2. Digital Modulation and Demodulation Techniques
Chapter 2
Digital Modulation and Demodulation Techniques
2.1 Why Digital Modulation
Modern wireless communication systems use digital modulation and demodulation
techniques. Advantages over analogue modulation:
Improved spectral efficiency
Increase in capacity (higher data rates, or more users)
Reduced power requirements:
- reduced transmitter power
- reduced antenna gain
- increased path loss tolerated (range increase)
Greater accuracy in transmitting and receiving messages in the presence of noise and
distortion (improved tolerance to cochannel interference and multipath effects)
Easier multiplexing of various forms of information (voices, data and video)
Greater security
Digital transmissions accommodate digital error control codes that detect and correct
transmission errors. Support complex conditioning and processing techniques such as
source coding encryption, and equalisation to improve performance of the overall
communication link.
Modulation is the process of encoding information from a message source in a manner
suitable for transmission. It generally involves translating a baseband message signal to a
passband signal at a much higher frequency (see Fig.2.1). Modulation can be done by
varying the amplitude, phase or frequency of a high frequency carrier in accordance with
the amplitude of the message signal. The modulating signal can be represented as a time
sequence of symbols or pulses, where each symbol has m finite states. Each symbol
represents n bits of information, where n=log2 m bits/symbol.
Demodulation is the process of extracting the baseband message from the carrier so that it
may be processed and interpreted by the intended receiver.
Factors influence the choice of a digital modulation scheme:
Provides low bit error rates at low received signal to noise ratio
Performs well in multipath and fading conditions
Performs well in an interference environment
Occupies a minimum of bandwidth
Easy and cost effective to implement
Performance of a modulation scheme is often measured by:
Power efficiency describes the ability of a modulation technique to preserve the fidelity of
the digital message at low power levels.
Bandwidth efficiency describes the ability of a modulation scheme to accommodate data
within a limited bandwidth.
A low bit-error-probability should be achieved in the presence of adjacent and cochannel
interferences, thermal noise and other channel impairments such as fading and
intersymbol interference.
1
2. Digital Modulation and Demodulation Techniques
Figure 2.1 (a) Baseband and (b) passband signals.
In the design of a digital communication system, very often there is a trade-off between
bandwidth efficiency and power efficiency. Adding error control coding to a message
increases the bandwidth occupancy (and this, in turn, reduces the bandwidth efficiency),
but at the same time reduces the required received power for a particular bit error rate,
and hence trades bandwidth efficiency for power efficiency.
When the signal passes through the channel, signal degradation by the following changes
its shape (see Fig.2.2):
Distortion resulted when the signal is passed through filters having insufficient bandwidth
Intersymbol interference (ISI) is the effect where one bit affects succeeding bits
Delay spread is the effect when multiple delayed versions of the original signal can be
received at the same time
Thermal noise from within the receiver itself or from manmade or natural interference
Adjacent channel interference due to other transmitters spilling over into the receiver
band
Cochannel interference due to distant transmitters operating at the same frequencies
Table 2.1 covers the applications for different modulation formats in both wireless
communications and video.
To understand and compare different modulation format efficiencies, it is important to
first understand the differences between bit rate and symbol rate. The signal bandwidth
for the communications channel needed depends on the symbol rate, not on the bit rate.
symbol rate =
bit rate
number of bits transmitted with each symbol
Bit rate is the frequency of a system bit stream. Take, for example, a radio with an 8 bit
sampler, sampling at 10kHz for voice. The bit rate, the basic bit stream in the radio,
would be 8 bits multiplied by 10k samples per second, or 80kbits per second.
The symbol rate is the bit rate divided by the number of bits that can be transmitted with
each symbol. If one bit is transmitted per symbol, as with BPSK, then the symbol rate
would be the same as the bit rate of 80kbits per second. If two bits are transmitted per
symbol as in QPSK, then the symbol rate would be half of the bit rate or 40kbits per
second.
If more bits can be sent with each symbol, then the same amount of data can be sent in a
narrower spectrum. This is why modulation formats that are more complex and use a
higher number of states can send the same information over a narrower piece of the RF
spectrum.
2
2. Digital Modulation and Demodulation Techniques
Figure 2.2 Waveforms in a typical digital communication system: (a) transmitted signal,
(b) distorted receive signal, (c) distorted signal with noise, (d) regenerated signal (delayed).
Table 2.1 Applications for different formats in both wireless communications and video.
An example of how symbol rate influences spectrum requirements can be seen in eightstate Phase Shift Keying (8PSK). It is a variation of PSK. There are 8 possible states that
the signal can transit to at any time. The phase of the signal can take any of 8 values at
any symbol time. Since 23=8, there are 3 bits per symbol. This means the symbol rate is
one-third of the bit rate. This is relatively easy to decode.
The symbol clock represents the frequency and exact timing of the transmission of the
individual symbols. At the symbol clock transitions, the transmitted carrier is at the
correct I/Q or magnitude/phase value to represent a specific symbol (a specific point in
the constellation).
3
2. Digital Modulation and Demodulation Techniques
2.2 Power Spectral Density of Digital Signals
With any modulation technique, the modulated bandpass signal can be expressed in the
form
{
}
s(t ) = Re g (t )e − j 2 πf ct
where g(t) is the complex baseband envelope, then the power spectral density of the
bandpass signal STX(f) is related to the power spectral density of the complex envelop S(f)
by
S TX ( f ) =
1
[S ( f − f c ) + S ( f + f c )]
2
2.3 Phase Modulation
Digital phase modulation generally changes the phase of the carrier to a number of
different phase angles.
Binary phase shift keying (BPSK) – carrier phase is either 0° or 180°
Quadrature phase shift keying (QPSK) – use one of the four different phase angles (45°,
135°, −45° and −135°) to represent two bits at a time
8-PSK – use eight phase angles to represent groups of three bits at a time
16-PSK – use sixteen phase angles to represent groups of four bits at a time
2.3.1 Binary Phase Shift Keying (BPSK)
Simplest form of digital phase modulation. Used in direct-sequence spread-spectrum
(DSSS) transceivers, pulse compression radars and deep space telemetry.
Phase of a constant amplitude carrier signal is switched between two values (0° and 180°)
according to the two possible signals corresponding to binary 1 and 0 respectively (see
Fig.2.3). The symbol rate is one bit per second.
BPSK is often referred to as an antipodal modulation, where each of the two binary
waveforms is the negative of the other. The binary waveforms are the unshifted carrier or
the inverted carrier (see Fig.2.4). This time domain response shows that the binary bit
stream inverts the phase of the carrier back and forth 0° or 180°. Each inversion of the
carrier causes a sharp transition in the time domain response. These transitions produce a
very wide transmitted spectrum.
Fig.2.5 shows a block diagram for a typical BPSK modulator. An oscillator produces an
unmodulated carrier that is fed to a double-balanced mixer. The non-return-to-zero (NRZ)
data is mixed with the carrier to form the desired BPSK signal. The transmitted output
spectrum is reduced by filtering the baseband modulation signal with the use of a lowpass
filter between the NRZ data input and the double-balanced mixer.
An amplifier is used to increase the transmitted signal level coming out of the modulator.
A final filter is used to eliminate the out-of-band harmonics of the signal produced by the
RF amplifier.
4
2. Digital Modulation and Demodulation Techniques
Figure 2.3: Phase domain of carrier for BPSK.
Figure 2.4: BPSK time domain waveforms.
5
2. Digital Modulation and Demodulation Techniques
Figure 2.5: BPSK modulator.
A diagram of a coherent BPSK demodulator is shown in Fig.2.6. The action of the
demodulator is the reverse of the modulator. Coherent demodulation implies that the
exact phase and frequency of the modulated signal is known at the receiver. The
modulated signal is applied to a double-balanced mixer, which is mixed with a LO having
the same frequency and phase as the modulated signal itself. Carrier recovery circuits are
used to produce this local carrier reference. These circuits use phase or frequency
information from the received signal to synchronise the local oscillator.
The received modulated signal can be written as
ri (t ) = B cos[2πf c t + ϕ i (t )]
where B is the amplitude of the received signal and ϕi(t) is the phase of the transmitted
signal, either 0° or 180°. Multiplying the LO signal by the received signal gives
s i (t ) = B cos[2πf c t + ϕ i (t )]cos(2πf c t )
B
{cos[4πf c t + ϕ i (t )] + cos[ϕ i (t )]}
2
The component at twice the RF frequency is removed by filtering, leaving
B
s i (t ) = cos [ϕ i (t )]
2
If ϕi(t) is 0°, then si(t) is 1. If ϕi(t) is 180°, then si(t) is −1. Thus, the original binary NRZ
signal is recovered by the demodulator.
=
6
2. Digital Modulation and Demodulation Techniques
Figure 2.6 BPSK demodulator.
The NRZ data signal resembles a square wave but alternates periodically between binary
1 and 0 in a random fashion. This characteristic means that the NRZ signal power spectral
density is smooth and resembles a sinx/x shape. For balanced +A and –A volt NRZ
signalling states,


