27

CHAPTER 2

QPSK VARIANT IDENTIFICATION USING BLIND AMR

2. 1 INTRODUCTION

Implementation of advanced information services and systems in

a crowded electromagnetic spectrum is a challenging task for

communication engineers. A spectrum of these signals may range from high

frequency (HF) to millimeter frequency band, and their format can vary

from simple narrowband to wideband scheme. Advanced signal processing

techniques are required for real time signal interception and processing

which are vital for decisions involving operations and tactical actions.

The existence of incompatible wireless standards in different

countries often inhibit deployment of global roaming facilities and

problems in rolling out new service features due to widespread presence of

legacy subscriber handset. The need for ability of radio to operate with all

standards in different geographical regions of the world has fostered the

growth of Software Defined Radio (SDR) concept. SDR technology

promises to solve these problems by implementing the radio functions as

software modules running on generic platform.

The advent of realizable SDR allows implementation of creative

transceiver designs which can dynamically adapt to communication channel

and user application. Instead of dedicated hardware designed to carry out a

rigid set of objectives, software implementation of hardware devices are

entirely flexible regarding their functionality. Supplementary information

28

transmitted is used to reconfigure SDR systems. An ideal use of this

flexible architecture is in the area of wireless networks where a node may

adapt to its environment and user objectives.

Wireless communication system in future will no longer be static

as each individual node in the network will have to acquire a dynamic route

to the intended destination. This dynamic network such as this is not

feasible with existing fixed architecture radio systems. SDR has been a

focal point to cope with the diversification of communication systems. SDR

implementation becomes preferable in maximally flexible systems. One

major advantage resulting from SDR terminal deployment is that, as

network topology changes the terminal can adapt to user requirements,

change the mode of operation, channels and access methods and request

new software upgrades if required without user intervention.

In SDR data communication parameters such as modulation

schemes, bandwidth can be selected on a per packet basis in response to

user constraint such as data rate. This leads to a significant improvement in

bandwidth used and power consumption and minimizing the need for

hardware as in Bose et al (2001). Since a single SDR system robustly

handles multiple modulations, modulation recognition is an important issue

for such system.

The key factor in SDR is the reconfigurable blocks that allow

easy changes in the radio fundamental characteristics such as modulation

type, operating bandwidth, multiple access schemes, source and channel

coding/ decoding methods, frequency spreading/ dispreading techniques,

and encryption/ decryption algorithm. The traditional hardware based radio

requires hardware changes to modify these fundamental characteristics.

29

SDR rapidly evolving as a 4G technology offers flexibility,

global mobility, service portability, wider bandwidth and higher bit rates at

lower cost. It represents a departure from traditional radio design with

reprogrammable radios, opening the way for new services and prolonging

the mobile wireless device lifespan. It consists of a receiver and or

transmitter where the received signal is digitized at some stage downstream

from antenna (digitization may occur at RF, IF or baseband) and then

processed using DSP techniques in flexible and reconfigurable functional

blocks to define the characteristics of the radio.

The general idea behind the SDR architecture is to perform a

considerable amount of signal processing in software instead of being

defined in hardware. This enables the radio to get adapted to change in

environment and user requirements by simply updating the software or by

using adaptable software systems. In such scenarios, a broadcaster could

change the appropriate modulation scheme according to the capacity of the

channel.

The integration of receivers for the software-based radio requires

the modulation identification at the receiver side. Meaning thereby, an

intelligent algorithm identifying the modulation must be running at the

receiver side.

Modulation Classification and Modulation Recognition are

specifically important for SDR which has shown promise to cope with the

variety of communication system. A receiver incorporating AMR will then

have to handle this in real time. This certainly needs identification of

modulation technique for the accurate reception of the signal. Blind

Modulation Recognition techniques can be used with an intelligent receiver

30

yielding an increase in transmission efficiency by reducing overhead as it

does not use any explicit signaling to indicate modulation signal. Current

applications have emerged the need for flexible intelligent communication

systems, where the automatic modulation recognition of the received signal

is a major task.

The task is to identify modulation type used to encode an

unknown radio transmission. The main task of this thesis is to recognize

simultaneously the various linear digital modulation type such as BPSK,

QPSK, OQPSK, 8-PSK and /4- DQPSK. The existing methods require

high SNR, assuming constant signal level and signal parameters are known

to the receiver. Thus the blind identification of modulation schemes like

BPSK, QPSK, OQPSK, 8-PSK and /4- DQPSK that can be desired by a

constellation is being done at lower SNR. The simulations are under taken

at varying SNR, channel model and data rate conditions.

The basic modulation types are identified based on constellation

diagram plotted based on inphase and quadrature phase components. A

further classification of QPSK and OQPSK based on eulidean distance

analysis is done. Further classification of /4-DQPSK and 8-PSK can be

done based on the relative phase difference between the adjacent samples.

