In a previous article, Linear & Rotational Encoding Methods, I discussed encoder quadrature signals. While interesting and useful, quadrature here – two square wave signals arranged at 90º to each other – simply indicates the position of a disk or linear slider by the quadrature pattern it produces. But what if you were to turn this concept on its head and produce two repeating signals at 90º out of phase with each other for signal generation?
What is QPSK Modulation?
This sort of arrangement is incredibly powerful in RF and data transmission applications. It allows for phase modulation (PM) of a signal, where a carrier wave’s phase is dynamically shifted to convey information. In Quadrature phase-shift keying (QPSK), two input carrier waves I (in-phase wave) and Q (quadrature wave) are switched between +1 and -1 as binary signals. This input sums to four distinct phase shift possibilities when combined.
In-Phase quadrature: QPSK waveform explanation
Consider the two waves at 90º to each other as shown in the sketch below:
The in-phase component I is a cosine wave that's in-phase with the unshifted carrier wave, while the quadrature component Q is a sine wave that's shifted at 90º with respect to the I wave. This could also be defined as an unshifted sine wave, which is naturally in quadrature with the cosine wave I. The solid lines represent each input wave multiplied by +1 for binary 1, while the dashed lines represent each wave multiplied by -1 for binary 0).
The sketch below shows the I and Q components each multiplied by one, while the red line represents the summation of both signals when added together. If the amplitudes of each are kept the same, this summed output carrier wave is shifted to the middle of both input waves at 45º.
Consider the first sketch again, and that with the simple input of +1 or -1 for each wave, you could produce a summed carrier wave that's at either 45º, 135º, 225º, or 315º – the midpoint between each active signal. The sketch below, for example, shows what happens when the I component is 1, and the Q component is 0, and that is multiplied by -1 to mirror this input. The new carrier output is thus shifted by 315º, midway in between 270º and 360º/0º as the cycle starts all over again.
QPSK constellation diagram & QPSK baud rate
Four distinct signal possibilities means that two bits can be transmitted in the same amount of time as one bit when transmitting a binary signal. In other words, two bits per signaling event gives a data rate of twice the baud rate, the difference between which is sometimes confused.
Plotting phase shift and amplitude at a discreet moment in time, you can generate a QPSK constellation diagram as shown below. Each of the four red dots represent a particular signal state, or phase shift. The four smaller circles represent the fact that if a signal varies to some extent via noise, the correct meaning can still be demodulated on the receiving end.
In this representation, it’s easier to point out that the shifted output is simply the addition of the cosine function of I plus the sine function of Q, multiplied by +1 or -1. If there was no Q component whatsoever, and I varied between +1 and -1, then the signal would switch from in-phase to 180º out of phase. This simpler QPSK modulation scenario can be used for binary phase-shift keying, or BPSK.
RF signal repeaters: beyond phase shift and 2 bits per signal?
We've covered quadrature in the context of binary signals that produce +1 and -1, but I and Q amplitudes can be anywhere in between. This means that not only can one transmit two bits per signal, but it could actually transmit much more data by varying the phase shifts in more than four states, as well as the total amplitude. QAM, or quadrature amplitude modulation, is one term for this sort of data encoding, of which there are many variations. The caveat here is that as more bits per signal are transmitted, the error tolerance is normally reduced, and the signal-to-noise ratio must be sufficiently good enough for the method chosen.
While this article gives a brief conceptual introduction to quadrature signal encoding, it’s a massive subject that would require significant study to truly grasp. However, with its wide range of applications, you could argue that it's more than worthy of exploration. Like the countless transistors powering your computer, phone, and perhaps even your toaster, it’s one of the unseen technologies that powers our connected world today!
