UNIVERSITY OF NAIROBI
CARRIER RECOVERY BY RE-MODULATION IN QPSK
PROJECT NO: PRJ 093
BY:
YEGO KIPLETING KENNETH
F17/1783/2006
SUPERVISOR: DR. V.K. ODUOL
EXAMINER: PROF. ELIJAH MWANGI
Project report submitted in partial fulfillment of the
requirement for the award of the degree of
Bachelor of Science in Electrical and Electronics Engineering
Report submitted on 18TH May 2011
Department of Electrical and Information Engineering
i
DEDICATION
To my parents and my family members, God bless you for your continued support.
ii
ACKNOWLEDGMENT
I would like to thank my project supervisor, Dr. V.K. Oduol, for his invaluable support and
guidance by providing ideas, useful hints and directions throughout the undertaking of the
project.
I would also like to acknowledge the efforts of my friends who helped me in proof reading this
report.
iii
TABLE OF CONTENTS
DEDICATION .................................................................................................................................................................... I
ACKNOWLEDGMENT ................................................................................................................................................. II
TABLE OF CONTENTS.............................................................................................................................................. III
LIST OF FIGURES.......................................................................................................................................................... V
LIST OF ABBREVIATIONS .................................................................................................................................... VI
ABSTRACT ................................................................................................................................................................... VII
CHAPTER ONE ..............................................................................................................................................................1
INTRODUCTION ...........................................................................................................................................................1
1.1 Background ......................................................................................................................1
1.2 Coherent demodulation .....................................................................................................2
1.3 Carrier Synchronization ....................................................................................................3
1.4 Project Objectives.............................................................................................................5
1.5 Report organization ..........................................................................................................5
2 CHAPTER TWO ...................................................................................................................................................6
CARRIER RECOVERY TECHNIQUES .............................................................................................................6
2.1 Overview ..........................................................................................................................6
2.2 Phase locked loop (PLL)...................................................................................................7
iv
2.3 Carrier recovery in BPSK .................................................................................................9
2.3.1 The squaring loop ....................................................................................................... 10
2.3.2 Costas Loop ................................................................................................................ 11
2.4 Carrier Recovery in QPSK.............................................................................................. 14
2.4.1 Carrier recovery by raising to the fourth power followed by PLL ................................ 16
2.4.2 QPSK Costas loop....................................................................................................... 17
2.5 Carrier recovery by re-modulation .................................................................................. 19
2.5.1 BPSK carrier recovery by re modulation ..................................................................... 22
2.5.2 Advantages of carrier recovery by re-modulation ........................................................ 23
2.5.3 Disadvantages of carrier recovery by re-modulation .................................................... 23
2.6 Comparison of the Carrier Recovery methods ................................................................. 23
3 CHAPTER THREE .......................................................................................................................................... 25
3.1 SYSTEM DESIGN ......................................................................................................... 25
3.1 The overall carrier recovery system block diagram .............................................................. 25
3.2 Description of the QPSK re-modulator ................................................................................ 26
4 CHAPTER FOUR .............................................................................................................................................. 28
4.1 QPSK Re-modulator output ............................................................................................ 28
4.2 QPSK Costas loop output ............................................................................................... 30
4.3 Comparison of the re-modulator and Costas loop ............................................................ 32
CHAPTER FIVE ......................................................................................................................................................... 33
CONCLUSION AND RECOMMENDATIONS ....................................................................... 33
REFERENCES ............................................................................................................................................................. 34
v
1 LIST OF FIGURES
Figure 1.1 QPSK constellation affected by carier phase/frequency offset………………………1
Figure 2.1 The PLL………………………………………………………………………………7
Figure 2.2 Model of the PLL…………………………………………………………………….8
Figure 2.3 The squaring loop block diagram…………………………………………………….10
Figure 2.4 BPSK Costas Loop…………………………………………………………………...13
Figure 2.5 The Conceptual Diagram of carrier recovery circuit…………………………………15
Figure 2.6 Raising to the fourth power followed by PLL………………………………………..16
Figure 2.7 M th-power loop for M-ary phase shift keying ……………………………………...17
Figure 2.8 QPSK Costas loop……………………………………………………………………17
Figure 2.9 The first re-modulation approach…………………………………………………….20
Figure 2.10 The second re-modulation approach ……………………………………………….21
Figure 2.11 Carrier recovery by re-modulation in BPSK………………………………………..22
Figure 3.1 The QPSK re-modulator loop…………………………………………………………….25
Figure 4.1 QPSK constellations after carrier recovery by re-modulation ……………………………….28
Figure 4.2 The received QPSK constellation before carrier recovery………………………….. 29
Figure 4.3 QPSK constellation after the Costas loop recovery technique………………………30
Figure 4.4 QPSK constellation before carrier recovery………………………………………….31
Figure A1: Simulink Model for the QPSK re-modulator ………………………………………36
Figure A2 Simulink model for QPSK Costas loop…………………………………………… 37
vi
LIST OF ABBREVIATIONS
AWGN Additive White Gaussian Noise
BPF Band Pass Filter
BPSK Binary Phase Shift Keying
CDMA Code Division Multiple Access
FH Frequency Hopped
GPS Global Positioning Satellite
I In-phase
LPF Low Pass Filter
MPSK M-ary Phase Shift Keying
OFDM Orthogonal Frequency Division Multiplexing
PLL Phase Locked Loop
PSK Phase Shift Keying
Q Quadrature
QPSK Quadrature Phase Shift Keying
SS Spread Spectrum
VCO Voltage Controlled Oscillator
vii
ABSTRACT
An important task for a digital communications receiver is to remove any frequency and phase
offsets that might exist between the transmitter and receiver oscillators. The method of correcting
the receiver carrier oscillator frequency and phase to match that of the transmitted signal is
referred to as carrier recovery. Carrier recovery creates a reference carrier from which the in-
phase and quadrature modulated components may be determined both in frequency and phase.