g 1 (t ) =  + A
î 0


g 2 (t ) =  − A
î 0
−
Tb
T
≤t≤ b
2
2
elsewhere
−
Tb
T
≤t≤ b
2
2
elsewhere
The Fourier transform of the g1(t) symbol is
S1 ( f ) =
∞
∫− ∞ g (t )e
− j 2 π ft
dt =
Tb / 2
∫− T
b
/2
Ae − j 2 π ft dt
Tb / 2
A
e − j 2 π ft d (− j 2 π ft )
∫
− j 2 π f − Tb / 2
A
sin (π fT b )
=
πf
=
Similarly,
S 2 (f )=
T /2
− j 2 π ft
dt
∫− T / 2 (− A )e
b
b
− A
sin (π fT b )
=
πf
The complete spectral density (neglecting the dc term and harmonics) of equiprobable
p(+A)=p(–A)=0.5 balanced NRZ random data is given by
S ( f ) = 2 f b p (1 − p )[S 1 ( f ) − S 2 ( f
=2

1
( 0 .5 )(1 − 0 .5 )  2 AT b
Tb

 sin π fT b 
= 2 A 2Tb 

 π fT b 
)]2
2
sin (π fT b )
πfT b


2
where Tb is the bit period, A is the amplitude of the signal, and f is the frequency.
The PSD for the BPSK signal at RF can be evaluated by translating the baseband
spectrum to the carrier frequency
PBPSK