2. 2 MODULATION RECOGNITION

HF communication is undergoing resurgence despite advances in

the long-range communication systems. Spectrum surveillance and

spectrum management organizations are monitoring HF spectrum to control

and enforce licensing. It requires a system capable of determining location

of source, separate valid signal from interference and noise and recognizing

31

signal modulation. In past, HF communication employed analog technique

in which signals received by antenna will be down converted to baseband

signals using filters, oscillators and discrete components. This baseband

signal is then passed through demodulator to extract the information

content. Techniques that are monitoring and detecting signals using

traditional methods would require numerous HF receivers, with the prior

knowledge of signals so as to choose the receiver of suitable type for a

bunch of transmitted signals.

In the conventional type of communication system design, the

modulation recognition relied heavily on operator interpretation of

measured parameters to classify the incoming signals. This method requires

information like IF waveform, signal spectrum, instantaneous amplitude

and instantaneous phase from transmitted signal. Here the received signal is

checked and displayed visually. These methods rely very much on the

operator’s skill and abilities. These limitations lead to the development of

more automated modulation recognizers. The later form of recognizer by

Pavlik (2005) and Ghani (1992) uses a bank of demodulators each designed

for a separate modulation type. This is semi-automatic, as an operator is

needed to listen to the output of the demodulator. This approach is, however

not practical anymore owing to the new digital communication techniques

employing RF signals including both data and voice.

A software receiver implementation facilitates much more

flexible and relatively inexpensive application design. This is important for

dynamically changing the function of radio and for reacting to the changes

in the intercepted signal such as the change of the modulation scheme

employed. To detect the received symbols correctly, the receiver has to

know the type of modulation being used in the transmitter. Therefore,

32

automatic detection of correct modulation scheme used in an unknown

received signal is required. After correctly recognizing the modulation

mode of the received signal, parameter estimation and demodulation can be

made further (Nolan et al 2002).

The type of communication modes and number of radio stations

are increasing rapidly in the mobile communication (Mitola 1995). Most of

these systems adopt communication technologies based on digital

modulation schemes. The knowledge on type of modulation scheme

provides valuable information and is crucial in retrieving the information

stored in the signal. Therefore efficient methods to discriminate them have

to be sort out. However, new transmission receiver systems need to classify

automatically digital modulation without specific information of the

transmitted signal. The efficient modulation detection schemes can provide

an insight into the channel and noise characteristics of the propagating

medium.

Digitally modulated signal like QPSK and its variants (OQPSK,

/4–DQPSK, 8-PSK) are employed for mobile and wireless communication

standards like IS-54, IS-95, IS-136, TETRA and 802.11. Such signals can

be found in interference identification and spectrum management,

identification of non-licensed transmitters, electronic warfare, surveillance

and threat analysis, control of communication quality etc. In

Communication Intelligence (COMINT) applications, the modulation types

are considered as signal signatures, Le Guen and Mansour (2002). A

practical SDR system needs automatic distinguishing of signals in order to

perform the task of recovering the message properly. Therefore, the

modulation recognition is an essential key to demodulate as well as to

decode and understand the transmitted message.

33

2. 2. 1 Modulation Classification

A modulation classifier is supposed to correctly choose the

modulation format of the incoming signal from a pool of N candidate

modulations. A desirable classifier should provide a high probability of

correct classification in a short observation interval, particularly for a large

range of SNR. Besides, it should have capabilities to recognize different

modulations in environment with diverse propagation characteristics,

robustness to model mismatches, real time functionality and low

computational complexities.

Automatic Modulation Recognition (AMR) of the detected

signal is an intermediate step between signal detection and demodulation.

Without any fore knowledge of transmitted data and many unknown

parameters at the receiver such as signal power, carrier frequency, phase

offsets, timing information, blind identification of modulation is a difficult

task as indicated by Hanzo et al (2002). This is more challenging in the real

world scenarios with multipath fading, frequency selective and time varying

channels.

According to Soliman and Hsue (1992) the design of a

modulation classifier essentially involves two steps:

Preprocessing the received data which is associated with the noise

removal, estimation of carrier frequency, symbol period, signal and

noise power, and equalization.

The selection and classification of modulation type based on

recognition algorithm.

34

Two methods, namely parameter signaling and blind detection

are being employed for modulation detection. Parameter signaling is where

modulation information is embedded within the transmitted data symbols. It

has the disadvantage of reducing data throughput due to signaling symbols.

In blind detection the estimate of the modulation schemes is done without

explicit signaling. It can be used to minimize the loss of useful data and

conserving the bandwidth. Thus it has the advantage of increased spectral

efficiency and improved throughput over traditional signaling schemes.

There are two approaches in blind identification problem. They are decision

directed and statistical pattern recognition based methods. The first

approach uses the probabilistic and hypothesis testing arguments to

formulate the modulation recognition problem. This approach is based on

the signal envelope characteristics, likelihood ratio, zero crossing, statistical

moments, square law and phase based classifiers. In pattern recognition

method, the classification process follows a step-by-step procedure of

feature extraction, reduction of feature space and classification based on

lower dimension feature space subsystem.