. The project describes the most commonly used methods of carrier recovery at the receiver of a
digital communication system. The carrier recovery methods studied in this project included the
Squaring Loop, the Costas Loop and the Re-modulator technique. The analysis of these methods
was done based on BPSK and QPSK signals. Comparison of the performances of these carrier
recovery structures was also done.
Re-modulation is done by first demodulating the incoming signal and then recovering the
message waveform. The baseband waveform is then used to re-modulate the incoming signal.
The main objective was to design carrier recovery by re-modulation for use in the demodulation
of QPSK signals. The re- modulator for this particular application was described and its
SIMULINK model developed. The resulting findings indicated that carrier recovery by re-
modulation can be used, for demodulation of the QPSK signals. The re-modulator approach was
shown to give better performance than squaring and the Costas loop.
1
CHAPTER ONE
INTRODUCTION
1.1 Background
For digital transmission using M-ary phase shift keying (MPSK), coherent detection is essential
in order to achieve full performance potential.
Digital modulation techniques may be classified into coherent and non coherent techniques,
depending on whether the receiver is equipped with a phase recovery circuit or not. The phase
recovery circuit ensures that the oscillator supplying the locally generated carrier wave in the
receiver is synchronized in both frequency and phase to the oscillator supplying the carrier wave
used to originally modulate the incoming data stream in the transmitter.[1]
Carrier recovery is the estimation of the phase and frequency of the carrier. This means that for
coherent detection the knowledge of both frequency and phase of the carrier is necessary. A
carrier recovery system is a circuit used to estimate and compensate for frequency and phase
differences between a received signal's carrier wave and the receiver's local oscillator for the
purpose of coherent demodulation. Figure 1.1 illustrates the effect of phase/frequency error on
QPSK constellation.
Figure 1.1 The QPSK constellation affected by carrier phase/frequency offset
2
The error arises because of the receiver demodulating with a constant phase error causing a fixed
rotational offset on the received symbol constellation. If left uncorrected, the tilt will degrade the
immunity of the receiver to noise by bringing the received signal points closer to the boundaries
of the decision regions. To correct the problem, a carrier recovery system is required.
In the transmitter of a communications carrier system, a carrier wave is modulated by a baseband
signal. At the receiver, the baseband information is extracted from the incoming modulated
waveform. In an ideal communications system the carrier frequency oscillators of the transmitter
and receiver would be perfectly matched in frequency and phase thereby permitting perfect
coherent demodulation of the modulated baseband signal. However, the transmitters and
receivers rarely share the same carrier frequency oscillator. Communications receiver systems
are usually independent of transmitting systems and contain their own oscillators with frequency
and phase offsets and instabilities [1]. Doppler shift may also contribute to frequency differences
in mobile radio frequency communications systems. All these frequency and phase variations
must be estimated using information in the received signal to recover the carrier signal at the
receiver and permit coherent demodulation.
1.2 Coherent demodulation
This type of detection requires the demodulator to estimate the carrier phase of the received
signal and to use it as a phase reference in the demodulation process [4]
The principle of a coherent receiver requires perfect knowledge of the frequency and phase of
the carrier wave. This is not available because of various fluctuations on the transmission link.
The receivers thus have a carrier recovery device allowing the frequency and phase of the
transmitted carrier to be estimated. The device is built around a PLL.
The assumption of coherence which requires perfect synchronization between the modulation
rate and the carrier frequency is however only rarely satisfied in radio transmission. A coherent
demodulator has to provide a synchronization function. Coherent demodulation requires the use
of a carrier on reception of the type cos (ωct+Фo) in phase with the transmission carrier.
Oscillator stability is imperfect. The receiver frequency has therefore to be locked to the
transmitter frequency. Perfect tuning is not possible, due to noise on the transmission channel.
3
Theoretical coherent demodulation is hard to achieve in practice. The reception carrier will be
produced from the pilot carrier or from the modulated signal. In most cases it is possible to
recover carrier at the cost of a negligible degradation in performance thus coming close to the
theoretical performance levels of coherent demodulation. The baseband part of the coherent
receiver include sampling meaning the transmission clock needs to be recovered assuming the
clock is perfect and free of jitter.
In some cases it may not be possible to extract a good phase estimate from the received signal.
For example if propagation delay varies with time, the oscillators in the modulator and
demodulator may not be sufficiently stable to guarantee a relatively fixed carrier phase over the
signaling intervals. Under this circumstance it is still possible to transmit digital information by
PSK and to demodulate it at the receiver if the information is encoded in to phase differences
between two successive signaling intervals; the resulting signal waveform from the modulator is
the differentially encoded PSK (DPSK)
1.3 Carrier Synchronization
Carrier synchronization in coherent MPSK receivers deals with the cancellation of the carrier
phase error provided by the phase detector. Most synchronization techniques are based on the
phase locked loop (PLL).
The carrier synchronization parameters include carrier frequency offset and carrier phase offset.
Carrier frequency offset is mainly caused by two mechanisms – the frequency instability in either
the transmitter or receiver oscillator, and the Doppler Effect when the receiver is in motion
relative to the transmitter. Carrier phase offset occur as a result of three major components in this
application, namely: the phase instability in oscillators, thermal noise such as AWGN and the
phase due to transmission delay.[1]
Carrier recovery occurs in two subsequent phases of acquisition and steady-state tracking. At the
start of signal reception, the synchronizer has no knowledge about the synchronization parameter
values. After some processing of the received signal, the synchronizer is able to deliver accurate
4
estimates of the synchronization parameters which are needed for reliable data detection. This
transition from a large initial uncertainty about the synchronization parameters to a small steady-
state estimation error variance is called carrier acquisition.
