I/Q Data in Communication Systems

 RF communication systems use advanced forms of modulation to increase the amount of data that can be transmitted in a given amount of frequency spectrum. Signal modulation can be divided into two broad categories: analog modulation and digital modulation. Analog or digital refers to how the data is modulated onto a sine wave. If analog audio data is modulated onto a carrier sine wave, then this is referred to as analog modulation. If analog audio data is sampled by an analog to digital converter (ADC) with the resulting digital bits modulated onto a carrier sine wave, this is digital modulation because digital data is being encoded. Both analog modulation and digital modulation are performed by changing the carrier wave amplitude, frequency, or phase (or combination of amplitude and phase simultaneously) according to the message data.

Amplitude modulation(AM), frequency modulation (FM), or phase modulation (PM) are all examples of analog modulation.  With amplitude modulation, the carrier sine wave amplitude is modulated according to the message signal. The same idea holds true for frequency and phase modulation.

  Figure 5. Time Domain of AM, FM, and PM Signals

Figure 5 represents various analog techniques—AM, FM, and PM—applied to a carrier signal. In the AM case, the message signal is the blue sine wave that forms the “envelope” of the higher frequency carrier sine wave. In the FM case, the message data is the dashed square wave.  As the figure illustrates, the resulting carrier signal changes between two distinct frequency states.  Each of these frequency states represents the high and low state of the message signal. If the message signal were a sine wave in this case, there would be a more gradual change in frequency, which would be more difficult to see. In the PM case, notice the distinct phase change at the edges of the dashed square wave message signal.

As such if  only the carrier sine wave amplitude changes with respect to time (proportional to the message signal), as is the case with AM modulation, we should see changes in the I/Q plane only with respect to the distance from the origin to the I/Q points.

 So Why Use I/Q Data?

Because amplitude and phase data seem more intuitive, it would seem that we should use polar amplitude and phase data instead of cartesian I and Q data. However, practical hardware design concerns make I and Q data the better choice in this matter.

It is difficult to vary precisely the phase of a high-frequency carrier sine wave in a hardware circuit according to an input message signal. A hardware signal modulator that manipulates the amplitude and phase of a carrier sine wave would therefore be expensive and difficult to design and build, and, as it turns out, not as flexible as a circuit that uses I and Q waveforms. To understand how we to avoid manipulating the phase of an RF carrier directly, we first return to trigonometry.

Figure 6. Mathematical Background of I/Q Modulation

According to the trigonometric identity shown in the first line of Figure 6, multiply both sides of the equation by A and substitute 2∏f_ct in place of α and φ in place of β to arrive at the equation shown in line 2.  Then substitute I for A cos(φ) and Q for A sin(φ) to represent a sine wave with the equation shown on line 3. Remember that the difference between a sine wave and a cosine wave of the same frequency is a 90-degree phase offset between them. The implications of this are very important. What this essentially means is that we can control the amplitude, frequency, and phase of a modulating RF carrier sine wave by simply manipulating the amplitudes of separate I and Q input signals. With this method, we no longer have to directly vary the phase of an RF carrier sine wave. We can achieve the same effect by manipulating the amplitudes of input I and Q signals. Of course, the second half of the equation is a sine wave and the first half is a cosine wave, so we must include a device in the hardware circuit to induce a 90-degree phase shift between the carrier signals used for the I and Q mixers.

Figure 7. Hardware Diagram of an I/Q Modulator

Figure 7. shows a block diagram of an I/Q modulator. The circles with an ‘X’ represent mixers—devices that perform frequency multiplication and either upconvert or downconvert signals (upconverting here). The I/Q modulator mixes the I waveform with the RF carrier sine wave, and mixes the Q signal with the same RF carrier sine wave yet with a 90-degree phase offset. The Q signal is subtracted from the I signal (just as in the equation shown in line 3 in Figure 6) producing the final RF modulated waveform. In fact, the 90-degree shift of the carrier is the source of the names for the I and Q data—I refers to in-phase data (because the carrier is in phase) and Q refers to quadrature data (because the carrier is offset by 90 degrees).

This technique is known as quadrature upconversion and the same I/Q modulator can be used for any modulation scheme. This is because the I/Q modulator is merely reacting to changes in I and Q waveform amplitudes, and I and Q data can be used to represent any changes in magnitude and phase of a message signal. The flexibility and simplicity (relative to other options) of the design of an I/Q modulator is the reason for its widespread use and popularity.