Recent developments in pulse-compression - Upgrading EISCAT UHF

Pulse-compression techniques are regularly used in high-power ionospheric incoherent scatter radars. For example, the EISCAT Tromsø has binary coding possibility. As I have understood pulse-compression, it is typically due to two factors:

1. High-power amplifier technology supports transmitting longer pulses with lower peak power instead of shorter pulses with very high peak power.
2. The wanted range resolution is of the order of microseconds or less while range extent of the target is typically milliseconds. Thus if we send microsecond pulse in millisecond intervals, the transmitter is nonoperational for a very large portion of time.

Because of these reasons, we use pulse-compression techniques in high-power radars, i.e. Barker codes, chirped signals etc.

SGO team has concentrated on designing a number of different coding and analysis techniques. The first significant breakthroughs were done already in 1980s with alternating coding development. During recent years, we have been working on perfect pulse-compression coding techniques. These codes were first reported in

[1] M. Lehtinen, B. Damtie, P. Piiroinen and M. Orispää, Perfect and almost perfect pulse compression codes for range spread targets, Inverse Problems and Imaging 3 (2009) 465-486.

A succession to this paper was reported in

[2] L. Roininen and M. S. Lehtinen, Perfect pulse-compression coding via ARMA algorithms and unimodular transfer functions, Inverse Problems and Imaging 7 (2013) 649-661.

The paper [1] included a crucial discussion on comparison of measurements developed by Petteri Piiroinen from University of Helsinki. This mathematical formalism gives us a solid background to compare different kinds of measurements and hence also coding techniques. Paper [2] shows the relation of the coding problem to the classical study of unimodular polynomials with constrained coefficients.

As [1] and [2] need amplitude and binary phase coding, we have not yet run any real measurements with these codes in high-power radars. Of course at some point we will do this also! However, in 2012, we ran a series of polyphase coded experiments with the Millstone Hill ISR in Massachusetts, USA. These were reported in Radio Science

[3]  I. I. Virtanen, F. Lind, L. Roininen, P. Erickson, W. Rideout, M. Orispää, J. Vierinen, and M. Lehtinen,  Polyphase-coded incoherent scatter measurements at Millstone Hill, Radio Science, 48 (2013).

To our knowledge, this was the first reported polyphase-coded ISR experiment.  Of course we want to do similar things with EISCAT system. Hence during the Finnish November EISCAT campaign, we discussed a possibility for doing quadriphase coded experiments by minor modifications of the current EISCAT UHF. This option is now available and we are going to schedule these experiments for the May campaign. Provided that everything will go ok, we will report these experiments in the web log and hope to publish them in peer-reviewed journals!

Naturally we are also continuing the development of the mathematical background for pulse-compression code comparison. This week, we are going to submit a paper on pulse-compression of continuous codes to Inverse Problems and Imaging. The reference is:

[4] L. Roininen, M. S. Lehtinen, P. Piiroinen and I. I. Virtanen, Perfect pulse compression coding via unimodular Fourier multipliers, manuscript in progress.

Hence, we are working on both the mathematical background of the pulse-compression techniques and upgrading the existing hardware to more advanced coding possibilities. And of course... The EISCAT_3D needs a whole lot more!

EISCAT UHF Klystrons!

SGO projects in Ethiopia

SGO is carrying out two collaboration projects in Ethiopia. We have mentioned these projects in web log previously, but maybe it is time to check out the projects in more detail.

For SGO, the most interesting thing in Ethiopia is that the geomagnetic Equator crosses Ethiopia. Hence this makes the Bahir Dar University an ideal spot for Equatorial studies. Our future plan is to both install instruments in the country (riometers, tomography receivers,...) and to make scientific collaboration with the BDU departments of mathematics and physics. The cunning plan is to educate the Ethiopian staff to carry out methodological research, which is based on rigorous mathematical modelling of geophysical measurements and to implement these methods in practice with modern measurement tools, such as software radios (USRPs) and the like.

Our Ethiopian projects are actually part of two big projects coordinated by the Department of Mathematics and Physics of Lappeenranta University of Technology. The third Finnish partner is the Department of Mathematics of Tampere University of Technology. The other African partners are from Tanzania, Uganda, Rwanda and Kenya. The projects are:

• Mathematics education and working life relevance in East Africa 2013-2015 (funded by Ministry for Foreign Affairs of Finland)
• East-Africa Technomathematics 2009-2015 (funded by Centre for International Mobility of Finland)

We have a project website at http://www.mafy.lut.fi/HEI-ICI/.