The second process is carrier tracking, which arises because the fluctuation of the
synchronization parameters over the burst cannot be ignored, because the frequency offset
estimated in the acquisition process is not perfectly accurate, and the residual frequency error
will accumulate phase error with time and cause a loss of phase synchronization. It leads to
severe problem in symbol detection. The carrier recovery system must make several estimates
per burst so that the variations of the carrier phase over the burst can be tracked.[8]
The PSK digital modulation scheme is widely used in modern communication especially in
satellite communications where M-ary PSK techniques are used for their bandwidth efficiency.
PSK is often used as it provides a highly bandwidth efficient modulation scheme.
The use of phase shift keying (PSK) has become a very popular method for digital signaling
because it represents a well-balanced trade off between energy and bandwidth efficiency.
Receivers for digital PSK expect to receive a signal of constant magnitude. This simplifies the
analysis of the signal and the design of appropriate receiver structures. The information
contained in a received PSK signal is, by definition, embedded either in the absolute or relative
phase of the received signal. Digital phase modulation results when all the binary digits from
information sequence {an} are mapped in to discrete phases of the carrier.
An M-shift keyed PSK (MPSK) signal is generated by mapping a block of k=log2M binary digits
of the sequence {an} in to one of the M corresponding phases of
ϴ=2π(m-1)/M, for i=1,2,…M.
The M-PSK signal is expressed as
sm(t)=Re{u(t)ejϴej2πft}
=u(t)cos[2πfct+ (m-1)] for m=1,2,…M
5
1.4 Project Objectives
The objectives of the project were to:
1. Study carrier recovery in digital communication systems and in particular those based on
QPSK and BPSK signals.
2. Compare the performance of re-modulation and Costas-based carrier recovery methods for
both BPSK and QPSK
3. Design and demonstrate a carrier recovery system by re-modulation for use in QPSK
demodulation.
1.5 Report organization
This chapter gives the introduction to carrier recovery. Chapter two describes the carrier
recovery methods particularly those based on BPSK and QPSK signals. Comparison of re-
modulator and Costas loop techniques has also being discussed in this chapter. Chapter three
describes the QPSK re-modulator receiver and its analysis. Chapter four provides illustration and
analysis of the results obtained by simulation while chapter five presents the conclusion and
suggestions made for future work. A list of references as well as appendix has been provided at
end of .the end of the project report.
6
2 CHAPTER TWO
CARRIER RECOVERY TECHNIQUES
2.1 Overview
In coherent demodulation process carrier recovery is a very important function. The carrier
recovery loop is needed because the carrier is suppressed in a digitally modulated spread
spectrum signal. In order to remove the carrier coherently, a carrier recovery tracking loop is
used to recover the carrier. This recovered carrier is use to remove the signal carrier. For a
carrier signal containing a dominant carrier spectral line, carrier recovery can be accomplished
with a simple band-pass filter at the carrier frequency and a phase-locked loop.
However, many modulation schemes make this simple approach impractical because most
signal power is devoted to modulation where the information is present and not to the carrier
frequency. Greater transmitter efficiency is achieved by reducing the carrier power. Different
methods must be employed to recover the carrier in these conditions.
The use of properly phased carrier is a requirement for coherent demodulation at the receiver.
There are a number of ways by which a carrier of proper phase and frequency may be generated
from the received signal depending on the type of modulation [5].
Some signals have carrier or other steady frequency component which may be filtered to provide
phase reference either directly or by use of PLL. In most cases however some form of non-linear
processing is required to get reference to maintain carrier phase. For BPSK a squaring circuit or
a Costas loop equivalent may be used. For QPSK, a fourth order circuit or higher order Costas
loop may be used. Another technique sometimes used is decision aided feedback where the
demodulated output is used to control re-modulation of the incoming signal stream eliminating
modulation to provide a reference carrier [3].
7
2.2 Phase locked loop (PLL)
The basic structure of a PLL used for synchronization is illustrated by figure 2.2-1
The PLL consists of mainly three modules namely: phase detector, low-pass filter, and a voltage-
controlled oscillator (VCO). These are connected to form a closed loop frequency feedback
control system. The feedback control system controls the phase of the VCO. [4]
Figure 2.1 The PLL
The output of the loop filter provides the control voltage vc (t) for the VCO.
The VCO is basically a sinusoidal signal generator having an output of the form
sin (4πfct +K∫ 푣(휏)푑휏∞ ) (2.1)
the loop filter is selected to have the following transfer function
H(s) = (2.2)
Where 휶 and 휷 are the design parameters controlling the bandwidth of the loop.
Let the input to the loop be sin (4πfct+2Ф) and let the output of the VCO be cos (4πfct+2Ф)
where Ф represents an estimate of the phase . The product of the signals generate an error signal
e(t)=cos(4πfct+2Ф) sin(4πfct+2Ф) (2.3)
LOOP FILTER
VCO PHASE DETECTOR
Input Output
8
= sin 2(Ф-Ф)+ sin(8πfct+2(Ф- Ф)) (2.4)
The loop filter is a low-pass filter and hence the high frequency component is eliminated leaving
only sin 2(Ф-Ф)
when Ф is close to Ф then
sin 2(Ф-Ф)≈ Ф-Ф (2.5)
By definition
2Ф= K∫ 푣(휏)푑휏∞ ) (2.6)
The PLL equivalent model can be approximated as
2 Ф
v(t)
2 Ф
Figure 2.2 Model of the PLL
The PLL is a key component of a carrier recovery loop as it enables the receiver to adaptively
track and remove the phase or frequency offsets. The purpose of the loop filter is to filter the
phase error signal in order to provide a control signal to the VCO. The error signal generated by
the phase detector is actually a noisy estimate of the phase error, i.e. the error signal consists of
an error term and a noise term.
ퟏퟐ sin2(Ф-Ф)
LOOP FILTER H(S)
K/s
9
The loop filter processes the phase error signal in order to generate a useful error while
suppressing the effect of the noise as much as possible. The values of the gain parameters chosen
for the loop filter control the loop bandwidth of the PLL. The size of the loop bandwidth
determines the range of error signal frequencies that the loop filter will pass.
