IQ Modulation

EARLY MODULATION FORMATS

There are three basic ways to modulate a waveform: Amplitude Modulation (AM), Frequency Modulation (FM) and Phase Modulation (PM). AM came first–it was easy to implement and easy to understand. In 1933, Edwin H. Armstrong developed Frequency Modulation, or FM, which proved to be less susceptible to noise than AM. You can experience this yourself–listen to an AM station during a thunderstorm when bursts of static electricity are causing interference in the station, and then switch to an FM station. You’ll find the noise level subsides dramatically.

(a)	(b)	(c)

Fig.1. Amplitude modulation (a), frequency modulation (b), and phase modulation (c).

Modern communications systems demand more information capacity, higher signal quality, greater security and digital data compatibility. AM and FM, while valuable modulation methods, have proven inadequate to match today’s needs for high-volume traffic. With millions of cell phone subscribers gobbling up more voice bandwidth, we need a modulation method that can efficiently transfer information in a reliable manner.

New modulation methods have been developed in the past few years–schemes that are simply combinations of the original three modulation methods. Combined with other digital techniques, these newly-affordable methods give us more efficiency, and have the added benefit of handling digital data as well as voice.

Why digital? Once the baseband voice signal has been digitized, we can do whatever we want with it. We can send it at any time, send it in bursts between other messages, or operate on it with a digital algorithm that requires fewer bits to be transmitted. Fewer bits mean more users can be accommodated.

IQ MODULATION

One modulation technique that lends itself well to digital processes is called "IQ Modulation", where "I" is the "in-phase" component of the waveform, and "Q" represents the quadrature component. In its various forms, IQ modulation is an efficient way to transfer information, and it also works well with digital formats. An IQ modulator can actually create AM, FM and PM. It works something like this:

When you modulate a carrier with a waveform that changes the carrier’s frequency slightly, you can treat the modulating signal as a phasor. It has both a real and an imaginary part, or an in-phase (I) and a quadrature (Q) part. Now construct a receiver that locks to the carrier, and you can decipher information by reading the I and Q parts of the modulating signal. The information appears on a polar plot as in Fig.2 below.

The I/Q plane shows two things:

1. What the modulated carrier is doing relative to the unmodulated carrier and…
2. What baseband I and Q inputs are required to produce the modulated carrier.

(a)	(b)

Fig. 2. Unmodulated (a) and modulated (b) carrier. The positive I axis is arbitrarily chosen to represent 0 degrees relative to the unmodulated carrier. In part (a), since the plot of the modulated carrier is relative to the unmodulated carrier, an unmodulated carrier appears as a fixed vector along the positive I axis. In part (b), a modulated carrier at the same frequency as the unmodulated carrier but offset by 45 degrees appears as a fixed vector at 45 degrees.

To produce the carrier in Fig. 2b, equal dc values would be required at the I and Q modulator inputs. Assuming unity gain in the modulator, to produce a carrier of unity amplitude at 45 degrees, the I and Q inputs must both be dc values of Q_dc = I_dc = +0.707.

The baseband inputs (those producing the information), must obviously vary over time, creating a difference between the modulated and unmodulated carriers. The modulator block diagram is shown below. The signal first goes through an A/D converter, is compressed, checked for errors and encoded, then sent through a filter to the IF and RF mixers:

Fig 3. IQ Modulator and transmitter chain. Baseband signal appears at left. Block "A" to the right of the A/D does compression and error-correction.

SIMULATIONS

This Java applet looks at an I/Q modulator by plotting vectors (phasors), waveforms, and symbols on the I/Q plane. (See explanations below the simulation.)

Simulation Explanations:

Simulation 1: Cosine on I axis
The first simulation, a cosine wave on the I axis, shows the modulated carrier's amplitude being varied sinusoidally. Perhaps not obvious is the fact that the phase changes 180 degrees each time the baseband-modulating signal crosses zero. Euler's identity is utilized to show that the modulating signal comprises both a positive and negative frequency component; otherwise the modulated carrier would not stay on the I axis.

The spectrum of the modulated carrier, shown in the upper left corner of the simulation screen, is that of double-sideband, suppressed-carrier amplitude modulation.

Simulation 2: Sine on Q axis.
The second simulation, a sine wave on the Q axis, shows a similar situation along the Q axis.

Simulation 3, 4: Modulate Both I and Q
If the I (cosine) and Q (sine) functions modulate the carrier simultaneously, the modulated carrier vector will rotate counterclockwise if I leads Q and clockwise if Q leads I. The counterclockwise rotation means that the modulated signal is at a higher frequency than the unmodulated carrier. Clockwise rotation means the opposite. The frequency offset is shown in the spectrum display.

The final three simulations illustrate quadrature phase-shift keying (QPSK), Pi/4 QPSK, and quadrature amplitude modulation (QAM).

Simulation 5: QPSK
In the case of QPSK, the I and Q inputs are momentary dc values. Note that occasionally the phase shift is 180 degrees. In this case, the modulated carrier is turned off briefly as the I and Q values go through V=0, i.e. go through the origin of the I/Q plane. To accommodate this situation, the transmitter output power amplifier must be linear over a wide dynamic range to prevent spectral splatter and therefore interference with adjacent frequency channels.

Simulation 6: Pi/4 QPSK
To avoid the problem of splatter, the NADC-TDMA system uses Pi/4 QPSK. That is, a second set of four possible phase states is utilized. One set is on the I/Q axes; the second is offset by 45 degrees. If the current symbol is on the I or Q axis, the next symbol must be off the axes, and vice versa. Another method to avoid the origin is offset QPSK (OQPSK). Here the change of Q (or I) is delayed by half a symbol period relative to I (or Q). (A symbol is a location on the I/Q plane; symbol period is the minimum length of time spent at a symbol.) OQPSK is not shown.

Simulation 7: QAM
QAM takes advantage of the fact that the greater the number of symbols, the greater the efficiency of the system. Occupied bandwidth is determined, mostly, by the symbol rate. So the more bits (the fundamental information units) per symbol, the higher the efficiency. The number of symbols required for a given system is 2ⁿ, where n is the number of bits per symbol. For 16 QAM, n = 4 and there are 16 symbols–each symbol represents four bits: 0000, 0001, 0010, etc.