The previous series on radio that I put together, back in the winter and
spring of ‘19, included
a very wide-ranging post on modulation
. It’s a worthwhile refresher to go back to read to get a feel for the
whole process of modulation, if some of this seems like it comes out of the
blue. Nevertheless, there were some important concepts that I dropped in
the effort to keep the post length a bit more reasonable.
The most important part of the posting is the idea of a “universal
modulator.” A universal modulator is nothing more than a multiplier
circuit that takes an RF input to be modulated splits the signal in two paths
which then go to two mixers. One side of the split is shifted in phase
by 90 degrees. The modulating signals, shown here as i and q (both as
time-varying functions), are applied to the low frequency ports of those
Let’s start with this concept. Any characteristic of the radio signal
can be modulated. Amplitude can be modulated (AM or SSB); the simplest
Amplitude Modulation is presence or absence of the transmit signal, On-Off
Keying. Frequency can be modulated (FM, FSK). Phase can be
modulated (analog PM, BPSK, QPSK, 8PSK, 16PSK). There are even types of
modulation that combine more than one kind; the most common of those being
Quadrature AM, like 64 or 128QAM (pronounced “kw-ahm”). Quadrature AM
modulates both the amplitude and phase of the signal to transfer data.
The only difference between generating AM, or SSB or 64 QAM is the way the
i(t) and q(t) signals are created and processed. If they’re kept
identical in phase and a DC offset added, full-carrier AM is generated.
If they’re left in quadrature, single sideband is produced. If Q is left
constant and I varies 180 degrees for modulation, BPSK is generated.
Everything is produced by the way those i and q signals are created.
Because of the concept of modulation by applying I and Q signals, Q can be
plotted versus I, producing what’s referred to as constellation. BPSK,
or Bi-Phase Shift Keying is simply shifting the phase of the carrier from no
shift to 180 degree shift for each symbol. The signal shifts from +1 to
-1 constantly to transfer the information. QPSK is Quadri-Phase Shift
Keying, shown here as varying I and Q at the same time, giving constellation
values at (1,1), (-1,1), (-1,-1) and (1,-1), or simply changing one axis at a
time (1,0), (0,1), (-1,0), (0,-1). 8PSK and 16PSK are what the names
imply: 8 and 16 values of amplitude and phase.
This isn’t the only interpretation. 16QAM is modulating both amplitude
and phase. There is 16 phase shift keying (16PSK), where the amplitude
remains constant and the constellation points are all on a circle of constant
amplitude but with (360 / 16 or) 22.5 degrees between the symbols.
This is 64QAM as it would be seen on a piece of test equipment. Each of
those dots represents a transmission and their random looking appearance
(spread out and not just a dot) is from the introduction of noise in the
channel. If it were pure phase noise
each of those would be short arc
centered on the origin (0,0) in the graph with the points farthest into the
corners being the longest arcs. These look to be amplitude noise and not
There are subtle changes to the constellations that affect not just the number
of constellation points but also the trajectories that the signal takes to get
between them. Below is a math simulation of a differential 8-phase shift
keying (D8PSK), which has become widely adopted in the aviation world.
In one application, data at 31.5 KBPS is used in a 16 kHz wide AM channel
previously used for voice, which has a 6 kHz bandwidth.
As I’ve been saying in almost every post, physics doesn’t allow something for
nothing. Perhaps in your wanderings around the ‘net you’ve come across
the concept that information is proportional to bandwidth. Simply, the
more information you’re sending in the same amount of time, the more bandwidth
the signal takes. I bet you know this even if you’ve never seen it
stated online. Voice channels take up more bandwidth than on-off keying;
video takes up more bandwidth than voice. Lower data rates take less
bandwidth than higher data rates.
The trade between the modulation types is that they convey more information in
the same bandwidth, but require higher amplitudes for the same bit error
rate. That means more signal power at the receiver, so transmit powers
may have to be higher and marginal signal strength might not work. The
complexity (read that as cost) of the transmitter and receiver go up.
For that cost, the D8PSK signal provides more digital data in the transmit
bandwidth than plain AM voice.
These curves are generically referred to as “waterfall curves.” It’s not
quite as vivid in this graph but for some of these modes, as the signal to
noise ratio (horizontal axis) goes up, the bit error rate (BER) falls off like
going over a waterfall. The signal to noise ratio is expressed as
“energy per bit to noise power spectral density ratio
” It’s calculated from the signal to noise ratio (SNR).
This is read by choosing an error rate you’re comfortable with; I’ll choose
10-4 because all three curves are on the chart. That means 1 bit in
10,000 is wrong. For BPSK, you’ll see where the blue curve intersects
that line, go down to the X axis and see it’s a little over 8 dB; I’ll call it
8.5. For the 16-PSK curve, you see it’s just over 16 dB. You get a
higher data rate but it costs you 7.5 dB more in the hardware
complexity. Adding 7-1/2 dB transmit power is expensive in the ham world, depending on the frequency and other requirements. On the other hand, if the receiver is reasonably well-designed, it's physically impossible to make one 7-1/2 dB more sensitive.