Noise Radar Technology
4.2 Clutter and direct signal cancellation
The detection scheme based on the matched filtering concept [39,53], described by (4.10) for the constant velocity case or (4.26) for the constant acceleration case, is optimal only in single object cases. In the case where there are more targets visible in the antenna beam, the signals originating from one target can be treated as additional noise when the filter is tuned to the second one. The sidelobes originating from the strong targets can then mask the weak target echo, as shown in Figure 4.15.
If only a weak target echo is present, the noise floor is low and the target echo is visible. In the case of presence of both weak and strong target echo, only the strong target peak is visible, and the weak one is masked by processing sidelobes.
103 102 101 100
10–1 10–2 10–3 a [m/s2]
10–2 10–1 100
ti[s]
101 Fc = 100 [MHz]
Fc = 1 [GHz]
Fc = 10 [GHz]
Fc = 100 [GHz]
Figure 4.14 Acceleration resolution versus integration time for different carrier frequencies
In the case of a single target, the detection range is limited in noise (and other) radars by receiver thermal noise. In the multi-target cases, the detection range can be limited by ground clutter or strong echoes, while the direct signal, strong echo returns, ground clutter echoes and distant targets’ weak echoes are received simultaneously. Such an effect is not present in pulse radars, as all of these com- ponents are separated in time, and range gain control can solve the dynamic pro- blem of noise radar.
4.2.1 Noise radar range equation
The echo power received by the noise radar receiver is equal to PR¼ PTGT
16p2R4LSoSR (4.31)
wherePTdenotes the effective transmitted power,GT is the transmit antenna gain, Sois the target radar cross-section,SRis the received antenna effective surface,Ris the range to the target andL denotes all the losses in the radar system, including transmission losses, propagation losses and receiving losses. This expression can be also presented in the form:
PR¼PTGTGRl2
ð4pÞ3R4L So (4.32)
where GR is the receiving antenna gain, and l¼cF is the wavelength of the transmitted signal.
60
40 20
–20
[dB]
–40
–60
0 50 100
Samples
150 200
0
Target 0 dB + Target –40 dB Target –40 dB
Figure 4.15 Masking effect in noise radar
In the single target cases, the target echo power has to be detected in the presence of receiver thermal noise
PN ¼kTRB (4.33)
whereTRis the effective system noise temperature (dependent on the temperature of the receiver, the receiver’s noise figure, antenna noise and outer space noise), B– the receiver bandwidth, andkis Boltzmann’s constant (1.3801023[J K1]).
The radar detection criterion can then be written as PTGTGRl2
ð4pÞ3R4L So>kTRBDo (4.34)
where Do is the detection threshold, usually having the value of 10–16 dB, depending on the assumed probability of a false alarm in the Neyman–Pearson detector. The maximum detection range can be predicted by the equation
Rmax¼
ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi PTGTGRl2So
ð4pÞ3LkTRBDo
4
s
(4.35) For a noise radar, after the matched filtering, the effective receiver bandwidth is reduced to the value 1=ti which is usually much lower than the original radar bandwidth B. In a typical case, the radar bandwidth is in the range of 1 MHz to 1 GHz, while the effective receiver bandwidth obtained by coherent integration is in the range of 0.1–1000 Hz. The effect of reducing receiver bandwidth in integration processing is called integration gain, which is equal to the time- bandwidth productBti. Applying the effective bandwidth to (4.35), one can obtain the final noise radar range equation as
Rmax¼
ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ETGTGRl2So ð4pÞ3LkTRDo
4
s
(4.36) whereET ¼PTtiis the total energy sent towards the target during the integration time.
In a multiple target scenario, when the filter is tuned to a distant target, the total noise power is now equal to
PN ¼kTRBþPRN (4.37)
where PRN is the sum of all received echo powers except for the one to which the filter is tuned. Each echo power is described by (31). IfPRN kTRB, then (4.34) for a two-target case, taking in consideration the integration gain, takes the form
PTGTGRl2
ð4pÞ3R4L So> PTGTGRl2
Btið4pÞ3R4NLSNDo (4.38)
whereRN is the range to the strongest near target (or clutter), andSN is the radar cross-section of this target.
As a result, the radar detection range is shortened to the value of Rmax¼RN
ffiffiffiffiffiffiffiffiffiffiffi SoBti SNDo
4
r
(4.39) Assuming that both the targets are of similar size, the integration gain is at the level of 50 dB, and the detection threshold is at the level of 10 dB, the noise radar detection range is limited to 10RN. The situation can be much worse when a near target or ground clutter radar cross-section is significantly higher than that of the target.