The value for this bandwidth has a direct impact on the performance of the PLL. If the value of
the loop bandwidth is large, the loop filter can pass a wide range of frequencies for the error
signal. A wide loop bandwidth will thus allow the PLL to track large frequency errors. However,
it will also pass a wider portion of the noise spectrum. The end result is a noisy control signal for
the VCO translating into a phase jitter on the locally generated signal. In contrast, a small value
for the loop bandwidth will limit the amount of noise that passes through the filter. The narrow
loop bandwidth will result in a better control signal for the VCO. However, the drawback of
using a narrow loop bandwidth is that the range of frequencies that the PLL can track is reduced
as well.[1]
2.3 Carrier recovery in BPSK
Binary Phase Shift Keying (BPSK) is one of the simplest digital modulation schemes. BPSK
systems employ a conventional Phase-Locked Loop (PLL) carrier recovery circuit in the
receiver. The modulated input is first squared by the circuit to remove the phase transitions, and
then the resulting signal is used as a reference for its Voltage Controlled Oscillator (VCO). The
frequency of the output is then divided by two to produce a carrier.
The three basic methods for BPSK carrier recovery are:
1) Squaring loop
2) Costas loop;
3) BPSK re-modulator
10
2.3.1 The squaring loop
One of the methods of generating a carrier from the received signal is to square the signal to
generate a frequency component at 2fc which can be used to drive a PLL tuned to 2fc.This is
illustrated below
s2(t) =m2(t)cos2(ωct+Ф)
= m2 (t) + m2 (t) cos (2ωct+2Ф) (2.7)
The double frequency component is the desired term since it contains a spectral line at 2fc. This
component is selected by a BPF tuned to 2fc where its output is used to drive a PLL.[5] The PLL
basically comprises a multiplier, a loop filter and a VCO. Let the input to the loop filter be
cos(2ωct+2Ф) and the output of the VCO be sin(2ωct+2Ф) where Ф represents the phase
estimate. The error signal is generated by the product of the two signals
e(t)= cos(2ωct+2Ф) sin(2ωct+2Ф)
= sin 2(Ф− Ф) + sin (4ωct+2Ф+Ф) (2.8)
The first technique relies on the fact that, because the BPSK modulation causes ±180° phase
transitions, its second harmonic will be phase-modulated by an ambiguous ±360°. The second
harmonic is an un-modulated carrier at twice the frequency. Dividing this second harmonic of
the carrier by two will result in a theoretically phase-coherent carrier.
Figure 2.3 The squaring loop block diagram
Output carrier reference
s(t) ( ) 2
BPF at 2fc
LOOP FILTER
÷ 2 VCO
BPF at fc
11
The input signal s (t) is expressed as
r (t)=x(t)+n(t) (2.9)
with x(t) being the transmitted signal and n(t) the AWGN with two-sided spectral density NO/2
For binary phase shift keyed (BPSK) system, the squaring of the signal
r(t) =m(t) sin(ωct+θo)+n(t) (2.10)
With noise n(t) and frequency θ0 results in frequency doubling and higher order noise terms.
The second order PLL following the squaring device tracks the 2nd harmonic term by driving the
VCO with control signal so that the difference between the VCO output frequency/phase and
input carrier component frequency phase is near minimum. The control signal is the average
error voltage from the phase detector (PD) output which gives a measure of phase and frequency
mismatch between the VCO output signal and the input signal. [8]
From control theory and negative feedback nature of phase locked loops, the overall closed loop
gain transfer function yields a low pass filter characteristic with 3 dB bandwidth corresponding
to the closed-loop natural bandwidth. A frequency divider-by-2 is inserted following the VCO
output to recover the original carrier frequency.
The advantage of the squaring-then divide circuit is that it is mathematically simple to analyze.
However, in practice, controlling the phase offset will be complicated and layout dependent; the
recovered carrier takes a different path from the demodulator path, and this creates a time
differential that will result in a phase error. Also, several filters are required, making it difficult
to maintain proper phase over the range of operating frequencies.
2.3.2 Costas Loop
An alternative circuit by which the carrier of BPSK or QPSK received signal may be recovered
is the Costas loop. This method of carrier recovery was developed by Costas. The Costas loop is
a phase-locked loop used for carrier phase recovery from suppressed-carrier modulation signals,
such as from double-sideband suppressed carrier signals. [1]
12
The Costas loop is commonly used for coherent carrier recovery from a received modulated
signal. The Costas loop should be able to acquire phase lock from a relatively small initial
frequency error. However, the pull-in time is expected to increase rapidly with the initial
frequency error, particularly as the signal-to-noise ratio in the loop approaches threshold.
Furthermore, the similarity to a phase-locked loop tends to break down for larger initial
frequency errors, in the sense that Costas loop acquisition can fail due to a tendency to false lock
to a data sideband, with the VCO frequency offset by half the data rate.
The tendency of a Costas loop to false lock, especially at a high loop signal-to-noise ratio can
also reduce the attempt to achieve acquisition by sweeping the VCO frequency over the range of
frequency uncertainty, since the offset frequency is reached before the correct frequency. While
the squaring method is a feed-forward technique, the Costas loop relies on feedback concepts
related to the Phase Locked Loop (PLL). The Costas loop offers an inherent ability to self-
correct the phase (and frequency) of the recovered carrier and, in the end; its implementation is
less complicated than the first technique. Its main disadvantage is involvement of a loop settling
time. The primary application of Costas loops is in wireless receivers. Its advantage over the
PLL-based detectors is that at small deviations in the error voltage the sensitivity of the Costas
loop is doubled making the Costas loop uniquely suited for tracking Doppler-shifted carriers
especially in OFDM and GPS receivers. [1]
Principle and the description of the Costas loop
The Costas loop that is suitable for BPSK demodulation is shown in the Figure 2.4. The system
involves two parallel tracking loops operating simultaneously from the same VCO. The first
loop, called the in-phase loop (or I arm), uses the VCO as in a PLL (Phase Locked Loop), and
the second, called the quadrature loop (or Q arm) uses a 90 degree shifted VCO. The I and Q
multiplier outputs are filtered by single pole Butterworth low pass filters. The I and Q arm filter
outputs are then multiplied together and the product is filtered to produce the loop error used to
control the VCO. The loop error should settle to a value when the loop is locked. A negative loop
error decreases the VCO increment resulting in a lower VCO frequency, and similarly, a positive
loop error increases the VCO increment resulting in a higher VCO frequency. The low pass
filters in each arm must be wide enough to pass the data modulation without distortion.
