BLIND SPEEDS IN MOVING TARGET INDICATOR RADAR SYSTEMS

If the target has an approach velocity towards or away from the source, the phase shift is not constant, this can be demonstrated as follows;

Say, at a particular instant in time, that the Doppler frequency is 2000 Hz, and the time for a pulse to return from the target is 124 m s (10 nautical miles). The phase difference between the transmitted and received carrier modulated signals will be f ₁ = 2000*124 m s = 0.248 cycles, or 1.5582 radians. When the next pulse is returned from the moving target, the target will now be, say, 123 m s away, or f ₂ = 2000*123 m s = 0.246 cycles, or 1.5457 radians. Thus, the phase shift of the modulating carrier frequency is definitely not constant for moving targets, as this example shows. There is a phase difference D f =1.5582 - 1.5457 = 0.0125 radians between the carrier frequency of successive pulses on the target. If the target happens to have a velocity, whose radial component results in a phase difference of exactly 2p radians of the carrier signal between successive pulses, it is the same as having no phase shift in the carrier signal at all. This means that the target is stationary or that the target appears stationary, and echoes from it are cancelled by the MTI action. The probing pulse can be considered as a sampling pulse. The first pulse to be considered samples the target position and returns information to the source in terms of the target's phase. Due to the Doppler effect, this phase can be considered to be;

The next pulse sent out from the source again samples the target position again and again returns information to the source in terms of the phase of the target.

Because the Doppler frequency does not change and so,

However, the difference in time , must be the difference between the sampling period of the first and second pulse, which makes it the inverse of the PRF. Because the source PRF remains the same, the movement of the target is detected by a change in the returned phase of the carrier, comprising the pulse, from one pulse to the next.

Also, the difference in phase between each sample , must be a cycle or multiple cycles of the carrier frequency, if the target is to appear stationary. Thus,
 
 

Considering the Doppler frequency shift observed by a source from a signal returning from an approaching target moving less than about 10% of the speed of light, that is;

That is,

This permits the blind speed to be expressed in terms of the source pulse repetition frequency (PRF) and the source carrier wavelength l .

That is,

where

= the blind speed

SOLUTION

From,

The lowest blind speed corresponds to n = 1. Thus, = 86.4 km/h.

Consequently, the lowest three blind speeds are 86.4, 172.8 and 259.2 km/h (for n= 1, 2 and 3). The fact that blind speeds exist need not be a serious problem, and does not normally persist beyond a small number of successive pulses. A target flying directly toward the radar set at a constant velocity could cause this, but it would be sheer coincidence, and a far-fetched one at that, for a target to do this accidentally. Intentionally, it could be possible that a wideband receiver and microprocessor on board the target (aircraft/missile) analyses the transmitted frequency and PRF, and adjusts its radial velocity accordingly. The solution to this problem would be to have a variable PRF. That presents no difficulty, but varying the delay in the MTI radar does. It can, however, be done by having two delay lines and compensating amplifiers. One of these can be a small delay line, having a delay that is say, 10 percent of the main delay. This second line will then be switched in and out on alternate pulses, changing the blind speed by 10 percent each time.
 
 
 
 
 
 

If the speed of the plane is within ± 1% of the blind speed, the plane changes from dark grey to light grey. If the speed of the plane is within ± 0.01% of the true blind speed, then the speed of the plane is considered to be at the blind speed and no plane is observed. In this case, a message indicating that the plane is travelling at, or near the blind speed, is printed on the screen.

Please keep the mouse arrow off of the "GO" button once activated, otherwise the plane will continue to traverse the screen.

For best results Netscape Gold should be used with a screen size of 800 x 600 pixels.