Of course going to Africa has many positive aspects for Finns, such as being in a nice climate during the slushy seasons or dark period "kaamos".  Actually the Bahir Dar weather is just like best Finnish summer weather, very pleasant indeed.

Admin block at the main campus of the Bahir Dar University.

Sodankylä and clouds... Part 2

Yesterday we claimed that we have record-level cloudiness in Sodankylä. So let us check out the data in more detail. In the Figure below, you may find the cloudiness and sunshine duration data given kindly by Rigel Kivi from FMI Sodankylä. It is notable that in February, we had a cover of clouds for a long period. Hence, if someone wanted to see the aurora borealis, then North America would have been a much better choice!

So why do we have this kind of weather? One explanation is that there is a high pressure in Russia and that does not move anywhere at all. It is locked! Hence we are getting warm air from south all the time!

It's cloudy, very cloudy indeed!

Latest results: Bayesian inversion on unstructured lattices

Our paper on prior modelling for Bayesian statistical inverse problems has been accepted for publication in Inverse Problems and Imaging. The reference is

[1] L. Roininen, J. M. J. Huttunen and S. Lasanen, Whittle-Matérn priors for Bayesian statistical inversion with applications in electrical impedance tomography, Inverse Problems and Imaging, Accepted March 2014.

The paper considers Gaussian smoothness priors on unstructured lattices. Such priors have been widely used in Bayesian inversion, however there has been a lack of systematic construction of proper integrable, computationally efficient and discretisation-invariant smoothness priors. In this paper, we show how to construct such priors via solutions of stochastic partial differential equations. The paper is a continuation for two earlier papers also published in IPI:

[2] L. Roininen, M. S. Lehtinen, S. Lasanen, M. Orispää and M. Markkanen, Correlation priors, Inverse Problems and Imaging 5 (2011) 167-184.

[3] L. Roininen, P. Piiroinen and M. Lehtinen, Constructing continuous stationary covariances as limits of the second-order stochastic difference equations, 7 (2013) 611-647.

The papers [2] and [3] offer convergence studies of the stochastic difference equations to some continuous objects. The paper [1] concentrates more on unstructured meshes, i.e. finite element approach, and is more application oriented with a strong emphasis on scientific computing. From a point of view of a geophysical observatory, the methods developed can be used especially in ground prospecting as well as in ionospheric tomography.

We will post a link to the full paper, as soon as it is online. Meanwhile below you may find the abstract of the paper. If you are interested in the topic, the authors will gladly respond to any questions or comments.

Whittle-Matérn priors for Bayesian statistical inversion with applications in electrical impedance tomography

Abstract:

We study flexible and proper smoothness priors for Bayesian statistical inverse problems by using  Whittle-Matérn Gaussian random fields. We review  earlier results on finite-difference approximations of certain Whittle-Matérn random field in $\mathbb{R}^2$. Then we derive finite-element method approximations and show that the  discrete approximations can be expressed as solutions of sparse  stochastic matrix equations. Such equations are known to be computationally efficient and useful in inverse problems with a large number of unknowns.

The presented construction of Whittle-Matérn correlation functions allows both isotropic or anisotropic priors with adjustable parameters in correlation length and variance.  These parameters can be used, for example, to model spatially varying structural information of unknowns.

As numerical examples, we apply the developed priors to two-dimensional electrical impedance tomography problems.

Sodankylä, the cloudiest place on Planet Earth?

The Sodankylä winter 2013-2014 has been characterised by relatively high temperatures, soft grey skies and snow/sleet/rain/... One peculiar thing is that we have not really seen the Sun this year. It has been only during couple days with nice February/March weather. Of course the positive point is that we have not had any really cold weather (like -30 C).

Today, I asked one of our FMI colleagues, how many hours of sunlight we had in February. We briefly checked the FMI databases and found out that during 1/2-3/3 we only had 4 days with some sunshine!!! Otherwise it has been grey! 