13
In-phase
Output
r(t)
Quadrature
Output
Figure 2.4 BPSK Costas Loop
The input to the Costas loop is the waveform expressed as
r (t) = (m(t)×sin (ωct + Ф (t)) + n(t) (2.11)
This incoming signal is multiplied by cos (ωct+Ф) in one channel and sin (ωct+Ф) in the other
channel to generate a coherent phase reference from suppressed carrier signal.[4]
where m(t) is the BPSK modulated signal and n(t) is the AWGN noise. The in-phase multiplier
generates
I(t) = m(t)× cosψe + nmc(t) (2.12)
while the quadrature multiplier generates
Q(t) = m(t) ×sinψe + nms(t) (2.13)
where the noise components nmc(t) and nms(t) are low pass demodulated noise processes in the
carrier noise n(t). The output of the multiplier is then:
I(t) Q(t) = m2(t) ×sin(2ψe)/ 2 + nsq(t) (2.13)
LPF
VCO
900
LPF
LOOP FILTER
14
where nsq(t) represents all the signal and noise cross-products. The multiplier of the Costas loop
can be thought of as allowing the bit polarity of the in-phase loop to correct the phase error
orientation of the tracking loop, thereby removing the modulation.[8]
The Costas loop is usually preferred over the squaring loop for PSK coherent detection because
of greater tolerance to shift in the carrier frequency and capability of wider bandwidth
operation.[5]
2.4 Carrier Recovery in QPSK
QPSK modulation is represented by shifts of 90o in the phase of the carrier. Quadrature phase
shift keying is a bandwidth conservation modulation scheme that uses four points on the
constellation diagram, equally spaced around a circle. With four phases, QPSK can encode two
bits per symbol, with Gray coding to minimize the bit error rate (BER) — twice the rate of
BPSK. Analysis shows that this may be used either to double the data rate compared to a BPSK
system while maintaining the bandwidth of the signal or to maintain the data-rate of BPSK but
halve the bandwidth needed.
The suppressed carrier signal of QPSK is recovered by frequency multiplication technique,
which regenerates the carrier signal and removes the modulation signal. The conceptual diagram
for QPSK carrier recovery circuit is shown in Fig. 2.5. The input band-pass filter at carrier
recovery circuit rejects the outside interference signal and spurious signal of band-pass signal.
The bandwidth of the filter depends on transmission data rate. The output band-pass filter of
fourth harmonic generating circuit is a narrow band-pass filter that is used to obtain the high
signal-to-noise ratio.
15
4th Harmonic Generating Circuit
Tracking filter
Figure 2.5 The Conceptual Diagram of carrier recovery circuit
Within the carrier recovery circuit, the fourth-law regenerator enhances the additive white
Gaussian noise and phase noise power by a factor of 16. The white Gaussian noise component is
further enhanced due to inter-modulation, which generates a quadrupling loss.
In most practical applications, efficient modulation techniques suppress the carrier completely as
this discrete carrier component (although useful as a tracking aid in coherent demodulation)
wastes transmitted energy. Since information is stored in sidebands, a narrow band phase locked
loop (PLL) is not capable of locking to any significant discrete component without the
undesirable effect of frequency and phase drift at the voltage controlled oscillator (VCO) output.
However, suitable nonlinear clock regenerators are combined with PLL to provide suitable
means for carrier recovery. The three basic types of carrier synchronizers used are: the Squaring
loop, the Costas loop and the Re-modulator.
BPFi
Hi(jω)
Frequency
Multiplier
(.)4
Frequency
Divider
/M
BPFL
H(jω)
Phase
Tracking
Circuit
16
2.4.1 Carrier recovery by raising to the fourth power followed by PLL
The Principle and description of the circuit
Input signal
Output
Carrier reference
Figure 2.6 Raising to the fourth power followed by PLL
When the signal is raised to the fourth power a line can be obtained at frequency 4fc.
Let s(t) be modulated signal, filtered by the receive filter, without thermal noise, and s(t) be its
baseband equivalent. Raising the signal s(t) to the fourth power, and retaining only frequencies
around 4fc, gives the signal :
s4(t)= Re[s4(t)e4jωt]. (2.14)
The corresponding error recovery circuit, with a phase locked loop, used for QPSK modulated
signals, is similar to the circuit considered for BPSK modulated signals. Squaring is replaced by
raising to the fourth power in order to eliminate the quaternary phase modulation and the loop
operates at frequency 4fc . The frequency of the signal produced by the loop is divided by 4 in
order to give the recovered carrier frequency fc..
For improved phase noise performance on the carrier recovery output, it is desirable to make the
loop bandwidth as small as possible before the VCO noise becomes dominant. However, at the
same time, a narrow bandwidth loop implies longer synchronization time and reduces capture
range due to multiple phase slipping. Thus a compromise must be reached for loop parameters
such as loop bandwidth, loop damping factor, phase noise, capture range and settling time.
Additionally associated to the squaring device is a squaring loss which must be minimized in
BPF at fo ()M
DIVIDE by M
VCO
LOOP FILTER
BPF at Mfo
BPF at fo ( ) 4
DIVIDE by 4
VCO
LOOP FILTER
BPF at 4fc
BPF at fc
17
order to achieve maximum signal to noise ratio. This is done using a pre-squaring filter. For any
M-PSK signal the general carrier recovery loop is given by figure 2.7.