(
)
( f ) = A T b  sin π f − f RF Tb
 π ( f − f RF )T b
2
7

 sin π ( f + f RF )T b
 + 

 π ( f + f RF )T b
2



2



2. Digital Modulation and Demodulation Techniques
The PSD of an unfiltered BPSK signal is plotted in Fig.2.7 for a data rate of 10Mbps and
a carrier frequency of 80MHz. The null-to-null bandwidth is found to be equal to twice
the bit rate (BW=2Rb=2/Tb). The first null occurs at a frequency equal to Rb away from
the carrier frequency and the amplitude of the first lobe is only 13dB down from its
carrier value.
Another important parameter of any digital modulation is how the probability of bit error,
PE varies with SNR. Fig.2.8 shows a BPSK received signal with and without noise. The
modulator decides whether the recovered signal was a 1 or –1 by sampling the waveform
at the centre of the bit period. This is easy to do when there is no noise added to the
signal. When noise is added to the signal, it is easy to make an error.
Fig.2.9 shows a plot of the probability of making a bit error versus the ratio of the energy
per bits over the noise power spectral density, Eb/N0. Eb/N0 is related to SNR as follows
Eb
ST b
S Bn
=
=
N 0 N / Bn N Rb
where S is the average signal power of the carrier and Tb is the bit period. Eb/N0 is equal
to SNR when the noise bandwidth of the receiver is equal to the data rate. This is a
theoretical result since the noise bandwidth of the receiver needs to be somewhat wider
than the bit rate to avoid intersymbol interference in the received waveform.
Binary modulation methods transmit one bit per signalling interval, with a bandwidth
efficiency of 1bps/Hz.
Differential Phase Shift Keying is a noncoherent form of phase shift keying which avoid
the need for a coherent reference signal at the receiver. Noncoherent receivers are easy
and cheap to build, and hence widely used in wireless communications. The input binary
sequence is first differentially encoded and then modulated using a BPSK modulator. The
received signal is compared with a delayed version of itself. Fig.2.10 shows both the
DPSK modulator and demodulator. The data must be differentially encoded prior to
modulation. If the original NRZ data stream is
0, 1, 1, 0, 1, 1, 1, 0, 0…
then the encoded NRZ data signal (assuming the initial bit was a 0) is
0, 1, 0, 0, 1, 0, 1, 1, 1…
From earlier equation, the delayed version of the signal can be written as
ri (t − Tb ) = B cos[2πf c (t − Tb ) + ϕ i (t − Tb )]
Multiplying the delayed and original signals together yields
ri (t ) = A cos [2 πf c t + ϕ i (t )]
After some algebra and lowpass filtering, we are left with
B2
cos[ϕ i (t − Tb ) − ϕ i (t )]
2
If the last angle and the present angle are both the same, then their difference is 0° and
the filtered output is 1. If the present angle and the last angle are different, then their
difference is 180°, and the filtered output is –1. The differential BPSK demodulator
performs a comparison detection directly on the modulated signal and thus does not
require a carrier recovery circuit. Since a delayed version of the received signal,
complete with added noise is used as a reference for demodulation, the PE performance
for DPSK is worse than that of coherently demodulated BPSK as shown in Fig.2.9.
[ri (t − Tb )ri (t )]LPF
=
While DPSK signalling has the advantage of reduced receiver complexity, its energy
efficiency is inferior to that of coherent PSK by about 3dB.
8
2. Digital Modulation and Demodulation Techniques
Figure 2.7 BPSK power spectral density.
2.3.2 Quadrature Phase Shift Keying (QPSK)
In the case of M-ary modulation methods, more than one bit may be transmitted per
signalling interval. This allows greater bit rates for the same bandwidth, at the expense of
a more complex system.
If we transmit M=2n symbols for each signalling interval, a bandwidth efficiency of
nbps/Hz can be achieved. If the symbol rate is Rs, then the effective is Rb=nRs. If we use
four states, where n=2 and M=4, then we transmit two bits, or four symbols for each
signalling interval. This is called quadrature phase shift keying (QPSK).
QPSK has twice the bandwidth efficiency of BPSK since two bits are transmitted in a
single modulation symbol. The modulated signal has four distinct phase states, such as
45°, 135°, −45° and −135°. Each value of phase corresponds to a unique pair of message
bits as shown in Fig.2.11. QPSK is used in applications such as early telephone modems,
satellite communications, global positioning system (GPS) and in some forms of code
division multiple access (CDMA). For a QPSK waveform, the binary sequence is
0, 1, 1, 0, 1, 0, 0, 0
To send a stream of symbols corresponding to these bits, we first separate the bits into
groups of two
01, 10, 10, 00
We can write the QPSK signal as
ri (t ) = A cos[2πf RF t + ϕ i (t )]
where A is the carrier amplitude, i is an integer (0, 1, 2, 3) and ϕI(t) is the instantaneous
phase angle of the modulated signal with respect to the unmodulated carrier. The value
ϕi(t) can be written as
π
ϕ i (t ) = (2i + 1)
4
9
2. Digital Modulation and Demodulation Techniques
Figure 2.8 Demodulated BPSK waveforms: (a) without noise, (b) with noise.
10
2. Digital Modulation and Demodulation Techniques
Figure 2.9 BPSK probability of bit error.
Figure 2.10 Differentially encoded/decoded BPSK (DBPSK): (a) DBPSK transmitter,
(b) DBPSK receiver.
11
2. Digital Modulation and Demodulation Techniques
Figure 2.11 Phase domain of carrier for QPSK (gray-coded).
A more common implementation used to perform QPSK modulation is shown in Fig.2.12.
The QPSK signal at the modulator output is normally filtered to limit the radiated
spectrum, amplified and then transmitted over the transmission channel to the receiver
input. The serial data stream is demultiplexed into even and odd components via the
serial-parallel converter (or demultiplexer). Each data component (now at half the bit rate)
is applied to a set of double-balanced modulators.
Lowpass filters can be used to bandlimit the transmitted spectrum. The set of doublebalanced mixers forms a quadrature modulator which can vary both the phase and
amplitude of the transmitted signal. Finally, the outputs from each double-balanced mixer
are added together and fed through an amplifier to a bandpass filter to removes any
harmonics of the modulated signal. QPSK can be regarded as two BPSK systems
operating in quadrature.
12
2. Digital Modulation and Demodulation Techniques
Figure 2.12 QPSK modulator.
13
2. Digital Modulation and Demodulation Techniques
Fig.2.13 shows a simplified block diagram of the quadrature modulator. The inphase and
quadrature components of the modulated signal can be written in their exponent forms
 e j 2 πf RF t + e − j 2 πf RF t 

I cos(2πf RF t ) = I 

2


j 2 πf RF t
− j 2 πf RF t
e

−e

Q sin (2πf RF t ) = Q

j
2


The output of the quadrature modulator is then
 e j 2 πf RF t + e − j 2 πf RF t 
 e j 2 πf RF t − e − j 2 πf RF t
 + Q
s(t ) = I 


2
2j



1
= (I − jQ )e j 2 πf RF t + (I + jQ )e − j 2 πf RF t
2
[
]




Letting
(I − jQ ) =
(I + jQ ) =
I 2 + Q 2 e jϕ
I 2 + Q 2 e − jϕ
where
Q
ϕ = tan −1  
I 
we can then write
 e j (2 πf RF t + ϕ ) + e − j (2 πf RF t + ϕ ) 

