe. By studying the lobes next to the main lobe the estimated change after the tapering matrix was applied was 15 dbi to 55 dbi. The other side is presented in Figure 3.1, and the estimated 34

3.1. PHASED ARRAY SYSTEM TOOLBOX CHAPTER 3. RESULTS change after the applied tapering matrix was from 15 dbi to 3 dbi. 4 4 3 3 2 2 1 1-1 -1-2 -2-3 -3-4 -4-5 -5-6 -6-1. -.8 -.6 -.4 -.2.2.4.6.8 Directivity [dbi] Directivity [dbi] 3D directivity pattern in u-v space 1. V (a) Without tapering. 4 3 3 2 2 1 1-1 -1-2 -2-3 -3-4 -4-5 -5-6 -6 Directivity [dbi] Directivity [dbi] 3D directivity pattern in u-v space 4 (b) With tapering. Figure 3.1: The directivity in UV-space. When both the waveform and the antenna pattern are analysed it is possible to move on further with the simulation of environment and targets. Using these settings for the radar system to simulate a received signal from two targets located at a distance of 7569 m and 1287 35

CHAPTER 3. RESULTS 3.1. PHASED ARRAY SYSTEM TOOLBOX m from the antenna. They are placed at 7.6 and 38.7 in bearing angle respectively. The speed vectors of the two targets were [ 1; ; ] and [1; 8; ] m/s (one of them approaches and the other goes away). This is presented in Figure 3.11. Simulated received data with PAS toolbox 8-4 7-5 6 Range bin -6 5-7 4-8 3-9 2-1 1-11 5 1 15 2 25 3 35 4 Pulse index Figure 3.11: Simulated received data with two targets. One can see in Figure 3.11 that there are two areas where the signal strength is stronger than the surrounding. These yellow dots are the return from the targets, while the blue is from noise. It is shown in Figure 3.12 how the simulated data has changed after pulse compression. Pulse compression on simulated data 8-3 7-4 6 Range bin -5 5-6 4-7 3-8 2-9 1-1 5 1 15 2 25 3 35 4 Pulse index Figure 3.12: The simulated data after pulse compression. One can see on the scale bar that the signal strength increased with 1 db. It is also possible to see a narrow line in the centre of the yellow areas. In order to easier see the result of pulse compression, a cross section was done for each target. The cross sections were taken at pulse indices where local maxima occur. In Figure 3.13 is the cross section shown at pulse index 166. 36

-2-3 Signal before and after pulse compression at pulse index 166 Received signal Pulse compressed signal -4 Power [db] -5-6 -7-8 -9-1 1 2 3 4 5 6 7 8 Range bin -2-3 Enlargement of the peak at pulse index 166 Received signal Pulse compressed signal -4-5 Power [db] -6-7 -8-9 5 1 15 2 25 3 Range bin

-2-3 Signal before and after pulse compression at pulse index 3 Received signal Pulse compressed signal -4 Power [db] -5-6 -7-8 -9-1 1 2 3 4 5 6 7 8 Range bin Enlargement of the peak at pulse index 3-3 Received signal Pulse compressed signal -4-5 Power [db] -6-7 -8-9 1 15 2 25 3 35 4 Range bin

-2 Pulse nr 1 Power [db] Power [db] -4-6 -8-1 1 2 3 4 5 6 7 8 Range bin Pulse nr 2-2 -4-6 -8 Power [db] -1 1 2 3 4 5 6 7 8 Range bin Integration over all pulses -2-3 -4-5 -6-7 -8 1 2 3 4 5 6 7 8 Range bin Integrated over all pulses -3-4 Power [db] -5-6 -7-8 5 1 15 2 25 Range bin

-2 Pulse nr 1 Power [db] Power [db] -4-6 -8-1 -2-4 -6-8 Power [db] -1 1 2 3 4 5 6 7 8 Range bin Integration over all pulses -2-3 -4-5 -6-7 -8-3 Integration over all pulses -35-4 -45 Power [db] -5-55 -6-65 -7-75 1 15 2 25 3 35 Range bin

Pulse nr 1 Power [db] Power [db] -5-1 -15-2 -25 1 2 3 4 5 6 7 8 Range bin -5-1 -15-2 Pulse nr 2-25 1 2 3 4 5 6 7 8 Range bin -5 Integration over all pulses Power [db] -1-15 -2-25 1 2 3 4 5 6 7 8 Range bin Integration over all pulses -4-5 Power [db] -6-7 -8-9 5 1 15 2 25 Range bin

3D response of targets in polar coordinates with threshold -8-1 -12-14 Power [db] -16-18 3D response of targets in polar coordinates with threshold -8-1 -12-14 Power [db] -16-18

