(a) Quantitatively describe the relationship between a symbol and a bit and the Bit Rate and the Baud Rate.
(b) Describe how digital information is conveyed using various digital modulation techniques (ASK or OOK,
FSK, PSK and QAM) and recognize their waveforms, bandwidth, and constellations.
(c) Using a phase diagram analyze a M-ary PSK signal to determine its symbols and bits per symbols.
(d) Discuss the effect of noise on M-ary PSK and how Quadrature Amplitude Modulation (QAM) overcomes these detrimental effects.
Try to remember all the way back to lesson on Analog to Digital Conversion. We mentioned that we had analog signals that we wanted to represent by digital signals. (i.e. Recording your Comm-O singing Mikey J’s Thriller on karaoke night.) Now your Comm-O prides himself in being a good singer, and decides he wants to broadcast his digital recording from karaoke night to the rest of the carrier group to raise morale (and maybe, just maybe, get selected to go to American Idol).
All he needs to do is transmit the digital signal. Right?
Free Space
0 1 1 1 0 0 1 1 0 1 1 1 1 1 1 1 1 0 0 1 1 0 0 1
WRONG! Haha. Of course it can’t be that easy. The digital binary (0 and 1) signals to which we are so accustomed are, typically, alternations between 0Vs and 5Vs (aka. DC voltage). It just so happens, and you can just trust me on this one, antennas don’t transmit DC voltage. voltage
1 0 1 1 0 1
5 V
0 V time
Binary digital signal represent 1 or 0 using switched pulses.
We must come up with a method to transmit the digital information using radio waves (continuous sine waves).
1

Does this equation look familiar?
1
0.5
0
 c
  
-0.5
A sinusoidal carrier can be modulated by varying its amplitude, frequency, or phase.
0 0.5
1 1.5
2 2.5
3 3.5
4
T ime (msec)
2 x 10
-3
 
1.5
1
0.5
0
-0.5
-1
-1.5
-2
0 0.009
0.01
1
0.5
0
-0.5
-1
0 0.5
1 1.5
2
T ime (msec)
2.5
3 3.5
0.001
Amplitude
0.007
0.008
Frequency x 10
-3
4
Phase
Now think about this question. What is it we are trying to transmit? Spectacular answer! Just 1s and 0s.
So, how do we go about representing 1s and 0s using amplitude modulation? That, my Midshipman, is the question that is about to be answered. Just as we can vary amplitude, frequency, and phase of a high-frequency carrier in accordance with an analog waveform, we can do the same to represent bits… and since bits shift values between 0 and 1, digitial modulation techniques to varying amplitude, frequency, and phase are referred to as
“ shift keying
.”
Amplitude Shift Keying (ASK)
The simplest digital modulation scheme is a form of ASK called on-off keying (OOK). This is analogous to
Morse code. A radio wave is transmitted when the binary signal is 1 and nothing is transmitted when the binary signal is 0.
Example
Draw a modulated OOK signal below the bit stream.
1 0 0 0 1 1
2

Before we continue, you need to learn some terms that are used frequently in communication systems. We already know from our mad binary skills that N bits can be used to represent 2
N values… and when we’re talking shift keying, the 2 N values are referred to as Symbols.
Each change in the amplitude is termed a Symbol .
S = 2 N , where and N is the number of bits transmitted per symbol.
S is the number of symbols
NOTE: Read this equation again and make sure you understand it. It is a major point that many people miss. In this example of OOK, there are only 2 symbols with 1 bit per symbol, either 1 or 0. We will show shortly that there are often times where there are many symbols and therefore many bits per symbol.
Don’t freak out – you really already know this. If you have 1 bit, you can either represent a 0 or a 1 – that’s it.
Since you can only represent 2 binary numbers, you have 2 symbols. If you have 2 bits, you have more options – you can represent 4 numbers (00, 01, 10, 11), and therefore, 4 symbols.
Since the Comm-O is ultimately interested in getting all those 0s and 1s out fast (and through the limited bandwidth available at sea) so that his karaoke night performance is available for everyone, the rate at which 0s and 1s are transmitted is important.
Bit Rate (R b
) is the speed of transfer of data, or the number of bits per second. Bit Rate is inversely proportional to Bit time (t b
) , or the time required to transmit a single bit.
R b

