Sheet 1 of 11 RADAR RAdio Detection And Ranging Part 1 of 2 Introduction Applications: Detection and Ranging of ground, sea and air targets Air Traffic Control (ATC) Guidance Tracking Meteorological applications Collision avoidance Speed measurement Remote sensing Why use microwave frequencies? 1. Low absorption by the atmosphere see Figure 1 • low attenuation below about 20 GHz, particularly below 10GHz • resonant peaks due to oxygen and water molecular absorption • at higher frequencies operate in 'windows' at about 35GHz, 94GHz etc • much lower absorption by fog, rain, snow at microwave frequencies than at optical frequencies Figure 1 Graph showing attemuation of a microwave signal through the atmosphere with varying conditions and frequencies 2. Antenna sizes • angular resolution limited by beamwidth • beamwidth determined by λ/D - D is antenna diameter - θ(radians) ≈ λ D • require D = 10λ for 6° beamwidth • suggests using high microwave frequencies to reduce antenna size, but a balance must be struck with the atmospheric attenuation Sheet 2 of 11 Types of radar 1. Bistatic separate transmit and receive antennas Monostatic same antenna for transmit and receive TX RX TX RX Bistatic (i) Bistatic (ii) Monostatic Figure 2 Monostatic and bistatic radar 2. CW radar transmits continuous wave (CW) • can detect objects, measures velocity from Doppler shift, but cannot measure range 3. FM-CW radar frequency-modulated CW transmitted signal • detects, measures range and radial velocity 4. Pulsed radar includes MTI (moving target indicator) and Pulsed Doppler • detects, measures range and velocity, but has blind speeds and ranges CW radar • can be bistatic or monostatic TX RX TX RX Bistatic (i) Bistatic (ii) Monostatic Figure 3 Monostatic and bistatic CW radar Sheet 3 of 11 • transmitter and receiver both operate continuously - hence no range measurement. Difficult to avoid Tx to Rx feed-through, even with separate antennas • measure radial velocity of target from Doppler shift fo Vr TX ⎛ 2.vr ⎞ fo + ⎜ ⎟ fo ⎝ c ⎠ Doppler shift Fig. 4. Doppler frequency shift for reflected signal Mix Tx and Rx signals to give difference frequency - the Doppler frequency ⎛ 2v ⎞ ⎛ 2v ⎞ fD = f0 + ⎜ ⎟ f0 − f0 = ⎜ ⎟ f0 ⎝ c ⎠ ⎝ c ⎠ • Ships radial velocity in range 0 to 30 knots typically i.e. 0 to 15ms-1 ∴ at an operating frequency of 2GHz, f D is in the range 0 to 200Hz Using homodyne detection, where the Rx and Tx signals are mixed directly to give the Doppler frequency problems arise due to flicker noise in the detectors and amplifiers because the noise power is proportional to 1/f and flicker noise is large at low frequencies such as 200Hz. Noise power density is Area for given bandwidth and is greater at lower 1/f Frequencies. Flicker noise Power density B.W f Fig. 5. Flicker noise versus frequency Sheet 4 of 11 A solution is to use heterodyne detection in which the Rx signal is mixed with a local oscillator (LO) with a frequency which differs from the Tx frequency by, for example, 30MHz. The received signal + LO generate an IF (intermediate frequency) output at 30 MHz which contains the same information - ie Doppler frequency shift - as the Rx signal. After amplification the Doppler frequency shift can be extracted by further mixing. (fo+fD) (fo+fD)- fLO ≈ 30MHz → RX amplify without flicker noise LO fLO Velocity ambiguity with CW radar Velocity ambiguity is the inability to distinguish between approaching and receding targets. It arises because in a mixer with an LO frequency f 0 input signals with frequencies f 0 + f D and f 0 − f D give the same IF frequency ie the same IF output is obtained for targets that are approaching or receding from the radar at the same radial speed. Velocity ambiguity can be removed by splitting the received signal into two equal components. A 90° phase change is applied to one of the components. After further mixing the relative phases of the two components gives the sign of the Doppler frequency. Thus approaching and receding