6.5.1 Transmitted signal
A radar works on the principle that the range of a target can be determined by measuring how long it takes for a radio pulse to travel from the transmitter to the target and back again. The transmitted signal s(t) is a continuous wave (CW) modulation of a carrier.
CW modulation can be thought of as an on-off keying of the carrier. In order to reduce harmonic distortion the carrier is in fact modulated with a Gaussian shaped pulsep(t) and so the transmitted signal is a linear multiplication of the Gaussian pulsep(t) with a carrier signal sin(2πf0t) or, in complex form exp[ı2πf0t], to create the following transmitted signal
s(t) =p(t) exp[ı2πf0t].
6.5.2 The received signal
For radar applications the received signal r(t) may be a superposition of several multi- path echoes (i.e. echoes which have travelled over various propagation paths between the transmitter and receiver) reflected at various ranges from various irregular features in the ionosphere. The received multi-path signalr(t) which is an attenuated and time delayed (possibly multiple time delays) replica of the transmitted signals(t). It can be represented as,
r(t) =
P
X
i=1
ais(t−τi) or
r(t) =
P
X
i=1
aip(t−τi) exp[ı2πf0(t−τi)], (6.1) where Σ shows that theP multi-path signals sum linearly at the receiving antenna, ai is the amplitude of the ith multi-path component of the signal, and τi is the propagation delay associated with multi-path i. After removing the carrier, the modified r(t), now represented byr1(t) becomes:
r1(t) =
P
X
i=1
αip(t−τi),
where the carrier phase of each of the multi-path components is now represented by a complex amplitudeαi which carries along the RF phase term andp= 1 whent=τ.
frequency pulse more than once. If the received signals are coherent then the signals can be added to achieve a cleaner and more detectable signal. Ifr1(τ) is the amplitude att=τ of reflections from parts of the ionosphere cτ2 away and one were to transmit a second pulse at the same frequency, then under steady state conditions, one would obtain an identical r2(τ) at the same time after the second pulse. If the target were moving, there would be a phase difference betweenr1 and r2 that would be determined by the velocity of the target and manifested as a Doppler shift in the signal.
6.5.3 The timing
The length of the transmitted pulse
In a standard radar, once the transmitter begins transmitting the receiver will saturate and so the transmitted pulse must be turned off before the first echoes are expected to arrive at the receiver. This determines the maximum length of the transmitted pulse. If a second pulse it to be transmitted for the purpose of determining the Doppler shift, then the transmitter should wait until the last possible echo has returned. This determines the pulse repetition rate of the radar.
This is not the case for a SuperDARN radar.
The intention of the radar is to record echoes from as far as 3555km away. This means that, in order not to contaminate echoes, the system should wait until the last possible echo has been received before it begins with the next pulse. This would mean that the system would have to wait 2dc seconds wheredis the range andcis the speed of light. This amounts to waiting 24 ms before transmitting the next pulse. Waiting this long means that you are only sampling the same region of ionosphere every 24 ms and subsequently according to Nyquist theory, can only resolve motions with a period of 21 Hz. At 12 MHz transmitted signal this translates into a maximum Doppler velocity of 263 m/s which is not suitable for polar ionospheric convection analysis.
To avoid this problem the SuperDARN radars will transmit pulses before the last expected pulse has returned. They achieve this by making use of a staggered pulse pattern with each pulse length being 300µs long and rely on the fact that, although there will be interference, the noise will decorrelate and be cancelled.
The staggered pulse pattern
The way the radar achieves a sampling rate high enough to resolve large Doppler velocities without having to wait for the echoes from the further ranges is to transmit pulses before the echoes from the farthermost ranges have returned. It achieves this by transmitting
CHAPTER 6. THE SUPERDARN RADAR 45
Figure 6.3: The staggered pulse pattern showing how the various ACF lags can be created from the seven pulses.
shown in figure 6.3.
In this example the first pulse is transmitted at what is known as lag 0 where a lag time is 2.4 ms. 9 lags later 21.6 ms, a second pulse is transmitted. 3 lags later 7.2 ms, the next pulse is transmitted, then 8 lags (19.2 ms), then 2 lags (4.8 ms), then 4 lags (9.6 ms) and finally 1 lag later, that is 2.4 ms, the final pulse is transmitted.
Transmitting before the last echoes have returned means that at some point in time one may be receiving echoes from two different pulses, and from possibly two significantly different regions of the ionosphere. This is where the nature of the pulse pattern becomes significant. It is assumed that the region of ionosphere of interest will remain coherent for the duration of the pulse pattern. If this is the case then a correlation between two different samples made at the same time after a pulse was transmitted, will be high for reflections from the same region and low if the echo is from different regions.
After the first pulse was transmitted, the receiver starts to make samples every 300µsand continues to do so until 24 ms after the last pulse. The 24ms is required for the last possible echo to return from 3555 km. This means that it takes approximately 90 ms to complete one pulse sequence. Once the pulse sequence has been completed, an auto correlation function is generated for each range [15]. The generation of the ACF is discussed in detail in appendix D.