Input signal
Output
Carrier reference
Figure 2.7 M th-power loops for M-ary phase shift keying
2.4.2 QPSK Costas loop
The structure of QPSK Costas loop is similar to that of BPSK case. The difference is in the way
the error voltage is generated.
Figure 2.8 QPSK Costas loop
BPF at fo ()M
DIVIDE by M
VCO
LOOP FILTER
BPF at Mfo
BPF at fo ()M
FREQ. ÷ M
VCO
LOOP FILTER
BPF at Mfo
BPF at fo
LPF
휋2
xs(t) LPF
−
VCO LOOP FILTER
SAMPLING DECISION
SAMPLING DECISION
Output sequence
LPF
x(t)
xc(t)
18
Demodulation is carried out with carrier recovery. Sampling of signals xc(t) and xs(t) provides
the demodulated sequences.
The received signal is a QPSK modulated signal with noise expressed as
x(t)=A(t)cos(ωct+ϴ(t))−B(t)sin(ωct+ϴ(t))+n(t) (2.16)
The phase error is defined by
Ф(t)=ϴo(t)−ϴ(t) where ϴo(t) is the recovered carrier phase.
xc(t)= (A(t)+nc(t))cosФ(t)−
(B(t)+ns(t))sinФ(t) (2.17)
xs(t)= (A(t)+nc(t))sinФ(t)+ (B(t)+ns(t))cosФ(t) (2.18)
The error voltage is generated as
ve(t)=xc(t)xs(t)(x2c(t)−x2
s(t)) (2.19)
The error voltage is given as
ve(t)= {[ 2[(A(t)+nc(t))2−(B(t)+ns(t))2]–(A(t)+nc(t))2(B(t)+ns(t))2]×sin4Ф(t)+
[A(t)+nc(t))2−(B(t)+ns(t))2]× (A(t)+nc(t))2(B(t)+ns(t)) cos4Ф(t)]} (2.20)
.The phase error is a function of 4 Ф (t). = 4 ϴo(t)- 4 ϴ(t) and modulation has therefore been
eliminated from this expression.[2]
The coefficient of the term in cos 4Ф (t) is low. It can even be zero in the absence of noise.
Minimization of the error voltage therefore requires minimization of the term sin 4Ф (t).
In the absence of noise with an unfiltered signal of amplitude A the error voltage is expressed as
ve(t) = sin4Ф(t) (2.21)
19
The characteristic of the equivalent phase detector is
f(Ф)=sin 4Ф (2.22)
The system has four stable and four unstable equilibrium points.
There is a fourth order ambiguity on the phase of the recovered carrier which is only defined to
within a multiple of 90o [2]
2.5 Carrier recovery by re-modulation
The re-modulator is a decision feedback approach where the carrier is recovered through a
combination of a PLL, modulator (or re-modulator) and demodulator. The basic operation is the
multiplication of the input signal by its demodulated baseband to retrieve the carrier. Similar to
the squaring loop, the re-modulator technique exhibits performance limitation in high speed
acquisition /synchronization. The inherited limitations are from loop dynamic action [2].
The underlying principle of re-modulation as a method of carrier recovery is to eliminate the
modulation of the received signal using the demodulated signal.
The two possible approaches include:
1. Modulation, by the demodulated signal, of a pure carrier produced by a voltage
controlled oscillator and comparison of the signal obtained in this way with the received
signal. This comparison provides an error voltage allowing the oscillator frequency to be
corrected. The method can be used for the case of BPSK modulation.
2. Re-modulation of the received signal by the demodulated signal. This operation
eliminates the modulation and provides an un-modulated carrier that can be filtered by a
filter or by a PLL. This method can be applied for the case of QPSK modulation.
The carrier is recovered through a combination of a phase locked loop, a re-modulator and a
demodulator. The basic operation is the multiplication of the input signal by its demodulated
20
baseband to retrieve the carrier. Since demodulation requires some form of carrier recovery, the
re-modulator approach inherently includes a PLL in the feedback path.
The first re-modulation approach allows demodulation of incoming signals and recovery of the
carrier signal In Figure. 2.9, the incoming signal is demodulated and the message waveform is
recovered. This baseband waveform is used to re-modulate the incoming signal; if the
waveforms are rectangular and time aligned, the re-modulation procedure removes the
modulation completely. The output of the balanced modulator has a pure carrier component at
the input frequency and the PLL tracks the component. The re-modulator is stochastically
equivalent to the polarity loop, that is, the hard-limited Costas loop.[6] The re-modulator,
however, is typically implemented at low frequencies and cannot be used for multiple data rates
due to time delays which affect the realization of a wide-band synchronizer.
Figure 2.9 The first re-modulation approach
Figure 2.10 illustrates another version of the re-modulator loop that imposes the recovered
message modulation on the VCO output so that both inputs to the phase detector are identically
modulated. The low-frequency product of two such waveforms results in a DC component of the
same amplitude as if the inputs had no modulation. This version of the re-modulation technique
can also be applied for QPSK carrier recovery and data extraction. Although stochastically
VCO
LPF
Td Delay
휋2
LPF
Input Output data
21
equivalent, the QPSK re-modulator loop has been shown to exhibit faster acquisition time when
compared to the conventional QPSK Costas loop. [7]
Figure 2.10 The second re-modulator approach
.