1 t b
Baud Rate (aka Symbol Rate) (R
S
) is the number of symbols transmitted per second, and is inversely proportional to the Symbol Period (T
S
) , or the time required to transmit 1 symbol.
R
S

1
T
S
R b
= R
S
* N (where N = log
2
S)
The bandwidth associated with OOK is:
The Bit Rate and the Baud (or Symbol ) Rate are related by the number of bits per symbol ( N ).
3

One digital modulation scheme down. What next?
Frequency Shift Keying (FSK)
The oldest form of modulation used in modems (Ah, good old dial-up), frequency-shift keying (FSK) is the name of the method used to represent a binary signal using frequency modulation.
With FSK, the binary bits are represented by different frequencies. The binary 0 has a lower frequency of 1070
Hz and the binary 1 has a higher frequency of 1270 Hz.
The lower frequency, binary 0, is called the space. The higher frequency, binary 1, is called the mark.
Similar to OOK, now we’re varying frequency.
Still representing a single bit, so only two Symbols .
S = 2.
To determine the bandwidth associated with FSK, it is important to utilize the frequency domain.
Now let’s take a closer look at the output of the modulator to get the Bandwidth.
+ R
R b
4

Example
You have an FSK transmitter using a carrier of 500 kHz sending 10 kbps and deviating 100 kHz, how much bandwidth do you need?
Of course, who still uses dial-up? What else is there?
Phase Shift Keying (PSK)
Another modulating option is phase modulation know as
Phase-shift keying (PSK)
For binary phase shift keying (BPSK), the carrier phase is shifted by 0

or 180

.
“1” the carrier phase is unchanged.
“0” the carrier phase is shifted by 180 
.
One difficulty in demodulating a BPSK signal is that the carrier must be recovered to determine the correct phase relationship.
To simplify demodulation, a version of BPSK known as Differential phase-shift keying (DPSK) can be used.
For DPSK, there is no absolute phase reference. At the receiver, the phase of one bit is compared to the phase of the previous bit: at the transmitter: at the receiver: logic 0

send the same phase if receive the same phase

logic 0 logic 1

change the phase if the phase changes

logic 1
(or vice-versa)
In other words, the receiver has to know if the first bit of the transmission is a 0 or 1. After that, if there is no change in the phase of the signal received, each bit received will be the same as the previous bit received. Once an
180 o
phase shift occurs, the receiver knows the bit has changed, either 0 to 1 or 1 to 0. This continues throughout the receipt of the signal being transmitted.
DPSK when compared to BPSK: is used in practice simplifies demodulation has bit errors that tend to come in pairs
Up to this point we have been looking at the possibility of one bit per symbol which means two symbols. As mentioned earlier, it is possible to have more than one bit per symbol. In order to represent this in an easier to understand pictorial, you are about to be introduced to another representation of the material you have learned.
Ready for the surprise?
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We can represent the BPSK signal using a phasor diagram which shows the two possible BPSK symbols .
The picture on the right is called a signal constellation diagram .
BPSK and DPSK are limited to transmitting just one bit per symbol .
We have finally gotten through three modulation techniques. Here is the crux. In today’s time, no one wants to wait on information. We want it now! How many times have you wanted to throw your phone across the room because of the annoyingly long time it is taking to download a Youtube video of Flavor Flav? I mean, really.
Think back to the beginning of this lesson. The Comm-O’s going to lose his job if the carrier group commander doesn’t get his morale improved soon!
There are a couple of ways to get this information across more quickly. On way is to send more bits per second. If we choose to use this path, you need to realize this means an increase in bandwidth. What did we say was a major limiting factor for communication systems? That’s right. Bandwidth. Sure, you can spend millions of dollars to get a little more bandwidth, but eventually the FCC will say, “No more.” So, what to do?
As Theo Huxtable used to say, “No Problem!”
We can preserve bandwidth if we keep the symbol rate the same and increase the number of bits per symbol .
Instead of transmitting just 2 possible phase shifts (0˚and 180˚), we could transmit 4 possible phase shifts per symbol (45˚, 135˚, 225˚, and 315˚).
This is called quadrature or quaternary PSK (4-PSK or QPSK).
Sweet. Now S can be greater than two.
QPSK
In QSPK, because there are 4 possible symbols and we are transmitting 2 bits per symbol .
[bits per symbol = log
2
(# of possible symbols)]
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Consider the bit stream below and the resulting QPSK signal. unmodulated carrier
QPSK signal
00
(45˚)
01
(135˚)
11
(225˚)
10
(315˚)
00
(45˚)
11
(225˚)
01
(135˚)
10
(315˚)
We’ve seen these equations earlier, but to re-emphasis:
2 N = S or log
2
S = N
Where N = number of bits per symbol
And S = number of symbols bit stream
What? Did I hear you correctly? You want to know if you can add even more bits per symbol. Absolutely!
M-ary PSK
We can further increase the number of bits per symbol by increase the number of possible phase shifts.
Consider the 8-PSK constellation below.
90
˚
180
˚
0˚
270
˚
How many bits per symbol are transmitted?
S=8 𝐥𝐨𝐠
𝟐
𝑺 = 𝟑 So 3 bits/symbol
8 PSK
Consider the bit stream below and the resulting 8-PSK signal.
000
(0 ˚)
010
(135˚)
111
(225˚)
100
(315˚)
001
(45˚)
Yeah baby! Let’s do that again. Give me more.
101
(270 ˚)
011
(90 ˚) unmodulated carrier
8-PSK signal
100
(315˚) bit stream
7

