1. Requirements of ISR Experiments
Ian McCrea

2. Requirements of an experiment
When we’re designing an experiment, we have to bear in mind six requirements:
Spatial Resolution
Range Extent
Lag Extent
Lag Resolution
Time Resolution
Accuracy
Unfortunately, these requirements are frequently contradictory!
Real experiment design is a compromise that gives acceptable (rather than
optimum) solutions to these requirements.

3. 1) Spatial Resolution
To measure the ionosphere properly, we need to measure it on at least the same
height scale as its own natural altitude variation. If we do not do this, we will
average height-varying parameters together and arrive at a result which fails to
represent any one altitude properly.
One measure of the rate of parameter change with height in the ionosphere is given
by the plasma scale height. Remember that the scale height is defined as an
e-folding distance, so ideally we want to have gates at significantly better
resolution than the scale height.
If we want gates separated by one quarter of the ionospheric scale height;
At E region altitudes; mi ~ 30 amu and Ti ~ Te ~ 200 K so Hp ~ 12 km and so we
should have gates separated by about 3 km.
At F region altitudes, mi ~ 16 amu and Ti ~ 1000 K Te ~ 2000 K so Hp ~ 150 km
and so it is acceptable for the gate separation to be ~ 40 km.
Ideally, we would want each gate to be independent (range ambiguity = gate
separation) although we could relax this where the scale height was large.

4. Constraining factors for an incoherent scatter radar experiment
Pulse length giving
resolution equal to
the scale-height.
ionospheric
correlation time,
τ1 for UHF
Possible values for
UHF experiment
ionospheric
correlation time,
τ1 for VHF
Time of flight for
radar pulse
Minimum pulse
length obtainable
from transmitter
Some constraining factors for incoherent scatter experiments, shown as
functions of height for typical ionospheric conditions.

5. 2) Range Extent
This is really about making sure that our measurements address the kind of physics
we are trying to understand.
In some experiments with specific scientific aims (e.g. PMSE studies, topside ion
outflows, wave coupling across the mesopause) it may be acceptable to probe only
a limited range of altitudes.
However, for general purpose experiments (e.g. the most frequently used Common
Programmes) we would like to survey the whole ionosphere from the lowest to the
highest altitudes where we can get useful signals.
This imposes the requirement that our experiment should include different types of
modulation such that:
1) E region data can be obtained with adequate range resolution and
range ambiguity
2) F region data can be obtained with adequate signal-to-noise.
Very long pulses can be used in the topside, where reange resolution is not a pressing
requirement to boost SNR to acceptable levels.

6. To use our radar optimally, we would like to transmit as much power as the duty
cycle of the transmitter allows.
To fulfill the requirement for different range resolutions and ambiguities, we ought
to transmit several different modulations (e.g. alternating code, long pulse, power
profile etc). We transmit each modulation on a different frequency.
Even though we can only transmit one frequency at a time, we can receive and
process signals on many frequencies simultaneously, since we have a multi-channel
system.
This means that the low-altitude modulations have to be transmitted last !
We’ll see later that there is one modulation scheme which is almost optimal for
all altitudes.

7. 3) Lag Extent
In order to get full information on the shape of our ACF, we have to sample the full
length of the function from the zero lag to where the correlation disappears to zero
(equivalent to the decay time of the plasma waves we’re scattering from).
The longest ACFs (narrowest spectra) are found in the E-region and the shortest
ACFs (broad spectra) come from the F-region.
Hence we need the largest lag extent at the
lowest altitude.
This is exactly the opposite of what we’d like,
given that for conventional long pulses, a long
delay time implies a large spatial ambiguity.
We can’t use long pulses at altitudes where
their spatial ambiguity exceeds the scale
height. However, short pulses won’t give us
a large enough lag extent.
We need to find some “trick” by which we
can get a large lag extent with a small range
ambiguity, and this is why we need pulse coding.

8. 4) Lag Resolution
It isn’t merely sufficient to sample the ACF out to a long enough lag. We also have
to sample it sufficiently frequently to define its shape.
Since our lags come from cross-products of samples, our shortest possible lag
spacing is going to be equal to our sample spacing.
However, the sample spacing is set by the post-detection filter we use, and this in
turn is determined by the modulation bandwidth as well as the spectral width.
If we OVERSAMPLE the filter, i.e. sample faster than twice the fastest frequency
which the filter allows through, we don’t gain any new information.
If we UNDERSAMPLE the filter, i.e. sample slowly so that we don’t sample the
full range of frequencies allowed through by the filter, then we’re losing
information. This is equivalent to determining the ACF with insufficient resolution.