The fabulous thing about FMI Sodankylä, is that they have lidar measurements of the cloudiness, hence the next step is to analyse cloudiness ratio in Sodankylä for whole winter. And I say, it has been extremely cloudy! From the atmospheric science point of view, we could ask why we have had so cloudy winter! Is it due to jet streams or something else? In addition, we know that in the North America, the winter has been really cold (the opposite of the European winter). What is the reason for this extremely boring weather phenomenon?

The brief moments, when we have seen the Sun in February 2014.

Software defined radio wide band wide beam riometer

During my visit to Finland a few weeks ago, I setup two computers with two different prototype radio frontends to test my idea of using a USRP N200 and a single LOFAR LBA antenna as a low cost riometer with next generation capabilities.

First of all, a riometer (Relative Ionospheric Opacity METER) is an instrument that measures the absorption of cosmic radio noise in the D-region of the Earth's ionosphere. We assume that the cosmic radio noise statistics are unchanged. Thus, we assume that at a certain time of celestial day, we should pick up the same cosmic radio noise power with our antenna beam, as it sees the same swath of sky. The only variations to this power is attributed to changes in ionospheric absorption, which is significant below 50-100 MHz.

In reality the radio sky isn't a completely stationary noise source. Occasionally there are radio emissions from the Sun, which are sporadically seen as spikes in power during the daytime in riometer data. Jupiter is also a strong and variable radio source, and its emissions might cause confusion when interpreting riometer measurements. These type of sporadic emissions need to be excluded from any ionospheric data products derived from riometer measurements.

The advantage of using a wide band for riometry is at least four fold:

1. More bandwidth = more statistics
2. We get a measure of the frequency dependent absorption, which contains information about the electron density height profile
3. More tolerance to interference, as we can find the noise floor around the interference, as long as it doesn't completely saturate the amplifiers. 
4. The wide band nature of the instrument allows us to more easily identify transient radio emission events, such as Solar or Jovian radio emissions.

Anyway, here are some of the initial results. This is simply a dynamic spectrum and a raw power plot derived from the dynamic spectrum. I have not attempted to yet fit a quiet day surface to extract the frequency dependent absorption, although there is no reason why this wouldn't be possible as we have already done it successfully with the LOFAR digital backend. 

The first ~five days of raw riometer power. Several auroral precipitation absorption events happened during this interval, which was a lucky coincidence, allowing us to not only verify that the daily cosmic radio noise variation is periodic, but that we can see D-region absorption. The blue curve is labeled "Army", because this RF frontend utilizes some pretty heavy duty US army surplus tuneable helical filters. The "Pelti" frontend is made from standard minicircuits boxed components. 

The dynamic spectrum between 25 and 50 MHz. Again, nearly five days of data and many absorption events. The strong interference at 36.9 MHz is the Sodankyla Geophysical Observatory meteor radar, which is located about 10 km from the riometer site. 

I'd like to acknowledge Tomi Teppo and Toivo Iinatti for their assistance in setting up these wide band wide beam riometers. 

Food for thought

Ack! It is weekend again and we've missed Photo-Friday. Sorry everyone. My, how the week has flown past. We've been busy with the Heppenaari Inverse Problems meeting, and the KAIRA team has been scattered travelling and processing the latest exciting results (yes, we've just made some serious breakthroughs and are working on it).

But it is weekend and the weblog has been neglected for two days now. Time to set things right!

Today's story is actually from last weekend. Yours truly decided to have a shot a making bread. The recipe was simple:

• All the flour remaining in the packet,
• One sachet of dry yeast (it said 11g on the packet),
• Water, until doughy (added carefully not to over do it),
• Spoon of sugar (granular, not cubed),
• Pinch of salt,
• Butter to grease the pot and tray.

The procedure was also simple:

Apart from the butter, put everything in the pot. Mix it by hand until it has made a serious mess. Turn it out and butter the pot/tray. Turn on the over for some random number (180 seemed like a good idea). Dump the dough in the pot and sit it on the stove over the oven, which was slowly warming up. When risen (exact time = enough to deal with some KAIRA e-mails), splot it into the tray and place it in the oven.

Leave it in the oven until force of appetite exceeds force of reason.

Dough in the pot. I didn't have a bowl or anything.

Rising dough in the pot. Note in the background the machine that solves equations.

After a second rising, it went into a buttered, glass baking tray.

Mmm... hot bread. Added lots of butter, and then toppings.

I think we could easily compete in the Great Finnish Bake-off, no?