Albert Einstein’s work has influenced and still influences, even today, mobility in cellular networks that we take for granted when applying cell site analysis. Mobile telecommunications is very lucky that it has a fantastic collection of grand luminaries whose influential work from the world of science and mathematics that underpins mobile communications. To understand Einstein’s influence it is useful to firstly understand the mobile radio background which CSA examiners, technicians and student can use to improve the art of performing cell site analysis. It does, though, require keeping a mindset to remain active at all times and that mindset is CSA needs to keep focused on how the mobile network is arranged to react to how the mobile phone is being used whilst moving around.
The goals of mobile network is to keep the mobile phone in touch with the network to maximum the network’s chances of providing services (e.g. revenue generation) to the subscriber customer. The network will do its very best to make coverage available when coping with outages (http://trewmte.blogspot.co.uk/2013/08/operational-audit-check-oac-is-part-of.html) as it will when radio coverage degrades (http://trewmte.blogspot.co.uk/2008/11/mobile-phones-and-fringe-coverage.html) until it can no longer sustain a revenue service to it (the mobile phone).
Importantly, the goal for available service intensifies the denser the urban area in which the mobile phone is to be found. Having to propagate coverage into a hostile environment requires operators to strive to meet that goal by saturating a particular geographical landscape with more mobile network infrastructure base stations and nodes.
The monitoring of the switched ON mobile phone that is in use is to ensure a base station/node is available, but that doesn’t just stop there though. Humans move around either as pedestrians on the pavement (sidewalk) or using some form of transportation. Therefore, the movement and the time (called dwell time) that a mobile phone remains in an area will have an influence upon the layer/s of mobile coverage that may be allocated for a particular call. You may remember the image below from a previous cell coverage discussion at my blog: http://trewmte.blogspot.co.uk/2009/08/cell-site-analysis-csa-images-part-2.html.
The above image is a useful guide to CSA examiners, technicians and students as it illustrates how a mobile network operator looks at designing coverage. The guidance it offers is that when conducting CSA merely conducting drive tests during site surveys is an entirely insufficient CSA method as a human walking does not do so at the speed of a human using transport. Whilst walking a person can stop and start dependent upon the intention or circumstances at that time. However, unless the transport is stuck in a traffic jam then we generally comprehend the transport to be moving more quickly/faster whilst on the road than the human on the pavement or crossing the road.
There have been a huge range of studies that have generated mobility models for incorporation into propagation models. These mobility models are based upon complex study, testing and/or mathematical data endeavouring to predict (mimic) a moving target from which conclusions are generated and later produced for simulation software. The simulation can then be added into programs for designing the coverage (cell planning) for particular geographical locations.
The image above is by Professor Sami Tabbane from his book detailing Planning Stages Of A Cellular Network: Radio Planning - propagation prediction tools.
Cell planning software tools amalgamate a wide range of models (or iterations of them) that the CSA examiner, technician and student maybe blinded to the compilations/combinations of mobility models that maybe incorporated into program. Identifying mobility models provides such needed knowledge, skill and experience that to ignore them might mean that a CSA examiner, technician and student conclusion/s about results obtained during or following site survey may be flawed. Below is a selection of mobility models that are well known:
- Brownian Mobility Model
- Random Waypoint Mobility Model
- Random Walk Mobility Model (including its many derivatives)
- Random Direction Mobility Model
- Random Gauss-Markov Model
- Gauss-Markov Mobility Model
- Markovian Mobility Model
- Incremental Mobility Model,
- Mobility vector model
- Reference Point Group Model (RPGM)
- Reference Point Group Mobility Model
- Pursue Mobility Model
- Nomadic Community Mobility Model
- Column Mobility Model
- Fluid Flow Model/Morales Mobility Model
- Exponential Correlated Random Model
- Exponential Correlated Random Mobility Model
- Map Based Model
- Manhattan Mobility Model
- Rush Hour (Human) Traffic Model
- Mission Critical Mobility Model
- Obstacle Mobility Model
- Smooth Random Mobility Model
- Post Disaster Mobility Model
- A Probabilistic Version of the Random Walk Mobility Model
- City Section Mobility Model
Einstein’s first described mathematically “The Random Walk Mobility Model” in 1926 [ http://users-phys.au.dk/fogedby/statphysII/notes/Einstein%27s-random-walk.pdf] which later became adopted and used for mobile telecommunications mobility. The Random Walk Mobility Model, its elements are widely used to create simulations, is sometimes also referred to as “Brownian Motion”.
The mathematical proposition states since many entities in nature move in extremely unpredictable ways, the Random Walk Mobility Model was developed to mimic this erratic movement. For this mobility model mobile node (MN), a common expression used for human (target) movement, moves from its current location to a new location by randomly choosing a direction and speed in which to travel. The new speed and direction are both chosen from pre-defined ranges, [speedmin; speedmax] and [0;2p] respectively. Each movement in the Random Walk Mobility Model occurs in either a constant time interval t or a constant distance travelled d, at the end of which a new direction and speed are calculated. If an MN which moves according to this model reaches a simulation boundary, it “bounces” off the simulation border with an angle determined by the incoming direction. The MN then continues along this new path.