Another limitation relates to the total dynamic range of the noise radar receiver. The power received by the radar is proportional to the integration gain, equating to 1=R4. If the radar has to observe two identical targets, one at a distance of 10 m and one at a distance of 10 km, the difference between the near and far echo power is 120 dB. Adding 10 dB of threshold, the required dynamic of the radar receiver is equal to 130 dB. This dynamic range requirement is defined after integration processing, but assuming 50 dB of integration gain, l80 dB of dynamic range in the analogue part, and an analogue-to-digital converter (ADC) is still required, which is a high number.
4.2.2 Ground clutter cancellation
In the presence of direct signal interferences and multiple targets, more sophisticated detection schema has to be used. The optimal solution to the masking problem is to solve the non-linear equation set for each sampling instancetj, presented by
XRðtjÞ ¼xðtjÞ þX
i
AiXT tj2ri
c
e4pðFtvit=cÞtj (4.40) whereAi,ri,viare complex amplitudes, ranges and range velocities of all observed targets, including ground clutter returns, for whichvi¼0. The mean-square solution gives the unknown vectors [Ai], [ri] and [vi]. This approach, although optimal, is computationally very inefficient and cannot be performed in real time. It requires the solving of a non-linear equation set. In real time, it is possible to apply a sub-optimal approach. The received signal consists of three signal groups: receiver thermal noise, ground clutter echoes and moving target echoes.
Under the assumption that the echo power originating from moving targets is much smaller than the echo power originating from ground clutter, it is possible to find the ground clutter parameters by solving the simplified equation set
XRðtjÞ ¼xeðtjÞ þX
i
AiXT tj2ri c
(4.41) which is related only to ground clutter. The equation set is still non-linear and difficult to solve. Further simplification is based on the assumption that the clutter is placed on an equal-spaced distance grid related to the sampling period ri¼iTs=2c.
Under such assumptions, the equation set (4.41) becomes linear versus the unknown clutter amplitude vector [Ai].
XRðtjÞ ¼xeðtjÞ þX
i
AiXTtðjiÞ
(4.42) The estimated clutter echo amplitudes [A^i] can be further used for ground clutter attenuation. The attenuation is performed by the subtraction of the modelled clutter echoes’ signals from the received signal, according to
XRremðtjÞ ¼XRðtjÞ X
i
A^iXTtðjiÞ
(4.43) and the cleaned signal can be used for moving target detection using (4.12) or (4.20).
The direct solution of (4.42) is still computationally inefficient, so several more computationally effective methods have been devised using an adaptive filter concepts, e.g. the block lattice filter orthogonalization of the signal base set {XTðtðjiÞÞ} and iterative block ground clutter removal.
Figure 4.16 shows an example of a noise radar observing moving targets on the road [9]. It also receives strong ground clutter originating from trees. In Figure 4.17, the cross-section of the zero Doppler beam of the ambiguity function before and after the application of clutter cancellation is presented. It is easily seen that the residual fluctuations at the level ofBt¼60 dB below the strongest return completely masks the weak targets. After clutter cancellation, the strongest components are attenuated by 70 dB, and the noise floor is decreased by more than 40 dB. The cross-ambiguity function of the received signal is shown in Figure 4.18. The direct signal interferences and ground clutter are visible out to a range of 150 m. All moving targets are masked by ground clutter.
Figure 4.16 Experimental noise radar used for the detection of road traffic. Two antennas of the radar, mounted on a trailer next to the road, is visible on the right-hand side
In Figure 4.19, the cross-ambiguity function of the received signal after clutter cancellation is presented. Clutter was cancelled up to the range of 560 m. Radar detections at the level of30 to10 dB are visible, together with the track of the co-operating target. The target echoes levels are 70 to 90 dB below the strongest
0 100 200 300
Range, R (m)
400 500 600
60 50 40 30
20 10
–30 –20 –10 0
Velocity, V (m/s)
10 20 30
Figure 4.18 Cross-ambiguity function of the received signal (without ground clutter cancellation) – only ground clutter visible. Grey scale in dB
60 Before adaptive filtering
After adaptive filtering
Residual fluctuations BT
Leakage Clutter 40
Cross-ambiguity function, |ψ(R,V = 0)| (dB)
20 0 –20 –40 –60 –80
0 50 100 150 200 250
Range, R (m)
300 350 400
Figure 4.17 Signal at the output of correlation processing before and after the application of the clutter cancellation algorithm
received signal component. The ground clutter at the distance of 600 m is also visible, together with the Doppler spread clutter at a distance of up to 150 m, caused by trees and canopy motion. The Doppler spread components can also be atte- nuated, which is described in detail in [54].