The objective of blind modulation detection is to determine the

type of modulation used within the information conveyed by the least

possible number of received samples. The empirical data provided by the

received noisy samples is the distance to the closest legitimate constellation

point of all the modulation schemes. In other words, given a noisy sample

there would be M errors where M is the number of modulation schemes

used. Therefore, the objective is to make use of the distribution of these

data or errors to make a statistical inference of the type of modulation used.

35

2. 3 SIGNAL MODEL AND CHANNEL MODEL

To transmit digital information on bandpass channels, sinusoidal

carrier is required to perform frequency translation of the transmitted signal

spectrum. By Chen et al (2005), a modulated signal can be expressed as,

cs t m t f t (2.1)

where exp 2 cf t --- complex carrier signal with frequency cf

m t --- complex envelope containing the message signal

j tm t a t e (2.2)

Re--- real apart

The modulated signal can also be represented in the form of

inphase (I) and quadrature phase (Q) components as

=I cos 2 cos 2c cs t t f t Q t f t (2.3)

Amplitude of message signal is given by

a t = 2 2m t Q t I t (2.4)

Phase of message signal can be calculated as

t = 1tan IQ tz t t (2.5)

The channel over which bandpass signal s(t), is transmitted and

received as bandpass waveform r(t) can be modeled as follows:

AWGN Channel

Rayleigh fading Channel

2. 3. 1 Additive White Gaussian Noise Channel (AWGN)

The most important and most analyzed digital communication

channel in practice is the AWGN channel. The output of the channel r(t) is

36

n(t)

r (t) s (t)

the sum of modulated signal s(t) and an uncorrelated gaussian noise n(t), as

shown in Figure 2.1. On transmission through the channel, noise gets

added to the transmitted signal so the received signal takes the form,

r t s t n t (2.6)

where n t --- channel noise

s t --- transmitted signal

The added noise is assumed to be uncorrelated with itself, as it is

white in nature. AWGN has the following characteristics (Haykins 1994):

Mean of noise signal is zero.

0E n t (2.7)

where E{.} --- Expectation

Auto correlation function of the noise is

* ( ) 2oE n t n t T N T (2.8)

Where 2oN --- Power spectral density of noise signal

----impulse function/ dirac delta function

By taking the mean of the received signal, the originally

transmitted signal is recovered, since the mean of the added noise is zero.

Figure 2.1 Model of AWGN Channel

2. 3. 2 Rayleigh Fading Channel

In a radio link, the RF signal from the transmitter may be

reflected from objects such as hills, buildings, walls or vehicles. Some of

37

these reflections will arrive at the receiver, giving rise to multiple

transmission paths at the receiver. Figure 2.2 shows some of the possible

ways in which multipath signals can occur. Each multipath signal will have

different propagation distance and thus a different phase rotation. The

relative phase of multiple reflected signals can cause constructive or

destructive interference at the receiver the mathematical expression of the

received signal r(t) on a Rayleigh fading channel is given by)j t

er t r t e s t n t (2.9)

where n t --- channel noise

s t --- transmitted signal

er --- Rayleigh distributed channel gain

--- uniformly distributed phase

This is experienced over very short distances (typically at half

wavelength distances), thus is given the name fast fading as told by

Rappaport ( 2002).

Figure 2.2 Model of Rayleigh fading channel

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2. 4 MODULATION TECHNIQUES

Modulation in the context of radio communication is a process of

varying some characteristics of a high frequency carrier wave with respect

to information signal in order to transmit it over a long communication

channel. A radio transmitter modulates the carrier signal before it is being

transmitted and the receiver performs a demodulation in order to restore the

baseband signal. The modulation can be classified as analog and digital

modulation based on the nature of carrier signal.

2. 4. 1 Digital Modulation

The advances over the last several decades in hardware and

digital signal processing have made digital transceivers much cheaper,

faster, and more power efficient than analog transceivers. Digital

modulation is the mapping of information bits into an analog signal for

transmission over the channel. Digital modulation offers the following

advantages over analog scheme:

High data rate

High spectral efficiency (minimum bandwidth occupancy)

High power efficiency (minimum required transmit power)

Robustness to channel impairments (minimum probability of bit

error)

Effective multiple access storages

Low power/ cost implementation

Powerful error correction techniques

Better data security and privacy

39

The two main categories of digital modulation are,

Amplitude and Phase modulation

It embeds the information bits into the amplitude or phase of the

transmitted signal which is more susceptible to variation from fading and

interference. This is also called linear modulation.

Frequency modulation

Since frequency modulation typically has constant signal

envelope and is generated using non-linear techniques, this modulation is

also called constant envelope modulation or non-linear modulation.