targets are distinguished. A system that achieves the removal of velocity ambiguity is shown in Figure 6. The outputs are called the I (In phase) and Q (Quadrature phase) outputs. With f D +ve Q output leads I by 90° approaching target With f D -ve Q output lags I by 90° receding target FM-CW radar • frequency modulate the CW signal to give range as well as velocity • the frequency is swept repeatedly between f 1 and f 2 • the range is found from the frequency difference between the transmitted and the returned signal - see figure 7 for a stationary target • if the target is moving there is an additional Doppler frequency shift. For an approaching target the frequency of the returned signal is increased. For m positive (m is the rate of change of frequency with time for the transmitted signal) the range frequency is decreased by the Doppler frequency, whereas for m negative the range frequency is increased by the Doppler frequency. Using both measurements both the range and radial velocity of the target can be obtained - see figure 8. Sheet 5 of 11 System to remove Velocity Ambiguity with CW Radar TX fo CW Tx LO at IF fo LO fIF (fd+fIF) <90 degrees fd < 90 degrees Q 90 RX fo-fIF degrees Amplifier fo+fd 3dB fd+fIF fIF (Approachin (fo-fd)-(fo-fIF) g target) = fd+fIF fd < 0 degrees (fd+fIF) < 0 degrees I With fd +ve (approaching target) Q output 90 degrees AHEAD of I output With fd -ve (receding target) Q output 90 degrees BEHIND of I output Figure 6 Sheet 6 of 11 FM-CW Radar Frequency-modulate CW signal to give range information. (1) Stationary target Tx Rx F2 Frequency ∆f ∂f T m= ∂t F1 2R C time t Figure 7 Tx frequency – increases with time ⎛ ∂f ⎞ f T = f1 + ⎜ T ⎟t = f1 + m.t ⎝ ∂t ⎠ Rx signal lags Tx signal by time to target and back TX R 2R TR = C Mixing Rx and Tx frequencies gives difference frequency ∆f ∆f ⎛ 2R ⎞ =m ∴ ∆f = f R = m⎜ ⎟ 2R ⎝ C ⎠ C Range frequency Sheet 7 of 11 (2) Moving target with FM-CW due to Doppler - additional frequency shift due to Doppler effect Tx Rx F2 fD fD Frequency Approaching target ∆fr F1 time fr – fD = ∆fr Figure 8 Approaching target : Rx signal frequency increased by fd Therefore ∆f (measured) = fR-fd ( for m positive ) = f+ For m negative ∆f (measured) = fR+fd = f- Therefore, fR = ½(f+ + f-) fd = ½(f- - f+) simultaneous equations Sheet 8 of 11 • ambiguity can arise between very close fast moving targets and slow moving distant targets. It may not be possible to decide whether the difference frequency is f R − f D or f D − f R. Pulsed radar • short pulses (pulse length ∼ 1µs) of RF radiation are transmitted with relatively long intervals ( T(PRF)) ∼ ms) between them. PRF is the pulse repetition frequency Τ ~ 1us Echo E1 TX T R = (2R)/C T/R T (PRF) ~ 10-3s RX Figure 9 Pulsed radar and radar pulses • the time delay between the transmitted and reflected signal TR gives the range to the target R TX 2R 1 TR = R= CTR RX C 2 Figure 10 Transmitted and reflected signals • each time delay of 1µs corresponds to an increase in range of 150m • a T/R cell is connected between the transmitter and the receiver to protect the sensitive receiver from the high power pulses from the transmitter. This disables the receiver during pulse transmission Sheet 9 of 11 • the maximum unambiguous range of the radar occurs when TR = T ( PRF ) . For longer ranges the echo returns after the transmission of the next pulse. R (unambiguou s ) = cT (PRF ) 2=c 2PRF • the blind range of the radar occurs when the echo signal arrives back when the next pulse is being transmitted and the receiver is disabled - ie TR = T ( PRF ) . This is the same as the maximum unambiguous range. • to avoid the blind range and to distinguish targets that are beyond the maximum unambiguous range a variable PRF should be used. If we combine the reflections from several pulses, targets with R < R(unambiguous) will all have the same time delay with respect to the transmitted signal, but those will appear to have a variable delay, because they actually