# Polar Modulation explained

“What do you actually do at work?” – ” Uh, well, this is hard to explain.  Today, I was doing optimization of DPD coefficients for 3G higher order modulation cases”. When people asking us highly specialzed engineers, scientists, or researchers about their work,  we are sometimes stuck and can’t explain what we are actually doing, but rather explaining very basic, undergraduate course topics, which leaves both us and them puzzled.

With this blog post I want to start a new series on my actual work, with a more educational vision: The desire to explain basic principles of my work to people with no background in electrical engineering, but with following articles including deeper explanation of advanced techniques. The first example seems to be randomly chosen, but this technique is actually used in data connections of the modern mobile phones (smartphones), so it’s definitely worth  explaining; I am talking about Polar Modulation.

### So, what is Modulation?

The goal of wireless communication is transmission and reception of information  with the help of electromagnetic waves over the air, without wires. For example in audio broadcasting, the electrical signal representing the sound is transmitted over the air and can be receipt at a distant place with a radio receiver. As several stations want to be heard, the radio spectrum is organized in channels, and each station is only allowed to send a signal in it’s own channel. A channel is a range of frequencies, and Modulation is the term for the mechanism of bringing the desired information into frequencies of the desired channel. It includes a frequency translation, in the example of a radio the audio signal spans frequencies up to 20 kHz,  but the carrier frequency is around 100 MHz (in FM radio). The eletrical device which forms the carrier signal out of the underlying signal is called a Modulator.

### What does Modulation actually do?

Let’s explain with a simple example: music. While the term modulation means something different in the context of music, we can use music to explain polar modulation. The art of music lies in the artful combination of notes with different volume. A piano player can play louder high notes and lower bass notes; but he can also play louder bass notes and lower high notes, both volume and key are completely inedependent. As you probably know from the physics course, each note has a different base frequency.  The piano player is therefore altering both the amplitude and the frequency of the generated sound completely independently.

In wireless communication, equally to the example of a piano, the concept of altering the frequency (phase) and the amplitude of a signal indenpendently also exists. If the signal is thought of as a vector, it can be represented with  both phase and magnitude, meaning in polar coordinates. Therefore we are talking about polar modulation. Let’s have a closer look at the modulation itself. The transmission signal T(t) can be described by a cosine-wave:

T(t) = A(t) cos(ωt+φ(t)),

where A(t) is the modulated amplitude, φ(t) is the modulated phase, and w is the carrier frequency. But wait, we were talking here about frequency, not phase, so how are they related?  The phase of a sinewave is changing over one period from 0 to 2*pi, the shorter the period thefaster it changes; and the higher the frequency.  As we are talking on change versus time, the frequency is therefore derivative of the phase with respect to time, ω = dφ(t)/dt.

If we now find a device which can generate a signal with tunable frequency and tunable amplitude, we can build a Polar Modulator. Such a Transmitter has been built a Raspberry Pi, I will talk about that in my next posts. If the Pi is up and running, I will show measurements, and describe both the general and uniqe properties of the polar modulator based on a Raspberry Pi.