2. 4. 2 Linear Modulation

In linear modulation, amplitude of transmitted signal s(t) varies

linearly with modulating digital signal m(t). As these techniques are more

bandwidth efficient than the non-linear techniques, they are attractive for

use in wireless communication system where there is an increasing demand

to accommodate more and more users within a limited spectrum. But as the

information bits are embedded into the amplitude or phase of the

transmitted signal, it is more susceptible to variations from fading and

interference. The linear modulated signal can be expressed as,

s t Re [ m t exp( 2 ) ] cA j f t

= t cos 2 - m t cos 2I c Q cm f t f t (2.10)

where A--- amplitude of signal

cf --- carrier frequency

mI(t), mQ(t)--- Inphase and Quadrature phase components of

Message signal.

The popular linear modulation types are pulse shaped QPSK,

OQPSK, /4-DQPSK and MPSK methods.

40

2. 4. 2. 1 Binary Phase Shift Keying (BPSK)

In BPSK the phase of constant amplitude carrier signal is

switched between two values according to possible signal m1 (binary 1) and

m2 (binary 0). The phase between the symbols is shifted by 180 .

s t 2 /T cos 2BPSK b b c cE f t for symbol 1 (2.11a)

= 2 /T cos 2b b c cE f t for symbol 0 (2.11b)

where bE --- Bit Energy

Tb --- Bit duration

2. 4. 2. 2 Quadrature Phase Shift Keying (QPSK)

In QPSK signaling two bits are being transmitted in a single

modulation symbol. Phase of carrier takes on any one of the four values 0,

/2, , 3 /2. Each value corresponds to a unique pair of message bits. The

modulated wave can then be,

s t 2 /T cos 2 1 / 2QPSK s cE s f t i (2.12)

= 2 /T cos 2 cos 1 / 2 sin 2 sin 1 / 2s c cE s f t i f t i

Where i=1,2,3…..M

sE --- Symbol energy

Ts --- Symbol duration

Also the average probability of error of QPSK is identical to

BPSK. It is bandwidth efficient system since twice the amount of data can

be sent within the bandwidth equal to bandwidth of BPSK. Different types

QPSK signal sets can be derived by simply rotating the constellation.

41

2. 4. 2. 3 Offset QPSK (OQPSK)

QPSK modulation with quadrature offset among the carrier

phase is referred to as OQPSK. The signaling is similar to QPSK except for

time alignment of even and odd bit stream. In QPSK even and odd bit

stream mQ(t) and mI(t) occur at the same time. Due to time alignment in

QPSK, phase transition occurs only once every Ts seconds. Phase transition

have a maximum shift of 180 if the value of both mQ(t) and mI(t) changes.

In OQPSK even and odd bit stream mQ(t) and mI(t) are offset at their

relative alignment by one bit period (half symbol period). Here bit

transitions occur every Tb seconds. Since transition instant of mQ(t) and

mI(t) is offset at any given time only one between the two bit streams can

change values. This implies that the maximum phase shift of transmitted

signals at any given instant is limited to 90 . Hence by switching phases

more frequently OQPSK signaling eliminates 180 phase transitions.

OQPSK has the same spectral properties as QPSK for linear amplification,

but has higher spectral efficiency under nonlinear amplification, since the

maximum phase transition of the signal is 90 , corresponding to the

maximum phase transition in either the inphase or quadrature branch, but

not simultaneously.

2. 4. 2. 4 /4- QPSK

Signaling points of modulated signal are selected from two

QPSK constellation which are shifted by /4 with respect to each other.

Switching between two constellation every successive bit ensures that there

is atleast a phase shift which is an integer multiple of /4 radians between

successive symbols.

42

Table 2.1 Phase shift between adjacent bits in /4-QPSK

Inphase component (Ik)

Quadrature phase component ( Qk)

Phase shift( k )

1 1 /4 0 1 3 /40 0 -3 /41 0 - /4

1 1cos cos( ) sin( )k k k k k kI I Q

1 1sin sin( ) cos( )k k k k k kQ I Q (2.13)

where 1k k k

1kI , 1kQ --- previous value of kI and kQ

k ---- phase shift related to Im and Im

kI and kQ takes one of the five possible values 0, 11,2

.

Information contained in /4-QPSK is completely contained in the phase

difference k of the carrier between adjacent symbols.

/4-QPSK offers a compromise between OQPSK and QPSK in

terms of the allowed maximum phase transition. Here maximum phase

transition is limited to 135 as compared to 180 for QPSK and 90 for

OQPSK. It preserves the constant envelope property better than other

schemes. As it can be detected non-coherently, the receiver design is

simplified. In presence of multi path spread and fading /4-QPSK performs

better than QPSK (Feher 1991).

Differentially encoded /4-QPSK is called /4-DQPSK. The

basic principle of differential modulations is to use the previous symbol as a

phase reference for the current symbol thus avoiding the need for a coherent

43

phase reference at the receiver. Specifically, information bits are encoded

with differential phase between current symbol and the previous symbol.