s(t ) = I 2 + Q 2 

2


= I 2 + Q 2 cos(2πf RF t + ϕ)
The quadrature modulator can be used to modulate both the amplitude and phase of the
carrier. If I and Q are chosen to be ±1, then the amplitude of the modulated signal is a
constant √2. Having I and Q equal to ±1, all phase angles lie along the 45° lines off the
axes. We can also use the quadrature generator to perform modulations that require both
amplitude and phase variation such as Quadrature Amplitude Modulation (QAM).
Fig.2.14 shows the time domain response for QPSK. The phase of the carrier can be
changed 0°, ±90° or 180° from its present value. The two bit streams in the bottom of the
plot correspond to the demultiplexed I and Q data streams. The unfiltered input data bits
cause abrupt changes in phase in the modulated carrier, like BPSK.
If the bit rate of the input data is Rb bits per second, the output symbol rate is Rs= Rb/2
symbols per second. Thus QPSK requires only half the channel bandwidth of BPSK to
transmit the same data rate, and therefore has a bandwidth efficiency of 2bps/Hz.
The transmitted power spectral density of a typical QPSK signal at a carrier frequency of
80MHz and a data rate of 10Mbps is shown in Fig.2.15. Because the average transition
between phase states is 90°, the bandwidth of the QPSK spectrum is half as wide as the
spectrum of a BPSK signal.
14
2. Digital Modulation and Demodulation Techniques
Figure 2.13 Quadrature modulator.
Figure 2.14 QPSK time domain waveforms.
The QPSK demodulator is simply the reverse of the modulator. Fig.2.16 shows a block
diagram of a typical QPSK demodulator which is simply two BPSK demodulators using
mixers with quadrature LO components to recover the I and Q signals. The received
signal is multiplied by cosine and sine versions of the local carrier. The carrier recovery
circuitry provides a local inphase reference precisely aligned in phase to the transmitted
carrier. Shifting the inphase signal by 90° generates the quadrature signal. The symbol
timing recovery circuitry extracts the data clock and samples the lowpass filtered outputs
at precisely the optimum position within the bit period. A data multiplexer re-interleaves
the data back into the serial bit stream.
15
2. Digital Modulation and Demodulation Techniques
Figure 2.15 QPSK power spectral density.
As before, we can write Eb/N0 as
Eb
S Bn
=
N 0 N Rb
In QPSK, we have created two data streams, each at half the rate of the original bit
stream and each having maximum amplitude of ±(√S)/√2, this gives
(
)
2
Eb
Bn
S/ 2
S Bn
=
=
N0
N
Rb / 2 N Rb
Therefore, the BER of QPSK is the same as that of BPSK. Fig.2.17 shows a plot of the
probability of bit error for QPSK versus Eb/N0, which is identical to BPSK.
A noise spike could very easily cause the resultant vector to fall into the wrong quadrant.
If we code the data properly, a symbol error will result in a single bit error and not two bit
errors. Fig.2.18 shows the symbols on the QPSK phase plane for different assignments of
bits. Because the noise is Gaussian by nature, it is much more likely that a noise spike
will cause the resultant vector to fall in an adjacent quadrant, rather than the opposite
quadrant.
If the symbols are coded as in Fig.2.18(a), then falling into an adjacent quadrant could
result in two bit errors. However, if we gray code the data as in Fig.2.18(b), then each
symbol error into an adjacent quadrant causes only one bit error. This is because an error
is most likely to result in a shift from the correct phase state to the immediately adjacent
phase, rather than the diametrically opposite phase. A gray code is a mapping of input bits
to output bits, such that only one output bit at a time changes for sequential input bit
changes. This leads to improved bit error rates.
16
2. Digital Modulation and Demodulation Techniques
Figure 2.16 QPSK demodulator.
17
2. Digital Modulation and Demodulation Techniques
Figure 2.17 QPSK probability of bit error.
Figure 2.18 Assignment of symbols for QPSK: (a) nongray-coded QPSK, (b) gray-coded
QPSK.
In most wireless communication systems, the QPSK spectrum would be too wide to meet
regulatory requirements and would also cause unwanted interference by spilling into
adjacent channels. The transmitted spectrum can be reduced by placing a very narrow
bandpass filter at the output of the modulator. This is not practical since the Q of the filter
would be very high as the transmitted frequency is much higher than the data rate. Such a
high Q filter would be difficult to build, expensive and would cause significant distortion
on the transmitted waveform due to rapid phase variations at the band edges. As there are
many channels, the filter has to be tunable.
18
2. Digital Modulation and Demodulation Techniques
A better way to limit the transmitted output spectrum is by filtering the baseband I and Q
modulation signals before applying those to the double-balanced modulators as shown in
Fig.2.19. The resulting transmitted spectrum of the filtered and unfiltered QPSK is shown
in Fig.2.20. The action of the filter greatly reduces the bandwidth of the transmitted
signal. Fig.2.21 shows the corresponding time domain signal for a baseband filtered
QPSK signal. The amplitude dips to zero every time a 180° phase change is encountered.
However, a 90° phase changes result in much lower amplitude variations.
In most wireless communication systems, the output of the modulator has to be amplified
before applied to the antenna. To get the highest efficiency from the transmit power
amplifier, it is common to run the circuit in nonlinear, Class C operation which consumes
little power when no signal is applied to it. When a signal is applied to the hardlimited
(compression or saturation) amplifier, most of the power is directly transferred to the load
resulting in maximum efficiency.
When a filtered QPSK signal is passed through a limited amplifier, much of the amplitude
variations in the time envelope are reduced. Fig.2.22 shows the spectrum of a QPSK
signal that has been first filtered and then limited. The limiting action of the amplifier
causes the spectral regrowth. In general, modulation schemes that have non-constant
envelopes suffer from spectral regrowth when passed through a hardlimited amplifier.
These types of modulations generally require linear amplifiers in the transmit path.
2.3.3 Offset Quadrature Phase Shift Keying (OQPSK)
In offset QPSK the two bit streams are staggered, so that both channels do not change
simultaneously, as shown in Fig.2.23. The transitions do not pass through the centre of
the constellation diagram, and hence the amplitude fluctuation is much reduced. Also, the
transitions within the constellation diagram now occur twice as frequently. This may
make symbol timing more difficult to acquire. Nevertheless, because the two channels
carry orthogonal signals and still have the same baud rate as conventional QPSK, the
bandwidth is not increased.
OQPSK waveform is more tolerant to limiting as the phase variations are more gradual.
OQPSK is identical to QPSK except that the Q data stream is offset from the I stream by
delaying it by an amount equal to the incoming signal bit duration. Since the transitions of
I and Q are offset, at any given time only one of the two bit streams can change values.
Fig.2.23 shows the phase domain, I and Q data streams and corresponding phase angles
for QPSK and OQPSK. The action of the one bit period delay in OQPSK causes no 180°
phase transitions. OQPSK is used as a building block for other modulations such as MSK.
Fig.2.24 shows the time domain response of OQPSK where all the phase transitions are
90°.
Figs.2.25 and 2.26 show the block diagrams of the OQPSK modulator and demodulator
respectively. The OQPSK modulator is identical to that of QPSK with the exception that
an extra bit period delay is inserted into the Q data stream. The OQPSK demodulator is
very similar to that of QPSK except for the extra bit delay that is inserted into the I data
stream to re-align the data.
In OQPSK, the signal trajectories are modified by the symbol clock offset so that the
carrier amplitude does not go through or near zero of the centre of the constellation. The
spectral efficiency is the same with two I states and two Q states. The reduced amplitude
variations allow a more power efficient, less linear RF power amplifier to be used.
19
2. Digital Modulation and Demodulation Techniques
Figure 2.19 Using premodulation lowpass filters to limit QPSK transmitted bandwidth.
The spectrum of an OQPSK signal is identical to that of a QPSK signal, both signals
occupy the same bandwidth. The staggered alignment of the even and odd bit streams
does not change the nature of the spectrum. Due to the similarities with QPSK, both the
power spectral density and the PE of OQPSK are the same as for QPSK. However, when
filtered and limited, OQPSK shows much smaller spectral regrowth than QPSK as shown
