Jonny and the Cell (pt. 2.5)

Much has happened since my fledgling foray into the world of wireless networking. After finding and confirming facts for over a month I set to work developing a method that could be used to assess the quality of existing networks yet still provide a firm basis for the design of new ones. I derived a set of equations that could be used to answer the most difficult questions I had about access point placement and then developed a tool to simplify the solutions. I began using a grid, optimized for multi-floor, multi-unit deployments, to predict where access points would need to be placed and provide documentation that field technicians could follow during deployment. And after all this I am still developing my method and still finding evidence of its predictive power.

While the method itself is not yet simple enough for a layman to take full advantage of it, the mechanism by which it softens the subtle complexities of RF modeling is not difficult to grasp. By a kind of averaging of the details, it becomes easier to intuitively grasp the most important information necessary for a wireless deployment: area of coverage given a particular level of service and the number of access points required to provide said coverage.

Nevertheless, the results produced by this method will initially make very little sense to those steeped in RF modeling. Perhaps the most troubling thing one will find in one of my diagrams is the use of isotropic, or circular, cell boundaries. How can such a naïve description of wireless range ever be used to reliably predict the propagation of a signal in the real world? The question is a valid one, and important, for it lies at the very heart of my method.

When recently asked about this apparent discrepancy, I felt I could not answer properly without explaining fully the method itself. And so I present my answer here, as it may be the best and perhaps only complete explanation I've given of this method and the rationale behind it. I admit the explanation lacks the rigor needed to support certain claims, but I think the conversational tone may better facilitate understanding. At least for now, it will have to do.
The reason I use an isotropic cell boundary is because it is impossible to make a truly accurate diagram with the information available to me.

In order to design wireless installations without resorting to guess work, I created a method that takes into account empirical data to determine access point locations using the ITU model. This method uses what I call a 'thick-air' model to describe the medium through which wireless signal propagates. That is, all obstructions and interfering signals are averaged within a given space to produce numbers that are close to real. I liken this to taking a floorplan and applying a strong gaussian blur, then measuring the color difference between the blur and the blank space.

In an existing installation, I look at two access points that are just able to 'see' one another. First, I obtain the signal level that each AP receives from the other. Then, after obtaining a scale drawing of the site, I measure the distance between the two access points. With a known receive signal level, distance, transmit signal level, antenna gain, frequency, and number of walls between, I use the ITU propagation model to solve for the Path Loss Exponent. This exponent corresponds directly to the exponent in the Inverse-Square Law of RF propagation.

The idea behind the Path Loss Exponent is that the exponent for an RF signal propagating through a vacuum will be '2', which is what we would expect given an inverse-square. However, in a medium, the exponent increases, thus causing the efficiency with which the signal travels to decrease sharply. Of course, the Path Loss Exponent assumes that the medium is homogeneous. But when used to measure path loss in a heterogeneous medium (a building), it can help abstract away many small, unhelpful details about the space.

For any existing installation, I take several measurements like this throughout the site and average the results. In this way, outliers hold less sway over the final design. I then look at the standard deviation--a very worthwhile thing to do when looking at a limited amount of data--just to make sure I haven't seen only the best or only the worst of a site. Buildings that exhibit particularly poor RF characteristics compared to the rest of the site are set aside so as to not influence other buildings that may have been built in different phases with different materials. To measure floor loss I find two access points directly on top of one another, then use a Path Loss Exponent of 2.1 (atmosphere) while adjusting the level of shadow fading until the distance as-solved matches the actual distance.

Once I have a general Path Loss Exponent for a site, I use a set of equations that I derived to determine the inter-access point distance given a target cell overlap. Once this is obtained, I create a two-floor or one-floor grid, depending on the floor loss I measured when determining the Path Loss Exponent. In this way, I take into account RF propagation in all three dimensions. The grid is then set as an overlay on top of the scale floor plan and adjusted until it produces realistic candidate locations for installation.

When I began working on this method, I predicted that the Path Loss Exponent would be substantially higher at one of our sites than the numbers that many sources recommended. I reasoned that this would be because, unlike a single dense home environment with an average Path Loss Exponent of 4.0, we work with many dense home environments that have been put together, one on top of the other. As it turns out, this is correct, and it results in Path Loss Exponents as high as 8.5 in a few places, though a good number for most sites appears to be right around 5.0.

In sites without an existing installation, I would prefer to have a site survey taken before making a design. But, having done quite a few of these, I have some reasonably conservative values that I can assume when I lack information. For the site in the picture, I have done precisely this, documenting the principle values that I used when making calculations in the annotated area, at the corner of the diagram.

I hope this explains the reason for the isotropic cells in the diagram. Please let me know if you have any further questions.
 Indeed I hope that clarifies a few things, but I realize an explanation with far more background and rigor is required. This may be a while in coming (http://wiki.wlandesign.dreamhosters.com/wiki/Main_Page is hardly begun). In the meantime, give my humble design tool a shot at http://wlandesign.co.cc/. It lacks a few features I'd like to see, but it is, as best I can tell, fully functional in IE, Firefox, and Safari. And getting anything to work in IE is bordering on miraculous.

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