The /4-DQPSK modulation can be achieved by differentially encoding

information bits, yielding to one of the four QPSK constellation points.

Then, every symbol transmission is shifted in phase by /4. This periodic

phase shift has a similar effect as the time offset in OQPSK. It has the

significant advantage of eliminating the need for a coherent phase

reference. It also reduces the amplitude fluctuations at symbol transitions

which makes the signal more robust against noise and fading.

2. 4. 2. 5 Mary PSK (MPSK)

In MPSK the information is encoded in the phase of the

transmitted signal. Thus the transmitted signal over one symbol time is

given as,

s t 2 /T cos 2MPSK s c iE s f t

= 2 /T cos 2 cos sin 2 sins c i c iE s f t f t (2.14)

Where the carrier phase i is given by /12 ii i=1,2,….M

Constellation of MPSK is two-dimensional with M message

points equally spaced on a circle of radius sE centered at origin.

Constellation mapping is usually done by gray encoding where the

messages associated with signal phases that are adjacent to each other differ

by one bit value. In this encoding method, mistaking a symbol for adjacent

one causes a single bit error.

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2.5 CONSTELLATION SHAPE

Vector space representation of digitally modulated signal

provides a graphical insight into the underlying complex envelope signal

structure of each possible symbol. Constellation diagrams have been the

traditional means for such representations. It is obtained by projecting the

signal on to an orthogonal vector space, the dimensionality of which is

determined by a specific modulation type. From the shape perspective, a

constellation shape can be characterized by a specific and regular pattern of

points on a multi dimensional grid. The constellation is a binary space,

zeros everywhere except on modulation state vectors. The constellation

diagram is the representation of inphase component (I) versus quadrature

component (Q) of complex envelope. The distance between two signals on

a constellation diagram relates how different modulation waveforms are

being differentiated by the receiver among all possible symbols even when

random noise is present.

Some of the properties like probability of error, bandwidth of the

modulation schemes can be inferred from the constellation diagram.

Bandwidth occupied by modulated signal decreases as number of signal

points increases. Therefore if a modulation scheme has a constellation that

is densely packed, it is more efficient than a modulation with sparsely

packed constellation. Probability of error is proportional to the distance

between closest points in a constellation. This implies that a modulation

scheme with a constellation that is densely packed is efficient than a

modulation scheme that has sparse constellation.

The signal space representation of quadrature components of an

intercepted signal is the graphical means of monitoring channel quality

45

variations. Constellation diagrams are commonly used to asses the

underlying signal structure of the received signal. The mean excursion of

the received signal points on the constellation diagram may be used as a

metric to determine whether the employed modulation scheme can be

supported over the time varying channel. Channel distortion resulting in ISI

and fading due to a moving signal source or receiver may also distort the

constellation shape of received signals.

There are three classes of modulation that represent different

geometric approaches to constellation construction.

Cubic constellation:

It is commonly used on simple data communication channels. The

construction of a cubic constellation directly maps a sequence of N=b bits

into the components of the basis vectors in a corresponding N- dimensional

signal constellation as shown in Figure 2.3. Examples of this constellation

are BPSK, QPSK modulation.

Figure 2. 3 Geometry of Cubic constellation

N=3 N=1 1

N=2

1

2

1 2

3

N=3

46

Orthogonal constellation:

It has an orthogonal signal sets as shown in Figure 2.4. Example of

this constellation is FSK modulation.

Figure 2.4 Geometry of Orthogonal constellation

Circular constellation:

It places data symbol vectors at equally spaced angles. Only the

phase of the signal changes with respect to the transmitted message, while

amplitude of the signal envelope remains constant. PSK is often used on

channels with non-linear amplitude distortion when signals that include

information content in the time varying amplitude would otherwise suffer

performance degradation from non-linear amplitude distortion. Example of

this constellation is M-PSK modulation. Figure 2.5 shows the circular

constellation diagrams.

Figure 2.5 Geometry of Circular constellation

2

N=2

11

N=3

2

3

X5

X2

XO

X7

X6

X1

X4

X3

47

If a modulated signal can be uniquely characterized by its

constellation it should also be identifiable by the recovered constellation at

the receiver. The recovered constellation of course, will be distorted in a

variety of ways depending on the specific receiver structure as well as

channel as indicated in Mobasseri (1999). Random noise of the channel

disturbs constellation vertices. The loss of phase lock in a coherent receiver

causes a fixed rotation or slowly spinning constellation. Errors in carrier

frequency tracking cause a local spin of individual constellation points.

Thus constellation can be demonstrated as a global signature that provides a

robust stable and broad means of modulation classification.