9. 5) Time Resolution and 6) Accuracy
These two are coupled ….
Ideally we’d like to measure our data at very high time resolution, so we could get information on very short timescale processes e.g. in aurora. 
Unfortunately the fact that we’re measuring a stochastic process means that we have to post-integrate a large number of measurements together before the expectation value of the ACF becomes visible above the random noise.
For a given Signal-to-Noise Ratio, the accuracy of a measured signal power improves as the square root of the observing time, according to the following formula:
Ps is the measured signal power
Pn is the noise power
b is the measurement bandwidth
n is the number of pulses transmitted in unit time
 is the pulse length
t is the integration time.
This accuracy calculation can ultimately be applied to the fitted plasma parameters.

10. Aliasing due to undersampling of data
Oversampling isn’t dangerous, but it is a waste of effort.
Undersampling can be a serious problem and lead to (very) wrong results.
The choice of filter we need has to be made with the required lag resolution in mind

11. For the plasma velocity,
We can optimise n by increasing the number of transmitted pulses up to the limit allowed by the radar duty cycle (note that this is not always possible if it doesn’t allow adequate time for reception).
Pn/Ps can be optimised by having a high-gain system, but is subject to variations in electron density.
The choice of b and  are dictated by what we are trying to measure.
In the analysis of our data, we have to choose a time resolution that gives us a high enough accuracy to determine reliable plasma parameters, but a high enough time resolution to make our measurements worthwhile.
Since we don’t know in advance what this will be, the standard approach is to use short pre-integrations (e.g. 5 seconds) which can be summed together afterwards if needed.

12. Parts of an experiment
The aim of our experiment is to measure lag profiles from the ionospheric scattered signal, so that we can fit profiles of plasma parameters. However, in order to do this, we have to measure other things as well…
Noise Background
All of our measurements, as well as containing the wanted signal, contain a large percentage of “background noise”. This is cosmic noise from the sky, electronic noise from the radar system, external interference etc.
We want to subtract this background from our wanted signal, and we first assume that the background noise is stationary with respect to time at least on the timescales of our measurement (milliseconds).
In this case, if we make an independent measurement of the background only (i.e. without the signal) in the same way as our signal+background measurement, we can subtract the two, leaving only the wanted signal.

13. We can measure the noise only by either:
a) Measuring the background before we transmit the signal, thus
ensuring no possibility of contamination.
b) Waiting until the signal pulse has propagated out of the ionosphere
before measuring the background.
If we further assume that the background is “white” i.e. that it is evenly spread in frequency across our passband, then we don’t need to measure the spectral shape of the background, only its power, so only the background zero lag has to be measured.

14. Noise Injection
Sometimes “noise” can actually be helpful to us. We can use a standard noise injection signal (i.e. an injected signal at known power) to calibrate the system.
To do this, the noise injection has to be broadband across all the used frequencies, and has to be measured in the same way as the signal+background and background.
Since any measurement of the injected noise will also contain the background, we have to subtract the background from our noise injection measurement before calibrating the radar by comparing the noise injection to the level of the wanted signal. Since the injected signal is broadband, only the zero lag has to be computed.
Thus many data dumps contain three distinct parts – signal, background and calibration (noise injection).

15. “Clutter”
Because the ionospheric signal is so weak, it is easy for it to be swamped by even low-amplitude signals from other sources. The most troublesome can be signals caused by the radar transmission reflecting from mountains etc, or from satellites and orbital debris.
These kinds of signals are known as “clutter”.
In Tromsø, because the radar is in a valley, any reflections from mountains that we get come from very close range, and are eliminated by gating the receiver correctly.
At Svalbard, because the radar is on a mountain, we can get reflections (e.g. via the radar side lobes) from mountains many tens of kilometres away (i.e. at ranges comparable to the ionosphere).
To eliminate these we use our knowledge that, while the correlation time of plasma waves is short (hundreds of microseconds) the correlation time of mountains is somewhat longer (millions of years).