Input
VCO
LPF
Td Delay
휋2
LPF
Output data
22
2.5.1 BPSK carrier recovery by re modulation
The structure for carrier recovery by re modulation for BPSK modulation is illustrated by figure 2.11
y(t)
vc(t)
ve(t)
Figure 2.11 Carrier recovery by re-modulation in BPSK
The low pass component of the error voltage is given by:
ve(t)= [(A(t)+nc(t))cos Ф(t)−ns(t)sin Ф(t)]×[(A(t)+nc(t))sin Ф(t)−ns(t)cos Ф(t)]
= [[ A(t)+nc(t))2−ns2(t)]sin 2Ф(t)+2A(t)+nc(t))ns(t)cos 2Ф(t)] (2.23)
The expression obtained is comparable to that obtained for the carrier recovery system by
squaring loop and also for BPSK Costas loop. There is a second order ambiguity on the phase of
the recovered carrier. The phase ambiguity in the recovered carrier is not due to a defect in
VCO
LOOP FILTER
LPF
휋2
LPF
휋2
VCO
LOOP FILTER
LPF
Received Signal x (t)
Demodulated output sequence
23
carrier recovery circuit but is intrinsically associated with the nature of the modulated signal
itself [2]
2.5.2 Advantages of carrier recovery by re-modulation
The re-modulator has a better tracking capability than the squaring loop. Unlike the re-modulator
approach, the PLL in the Squaring loop must be able to track twice the amount of root mean
square jitters due to the phase magnification effect in the frequency doubler.[6]
2.5.3 Disadvantages of carrier recovery by re-modulation
Carrier recovery by re-modulation requires precise delay matching in the re-modulator path due
to the low pass filter group delay.
2.6 Comparison of the Carrier Recovery methods
Table 2.1 Carrier recovery methods, advantages and disadvantages [6]
Recovery
Method
Advantages Disadvantages
Squaring
Loop
Easy to implement. The Loop offsets cause phase
offset on the recovered carrier.
It has limited acquisition time due
to loop bandwidth.
Requires extra SNR at input due
to doubled RMS jitter.
It is prone to false lock.
Costas Loop Better performance than the
Squaring loop.
The Costas loop is easy to
implement
Limited acquisition time due to
loop bandwidth
The In-phase and Quadrature
arm must be matched carefully.
24
.
.
Re-
modulator
It has better tracking
capability than Squaring
loop.
It has a faster acquisition
time than the Costas loop.
Requires precise delay matching
in the re-modulator path due to
the low-pass filter group delay.
Its acquisition time is limited due
to loop bandwidth.
25
3 CHAPTER THREE 3.1 SYSTEM DESIGN
3.1 The overall carrier recovery system block diagram
The structure for carrier recovery by re-modulation for QPSK is illustrated in figure 3.1
n(t)
s(t) x’(t)
x(t) xc(t)
yc(t)
xs(t) ys(t)
y(t)
vc(t) ve(t)
cos(ωot+ϴo)
Figure 3.1 The QPSK re-modulator loop
sin(ωot+ϴo)
VCO
LPF
LOOP FILTER
π/2
LIMITER
π/2
LPF LIMITER
26
3.2 Description of the QPSK re-modulator
The QPSK signal plus noise is sent to the two multipliers of the upper branch (in-phase) and the
lower branch (quadrature) respectively. The in-phase branch multiplies the input signal by the
output of the VCO while the quadrature branch multiplies the input signal by the output of the
VCO after a phase shift. The output of the multipliers of the in-phase and the quadrature
branches are then passed through low-pass filters to eliminate high frequency components of the
signal and then passed through the limiters.
The error signal is filtered by the loop filer whose output is the control voltage which controls
the phase and frequency of VCO.
If the QPSK modulated signal is perturbed by a white Gaussian noise n (t) of spectral density
NO/2 then the received signal is given by :
x(t)=s(t)+n(t) (3.1)
x(t)= Acos(ωct+ϴ)−Bsin(ωct+ϴ)+n(t) (3.2)
Multiplication of the received signal by the recovered carrier and low-pass filtering gives the in-
phase component
xc(t)= 1 2[(A(t)+nc(t))cosФ(t)−(B(t)+ns(t))sinФ(t)] (3.3)
and the quadrature component expressed as
xs(t)= 2[(A(t)+nc(t))sinФ(t)+(B(t)+ns(t)cosФ(t)] (3.4)
A phase shift of 2 in the received signal x (t) gives
x’(t)= (A(t)+nc(t))sin(ωct+ϴ)−(B(t)+ns(t))cos(ωct+ϴ) (3.5)
Re-modulation results in:
yc(t)=x’(t)sgn(xc(t)), (3.6)
ys(t)=x(t)sgn(xs(t)) (3.7)
27
The multiplier mixes the incoming QPSK signal plus noise and the recovered carrier signal
leaving only the message signal after the multipliers.
If the incoming QPSK signal and the regenerated QPSK signal are identical then the loop
continuously locks. To extract the low frequency QPSK message signal from the multiplier, a
low-pass filter is used to reduce power consumption and the number of external discrete
components required.
The re-modulation process occurs at the multipliers and the result is re-fed in to the PLL phase
detector. The PLL tracks the frequency with the phase and outputs the same frequency but
different phase. The difference in the phase is due to controlled offsets in the system including
PLL offsets.
28
4 CHAPTER FOUR
SIMULATION RESULTS AND ANALYSIS
The SIMULINK model of the re-modulator and the Costas lop were established and the
theoretical simulation obtained. The loop parameters were set according to the models.
4.1 QPSK Re-modulator output
Figure 4.1 gives the QPSK constellation observed after carrier recovery by re-modulation
Figure 4.1 QPSK constellations after carrier recovery by re-modulation
29
The QPSK constellation at the receiver in before carrier recovery was as shown in Figure 4.1
Figure 4.2 The received QPSK constellation before carrier recovery.
The phase difference between the input and the regenerated QPSK signal a the receiver is 0.
Figure 4.1, shows that there is no carrier phase/ frequency offsets in the constellation at the re-
modulator output since the carrier recovery circuit has already corrected any carrier offsets .
The simulation results show that the re-modulation approach can be used to achieve
synchronization for demodulation of QPSK signals.