Let the received bandpass signal r(t) is given by,

=I cos 2 cos 2c cr t t f t Q t f t (2.15)

where I t --- Inphase component

Q t --- Quadrature phase component

By Complex envelope notations, the modulated signal can be

( ) exp 2e cr t RP r t f t (2.16)

where Ier t t jQ t

RP---- Real part

The complex envelope baseband signal re(t), obtained from

bandpass signal r(t), is used to generate the constellation points which

wander in the signal space anywhere inside a Gaussian distributed noise

cloud centered around prototype message points, in a complex random

fashion. Assuming perfect carrier synchronization and timing recovery and

employing I-Q demodulation

I , , ,I Q I I Q Qr k k Q k r k r k s k n k s k n k (2.17)

48

The sequence of the signal samples are collected at the receiver.

Then matching of the received signal sample with the available prototype

constellation is checked. In identification using constellation the received

signal points on a two-dimensional signal space has four quadrants,

represented as Q1, Q2, Q3 and Q4. The sign of the received signal points

,I Qr k r k indicates the quadrant in which received symbol is falling.

After computing the respective quadrant, the signal points are plotted as

shown in Figure 2.6. The constellation diagram obtained is compared with

the prototype constellation available.

Figure 2.6 Constellation Space of BPSK, QPSK, 8-PSK Modulation

Computation of ,k mD can be simplified by confining the search to

the quadrant in which r(k) lies. For example, as shown in Figure 2.7 if r(k)

lies in first quadrant Q1, then distance can be computed only from the

quadrant which it lies find Dk,8 as calculated by Naik et al(2005).

, ,min mink m m k mD r k s d m=1,2,------M (2.18)

2 2 2

1 1 1

49

Figure 2.7 Euclidean Distance Vector Calculation for MPSK

2. 6 EUCLIDEAN DISTANCE BASED RECOGNITION By analyzing the phase transitions of QPSK it is noted that the

phase transition between the adjacent bits in a symbol shifts from 90o to

180o. OQPSK signaling is similar to QPSK signaling, except the time

alignment bit responsible for generating the odd and even bit stream differs

by a half-symbol period. This implies that the maximum phase shift over a

transmitted signal at any given time instant is limited to ± 90o with reference

to Haykin (1994) and Rappaport (2002). It is observed that, for QPSK

signal there is bi-directional phase transition from signal point 1s to 3s or 2s

to 4s and vice versa as shown in Figure 2.8.

Figure 2.8 Possible path for switching between the message points

QPSK and OQPSK

S2 S1

S3 S4

1

3

QPSK

S2 S1

S3 S4

1

2

OQPSK

50

Hence the relative Euclidean distance denoted by rD between

the adjacent received signal symbol in a frame for QPSK is greater than

OQPSK signal. According to Naik et al (2005) the moment rM of received

signal symbols in a frame is represented as

4

1

1 ( )N

r r

k

M D kN

(2.19)

where Dr = ( ) ( )r i r j for 1 k N , 1 i N 1and j i 1

Euclidean distance between two symbols in a frame length of N

symbol is given byD (k)r .Therefore the signal having greater rD will be

boosted and the signal with smaller rD will be minimized. To distinguish

between QPSK and OQPSK signal, the fourth order moment rM is

obtained at each SNR value. Using the equation (2.20) the threshold on

moment rm is

( )2

r rqpsk oqpskr

m

M M (2.20)

By comparing received moment with available rm a clear

distinction between QPSK and OQPSK can be achieved.

2. 7 PHASE DIFFERENCE BASED RECOGNITION

In a /4-DQPSK modulation, constellation is formed by

superimposing two QPSK signal constellations offset by /4 relative to

each other resulting in eight signal phases. The carrier phase of the

successive symbols is alternatively picked from one of the two QPSK

constellations shown in Figure 2.9. During each symbol period a phase

angle from only one of the two QPSK constellations is transmitted. This

results in the maximum phase transition of 135°. The phase transition from

one symbol to the next is restricted to /4 and 3 /4.

51

8-PSK system is a type of Mary PSK with M=8. Constellation of

8-PSK is two dimensional and M message points are equally spaced on the

circle. Figure 2.10 depict the relative phase distribution of 8-PSK and /4–

DQPSK.

Figure 2. 9 Constellation of the dibits of /4 – DQPSK

An approach to classify, /4–DQPSK and 8-PSK signal is based

on the relative phase of the received symbols in a frame. Phase of received

signal r(k) is given as1 tan ( ) ( )r Q Ik r k r k where 1 < k < N (2.21)

Figure 2.10 Relative phase distributions of /4 – DQPSK and 8-PSK

8 - PSK

67.5 45 22.5

90

112.5

135

157.5

S1

S6

S2

S4

S5

S7 S8

S3

/4 – DQPSK

S3

S2

S4

S5

S6 S7

S8

157.5

125

67.5 22.5

2

1

2

1

52

Relative phase difference denoted by rP between each received

symbol in a frame is represented as

P rr ri j where 1 < i < N-1 , j = i + 1 (2.22)