in Fig.2.27 for a plot of the time domain response of a baseband filtered OQPSK signal.
The amplitude fluctuations are greatly reduced. When the signal is passed through a
limiting amplifier, its spectral regrowth is much lower than that of QPSK as shown in
Fig.2.28.
2.3.4 π/4 Quadrature Phase Shift Keying (π/4 QPSK)
π/4 shifted QPSK modulation is a quadrature phase shift keying technique which offers a
compromise between conventional QPSK and OQPSK in terms of the maximum phase
variations. The maximum phase change is limited to ±135°, as compared to 180° for
QPSK and 90° for OQPSK. Hence, the bandlimited π/4 QPSK signal preserves the
constant envelope property better than bandlimited QPSK, but is more susceptible to
envelope variations than OQPSK.
An extremely attractive feature of π/4 QPSK is that it can be noncoherently detected
which greatly simplifies receiver design. In addition, π/4 QPSK performs better than
OQPSK in the presence of multipath spread and fading. The spectral regrowth is reduced
since the instantaneous phase transitions are limited to ±135°.
Very often, π/4 QPSK signals are differentially encoded to facilitate easier
implementation of differential detection or coherent demodulation with phase ambiguity
in the recovered carrier. With differentially encoded, π/4 QPSK is called π/4 DQPSK. It
has been adopted for U.S. and Japanese digital cellular TDMA radio standards.
In a π/4 QPSK modulator, signalling points of the modulated signal are selected from two
QPSK constellations which are shifted by π/4 with respect to each other. Transitions must
occur from one constellation to the other. This guarantees that there is always a change in
phase at each symbol, making clock recovery easier. Fig.2.29 shows the two
constellations along with the combined constellation where the links between two signal
points indicate the possible phase transitions. Switching between two constellations,
every successive bit ensures that there is at least a phase shift which is an integer multiple
of π/4 radians between successive symbols.
20
2. Digital Modulation and Demodulation Techniques
Figure 2.20 QPSK transmit power spectral density: (a) unfiltered (10Mbps data rate, 80MHz
carrier), (b) baseband filtered (10Mbps data rate, 80MHz carrier, 2.5MHz Gaussian lowpass
premodulation filter).
21
2. Digital Modulation and Demodulation Techniques
Figure 2.21 Time domain waveform of baseband filtered QPSK transmit signal.
A conceptual implementation block diagram of basic π/4 QPSK modulator architecture is
given in Fig.2.30. The input bit stream is partitioned by a serial-to-parallel converter into
two parallel data streams mI,k and mQ,k, each with a symbol rate equal to half that of the
incoming bit rate. The kth inphase and quadrature pulses, Ik and Qk, are produced at the
output of the signal mapping circuit over time kT≤ t≤ (k+1)T and are determined by their
previous values, Ik−1 and Qk−1, as well as θk. Ik and Qk represent rectangular pulses over
one symbol duration having amplitudes given by
I k = cos θ k = I k −1 cos φ k − Qk −1 sin φ k
Qk = sin θ k = I k −1 sin φ k + Qk −1 cos φ k
where
θ k = θ k −1 + φ k
The relationship between φk and the input symbols is given in Table 2.2 below.
Information bits mI,k and mQ,k
Phase shift φk
11
π/4
01
3π/4
00
-3π/4
10
-π/4
The information in a π/4 QPSK signal is completely contained in the phase difference φk
of the carrier between two adjacent symbols. It is possible to use noncoherent differential
detection even in the absence of differential encoding.
22
2. Digital Modulation and Demodulation Techniques
Figure 2.22 QPSK transmit output spectrum with baseband filtering: (a) without limiting,
(b) with limiting (amplifier 10dB into compression).
23
2. Digital Modulation and Demodulation Techniques
Figure 2.23 QPSK and OQPSK I/Q data waveforms with their corresponding phase angles.
Figure 2.24 OQPSK time domain waveforms.
24
2. Digital Modulation and Demodulation Techniques
Figure 2.25 OQPSK modulator.
25
2. Digital Modulation and Demodulation Techniques
Figure 2.26 OQPSK demodulator.
26
2. Digital Modulation and Demodulation Techniques
Figure 2.27 Time domain waveform of baseband filtered OQPSK transmit signal.
The IF differential detector shown in Fig.2.31 avoids the need for a local oscillator by
using a delay line and two phase detectors. The received signal is converted to IF and is
bandpass filtered. The bandpass filter is designed to match the transmitted pulse shape, so
that the carrier phase is preserved and noise power is minimised. The received IF signal is
differentially decoded using a delay line and two mixers. The bandwidth of the signal at
the output of the differential detector is twice that of the baseband signal at the transmitter
end.
2.4 Frequency Modulation
In phase modulations, the phase of the carrier is abruptly changed to a new value in
response to the input data signal. This can result in a wide transmitted spectrum and can
also result in spectral regrowth if the signal does not have a constant envelope. Multiple
phase angles are used to represent groups of bits and thus reduce the effective symbol rate
at the transmitter.
Smoothly changing the phase angle from one value to another will result in a transmitted
signal having constant amplitude. A constant amplitude signal would be impervious to the
effects of filtering/hardlimiting and spectral growth.
27
2. Digital Modulation and Demodulation Techniques
Figure 2.28 OQPSK transmit output spectrum with baseband filtering: (a) without limiting,
(b) with limiting (amplifier 10dB into compression).
28
2. Digital Modulation and Demodulation Techniques
Figure 2.29 Constellation diagram of a π/4 QPSK signal: (a) possible states for θk when
θk−1=nπ/4, (b) possible states when θk−1=nπ/2, (c) all possible states.
Figure 2.30 Generic π/4 QPSK transmitter.
29
2. Digital Modulation and Demodulation Techniques
Figure 2.31 Block diagram of an IF differential detector for π/4 QPSK.
Smooth, continuous phase modulation corresponds to frequency modulation. The constant
envelope family of modulations has the main advantages of employing power efficient
Class C amplifiers without introducing degradation in the spectrum occupancy of the
transmitted signal. In situations where bandwidth efficiency is more important than power
efficiency, frequency modulation is not well-suited.
2.4.1 Minimum Shift Keying (MSK)
MSK is a binary digital FM modulation technique with a modulation index of h=0.5. It
has the following fundamental properties:
Constant envelope suitable for nonlinear, power efficient amplification
Coherent and noncoherent detection capability
Spectral main lobe is 50% wider than that of QPSK signals. First spectral null is at
(f−fc)Tb=0.75 instead of (f−fc)Tb=0.5.
MSK can be thought of as either a phase or frequency modulation. Fig.2.32 shows the
phase domain plot for MSK. The carrier phase changes phase by ±90° over the course of
a bit period. Note that between symbols the phase changes linearly with time, and the
amplitude remains constant, so between symbols the signal moves evenly around the
circle from one constellation point to another.
Since a frequency shift produces an advancing or retarding phase, frequency shifts can be
detected by sampling phase at each symbol period. Phase shifts of (2N+1)π/2 radians are
easily detected with an I/Q demodulator. At even numbered symbols, the polarity of the I
channel conveys the transmitted data, while at odd numbered symbols the polarity of the
Q channel conveys the data.
Suppose the carrier phase at the beginning of the data period is 0°. If the next data bit is a
1, then the phase smoothly advances by 90° by the end of the bit period. If the data bit
remains a 1, then the phase advances another 90° to 180°.
Instead, if the next bit were a 0, then the phase would smoothly retard by 90° to −90°.
Again, if the data were to remain at 0, then the phase would continue to retard itself by
another 90°.
30
2. Digital Modulation and Demodulation Techniques
Figure 2.32 Phase domain of carrier for MSK.
The orthogonality between I and Q simplifies detection algorithms and hence reduces
power consumption in a mobile receiver. The minimum frequency shift which yields
orthogonality of I and Q is that which results in a phase shift of ±π/2 radians per symbol
(90° per symbol).
Since the phase will continue to advance or retard itself over the course of each bit period,
the derivative of the phase or frequency is varied. In this way, MSK can also be
considered a frequency modulation. Used in satellite communications, military tactical
radio, ELF underwater communications and the GSM (Global System for Mobile
Communications) cellular standards.
The MSK phase trellis in Fig.2.33 shows the phase plotted over time. The phase angle
changes smoothly by 90° over each bit period.
We can write the MSK signal as
t
π 