CHAPTER 3. RESULTS 3.1. PHASED ARRAY SYSTEM TOOLBOX it is better to do for the maximum value. The simulated values are compared with the estimated from Figure 3.13 and 3.15 is presented in Table 3.1. Table 3.1: Comparison between simulated and estimated value from maximum value. Target First Second Simulated range [m] 7569 1287 Estimated range [m] 7625 1285 Difference [m] 56 43 One can see that using that by using the estimated maximum value, it is more consistent with the simulated. Both targets were estimated to the same radial velocity, namely 46.5 m/s. The difference in time required for signal processing using the current model and implementation with PAS system is present in the table below. Table 3.2: Time required for different moments in the signal process. Process Pulse compression GCG Pulse compression Air Time current model [s].124.2413 Time PAS [s].7277 1.2293 Difference [s].637.988 The TVG system object was not successfully implemented in the current system and thus could not compare the time required. Using the current model to simulate the received signal with a target located 388.3 m from the radar in order to compared with PAS simulation in Figure 3.11. In order to compare the PAS toolbox with the current model, a received signal was simulated with the same properties. A target was simulated 388.3 m from the radar system. The data simulated with the current system that should be compared with the PAS simulation in Figure 3.11, is presented in Figure 3.27. Simulated data with current model 18 2 2 16 18 18 14 16 16 14 14 12 12 1 1 1 8 8 Power Range bin 12 8 6 6 6 4 4 2 2 4 2 5 1 15 2 25 3 35 Pulse index Figure 3.27: The simulated data with one target present with current model. 44

3.1. PHASED ARRAY SYSTEM TOOLBOX CHAPTER 3. RESULTS The simulated image shows similar behaviour to the one with PAS. One can see an area where the signal is stronger than the surrounding, where the plane is, and the blue area with noise. This data was also treated with pulse compression. The result of it is presented in Figure 3.28. Data after pulse compression 16 7 14 6 5 1 8 4 6 3 4 2 2 1 5 1 15 2 35 3 25 Power Range bin 12 4 Pulse index Figure 3.28: The simulated after pulse compression. There is one major difference between Figure 3.12 and 3.28. One can see that the yellow area became much more narrow for the current model than for the PAS toolbox. By taking a cross section at the pulse index where the maximum signal strength occurs, the effect of pulse compression can be shown. It can be seen in Figure 3.29 how the signal increased in strength and became narrower after pulse compression. Signal before and after pulse compression at pulse index 121 8 Received signal Pulse compressed signal 7 SNR/Noise floor [db] 6 5 4 3 2 1 2 4 6 8 1 12 14 16 18 Range bin Figure 3.29: Profile of the data before and after pulse compression at pulse index 121. After pulse compression, the position of the target is estimated at a distance of 3884.1 m. The difference between the simulated distance and the estimated were roughly 4 m. Using a large number of simulation (1), the average difference between simulated and estimated distance 45

Bearing Plane orientation degrees, and wing angle 9 degrees 1 Plane front Plane back Apex of left wing.5 Left engine Apex of right wing Right engine Bearing Plane orientation degrees, and wing angle 11 degrees 1.5 -.5 -.5-1 985 99 995 1 15 11 115 12 Range -1 985 99 995 1 15 11 115 12 Range Plane orientation degrees, and wing angle 13 degrees 1 Plane orientation degrees, and wing angle 15 degrees 1.5.5 Bearing Bearing -.5 -.5-1 985 99 995 1 15 11 115 12 Range -1 985 99 995 1 15 11 115 12 Range

Plane orientation 45 degrees, and wing angle 11 degrees 1.5 Plane orientation 9 degrees, and wing angle 11 degrees 1.5 1 1.5.5 Bearing Bearing -.5 -.5-1 -1-1.5 99 995 1 15 11 115 Range -1.5 985 99 995 1 15 11 115 Range Plane orientation 11 degrees, and wing angle 11 degrees 1.5 Bearing 1.5 -.5-1 -1.5 985 99 995 1 15 11 Range Plane orientation 18 degrees, and wing angle 11 degrees.8 Bearing.6.4.2 -.2 -.4 -.6 -.8 985 99 995 1 15 11 Range

Two simulated plane target with a different orientation 9 12 1 6 15 3 5 18 21 33 24 3 27

Elevation Elevation.18.16.14.12.1.8 15.1 15. 14.9 14.8 Bearing angle.17.16.15.14.13.12.11.1 421 425 424 423 422 Range [m] Estimation of plane Estimation of point Simulated point Bearing angle Range [m].9.9 4215 422 4225 423 4235 424 4245 14.8 14.85 14.9 14.95 15. 15.5 15.1 Range [m] Bearing angle Elevation 15.1 15.5 15. 14.95 14.9 14.85 14.8 4215.17.16.15.14.13.12.11.1 422 4225 423 4235 424 4245

Data for point target at range bin with maximum power Data for point target at range bin + 1 Data for point target at range bin - 1 Bearing correction with new estimation for point target Bearing correction with current model for point target Data for plane target at range bin with maximum power Data for plane taget at range bin + 1 Data for plane target at range bin - 1 Bearing correction with new estimation for plane target Bearing correction with current model for plane target Power as function of bearing angle 128 Range number 127 126 3 25 2 15 Power 1 5 5 1 15 2 Bearing angle 25 3

Power as function of bearing angle 124 Range number 123 122 121 7 6 5 4 3 2 1 Power 5 1 15 2 25 Bearing angle 3

3 Power as function of bearing angle 25 2 Power 15 1 5 5 1 15 2 25 3 Bearing angle Power as function of bearing angle 25 2 Power 15 1 5 16 17 18 19 2 21 22 23 Bearing angle

7 Power as function of bearing angle 6 5 Power 4 3 2 1 5 1 15 2 25 3 Bearing angle

Power as function of bearing angle 6 5 4 Power 3 2 1 17 18 19 2 21 22 23 Bearing angle

9 113 85

1 x 99.25