The relative phase distribution of 8-PSK is 0, /4, /2, 3 /4, ,

5 /4, 3 /2 and 7 /4. Whereas relative phase distribution of /4-DQPSK is

0, /4, 3 /4, 5 /4 and 7 /4. Hence, to identify the modulation type three

counters C1, C2 and C3 have been placed at /2, and 3 /2 phase locations

respectively. The basic function of these counters is to count the number of

received symbols falling within the corresponding phase angles over a

frame. It is observed that, without any noise and fading, for a /4 – DQPSK

signal there is no relative phase value at /2, and 3 /2 and hence the three

counter values are zero. For 8-PSK there is some value in each counter. The

counter values are calculated and threshold ( a ) is computed using

equation (2.23)

41 2 3 1 2 38( ) 3 ( ) 3 2a

PSK DQPSKc c c c c c (2.23)

The relative phase distribution of the received signal in an

AWGN and multipath fading is obtained and compared with the available

threshold value. Modulation type is identified as 8-PSK, if it satisfies

equation (2.24) or else the modulation type is declared as /4-DQPSK.

1 2 3 8( ) 3

PSKc c c >

41 2 3( ) 3DQPSK

c c c (2.24)

53

2. 8 RESULTS AND DISCUSSION

This section presents simulation results on the performance of

the proposed method executed in MATLAB. The simulation conditions are

shown in Table 2.2.

Table 2.2 Simulation conditions

Modulation Types BPSK, QPSK, OQPSK, 8-PSK, /4-DQPSK

Recognition MethodConstellation shape based analysis Euclidean distance analysisAdjacent bit Phase difference analysis

Channel TypeAWGN Rayleigh Fading No noise

SNR(db) 0 to 30

Number of samples 100 to 5000 bits

From the sequence of N received signal samples r(k), the inphase

(I) components and quadrature phase components (Q) are extracted. The

constellation diagram of received symbols is plotted with I component

versus Q component. Constellation diagram of BPSK signaling shows that

majority of signal points will be confined to any one of the two quadrants

Q1 and Q3 or Q2 and Q4. Signal points of BPSK are scattered around the

symbols s2 and s6 or s4 and s8 respectively. In QPSK modulation, signal

points are confined to one of the four quadrants Q1, Q2, Q3 and Q4. In this

case signal points are scattered around the four symbols s2, s4, s6 and s8. If

8-PSK signaling is used, signal points are confined in any one of the four

quadrants Q1, Q2, Q3 and Q4. In this case signal points are scattered around

the eight symbols s1, s2, s3, s4, s5, s6, s7 and s8. Based on the fashion in which

the symbols scattered in signal plot the type of modulation of the received

54

signal can be identified. The simulation results are shown in Figure 2.11

under AWGN and multipath fad conditions for varying SNR values.

Figure 2.11 Constellation based recognition of BPSK, QPSK and

8-PSK at SNR 5dB AWGN and fad

Once the basic modulation types are identified based on

constellation diagram, further classification based on eulidean analysis is

done. Constellation diagram with four signal points will be recognized as a

-2 -1.5 -1 -0.5 0 0.5 1 1.5 2-2

-1.5

-1

-0.5

0

0.5

1

1.5

2

I comp

8PSK FAD scatter at SNR 7

55

QPSK signal. Since QPSK and OQPSK signal has the same constellation

diagram they cannot be distinguished by this method. Euclidean distance

between the adjacent received symbols in a frame can be used as a measure

to distinguish QPSK and OQPSK. The fourth order moment of the received

signal is calculated and compared with the available threshold value rm.

Modulation shall be identified as QPSK if the moment lies above the

threshold or else as OQPSK. The results of the simulation for 25 runs

carried out with N=2000 samples at each SNR is plotted in Figure 2.12

under AWGN and multipath fading conditions.

Figure 2.12 Fourth order moment of QPSK and OQPSK in AWGNand Rayleigh fad

The constellation diagram with eight signal points may be

identified as 8-PSK. Since both 8-PSK and /4-DQPSK has the same

constellation diagram they cannot be distinguished by the method based on

56

constellation shape analysis. Further classification can be done based on the

relative phase difference between the adjacent samples. The critical phase

difference values ( /2, and 3 /2) used for distinguishing /4-DQPSK and

8-PSK are measured using the respective counters. The counter values are

compared with the threshold values. The recognition accuracy is obtained

by averaging the number of detecting the signal over the total number of

runs carried out. The results are tabulated in Table 2.3 and 2.4 under

AWGN and multipath fad environment at various SNR and sample values

respectively. The results are recorded for iterations carried out at 10, 25 and

50 runs for particular SNR and a specific sample value.