s i (t ) = A cos 2πf RF t + ∫ d (t ) dt 
−∞
2 

π


= A cos 2πf RF t + ⋅ (± 1) ⋅ t + ϕ 0 
2


where d(t) gives rise to the ±1 term in the above equation.
Assume that d(t) changes from one bit period to another, the frequency will be higher in
one case. And when the input changes, the frequency will be lower. We can write this as
∆w ∆ϕ(t ) 1 π / 2 1 Rb
∆f + =
=
⋅
=
⋅
=
∆t 2π Tb 2π 4
2π
R
∆w ∆ϕ(t ) 1 − π / 2 1
=
⋅
=
⋅
=− b
Tb
∆t 2π
2π
2π
4
where Rb=1/Tb is the bit rate and Tb is the bit period. The effective frequency difference
is given by
R
∆f + − ∆f − = b
2
∆f
−
=
31
2. Digital Modulation and Demodulation Techniques
Figure 2.33 MSK phase trellis.
Therefore, the frequency difference in MSK corresponds to a 90° phase advance or lag
over a bit period is equal to half the bit rate. The word minimum corresponds to the
minimum frequency difference between the “mark” and “space” frequencies, which can
be coherently demodulated.
If the data stream in Fig.2.34 does not change, then the I and Q modulation signals are
simply two sinusoids 90° out of phase with one another. Simply look at any point on the
unit circle and determine what values of I and Q are required for that phase angle. If the
next bit is a 1, find a point on the unit circle that corresponds to 90° more of the phase
angle. This will dictate what the I and Q modulation signals should look like. As the data
stream changes value, the I and Q signals will look like half-period sinusoids.
This is better illustrated in the time domain waveforms in Fig.2.35. At the bottom of the
plot, the I and Q values are shown as rectangular data pulses. After passing through
special pulse-shaping filters, the I and Q signals become ‘half-sinusoidal” in nature. The
corresponding output signal is indeed constant envelope, with its frequency changing
from a slightly higher to a slightly lower value.
A block diagram of an MSK modulator is shown in Fig.2.36. It is identical to an OQPSK
modulator except for the special pulse-shaping filters. The input to the filter simply
reverses the polarity of the output signal at the end of each symbol period.
32
2. Digital Modulation and Demodulation Techniques
Figure 2.34 I and Q waveforms corresponding to MSK phase trellis shown in Fig.2.33.
Figure 2.35 MSK time domain waveforms.
Fig.2.37 shows a block diagram of the MSK demodulator. It is identical to an OQPSK
modulator. The lowpass filters shown are implemented as matched filters that are shaped
to allow the signal itself to pass with little or no attenuation and reject all other
waveforms (including noise).
33
2. Digital Modulation and Demodulation Techniques
Figure 2.36 MSK modulator.
34
2. Digital Modulation and Demodulation Techniques
Figure 2.37 MSK demodulator.
35
2. Digital Modulation and Demodulation Techniques
We can produce an MSK signal via standard FM circuitry. In Fig.2.38, the bit stream is
fed directly into the modulation input of a VCO. The modulation index for an FM signal
is given by
∆f
h ≡β=
fm
where the variable h is more commonly used as the index of modulation for digital
signals and β is the more familiar FM (analogue) index of modulation. ∆f is the total
frequency difference and fm is the modulation frequency. For MSK, we set the level of
the modulating signal into the VCO to produce a modulation index, h, of 0.5.
Fig.2.39 shows the time domain response of MSK with the modulated carrier being
shown at the top of the plot. The phase changes linearly 90° over the course of a bit
period and this is shown in the second trace. The relative slope is the same for a logic 0 as
it is for a logic 1, only with a negative slope. The input data stream is shown at the lower
portion of the plot.
A plot of the power spectral density of an MSK signal compared to that of an unfiltered
QPSK signal is shown in Fig.2.40 for a carrier frequency of 80MHz and a data rate of
10Mbps. The MSK spectrum falls off much more rapidly than the QPSK spectrum due to
the fact that the MSK signal is continuous inphase. Although the phase is continuous in
MSK, the frequency is not. It is this discontinuous frequency that results in a wider power
spectral density with sharp nulls.
Fig.2.41 shows a plot of bit error probability versus Eb/N0. The curve is the same as that
of BPSK and QPSK as MSK can be viewed as QPSK with special pulse-shaping filters
acting over two bit periods.
Fig.2.42 shows a plot of an MSK signal in the time domain which shows that MSK is a
true constant envelope modulation with no amplitude fluctuations. This is a desirable
characteristic for improving the power efficiency of transmitters. Amplitude variations
can exercise nonlinearities in an amplifier’s amplitude transfer function, generating
spectral regrowth, a component of adjacent channel power.
Fig.2.43 shows a plot of the MSK signal before and after hardlimiting. There is
essentially no spectra regrowth and this makes MSK very attractive in applications where
saturated power amplifiers are employed.
2.4.2 Gaussian Minimum Shift Keying (GMSK)
GMSK has a very narrow transmitted spectrum, yet exhibits very little intersymbol
interference and is tolerant to hardlimiting. It is a derivative of MSK where the bandwidth
required is further reduced by passing the modulating waveform through a Gaussian filter.
The Gaussian filter minimises the instantaneous frequency variations over time. GMSK is
a spectrally efficient modulation scheme and is particularly useful in mobile radio
systems. It has a constant envelope, spectral efficiency, good BER performance and is
self synchronising.
36
2. Digital Modulation and Demodulation Techniques
Figure 2.38 Using a voltage-controlled oscillator (VCO) as an MSK modulator.
Figure 2.39 Time domain waveforms from VCO-based MSK modulator.
37
2. Digital Modulation and Demodulation Techniques
Figure 2.40 MSK versus QPSK power spectral density.
Figure 2.41 MSK probability of bit error.
38
2. Digital Modulation and Demodulation Techniques
Figure 2.42 Time domain waveform of baseband filtered MSK transmit signal (using 5MHz
Gaussian lowpass filter).
To retain a constant envelope, coherent and noncoherent detection capability and increase
the spectral efficiency, the transmitted spectrum of MSK is narrowed by filtering the
modulation signal through a lowpass filter, before applying it to the VCO. The lowpass
