The easiest way to understand a ranging radar system, is by studying a puls radar. A
DUPLEXER Time control Signal processor Receiver Transmitter/ modulator Transmitted puls Puls echo RANGE [meters]
τ = Round trip time/ delay [seconds] BASIC PULS RADAR
Figure A.2.: Basic puls radar, with single puls operation
basic puls radar configuration is shown in figure A.2, which is based on figure 1.5 from [16]. More comprehensive block diagrams for both puls and CW -radars are given in [38, chap.3] and [16, chap.3], for better understanding of the specific radar designs. The transmitter modulates a rectangular puls of length ∆t with a sine wave and a duplexer
A.2. Range Sensing 163
enables transmission through the antenna. Meanwhile transmitting the duplexer isolates the receiver which is optimized to receiving weak echoes. In this way the receiver is protected from the high power puls transmission. A antenna directs the puls in the wanted direction depending on its pointing direction and antenna directivity. The puls propagates until it hits a reflecting structure, that backscatters a part of the puls energy towards the radar. The weak echo puls is then intercepted by the same antenna structure and coupled through the duplexer to the receiver. This type of configuration that uses the same antenna for transmitting and after reception of the echo, the signal is processed by a signal processor. Thru the whole operation a timing device have control over the occurring events. By using the timing information between transmission and reception, one can sort out the delay (τ ) from the reflection of target often called round trip time. Since electromagnetic waves travel at the speed of light, the range can be extracted.
τ = 2R c ⇓ R = cτ
2 (A.1)
Extraction of range is also possible in CW-type radars but they have to modulate their waveform in order to make an time mark to obtain the round trip time.
To be able to follow the target and to detect new targets that arrives within the radars maximum range Rmax, several pulses need to be send after another in pulsed radars.
The time between transmitted pulses (P RI) needs to be such that the previous puls has been received by the radar. The rate (P RF ) at which pluses are to be transmitted is determined by the longest range that targets are expected. This range will be given by the radar equation( A.24), that describes the systems performance to receive power or to gain a signal-to-noise ratio (SN R) at a specific range. A problem arise in pulsed radars when the PRI is to short and that echoes beyond Rmaxwill arrive after the next puls is
transmitted. This will lead to range ambiguity, and the radar can mistake earlier echoes as close targets. Such echoes are often referred to as Second-time-around echoes or even earlier transmitted pulses as Multiple-time-around echoes. Typical situations that could lead to such conditions is, bad radar design, big reflectors beyond Rmax, unpredictable
propagation conditions like Ducting or high-prf puls-Doppler radar, where this is a calculated disadvantage in order to achieve other preferable conditions. Figure A.3 shows the situation of a typical medium-range radar with rectangular modulated sine waves and the important puls parameters [38, p.4]. If the PRI is assigned variable Tp, it is defined
by Tp = f1p, where fp is the PRF. The unambiguous range is then defined as
Run = cTp 2 = c 2fp (A.2)
In prospect of figure A.3 the duty cycle is given as the ratio of time transmitted over the time that could be used for transmission, duty cycle = ∆tT
p, where ∆t is the puls width. Average power will show the effectiveness of the systems power utilization within a PRI and is therefore a perfered measurement of power compared to the peak power (Pt). To
P O W E R TIME 1 MW peak power Target echo 10-12 W Duty cycle = 0.001 ∆t= 1 μs PRI = 1 ms
Figure A.3.: Typical puls configuration of a medium range surveillance radar
the received average power and thereby improve detection of targets. Pavg =
Pt∆t
Tp
= Pt∆tfp (A.3)
Another consideration concerning the puls width and the use of puls trains, is the ability to discriminate multiple targets within the unambiguous range. To get a good range resolutiona narrow puls is needed, which will decrease the average power if not puls trains are applied. Range resolution is defined in equation A.4. The receiver bandwidth, is in most radars designed such that B ≈ ∆t1 . The range resolution is the shortest distance between two targets that can be discriminated as singular targets.
∆R = c∆t 2 =
c
2B (A.4)
Consequence the puls radar bandwidth needs to be large in order to get a good range resolution. Similarly this equation holds for CW type radars that enable ranging, and that they need to have a large modulated bandwith to have sufficient range resolution.