Table 2.3 Recognition accuracy with AWGN

SNR(db)

No of

bits

THRESHOLD NO OF ITERATIONS 24 49 99

1 2 3 8-PSK

/4- DQPSK

8-PSK

/4-DQPSK

8-PSK

/4-DQ PSK

3

100 6.02 6.2 6. 4 80.6 79.3 91.7 80.1 89.9 80.3300 19.59 18.8 19.22 86.9 82.3 95.6 82.1 97.3 83.9600 38.1 37.07 38.01 94.3 89.9 100 91.9 100 87.21500 96.08 98.02 97.35 100 95.3 100 93 100 89.7

6

100 6.13 6.3 6.14 87.5 87.5 93.8 87.7 93.9 90.9300 19.64 19.07 19.22 100 95.8 100 79.5 98.9 89.9600 38.82 37.17 38.25 100 87.5 100 93.8 100 87.81500 96.33 98.27 97.53 100 95.8 100 95.9 100 93.9

8

100 6.34 6.16 6.34 100 91.6 93.8 91.8 89.8 91.9300 19.67 18.87 19.03 100 95.8 100 83.6 97.9 91.9600 38.93 38.51 38.42 100 91.6 100 93.8 100 84.81500 98.63 98.56 98.59 100 87.5 100 83.6 100 88.8

12

100 6.35 6.13 6.17 95.8 75 91.8 93.8 93.9 88.8300 18.54 18.94 18.65 100 79.1 100 97.9 100 87.8600 37.52 38.02 37.97 100 75 100 89.7 100 84.81500 92.29 94.53 95.51 100 87.5 100 87.7 100 89.8

57

Table 2.4 Recognition accuracy with fading

SNR (db)

No of

bits

THRESHOLD NO OF ITERATIONS 24 49 99

1 2 3 8-PSK

/4-DQPSK

8-PSK

/4-DQ PSK

8-PSK

/4-DQPSK

3

100 6.08 6.2 6.22 93.8 82.3 94.3 83.2 95.1 83.4300 19.02 19 19.10 94.2 90.5 95.7 89.2 95.8 89600 38.2 37.36 37.55 100 90.8 100 85 100 89.2

1500 95.2 96.18 96.2 100 92.2 100 85 100 89.3

6

100 6.28 6.3 6.2 95.83 87.5 97.96 85.71 96.97 87.88300 19.47 19.15 19.09 100 91.67 100 81.63 100 78.79600 38.04 37.86 37.65 100 87.5 100 83.67 100 80.81

1500 95.7 96.81 96.03 100 79.17 100 83.67 100 78.79

8

100 6.06 6.16 6.27 91.67 79.17 89.8 83.67 91.92 81.82300 19.84 19.53 19.64 100 79.17 100 83.67 100 83.84600 38.57 38.72 38.52 100 87.5 100 81.63 100 83.84

1500 96.62 96.11 96.43 100 75 100 83.67 100 84.85

12

100 6.85 6.53 6.37 100 87.5 97.96 87.76 98.99 81.82300 19.75 19.8 19.66 100 87.5 100 85.71 100 83.84600 37.74 38.7 38.8 100 87.5 100 81.63 100 82.83

1500 97.47 97.04 96.48 100 79.17 100 81.63 100 82.83

In this thesis a blind automatic modulation recognition technique

for classifying the variants of QPSK is proposed. This can particularly be

used for SDR system that responds to the instantaneous change in

modulation modes.

Proposed algorithm is capable of identifying almost all variants of

QPSK modulation modes that follow a linear digital modulation

(BPSK, QPSK, OQPSK, 8-PSK, /4- DQPSK) with a specific

constellation.

Modulation identification is a blind process. The largest advent is

that it does not require any preliminary information of signal for

58

automatic estimation. Hence the available bandwidth for

transmission of information signal is increased.

It uses a deterministic method to speed up the identification

process. This is required, when algorithm is adapted to the adaptive

communication systems. The deterministic method identifies the

branch of tree-structured algorithm from properties of received

signal. (The computation time of signal analysis can be mitigated

dramatically.)

The proposed algorithm overcomes some of the disadvantages of

the existing algorithms which are SNR dependent and has shown

better result.

Certain assumptions like perfect carrier recovery, and

synchronization are made for the extraction of constellation points

from the received signal. Hence no pre-processing of received

samples is done.

The basic recognition is done based on the shape of constellation

diagram. QPSK variants with 2, 4 and 8 signal points are identified as

BPSK, QPSK and 8-PSK respectively. The results show that at high SNR

identification of symbol points clouded over constellation at particular

points. But for low SNR the shape of constellation diagram can be

improved by increasing the number of samples. The proposed algorithm is

able to identify the basic modulation at a low SNR of 3dB with 5,000

samples. Variant of OQPSK and QPSK is identified based on Euclidean

distance calculation between the adjacent bits. This method of classification

is able to recognize the signal with 100% efficiency at SNR

59

AWGN and for multipath fad signal with number of samples N=2000 for 8-

PSK. /4-DQPSK and 8-PSK can be differentiated based on relative phase

difference between adjacent bits. The algorithm can identify 8-PSK under

almost all conditions and /4-DQPSK can be identified at low SNR of 3dB

with 100% accuracy. Thus conclusion can be made that these computation

methods shows good results even in lower SNR (upto 3dB).