30
4.2 QPSK Costas loop output
The QPSK signal recovered using the Costas loop was as illustrated by Figure 4.3
Figure 4.3 QPSK constellation after the Costas loop recovery technique
31
Figure 4.4 QPSK constellation before carrier recovery
The symbol points in the output constellation after carrier recovery by Costas loop are more scattered around their positions showing that they are more affected by noise. This shows that the Costas loop under these conditions produces a noisier signal than that of the re-modulator.
32
4.3 Comparison of the re-modulator and Costas loop
By analyzing the scatter plots after carrier recovery it can be noticed that the two schemes
recover the frequency and phase offsets which allow the received symbols to recover their initial
positions. From the scatter plots obtained it can be seen that the performance of the QPSK re-
modulator is better than the Costas loop method. The received symbols by the Costas loop
method are more scattered around the ideal symbol position implying that noise still affects each
received symbol. However for the case of the re-modulator the symbols are more concentrated
around their ideal positions hence better performance.
33
CHAPTER FIVE
CONCLUSION AND RECOMMENDATIONS
Carrier recovery methods studied in this project included the squaring loop, the Costas loop and
the re-modulator. These techniques were studied based on BPSK and QPSK signals. Comparison
of the performances of these loops was also done. In this project a carrier recovery system by re-
modulation was presented and its SIMULINK model developed. It was shown that the re-
modulation approach of carrier recovery could be used in the demodulation of QPSK signals.
From the constellation results, it was observed that carrier recovery by re-modulation gives better
performance than the Costas loop method.
Further work can be done to look into how carrier recovery by re-modulation can be applied in
transmission systems such as spread spectrum (SS), TDMA, CDMA, and frequency hopped (FH)
for fast synchronization. Differential encoding of the QPSK signal can also be done and its
results compared with the re-modulation technique.
34
REFERENCES [1]. Spilker James. J, Jr., Digital communications by satellite 1977 by Prentice Hall
Inc.Englewood Cliffs, New Jersey.
[2] Bic J.C.,.Duponteil D., Imbeaux J.C Elements of digital communication John Wiley & Sons
,1991
[3]Ulrich L. Rhode and T.T.N. Bucher Communication Receivers Principles and Design
Mc Graw- Hill Company©1988.
[4] Proakis, J. Digital Communications, 3rd edition © 1995. McGraw-Hill Inc.
[5].Smith.R.David. Digital Transmission Systems © 1985 New York, Van Nostrand Reinhold
[6] Kamilo Feher, and Gary L. Do “An Ultra First Carrier Recovery versus Traditional
Synchronizers,” IEEE Transactions on Broadcasting, Vo. No. 42, Issue No. 1, March 1996 pp.
49.
[7] Glover, I.; Grant, P. Digital Communications, 2nd edition, © 2004 Pearson Education Ltd.
[8]. Lindsey W.’ C. and Simon M. K, Telecommunication Systems Engineering. © 1973
Englewood Cliffs, NJ: Prentice-Hall
[9] Haykin Simon, Communication Systems, 4th edition, © 2001, John Wiley and Sons, Inc.
printed by Hamilton Printing Company, New York, United States of America.
[10] C.L. Weber, "Demod-Remod Coherent Tracking Receiver for QPSK and SQPSK," IEEE
Transactions on Communications, Vol. No-28, Issue No. 12, December 1980 pp. 1952-1954.
[11] Andy D. Kucar and Kamila Feher, “Performance of Multi-level modulation systems in the
presence of phase noise,” International Conference Communication. Proc., vol. I , June 1985, pp.
511-514.
35
[12] J. Mark Steber, "PSK Demodulation Techniques Provide Lowest Probability of
Error," Microwave Systems News, June 1984 pp. 150-176.
[13] Y. W, Kim and J. H. Jo, “Phase noise allocation for digital satellite broadcasting system,”
/EEE Trans. Consumer Electronics, vol. 43, no. 3, 1997, pp 308-314.
[14] Yamamoto H, Hirade K, and Watanabe Y, "Carrier Synchronizer for Coherent Detection of
High-Speed Four-Phase-Shift-Keyed Signals," IEEE Transactions on Communications, Vol.
COM-20, No. 4, August 1972, pp. 803-807.
[15] A. G. Burr, “Comparison of coherent and non-coherent modulation in the presence of phase
noise,” ZEE Proceedings-1, vol. 139, no. 2, January 1992, pp. 147-155.
36
5 APPENDIX Simulink model for QPSK re-modulation
Figure A1: Simulink Model for the QPSK re-modulator
CARRIER RECOVERY BY RE-MODULATION
PLL
scope2
scope1
Summer
Sign 2
Sign 1
Real to complex 2
Out1
Random IntegerGenerator
RandomInteger
QPSKModulatorBaseband
QPSK
PhaseShifter
In
Ph
ComplexPhase Shift
PD
MUX4MUX 3
MUX 2
MUX 1
LoopFilter
FDATool
LPF2
Lowpass
LPF 1
Lowpass
Constant 1
pi /2
Constant
pi /2
Complex to real 2
In 1Out1
Complex to real 1
In1Out 1
Complex to real
In 1Out1
AWGNChannel
AWGN
Phase Shifter
In
Ph
ComplexPhase Shift
VCO
Discrete -TimeVCO
37
Figure A2 Simulink model for QPSK Costas loop
QPSK COSTAS LOOP
constant pi /2
Summer
Sign 1
Sign
Real -Imag toComplex 2
ReIm
Real -Imag toComplex
ReIm
Random IntegerGeneratorRandom
Integer
QPSKModulatorBaseband
QPSK
Product 2
Product 1
Product
PhaseShifter
In Ph
ComplexPhase Shift
Output Scope
LPF5
Lowpass
LPF 2
Lowpass
LPF 1
Lowpass
L00P FILTER
LowpassInput Scope
Complex toReal -Imag 1
ReIm
Complex toReal -Imag
ReIm
AWGNChannel
AWGN
VCO1
Discrete -TimeVCO
VCO
Discrete -TimeVCO