filter must have a well-behaved time domain response such as the Gaussian filters. The
frequency response of a Gaussian lowpass filter is Gaussian in nature and follows the
following relation
−
1
(τω )2
H (ω) = τ ⋅ 2π ⋅ e 2
where ω is the frequency in rad/sec and τ is a constant.
The time domain response of a Gaussian filter is Gaussian as well. Taking the inverse
Fourier transform of the spectrum
h(t ) =
1
− (τω )2
1 ∞
1 ∞
− jωt
2
(
)
H
e
dt
e
e − jωt dt
2
ω
⋅
=
τ
⋅
π
⋅
2π ∫−∞
2π ∫− ∞
=e
1 t 
−  
2 τ 
2
Fig.2.44 shows the plots of both the time domain and frequency responses of a Gaussian
lowpass filter. Both curves have the same bell-shaped response.
Fig.2.45(a) shows a block diagram of a GMSK modulator. It is identical to the VCObased version of the MSK modulator except for the lowpass modulation filter. The
relative bandwidth, BT of the filter is
BW−3dB
= BW−3dB ⋅ Tb
BT =
Rb
39
2. Digital Modulation and Demodulation Techniques
Figure 2.43 MSK transmit output spectrum with baseband filtering: (a) without limiting,
(b) with limiting (amplifier 10dB into compression).
40
2. Digital Modulation and Demodulation Techniques
Figure 2.44 Gaussian lowpass filter waveforms: (a) impulse response, (b) frequency response.
41
2. Digital Modulation and Demodulation Techniques
Fig.2.45(b) shows a simple noncoherent demodulator for demodulating GMSK.
Applications for GMSK include the Global System for Mobile communication (GSM)
with BT=0.3, and the Digital European Cordless Telephone (DECT) with BT=0.5.
The time domain response of GMSK with BT=0.5 is shown in Fig.2.46. The top trace
shows the modulated signal. As in the case of MSK, GMSK is a constant envelope
modulation. In contrast to MSK, the second trace shows that the phase has a smooth slope
due to the action of the Gaussian lowpass filter. The filter also smoothes out the input bit
stream, removing the sharp transitions in the data.
The action of the filter has a radical effect on the transmitted spectrum. Fig.2.47 shows a
plot of the power spectral density for various GMSK signals having different relative
filter bandwidths. If no filter is use as in MSK, then BT=infinity. The figure shows that a
filter having a bandwidth equal to half the data rate (i.e. BT=0.5) rolls off much faster in
frequency than MSK. Using filters with smaller relative bandwidths causes even faster
roll-off.
As the relative filter bandwidth is lowered, more and more intersymbol interference (ISI)
is imparted to the waveform. The eye diagram gives a qualitative indication of the amount
of ISI on the waveform. As noise or ISI increases, the eye begins to close, increasing PE.
Fig.2.48(a) shows the time domain response of a GMSK modulation signal with a BT=0.5
filter. The amplitude of the modulation waveform is equivalent to the instantaneous
frequency deviation of the carrier. Fig.2.48(b) shows an eye diagram of this same signal
taken over many more bit periods. Very little ISI is seen in the waveform for a filter
having a bandwidth of half the bit period (BT=0.5).
Fig.2.49(a) shows the time domain response for a BT=0.25 filter (quarter of the bit rate).
The alternating strings of 0s and 1s result in waveforms that are nowhere near the full
value of the original, unfiltered signal. The eye diagram shows this effect much more
clearly. At the sampling instant (near t=0), the eye is almost closed. It is easy to see that
very little noise will cause a bit error in this case.
The output of the noncoherently demodulated GMSK signal is equivalent to the
instantaneous frequency deviation of the signal. For low values of BT, the eye is almost
closed. Therefore, a relatively high SNR must be maintained if bit errors are to be kept
low.
Fig.2.50 shows a block diagram of a coherent GMSK demodulator that is identical to that
of MSK. A predetection Gaussian bandpass filter is used at the input of the demodulator.
The lowpass filters can be implemented as matched filters for better performance.
Fig.2.51 show a plot of the amount of degradation in performance of a GMSK signal for
different values of BT. We need to increase Eb/N0 by only 1dB over that of coherently
demodulated MSK to maintain the same PE performance when BT=0.215.
The reason for this result is that when we coherently demodulate the GMSK signal, we
are looking at the phase of the signal over two or more bit periods. Fig.2.52 shows the eye
diagrams for both the I and Q portions of a coherently demodulated GMSK signal for
BT=0.5. The eye diagrams are relatively open. If we reduce BT to 0.25, there is some
closing of the eye as shown in Fig.2.53, but the waveforms are remarkably good as
compared to that for noncoherent demodulation. This is the reason in Fig.2.51 shows little
degradation over coherent MSK, even for low values of BT.
42
2. Digital Modulation and Demodulation Techniques
Figure 2.45 Gaussian lowpass filtered MSK (GMSK): (a) GMSK modulator (noncoherent),
(b) GMSK demodulator (noncoherent).
43
2. Digital Modulation and Demodulation Techniques
Figure 2.46 GMSK time domain waveforms.
Figure 2.47 GMSK power spectral density for different relative filter bandwidths (BT).
44
2. Digital Modulation and Demodulation Techniques
Figure 2.48 GMSK demodulated waveforms (noncoherent): (a) recovered bit stream
(BT=0.5), (b) eye diagram (BT=0.5).
45
2. Digital Modulation and Demodulation Techniques
Figure 2.49 GMSK demodulated waveforms (noncoherent): (a) recovered bit stream
(BT=0.25), (b) eye diagram (BT=0.25).
46
2. Digital Modulation and Demodulation Techniques
Figure 2.50 Coherent GMSK demodulator.
47
2. Digital Modulation and Demodulation Techniques
Figure 2.51 Theoretical Eb/N0 degradation of GMSK as a function of BT compared to ideal
coherent demodulation.
Figure 2.52 Eye diagrams for coherently demodulated GMSK (BT=0.5): (a) I-channel,
(b) Q-channel.
48
2. Digital Modulation and Demodulation Techniques
Figure 2.52 (continued).
Figure 2.53 Eye diagrams for coherently demodulated GMSK (BT=0.25): (a) I-channel,
(b) Q-channel.
49
2. Digital Modulation and Demodulation Techniques
Figure 2.53 (continued).
2.5 Viewing a Digitally Modulated Signal
2.5.1 Time and Frequency View
There are a number of different ways to view a signal. This simplified example is an RF