In A Survey of Mobility Models for Ad Hoc Network Research the authors Camp, Boleng and Davies comment that many derivatives of the Random Walk Mobility Model have been developed including the 1-D, 2-D, 3-D, and d-D walks. In 1921, Polya proved that a random walk on a one or two-dimensional surface returns to the origin with complete certainty, i.e., a probability of 1.0. This characteristic ensures that the random walk represents a mobility model that tests the movements of entities around their starting points, without worry of the entities wandering away never to return. The 2-D Random Walk Mobility Model is of special interest, since the Earth’s surface is modelled using a 2-D representation.
So how might a CSA examiner, technician or student apply Einstein’s Random Walk Mobility Model? One key element to remember that this model is a memory-less mobility pattern because it retains no knowledge concerning its past locations and speed values. The current speed and direction of an MN is independent of its past speed and direction. This characteristic can generate unrealistic movements such as sudden stops and sharp turns which if undesired for simulation purposes can be addressed using e.g. Gauss-Markov Mobility Model. Because there is a memory-less occurrence of random movements it is the investigation into the mobile phone usage that requires analysis.
Points to consider for that analysis can be those that I raised to the 2005 consultation by the Legal Services Commission regarding the Use of Experts in Public Funded Cases:
In any assessment of the evidence the Defence expert at first instance seeks to correlate all the evidence to identify consistency or discrepancy regarding the data from the devices compared to the data obtained from mobile network operators and/or third parties. To assess that against the opinion of the Prosecution expert and/or the findings of the examiner at first instance. To then check the information against the Defence case. Eliminate the points agreed and to deal with those aspects concerning usage and the services obtained against the radio network in the geographical locations where the mobile telephone is alleged to have been. For instance, information not seen or ignored could result in an inaccurate opinion. By way of illustration, a Defendant is alleged to have been at a certain location where a murder occurred and cell site identity of the Mast used to make/receive mobile calls is presented as a justification for the Defendant being at the location. Experience teaches one not to accept that as absolute, but to consider the radio coverage and how the Defendant might use there mobile phone is daily life. The key is 'daily life', referring to regular or irregular movements of the human being in a locale and the purposes of him/her being there. An experienced Defence expert should be looking for evidence that may assist where the Defendant may have been so as to assess that evidence against the allegation. That can require knowing for instance whether the Defendant visited a burger bar outlet or café. Knowing whether the defendant used a cash machine, purchased petrol or used their Nectar card and so on. Knowing the aforementioned information it is then required to conduct a site visit and conduct radio test measurements at those locations identified by the Prosecution and Defence, where these types of events took place. A Prosecution expert is unlikely to know aspects of the Defence case as the Defendant's Proof of Evidence comes after the case material has been served and the Defence's consideration of it. Proof of Evidence is never served to the Prosecution expert or to the examiner for that matter.
Another key element to be reminded for the site survey is if the specified time (or specified distance) an MN moves in the Random Walk Mobility Model is short, then the movement pattern is a random roaming pattern restricted to a small portion of the simulation area. Some simulation studies using this mobility model set the specified time to one clock tick or the specified distance to one step. This can require taking account of e.g. Location; Time of Day/Night; Call duration [sCall;eCall]; Base stations/nodes used and so on.
Using the cell coverage layers image at the beginning of the discussion we can use a description of a dense urban area (e.g. a high street) and the target (mobile phone user) is a pedestrian on the pavement/sidewalk. In the vicinity, at below roof level, are three micrcocells (uBTS) providing lower layer coverage.
All things being equal the MS moving in a uniform linear direction may pass (handover) a call from BTS1 to BTS2. Bearing in mind we are discussing Random Walk Mobility Model the target whilst walking changes direction (turns left) which brings the MS into an area covered by BTS3. It maybe along the road covered by BTS3 there is a shop window the target stops to look in whilst chatting on the phone or decides to use a ATM cash machine to withdraw cash which is next to the shop. The call records show BTS1 and BTS 2 are used for the shop window browsing but BTS1 and BTS 3 have been used for the ATM cash machine usage. Why might this occur?
Microcell coverage usage has parameters included to detect the speed of the MS/dwell time of the MS in an area. The key is slow MS movement in an area is handled differently by the network than a fast MS movement. In this regard the network may apply techniques for homogeneity of speed discrimination in lower layer and upper layer cells. The network does this because the MS speed is detected based upon the signals received by the network. Microcell coverage has problems with street corners and can create fast ping-pong effect in the network to handover between Microcells; hence why I have often stated previously to this discussion that Microcells don’t go around corners.
A coping mechanism in the network is to use emergency handover (HO) to an upper layer of coverage that is more suited to handle traffic signalling for a period of time to decide the best handover candidate for the rest of an MS call.
The use case of BTS1 and BTS2 for the shop window scenario could be as a consequence that the shop was on the corner of the road and the period of target static time was short due to one to three steps (clock ticks) where as the BTS1 to BTS3 dwell time for the ATM cash machine scenario was much longer and requires handover via an upper layer cell down to BTS 3 to remove/reduce chances of fast ping pong on street corners and subsequent call drop.
Whilst the above discussion used Einstein’s Random Walk Mobility Model there are other Mobility Models that have been highlighted and each can be used to good effect to broaden CSA examiners, technician and student knowledge skills and experience.