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Cambridge University Science Magazine

You have arranged to meet a friend in a busy high street in London. She isn’t answering her phone, and you haven’t got a hope of finding her just by wandering around. Wouldn’t it be handy if you both had mobile phones that could be instantaneously and accurately positioned? The applications for such a technology are endless: keeping a watchful eye on your children; tracking goods and deliveries; seeing exactly where the bus you are waiting for is (and being able to decide whether to wait for it any longer); navigating when you are lost; finding a cash machine, petrol station or hotel; and perhaps, crucially, enabling the emergency services to locate you immediately when you call them.

ImageCurrently, any mobile phone can be positioned to within the cell it occupies, i.e. the area of coverage of the base station that is serving the mobile phone at a given moment (see figure below). This is called the Cell-ID method. In rural areas, where there are few tall buildings to block signals, powerful macrocell transmitters can be used to provide coverage for 35 kilometres or more. Within cities, where buildings are densely packed, macrocell coverage is enhanced by placing microcell transmitters every few hundred metres or so. There are even picocell transmitters in use inside buildings, in tunnels and on cruise-liners to provide coverage within a 50-metre range. However, Cell-ID determines only the position of the base station that is serving your phone, and so the accuracy is dependent on the range to the base station. If a person happens to be using the tube, being served by picocells, they can be located quite accurately, but in most cases you cannot rely on Cell-ID to give a useful position fix. It is only adequate for tracking goods and looking up information on the local area. Vodafone, for example, uses Cell-ID for their Find and Seek service, which is regularly used by the police to determine the last known position of an abducted person.

Improved accuracy can be achieved by combining Cell-ID with further information from the network. Whilst making calls on the move, your mobile is constantly monitoring the network, deciding when it needs to be handed over to a new serving base station. The changeover is determined by the signal strengths of the nearby base stations. The time it takes for signals to get to and from the base stations (the Timing Advance, TA) is also measured. Enhanced Cell Global Identity (E-CGI) uses these measurements to make a more accurate estimate of the position of the mobile. The accuracy is better than Cell-ID, but is limited by the large error in relating signal strength directly to distance and by the resolution of the TA timings. Signal strength is strongly affected by the environment the phone is in: moving a few metres in open space outside will not change the signal strength significantly, but moving a few metres into a building from outside causes a noticeable reduction. Signal strength, therefore, can provide only a very rough estimate of the distance from the phone to a base station.

TA allows your mobile to compensate for the time-of-flight of the signals to and from the base station. This is needed to prevent the signals from all mobiles using a particular base station at a given moment from arriving at different times depending on their distances from the base station, as these times would keep changing if the mobiles were moving. Each kilometre of distance delays the signals by a little over 3 microseconds, so a busy cell would have to deal with signal delays ranging from almost zero, for a caller right next to the base station, to 100 microseconds, for someone right at the edge of a rural cell. The additional processing performed by the base stations would increase costs and complexity considerably. To overcome this, the handsets are asked by the base station to advance their times of transmissions (by the TA value) so that everyone’s signals arrive when the base station is expecting them. These timing adjustments correspond to an error of 570 metres on the ground — helpful for positioning purposes, but still not that accurate.

ImageTriangulation has always been a straightforward positioning method in navigation, but is not very practical in a mobile phone system. One must calculate the directions from which the signals arrive at the mobile or at the base station. A large antenna (or two smaller antennas fixed a long way apart) is needed in order to measure this. Such an arrangement is sensitive to the direction of arrival of a signal, and the larger the antenna — or the wider apart the two smaller ones —the finer the angular resolution. Large antennas are impractical for mobile phones and large antenna arrays on the base stations further increase costs and complexity.

Another idea is to equip mobile phones with small Global Positioning System (GPS) receivers so that you can use your phone like a ‘sat-nav’ device in a car. GPS works out your position via satellites orbiting the Earth. There are 24 active satellites in the GPS constellation, but at any one time a GPS device can generally only see about one-third of them. Positioning this way requires direct lines of sight to at least three satellites, as their signals are very weak by the time they reach the Earth’s surface. GPS works with high accuracy outdoors in rural and suburban areas where there is always a reasonably good view of the sky. However, if the phone is in your pocket or bag, or you are indoors or in an area where the sky is obscured by tall buildings, the system does not work — a serious limitation when considering the typical scenarios for positioning a call to the emergency services, or locating an abducted or lost person. This is partly ameliorated by adding ‘assistance’ to the system, in which the GPS receiver is told where to look for satellite signals by messages sent from a central point in the mobile phone network. However, even with assistance the reception is often very poor and the caller has to wait a long time for a position fix, if one is available at all.

The most promising technique today is called Matrix and was invented here in Cambridge. Matrix was developed by Dr Peter Duffett-Smith of the Cavendish Laboratory as an offshoot of positioning work he did during a radio astronomy project. Dr Duffett-Smith was using a technique called aperture synthesis to study distant radio sources. The method involved simultaneously gathering data with two or more radio telescope antennas that were separated by some distance. The resolution of the images improves as that distance increases. However, for the method to have worked the distance between the antennas had to be known to the nearest metre, even when they were more than 1000 kilometres apart. Duffett-Smith found that not only could he use public broadcast FM radio signals, such as BBC Radio, to position a radio receiver attached to his telescope, but that this technique could be adapted to position any mobile radio device. In order to develop this technique for mobile phones he established Cambridge Positioning Systems Ltd. However, mobiles just measure the intensity of the signals they receive on one channel, whereas Duffett-Smith’s original technique required phase measurements on multiple channels. Matrix gets around this problem by solving a set of non-linear simultaneous equations using timing measurements made by the handsets on signals received from the base stations. A derivative of this system is Solo Matrix: a single handset can be positioned as long as it is moving, building up its own network timing model with the data it gathers on the move.

Another enhancement of Matrix currently under development is called Enhanced GPS (E-GPS), which combines the high accuracy of GPS in rural areas with the high availability of Matrix in urban areas. The timing data gathered during Matrix calculations can also provide assistance data for a faster GPS fix.

The Matrix equations assume that signals travel in straight lines directly to the mobiles from the base stations, but in urban areas and indoors the signals can undergo reflections and diffractions before reaching the mobile, leading to longer, more complicated propagation paths. By determining what the dominant delay processes are, and when signals transmit straight through a building and when they do not, these extra time delays can be modelled and incorporated into Matrix and E-GPS in order to improve the positioning accuracy further. Truly, the Matrix revolution is coming.

For more information on Matrix go to

Ramsey Faragher is a PhD student in the Department of Physics