Lecture 8. Radar Equation. Dr. Aamer Iqbal Bhatti. Radar Signal Processing. Dr. Aamer Iqbal Bhatti

Transcription

1 ecture 8 Radar Equation 1

2 Power received from a point target in absence of noise. PT G PR W / m (4 ) R If the received power from interfering sources is known, the signal-to-interference ratio is found by dividing signal power by interfering power. PR PT G IR P ( 4 ) R P I I

3 Radar single antenna is represented by two different but related parameters: Gain and Affective Aperture. IR P G T 1 4R 1 4R A E 1 P I Radar ERP Power/Area of radar at target ERP of target Power/Area of target power at radar Power from target captured by radar IR 3

4 There are three kinds of losses exist in radars: ystem osses: Exists within the system itself. Propagation Path osses: osses in the medium. Ground Plane osses: Caused by multiple signal path. P G ( 4 ) R P T IR :ystem osses A :Propagation Path osses GP :Ground Plane osses I A GP

5 If more than on hit is processed, the signal to interference ratio can be increased. A processing gain is applied to the radar equation. P G ( 4 ) R T IR G P G P =Processing Gain (usually >>1). Interfering power is internally-generated noise. I P A GP 5

6 The noise power generated within the radar, taken as a source at the input to the antenna. P Ni kto BF The signal-to-noise ratio for multiple hits processed together is PT G GP N ( 4 ) R KTo BF AGP The processing gain for noise interference is given by N G P ( N ) N = Number of hits processed together as a look. i = The integration oss. i 6

7 It is useful to consider the relationship between pulse width and bandwidth for gated CW waveform. B 1 Replacing B and G P in equation given on last slide. N ( PT N ) G (4 ) R KT F o A GP i The first three factors in numerator are the look energy. 7

8 ignal-to-noise or signal-to noise jamming ratio is directly proportional to look energy regardless of the waveform (Discussed later). ( PT N ) G N (4 ) R KT F PAVG = Average Power = Dwell or look time T D N N (4 ) (4 ) 3 3 P R T KT AVG 4 o o D o WG 4 R KT F A A G F A GP GP GP i i i 8

9 NR in terms of P AVG is useful with pulsed, CW, and pulse Doppler waveforms. Energy view of NR is one of the requirements of ow Probability of Intercept (PI) radar. PI radar : A radar that can see but can not be seen. PI is based on the fact that Target echo detection is done with illumination energy. Interception is done with peak power. o PI requires low peak power but high energy waveform. 9

10 A multimodal airborne radar has the following specifications in one of its modes. (high PRF single target track). Transmitted Power Pulse Width PRF Antenna Gain Frequency Rx NF ystem oss Propagation Path oss Ground Plane oss 10kW 1.µs pps 35dB 10.5GHz(λ=0.086m) 3.5dB 1.4dB 1.6dB 0 db Find the single hit NR for a m target at 55 nmi. 10

11 N ( 4 ) 3 PT G G 4 R KT BF All factors must be in ratio form. Antenna gain is 3160, the noise factor is.4, the system loss is 1.38, the propagation loss is 1.45, the range is m, and the ground plane loss is 1. The NR for single hit (N =1) using above equation will be 0.051(-1.9dB). Example 3-: If the same radar can coherently integrate 048 pulses with 1.6dB integration loss i. The integrated NR will be 7 or 18.6dB. o P A GP 11

12 One of the primary uses of the radar equation is the prediction of the maximum range at which a particular target can be detected. Maximum range is found where the NR is the minimum. Example 3-3: Find the maximum range at which the radar of previous examples can detect a 10m target if the minimum NR is 16dB. For (a) a single hit, (b) a 048-hit look. (a) Maximum range for single hit is 8800m (15.6nmi). (b) For 048 hits it is m (95.5nmi). 1

13 Target echoes for different NR s given below the figure. The number in parentheses is the ratio of the rms signal voltage to the rms noise voltage and is the square root of NR. 13

14 A factor of the radar equation can be isolated which represents all system parameters which are inconvenient to express in db, called the space gain or space loss. PT G G IR PI A The space gain is therefore. The space loss is P GP ( 4 ) R ( m (4 ) R G R PACe ) R PACE (4 ) 3 R 4 m 14

15 A hypothetical high power early warning radar has the following specifications. Transmitted Power Type Antenna 15MW Monostatic Antenna effective aperture 30 m Antenna Gain Frequency Rx NF ystem oss Propagation Path oss Processing Gain to Noise Minimum NR Ground Plane oss 94-ft diameter array (46.5dB) 1GHz 1.1dB(1.9) 1.0dB(1.6) 1.3dB(1.35) 9dB(800) 14dB(5.1) 0 db(1.0) 15

16 Estimate the following. a) The signal power received from a single hit on a -11.4dBsm target at a range of 000km. b) The noise power present in radar. c) The NR for this target for a single hit. d) The NR for this target for given processing gain. e) The maximum range at which this target can be detected. olution. a) 3.6 * W(-114.4dBm). b) 5.16 * W (-11.9dBm). c) dBm-(-11.9dBm)=-1.5dB which is not sufficient for detection. d) -1.5dB+9dB=7.5dB. e) Maximum range will be 4350km. 16