16 PSK
We could further increase to 4 bits/symbol using 16-PSK.
What’s S now? Yep, S = 16.
Wow, those dots are getting close together. At this rate, I imagine those dots will soon be touching. If that’s your thought, you might be on to something.
To demodulate 16-PSK, the receiver must determine the phase within
 11.25˚. Think about it. If you have 16 symbols, you have 360 o
/16 = 22.5
o
between each symbol. That leaves you a buffer of
 11.25˚ on either side of a symbol.
11.25
22.5
o o
As we’ve mentioned so many times, the number 1 most limiting factor of communication systems is noise. In all transmissions, the received signal will be degraded by noise.
This can be depicted in the phasor domain (constellation diagram) as follows.
A BPSK receiver must make a decision to determine the phase of a received signal to determine the corresponding binary signal.
8

Now consider the same noise in the presence of a QPSK or 8-PSK signal.
Noise effects (8-PSK)
So is this it? We’re limited to just a few symbols. Or did someone so handsome, so smart think of a method to overcome, to an extent, the limitations noise is playing on our abilities to transmit?
Think about it for a second. Up to this point, we have manipulated amplitude, frequency, or phase.
What if, and I mean WHAT IF, we were to change, say, phase and amplitude at the same time. I know. Crazy. Right?
CRAZY AWESOME!!!!!
Quadrature Amplitude Modulation
In order to increase the distance between points in the signal constellation, another option is to modulate both the amplitude and the phase.
This is called Quadrature Amplitude Modulation (QAM)
9
8-QAM

8-QAM
Consider the bit stream below and the resulting 8-QAM signal. Note that there are both phase and amplitude changes.
And it doesn’t stop there.
Higher level QAM signals
QAM signals can be extended to have a larger number of signal symbols, which then gives a much higher bit rate
(because there are more bits per symbol).
64-QAM and 256-QAM are common in cable modems, satellites, and high-speed fixed broadband wireless.
In 256-QAM, you find that for each symbol you are transmitting (2
8
=256) 8 bits of information. What that means is for the same bandwidth, you are sending 8 times more information when you use 256-QAM than when you use
OOK, FSK, or BPSK.
Now that’s powerful!
All that singing the Comm-O wants the carrier group to hear gets sent out at a high bit rate, morale is up, and everyone is happy.
10

Example
Using the signal constellation below, answer the following questions. a) What type of modulation does this represent?
90˚ b) How many symbols are represented? c) How many bits per symbol can be used?
180˚ d) If the Baud Rate is 10,000 symbols/second. What is the bit rate? e) Would 16 QAM be more of less susceptible to noise than this signal?
270˚
Example
Label the modulation schemes.
LCDR Jesse Atwood, Capt Ryan Whitty, USMC, LCDR Jennie Wood, CDR Hewitt Hymas
Help us improve these notes! Send comments, corrections and clarifications to atwood@usna.edu
0˚
11