What is the I&Q modulation principle? Perhaps it’s easier to start with what it’s not.
I&Q is not another type of modulation scheme, but rather a smarter way to implement radio frequency (RF) modulations and demodulations on digital signals. Though it is best known for its use with quadrature amplitude modulation (QAM), which we covered in the previous post, I&Q modulation can be used to augment any of the digital RF modulation schemes we’ve covered so far—that is, amplitude, frequency, and phase shift keying, or ASK, FSK, and PSK, respectively.
To demystify that famous “I&Q” terminology, we will build on the foundation of our college-level learnings about sine function, rotating vectors, and cartesian and polar representations, ending up with a constellation diagram of complex I and Q modulators and demodulators. But first: A quick recap of all we’ve learned so far.
We have seen how complex modulation schemes with multiple levels (M_ary) and scheme combinations (ASK+PSK+FSK) give rich symbols that can transport several bits at once. For example, a 1024 -QAM signal combining both amplitude and phase modulations give a data flow of 10 bits coded per symbol.
Figure 1 – 1024 QAM data structure
As previously highlighted, it can be challenging to implement modulators and demodulators capable of differentiating close-together symbols. A 1024-QAM with 128 or 256 possible phases will end up with an angle spacing of only 2.8 or 1.4 degrees, which is nearly impossible for any phase generator to achieve.
Thus, we turn to I&Q modulation.
A sinewave can be associated with a rotating vector in a 2-dimensional plane as seen in Figure 2. RF engineers typically refer to the horizontal X axis as the “in-phase” or “I” axis. The vertical axis Y is called the “quadrature” or “Q” axis because it’s opposed to the in-phase axis by 90°.
Figure 2 – Association of the sinewave and rotating vector in an I&Q plane
There are three elements to the rotating vector. Length A corresponds to the signal amplitude (green), the phase of the signal is represented as an angle ϕ versus the x-axis (blue), and a rotation speed ω (red) is applied around the plane origin (0:0).
By ignoring the vector rotation and plotting only the vector terminations on the plane, we create a constellation diagram. These diagrams give immediate visibility into ASK and PSK modulations. However, FSK signals are more difficult to show in a static form because they require rotation speed data.
Figure 3 – Examples of constellation diagrams
As emphasized in the first section, the more complex the symbols, the greater the risk of overlaps.
For example, on an 8-PSK signal, the carrier can take 1 of 8 possible phases, each 45° apart. But on a 512-PSK, the transmitter and receiver must have enough precision to discriminate between angles smaller than 1° each—quasi-impossible to achieve! That is why we need I&Q modulation.
Figure 4 – Examples of complex I&Q constellations: 16-QAM on the left and 256-QAM on the right. CC via Wikimedia Commons
Instead of one vector bearing the amplitude and the angle information, in I&Q modulation we have two amplitudes: one in the I axis and one in the Q axis. Both amplitudes together define the full modulation, as we’ll see below. The real revolution of I&Q is that any modulation can be produced without ever generating an angle.
Consider a modulated signal in two parts: its projection to the real axis, or “I,” and to the imaginary axis “Q.” Knowing this, we can modulate the signal using just two amplitude variations.
If we “freeze” the moving vector in the plane, then we can define it using either its polar representations (length and angle) or cartesian coordinates (x and y). The cartesian or rectangular view is simply the projection of the vector on the horizontal axis I and on the vertical axis Q.
Figure 5 – Polar and Cartesian Representations of a vector
The two representations are equivalent, and it is easy to convert from one form to the other. However, the cartesian form is much preferred because it is easier to produce a precise angle in this representation, and because it uses like elements: amplitude for both Ax and Ay.
From Polar to Cartesian (or I&Q): Ax = A.Cos(ɸ) and Ay = A.Sin(ɸ)
From Cartesian (or I&Q) to Polar: A = (Ax² + Ay²)1/2 and ɸ = Artg(Ay/Ax)
We know any modulated signal y(t) = A.cos (2πfct + ɸ) can be developed following the trigonometric formula:
cos(α + β) = cos(α).cos(β) - sin(α).sin(β)
We can rewrite y(t) as:
y(t)= A.cos (2πfct + ɸ) = A.cos (2πfct).cos(ɸ) - A.sin (2πfct).Sin(ɸ)
Figure 6 – I and Q signals
By putting A.cos(ɸ) as I and A.sin(ɸ) as Q, as in Figure 6, we have:
y(t) = I. cos (2πfct) – Q. sin(2πfct)
since sine is phased out by -90° versus cosinus:
y(t) = I. cos (2πfct) + j.Q. cos(2πfct) (Refresh j is the +90° operator)
Thus, we translate the I&Q equation into the following hardware, which uses two identical channels I and Q to modulate the signal.
Figure 7 – I & Q modulation implementation
At the receiver side, the demodulation is also handled via the I and Q channels.
Figure 8 - I&Q Demodulator Implementation
We have completed this long journey reviewing the modulation schemes used to imprint data on a carrier by changing its amplitude, frequency, and/or phase either separately or together. In this last chapter, we introduced the I&Q concept as a smarter way to implement modulation and demodulation by considering any modulated signal with its cartesian parameters I & Q instead of amplitude and angle. We hope you enjoyed those 7 modules of the series.
There are still many things that can be said about modulation techniques. For example, we could spend several posts just exploring techniques for rectangular signal modulation, such as pulse width modulation (PWM) and pulse amplitude modulation (PAM)... but that's a topic for another series!
