ANEKA INFO TEKNIK: DIGITAL MODULATION ; DIFFERENT WAYS OF LOOKING AT A DIGITAL MODULATED SIGNAL TIME AND FREQUENCT DOMAIN VIEW

5. Different ways of looking at a digitally modulated signal time and frequency domain view

There are a number of different ways to view a signal. This simplified example is an RF pager signal at a center frequency of 930.004 MHz. This pager uses two-level FSK and the carrier shifts back and forth between two frequencies that are 8 kHz apart (930.000 MHz and 930.008 MHz). This frequency spacing is small in proportion to the center frequency of 930.004 MHz. This is shown in figure 24 (a). The difference in period between a signal at 930 MHz and one at 930 MHz plus 8 kHz is very small.
Even with a high performance oscilloscope, using the latest in high-speed digital techniques, the change in period cannot be observed or measured.

Figure 24. Time and Frequency Domain View

In a pager receiver the signals are first downconverted to an IF or baseband frequency. In this example, the 930.004 MHz FSK-modulated signal is mixed with another signal at 930.002 MHz. The FSK modulation causes the transmitted signal to switch between 930.000 MHz and 930.008 MHz.
The result is a baseband signal that alternates between two frequencies, –2 kHZ and +6 kHz. The demodulated signal shifts between –2 kHz and +6 kHz. The difference can be easily detected.
This is sometimes referred to as “zoom” time or IF time. To be more specific, it is a band-converted signal at IF or baseband. IF time is important as it is how the signal looks in the IF portion of a receiver. This is how the IF of the radio detects the different bits that are present. The frequency domain representation is shown in figure 24 (c). Most pagers use a two-level, Frequency-Shift-Keying (FSK) scheme. FSK is used in this instance because it is less affected by multipath propagation, attenuation and interference, common in urban environments. It is possible to demodulate it even deep inside modern steel/concrete buildings, where attenuation, noise and interference would otherwise make reliable demodulation difficult.

5.1 Power and frequency view
There are many different ways of looking at a digitally-modulated signal.
To examine how transmitters turn on and off, a power-versus-time measurement is very useful for examining the power level changes involved in pulsed or bursted carriers. For example, very fast power changes will
result in frequency spreading or spectral regrowth. This is also known as frequency “splatter”. Very slow power changes waste valuable transmit time, as the transmitter cannot send data when it is not fully on. Turning on too slowly can also cause high bit error rates at the beginning of the burst. In addition, peak and average power levels must be well understood, since asking for excessive power from an amplifier can lead to compression or clipping. These phenomena distort the modulated signal and usually lead to spectral regrowth as well.

Figure 25. Power and Frequency View

5.2 Constellation diagrams
As discussed, the rectangular I/Q diagram is a polar diagram of magnitude and phase. A two-dimensional diagram of the carrier magnitude and phase (a standard polar plot) can be represented differently by superimposing rectangular axes on the same data and interpreting the carrier in terms of in-phase (I) and quadrature-phase (Q) components. It would be possible to perform AM and PM on a carrier at the same time and send data this way; it is easier for circuit design and signal processing to generate and detect a rectangular, linear set of values (one set for I and an independent set for Q).

Figure 26. Constellation Diagram

The example shown is a π/4 Differential Quadrature Phase Shift Keying (π/4 DQPSK) signal as described in the North American Digital Cellular (NADC) TDMA standard. This example is a 157-symbol DQPSK burst.

The polar diagram shows several symbols at a time. That is, it shows the instantaneous value of the carrier at any point on the continuous line between and including symbol times, represented as I/Q or magnitude/phase values.

The constellation diagram shows a repetitive “snapshot” of that same burst, with values shown only at the decision points. The constellation diagram displays phase errors, as well as amplitude errors, at the decision

points. The transitions between the decision points affects transmitted bandwidth. This display shows the path the carrier is taking but does not explicitly show errors at the decision points. Constellation diagrams

provide insight into varying power levels,the effects of filtering, and phenomena such as Inter-Symbol Interference.

The relationship between constellation points and bits per symbol is

M=2ⁿwhere M = number of constellation points

n = bits/symbol

or n= log₂(M)

This holds when transitions are allowed from any constellation point to any other.
5.3 Eye diagrams
Another way to view a digitally modulated signal is with an eye diagram. Separate eye diagrams can be generated, one for the I-channel data and another for the Q-channel data. Eye diagrams display I and Q magnitude
versus time in an infinite persistence mode, with retraces. The I and Q transitions are shown separately and an “eye” (or eyes) is formed at the symbol decision times. QPSK has four distinct I/Q states, one in each
quadrant. There are only two levels for I and two levels for Q. This forms a single eye for each I and Q. Other schemes use more levels and create more nodes in time through which the traces pass. The lower example is a 16QAM signal which has four levels forming three distinct “eyes”. The eye is open at each symbol. A “good” signal has wide open eyes with compact crossover points.

Figure 27. I and Q Eye Diagrams

5.4 Trellis diagrams
This figure is called a “trellis” diagram, because it resembles a garden trellis. The trellis diagram shows time on the X-axis and phase on the Y-axis. This allows the examination of the phase transitions with different
symbols. In this case it is for a GSM system. If a long series of binary ones were sent, the result would be a series of positive phase transitions of, in the example of GSM, 90 degrees per symbol. If a long series of binary zeros were sent, there would be a constant declining phase of 90 degrees per symbol. Typically there would be intermediate transmissions with random data. When troubleshooting, trellis diagrams are useful in isolating missing transitions, missing codes, or a blind spot in the I/Q modulator or mapping algorithm.