# Is there still a logical flaw in Apple's maths?

Apple's explanation of why the iPhone 4 shows a drop in reception when you grip it 'in a certain way' has me even more confused.To a phone, as Simon puts it, you are a large bag of salt water.

Apple's explanation of why the iPhone 4 shows a drop in reception when you grip it 'in a certain way' has me even more confused.

To a phone, as Simon puts it, you are a large bag of salt water. If you use a large bag of salt water to bridge the two antenna in a phone, you reduce the signal. FCC tests mandate that the antenna in a phone be as far away from the brain as possible, so instead of the pull-up antenna of days gone by the antenna are moving further and further down. The antenna on the iPhone are a little more exposed that usual due to the industrial design of the phone. Put it all together and yes, you're going to have some people bridging the antenna (especially when you see that the line of the antenna is almost a guide as to where to hold it to worst effect).

That's what Apple means when it says "To start with, gripping almost any mobile phone in certain ways will reduce its reception by 1 or more bars."

But when it goes on to explain the "dramatic drop in bars" that some people see, the logic doesn’t work for me. "We were stunned to find that the formula we use to calculate how many bars of signal strength to display is totally wrong," says Apple. "Our formula, in many instances, mistakenly displays two more bars than it should for a given signal strength."

So, I should be seeing a signal of two but I see a signal of four. I grip the phone 'in a certain way' and the bars drop - but by how much? Unless by gripping the phone 'in a certain way' I am actually fixing the incorrect algorithm, then if the signal was two (shown as four) and is now zero - wouldn't the algorithm now be showing two? If my grip is sufficient to drop the display to zero, isn't that equivalent to minus two in Apple's algorithm? In which case, hasn't the signal actually gone down by four bars after all?

Mary

The problem, of course, is not knowing just how Apple calculates signal strength. It's all in the algorithm, converting the received signal strength into those bars.

RF engineers measure signal strength in dBm, a logarithmic scale that has the advantage of being allowing engineers to display both very large and very small numbers in very little space, by referencing everything to 1mW. That means that 0dBm is equivalent to 1mW of received power - roughly the output of a Bluetooth radio at a range of 1m.

0dBm is actually a lot of power for a mobile phone to be receiving. You can expect a phone to be receiving around -10dBm or about 100μW. That's not very much at all, and the signal strength fluctuations resulting from the complex RF environment mobile phones operate in can mean significant variations down from that. But a big change in received power is only a small change in the measured dBm.

It's quite easy to imagine a group of software engineers being given a set of numbers by RF engineers to expect that this nice linear dBm scale is in fact a nice linear measure of power. When writing the code needed to converting those negative dBm numbers into a bar chart, it's also easy to see those software engineers using (say) a 3dBm drop in signal to remove one bar, not actually realising that that 3dBm drop is actually a 50% drop in the signal strength received by the phone.

That approach leaves the phone showing an artificially high signal strength. By the time you've had a 6dBm drop and removed two bars, the phone is actually receiving only around 25% of the power it had at the full five bars.

So is this the problem Apple has with displaying "too many" bars for a specific signal strength? It's certainly a likely one, but given Apple's passion for secrecy it's an answer we're unlikely to ever get...

The radio world has always had trouble talking to the digital world. Way back when, straight out of university, I spent some time working as a power RF engineer, designing elements of 30KW+ radio transmitters. The analogue wireless world is a messy place, and one that doesn’t translate well to the digital realm (at least not without a lot of domain knowledge). The software members of our team were RF engineers first, code jockeys second - which made communicating the complexities of radio a lot easier.

So how can Apple fix the problem of its bars? Getting the maths right in the first place will be one way to solve the problem. The other? Maybe it's time for Apple's RF engineers to actually write the code that shows the users just what the phone is doing…

--Simon