List of Abbreviations

CHAPTER-1

INTRODUCTION

GMSK RADIO MODULATION 1

INTRODUCTION

This chapter introduces basic concepts of modulation like analog,

digital, radio etc and concepts of GMSK and its origin.

1.1 MODULATION

In telecommunications, modulation is the process of varying a

periodic waveform, i.e. a tone, in order to use that signal to convey a

message, in a similar fashion as a musician may modulate the tone

from a musical instrument by varying its volume, timing and pitch.

Normally a high-frequency sinusoid waveform is used as carrier

signal. The three key parameters of a sine wave are its amplitude

("volume"), its phase ("timing") and its frequency ("pitch"), all of which

can be modified in accordance with a low frequency information

signal to obtain the modulated signal.

A device that performs modulation is known as a modulator and a

device that performs the inverse operation of demodulation is known

as a demodulator (sometimes detector). A device that can do both

operations is a modem (a contraction of the two terms).


1.2 ANALOG MODULATION

The aim of analog modulation is to transfer an analog lowpass

signal, for example an audio signal or TV signal, over an analog

bandpass channel, for example a limited radio frequency band or a

cable TV network channel.

1.2.1 MODULATION TECHNIQUES

Common analog modulation techniques are:

• Angular modulation

Phase modulation (PM)

Frequency modulation (FM)

• Amplitude modulation (AM)

Double-sideband modulation with unsuppressed carrier (used

on the radio AM band)

Double-sideband suppressed-carrier transmission (DSB-SC)

Double-sideband reduced carrier transmission (DSB-RC)

Single-sideband modulation (SSB, or SSB-AM)

Single-sideband suppressed carrier modulation (SSB-SC)

Vestigial-sideband modulation (VSB, or VSB-AM)

Quadrature amplitude modulation (QAM)


1.3 DIGITAL MODULATION

The aim of digital modulation is to transfer a digital bit stream over

an analog bandpass channel, for example over the public switched

telephone network (where a filter limits the frequency range to

between 300 and 3400 Hz) or a limited radio frequency band.

1.3.1 MODULATION TECHNIQUES

The most common digital modulation techniques are:

• Phase-shift keying (PSK)

• Frequency-shift keying (FSK)

• Amplitude-shift keying (ASK)

Quadrature amplitude modulation (QAM) a combination of PSK and

ASK

• Polar modulation like QAM a combination of PSK and ASK.

• Continuous phase modulation (CPM)

Minimum-shift keying (MSK)

Gaussian minimum-shift keying (GMSK)

• Orthogonal frequency division multiplexing (OFDM) modulation,

also known as discrete multitone (DMT).

• Wavelet modulation

• Trellis coded modulation (TCM) also known as trellis

modulation


1.4 RADIO MODULATION

Signals sent by radio (or over long wires or when stored on magnetic

media) must be modulated with some method that prevents their

signal from degrading before the signals can be received. A

transmitter and receiver must use the same mode of modulation to

successfully communicate. Some of these are digital modulations,

which typically modulate data to intermediate frequencies, which are

then modulated to radio frequencies using another modulation mode

such as FM or AM. [1,2,3,4,5]

1.5 CPM (CONTINUOUS PHASE MODULATION)

CPM is a method for modulation of data commonly used in wireless

modems. In contrast to other coherent digital phase-modulation

techniques where the carrier phase abruptly resets to zero at the start

of every symbol (e.g. M-PSK), with CPM the carrier phase is

modulated in a continuous manner. For instance, with QPSK the

carrier instantaneously jumps from a sine to a cosine (i.e. a 90

degree phase shift) whenever one of the two 5 GMSK RADIO

MODULATION message bits of the current symbol differs from the

two message bits of the previous symbol. This discontinuity requires

a relatively large percentage of the power to occur outside of the

intended band (e.g., high fractional out-of band power), leading to

poor spectral efficiency. Furthermore, CPM is typically implemented

as a constant-envelope waveform, i.e. the transmitted carrier power is

constant.


Therefore, CPM is attractive because the phase continuity yields high

spectral efficiency, and the constant-envelope yields excellent power

efficiency. The primary drawback is the high implementation

complexity required for an optimal receiver.

Each symbol is modulated by gradually changing the phase of the

carrier from the starting value to the final value, over the symbol

duration. The modulation and demodulation of CPM is complicated by

the fact that the initial phase of each symbol is determined by the

cumulative total phase of all previous transmitted symbols, which is

known as the phase memory.

Therefore, the optimal receiver cannot make decisions on any

isolated symbol without taking the entire sequence of transmitted

symbols into account.