pager signal at a centre frequency of 930.004MHz. This pager uses two-level FSK and the
carrier shifts back and forth between two frequency that are 8kHz apart (930.000 and
930.008MHz). This frequency spacing is small in proportion to the centre frequency of
930.004MHz. This is shown in Fig. 2.54(a).
The difference in period between a signal at 930MHz and one at 930MHz plus 8kHz is
very small. Even a high performance oscilloscope, using the latest in high-speed digital
techniques, the change in period cannot be observed or measured.
In a pager receiver, the signals are first down-converted to an IF or baseband frequency.
In this example, the 930.004MHz FSK-modulated signal is mixed with another signal at
930.002MHz. The FSK modulation causes the transmitted signal to switch between
930.000 and 930.008MHz.
The result is a baseband signal that alternates between two frequencies, −2kHz and
+6kHz. The demodulated signal shifts between −2kHz and +6kHz. The difference can be
easily detected.
This is sometimes referred to as “zoom” time or IF time. To be more specific, it is a bandconverted 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 Fig. 2.54(c).
50
2. Digital Modulation and Demodulation Techniques
Figure 2.54 Time and frequency domain view.
Most pagers use a two-level 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.
2.5.2 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 (as shown in Fig.
2.55) 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.
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. These phenomena distort the
modulated signal and usually lead to spectral regrowth as well.
2.5.3 Constellation Diagrams
The rectangular I/Q diagram is a polar diagram of magnitude and phase. A twodimensional diagram of the carrier magnitude and phase can be represented differently by
superimposing rectangular axes on the same data and interpreting the carrier in terms of
inphase (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).
51
2. Digital Modulation and Demodulation Techniques
Figure 2.55 Power and frequency domain view.
The example shown in Fig. 2.56 is a 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 affect 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 intersymbol interference.
The relationship between constellation points and bits per symbol is
M = 2n
where M = number of constellation points
n = bits/symbol
This holds when the transitions are allowed from any constellation point to any other.
2.5.4 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 in Fig. 2.57 and an “eye” 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. A
good signal has wide open eyes with compact crossover points.
52
2. Digital Modulation and Demodulation Techniques
Figure 2.56 Constellation diagram.
Figure 2.57 I and Q Eye diagram.
2.5.5 Trellis Diagrams
Fig. 2.58 is called a trellis diagram. It shows time on the x-axis and phase on the y-axis.
This allows the examination of the phase transitions with different symbols.
In the 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 90° per symbol. If a long series of binary
zeros were sent, there would be a constant declining phase of 90° 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.
2.6 Sharing the Channel
The RF spectrum is a finite resource and is shared between users using multiplexing or
channelisation. Multiplexing is used to separate different users of the spectrum such as
frequency, time, code and geography. Most communications systems use a combination
of these multiplexing methods.
53
2. Digital Modulation and Demodulation Techniques
Figure 2.58 Trellis diagram.
2.6.1 Multiplexing-Frequency
Frequency Division Multiple Access (FDMA) shown in Fig. 2.59, splits the available
frequency band into smaller fixed frequency channels. Each transmitter or receiver uses a
separate frequency. This technique has been used since 1900 and is still in use today.
Transmitters are narrowband or frequency-limited. A narrowband transmitter is used
along with a receiver that has a narrowband filter so that it can demodulate the desired
signal and reject unwanted signals, such as interfering signals from adjacent radios.
2.6.2 Multiplexing-Time
Time division multiplexing involves separating the transmitters in time so that they can
share the same frequency. The simplest type is Time Division Duplex (TDD) as shown in
Fig. 2.60. This multiplexes the transmitter and receiver on the same frequency. TDD is
used in a simple two-way radio where a button is pressed to talk and released to listen.
This kind of time division duplex is very slow.
Modern digital radios like CT2 and DECT use Time Division Duplex but they multiplex
hundreds of times per second. TDMA (Time Division Multiple Access) multiplexes
several transmitters or receivers on the same frequency. TDMA is used in the GSM
digital cellular system and also in the US NADC-TDMA system.
2.6.3 Multiplexing-Code
CDMA (Code Division Multiple Access) is an access method where multiple users are
permitted to transmit simultaneously on the same frequency (see Fig. 2.61). Frequency
division multiplexing is still performed but the channel is 1.23MHz wide. In the case of
US CDMA telephones, an additional type of channelisation is added, in the form of
coding.
In CDMA systems, users timeshare a higher-rate digital channel by overlaying a higherrate digital sequence on their transmission. A different sequence is assigned to each
terminal so that the signals can be discerned from one another by correlating them with
the overlaid sequence. This is based on codes that are shared between the base and mobile
stations.
54
2. Digital Modulation and Demodulation Techniques
Figure 2.59 Multiplexing-frequency.
Figure 2.60 Multiplexing-time.
2.6.4 Combining Multiplexing Modes
Another kind of multiplexing is geographical or cellular as shown in Fig. 2.62. If two
transmitter/receiver pairs are far enough apart, they can operate on the same frequency
and not interfere with each other.
In most of the common communications systems, different forms of multiplexing are
generally combined. For example, GSM uses FDMA, TDMA, FDD and geographic.
DECT uses FDMA, TDD and geographic multiplexing.
55
2. Digital Modulation and Demodulation Techniques
Figure 2.61 Multiplexing-code.
Figure 2.62 Multiplexing-geography.
56