A Tale of Two Wireless Companies

Honest Abe and Tricky Dick both started wireless companies selling equipment for wireless broadband access networks for deployment in urban areas. (These characters are entirely fictional and any resemblance to actual persons, living or dead, is entirely coincidental.) Because the buyers want equipment which will cover as large an area as possible, the range of their equipment is a very important selling point. As it happens they are using absolutely identical equipment, but you will not have suspected that reading their sales literature. Here are some quotes from that literature.

1. Quoting system range

Abe: “our system has a typical range of 0.5 miles”
Dick: “our system has a range of 25 miles”

Both statements are true. Abe is quoting the range of a typical deployment, taking into account the high path loss in an urban environment, effects of interference from other cells, and a fading margin. Dick is quoting range for a single cell under line of sight free-space propagation conditions. The 25 mile range, while technically true, is completely useless as an indicator of what one may expect in a real deployment.

2. Quoting coverage

Abe and Dick reported the area covered by their (identical) systems located on the same rooftop in San Francisco. Abe reported that the area covered was 1 square mile. Dick reported that the area covered was 4 square miles. Both statements are true. How can that be?

Wireless coverage is never perfect. In any given area there are always some users who can not communicate with the basestation because they are in a “bad spot”. In other words there is always some probability that a random user will not get connection. This is referred to as the “outage probability”. The smaller the cell size, the closer the users are to the station and the smaller is the outage probability. The larger the cell size, the larger the outage probability. Abe reported the coverage area for an outage probability of 2%, i.e. 98% of users in that area will get connection. Dick reported the coverage area for an outage probability of 30%, i.e. only 70% of users in that area will get connection. Of course he neglected to mention this.

3. Range increase due to SNR improvement

The engineers at both companies worked hard and were able to improve the equipment to get a 6 dB SNR gain. In other words, the new equipment could now overcome a path loss 4 times bigger than the old equipment (for both companies). Here is how they reported this.

Abe: our new equipment has a 40% larger range than before.
Dick: our new improved equipment had double the range and quadruple the coverage.

Both statements are correct. In a typical urban scenario pathloss is approximately proportional to the fourth power of the distance. Thus, a four-fold SNR improvement translates into a range increase by a factor equal to the fourth root of 4, which is 1.41. Hence the range increase is approximately 40%. Dick is reporting what happens under free space propagation where pathloss is approximately proportional to the square of the distance. Thus, a four-fold SNR improvement translates into a range increase by a factor equal to the square root of 4, which is 2.00. Hence the range doubles. The buyer of the equipment will of course only experience the 40% range increase, at best.

4. Quoting maximum range

Abe and Dick reported the maximum range of their (identical) system located on the same rooftop in San Francisco, facing Market street. Range was measured along Market street. Abe reported a maximum range of 1 mile . Dick reported a maximum range of 2 miles. Both statements are true. How can that be?

Most wireless systems have adaptively adjustable data rate. The system used by Abe and Dick could vary its data rate from 0.1 MBPS to 20 MBPS. The lower the data rate, the less receive SNR is required and the longer the range. Now the customers using these systems needed a minimum data rate of 1 MBPS. A data rate of 0.1 MBPS was of no use to them at all. When Abe measured maximum range he measured it as the largest distance at which the system could reliably sustain 1 MBPS – the minimum data rate required by the users. Dick on the other hand measured range for 0.1 MBPS, which was twice as large. Of course this is not something he mentions when reporting the maximum range.

So what happened you may ask? Equipment buyers were very impressed by the superior performance of Dick’s wireless system and his business grew and prospered. Abe struggled for several years and eventually went out of business. He is now teaching wireless communications at a local community college and is heavily into yoga and meditation.

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