16. Instead of sending one sounding modulation, we transmit two, spaced apart by more than the correlation time of the plasma waves and less than the correlation time of mountains.
Before we start to form lags etc from the two sample streams, we first subtract one from the other. This eliminates the clutter, which is present to the same degree in both, but since the wave process is stochastic, we can form the same expectation value by correlating and integrating the result of the subtraction as we could from either of the individual data streams. The difference is that the result of the subtraction contains no clutter.
This is known as the “moving target method” and is a standard process in non-ionospheric radars.

17. Satellites
At the other end of our range coverage, we can get large coherent echoes if our transmitted pulse strikes a satellite (remember that the illuminated volume can be thousands of km3).
However, it may be that satellites are only instantaneously in the beam. Certainly they are moving rapidly through the sidelobe pattern, so we can’t use the moving target method here.
For topside data (where satellite contamination is a real problem) we have to do some post-processing of the data to find and eliminate satellite events. Failure to eliminate even a short-lived event can have a serious effect on long data integrations.

21. “Self-Clutter”
Note that if the experiment is not well designed, some of our transmissions can occur as “clutter” in the reception of others.
Consider the simple case of a two-pulse experiment, where the pulses are transmitted very close together.
Two dimensional ambiguity functions
of a two-pulse code
Note that for the zero lag, the signal is ambiguous, because the range ambiguity of both pulses appears at ionospheric ranges.
In some applications (e.g. multipulse codes) this is an unwanted by-product, but a price worth paying to get small (unique) spatial ambiguities at the other lags.
The fact that we generally transmit several modulations consecutively before receiving explains why we need a multi-frequency radar !

22. A Timing Diagram for a Simple Radar Experimentms
Transmitted pulse
Reception windows
Calibration signal
Calibration reception

23. Writing out the data
In principle, it doesn’t matter in what sequence we write the output data, provided we know which bits are which. In practise, it is usually done in one of two ways.
1) As Pre-correlated ACFs
i.e. lag 0, lag 1, lag 2……lag n from range gate 1, followed by
lag 0, lag 1, lag 2…....lag n from range gate 2 ………
…….. lag 0, lag 1, lag 2……lag n from range gate n.
This was usually the data format for EISCAT mainland, pre-renovation data.
Note that most data dumps contain data dump from more than one pulse scheme, and most pulse schemes contain separate sets of gates for signal, background and calibration.
All the pre-gated data are written out in EISCAT LDR (Logical Data Record) binary format.

24. 2) As lag profiles
The structure is implied from the name:
Lag 0 from range gate 1, gate 2, gate 3………. gate n, followed by,
Lag 1 from range gate 1, gate 2, gate 3………. gate n, followed by
Lag 2 from range gate 1, gate 2, gate 3………. gate n, …………to….
Lag n from range gate 1, gate 2, gate 3………. gate n.
This is equivalent to writing out the lag profile matrix, and is probably the preferred method, as it allows the data analyst to make his/her own decision about gating.
This format can be found in ESR data and data from the post-renovation mainland system.
All the lag profile data dumps (almost) are written out in MATLAB (v5) format.
During this course, we’ll see several examples of each type.

25. Data Dump with Pre-gated ACFs (e.g. CP1KT)
Data Dump with Lag Profiles (e.g. GUP3)

26. Summary
We’ve now covered the basic principles of radar operations and experiment design
Can now apply these ideas to real experiments and data
If you haven’t grasped everything in the last 3 hours of lectures – don’t worry !
These concepts will come up many times during this week !

29. When we compute a zero lag from a sample, we are essentially multiplying a
sample by itself and so our zero lag comes from a spread of ranges.
At a time, t1, the signal that we receive from the leading edge of the pulse comes
from a height of c(t1-t0)/2, while the trailing edge comes from a height of c(t1-τ)/2.
Range
Time τ t0 t1
c(t1-τ)/2
c(t1-t0)/2

30. If we now consider a subsequent sample, taken at time t1+δt, the heights of the
leading and trailing edges are c(t1-t0 +δt)/2 and c(t1-τ +δt)/2.
So for every subsequent sample, the spread of ranges is the same, but the range
moves up by δt/2.
Remember that δt, the sampling interval, is set by our choice of filter, not
(necessarily) by our requirements in probing the ionosphere.
Range
Time τ t0
t1+δt
c(t1-τ +δt)/2
c(t1-t0+δt)/2