originated from an earlier transmitted pulse. T1 T2 T3 T Will move if R > R (unambiguous) E1 E2 E1 E2 Fixed for all transmission pulses if R < R (unambiguous) combine Figure 11 Use of variable PRF to distinguish targets beyond the unambiguous range • the radar range resolution is the ability of the radar to distinguish two targets with similar ranges. The resolution is determined by the pulse duration τ . The smallest time interval that the radar can resolve is τ which gives a range resolution of cτ 2 . If τ = 1µs the range resolution is 150m. T1 T2 τ R = ½.CTR AR = ½.C(A.TR) τ Figure 12 Radar resolution Sheet 10 of 11 • the angular resolution of the radar is determined by the beamwidth of the antenna, which is in turn set by the frequency of operation and the antenna diameter θ (radians)≈ λ/D. Blind speeds with pulsed radars If the frequency of the echo signal is measured the target radial velocity can be determined as well as its range. The sketches below show the time domain and the frequency domain forms of the transmitted pulses. τ 2 ⎛ sin(x) ⎞ sin x 2 = ⎜ ⎟ ⎝ x ⎠ Time P(f) Domain Line spectrum 1 ∆f1 = = PRF T(PRF ) PRF fo f 1 fo − fo 1 Frequency domain Transmitted Waveforms τ fo + τ Figure 13 Time and frequency domain forms of a radar pulse train In the frequency domain the pulse contains frequency components with spacing ∆f 1 = ( PRF ) from the transmitted frequency f 0 . If the Doppler-shifted echo signal falls on one of these frequency components it cannot be distinguished, and so the radar is 'blind' to the corresponding radial velocities - ie to velocities that give f D = n∆f1 =n( PRF ) where n = 1, 2, 3, etc. Blind speeds ⎛ 2.v r ⎞ c.n(PRF) f D = n(PRF) = ⎜ ⎟ fo ; v r (blind) = ⎝ c ⎠ 2 fo 3x108 x n x 103 eg fo = 10GHz; PRF= 1KHz vr = 10 = 15n....15ms −1 ; 30ms −1 ; 45ms −1 2x10 Sheet 11 of 11 For a pulsed radar with a frequency of 10GHz which transmits pulses at millisecond intervals -1 -1 -1 -1 (PRF = 1kHz) the blind speeds are 15 ms , 30 ms , 45 ms etc. 15 ms is about 30mph, so in some applications there would be many blind speeds within the speed range of interest eg aircraft. To avoid problems due to blind speeds the radar must be operated so that they do not fall into the range of interest. This can be achieved by increasing the PRF. However, this reduces the unambiguous range and so a compromise must be reached. -1 Example: Blind speeds less than 1500mph ( 670 ms ) are to be avoided. For a radar operating at 10GHz this corresponds to a Doppler shift, and hence a PRF of 45kHz. This PRF gives an unambiguous range of only 3.3km. The value of the Doppler frequency, and hence the PRF, could be reduced by operating the radar at a lower frequency -eg 2GHz -but this might mean using a larger antenna to give the same angular resolution. Two broad categories of pulsed radar are 1. MTI (Moving Target Indicator) radar • distinguishes moving targets from the stationary background by Doppler shift. Only those echoes with a frequency shift are displayed. The reflections from the background are known as clutter. • MTI uses a low PRF to avoid range ambiguity, and gives a large range • the blind range is small because the receiver is only disabled for a small % of the time • 'blind' to many speeds, starting from quite low speeds • the low PRF reduces the number of hits per target as the radar beam is scanned. This reduces the radar sensitivity. 2. Pulse Doppler radar • uses high PRF to avoid blind speeds • short unambiguous range, more extended blind range • more hits per target increases sensitivity Note: Hits per target gives the number of pulses that hit the target as the radar beam is scanned. The signal at the receiver is averaged over several pulses to average out the effects of noise. The radar sensitivity increases with the number of hits per target. If a beam with width 2° is scanned at 36° per second a target will be in the beam for 1/18 seconds. With a PRF of 300Hz the number of hits per target will be 300/18 = 15.