1.6 MSK (Minimum-shift keying )

MSK is another name for CPM with an excess bandwidth of ½ and a

linear phase trajectory. Although this linear phase trajectory is

continuous, it is not smooth since the derivative of the phase is not

continuous. The spectral efficiency of CPM can be further improved

by using a smooth phase trajectory. This is typically accomplished by

filtering the phase trajectory prior to modulation, commonly using a

Raised Cosine or a Gaussian filter. The raised cosine filter has a

strictly finite duration, and GMSK RADIO MODULATION can yield a

full-response CPM waveform that prevents Inter symbol Interference

(ISI).

1.7 GMSK ( Gaussian Minimum Shift Keying )

GMSK is a digital modulation scheme which uses Gaussian instead

of sinusoidal pulse shapes and commonly used in wireless, mobile

communications. GMSK is derived from MSK. In MSK we replace the

rectangular pulse with a sinusoidal pulse. Obviously other pulse

shapes are possible. A Gaussian-shaped impulse response filter

generates a signal with low side lobes and narrower main lobe than

the rectangular pulse. Since the filter theoretically has output before

input, it can only be approximated by a delayed and shaped impulse

response that has a Gaussian - like shape. This modulation is called

Gaussian Minimum Shift Keying (GMSK).


The relationship between the premodulation filter bandwidth, B and

the bit period, T defines the bandwidth of the system. GSM designers

used a BT = 0.3 with a channel data rate of 270.8 kbs. This

compromises between a bit error rate and an out-of-band interference

since the narrow filter increases the intersymbol interference and

reduces the signal power.


1.8 NOISE IN COMMUNICATION SYSTEM

Noise is one of the factors that affects the information being

delivered. It can create interference, alter the integrity of the signal

and sometimes even degrade the signal to an unrecognizable

pattern. Noise can come from a variety of sources, and can be

external or internal. Sources of external noise can be man-made such

as motors or ignition systems, can come from the atmosphere or

even sometimes from outer space. Internal noise, on the other hand,

can be classified as Thermal or Johnson noise due to the thermal

interaction of particles in a conductor, Transistor noise caused by the

random paths of motion in semiconductors, or Low Frequency noise

called also "flicker" which occurs due to changes in dc current levels

at low frequencies.

It is very difficult to measure Noise, and there exist only a few

empirical formulas which can be applied only to specific instances of

Noise, one of the examples being Thermal Noise.

The two figures below show how some small amount of Noise can

affect a signal's shape. On the left figure the Noise "rides" on the

original signal affecting its smoothness, the figure on the right

displays the signal without any Noise.


Figure 1.8.1 Effect Of Noise On Signal

Noise is an important factor in any communication modeling. For

idealing the effect of noise in wireless medium, a good selection of

modulation scheme is required. GMSK is a good candidate to reduce

the effect of noise. Next chapters illustrate GMSK in greater detail.


CHAPTER-2

THEORY OF

GAUSSIAN MINIMUM SHIFT

KEYING


GAUSSIAN MINIMUM SHIFT KEYING

In this chapter GMSK and other Digital modulation scheme which are

earlier used are discussed in detail .GMSK uses Gaussian Filter

which is also discussed.

2.1 DIGITAL MODULATION AND GMSK

A brief introduction to digital modulation schemes is given, showing

the logical development of GMSK from simpler schemes. GMSK is of

interest since it is used in the GSM system. The phase and amplitude

relations between carrier cycles over a data bit are developed,

enabling rigourous modelling of ensemble fields to be carried out.

2.1.1 Amplitude Shift Keying

Amplitude-shift keying (ASK) is a form of modulation that

represents digital data as variations in the amplitude of a carrier

wave.The amplitude of an analog carrier signal varies in accordance

with the bit stream (modulating signal), keeping frequency and phase

constant. The level of amplitude can be used to represent binary logic

0s and 1s. We can think of a carrier signal as an ON or OFF switch.

In the modulated signal, logic 0 is represented by the absence of a

carrier, thus giving OFF/ON keying operation and hence the name

given.


Like AM, ASK is also linear and sensitive to atmospheric noise,

distortions, propagation conditions on different routes in PSTN, etc.

Both ASK modulation and demodulation processes are relatively

inexpensive. The ASK technique is also commonly used to transmit

digital data over optical fiber. For LED transmitters, binary 1 is

represented by a short pulse of light and binary 0 by the absence of

light. Laser transmitters normally have a fixed "bias" current that

causes the device to emit a low light level.

This low level represents binary 0, while a higher-amplitude lightwave

represents binary 1.

2.1.2 Frequency Shift Keying

Frequency-shift keying (FSK) is a form of frequency modulation in

which the modulating signal shifts the output frequency between

predetermined values. Usually, the instantaneous frequency is shifted

between two discrete values termed the mark frequency and the

space frequency. Continuous phase forms of FSK exist in which there

is no phase discontinuity in the modulated signal. The example

shown at right is of such a form. Other names for FSK are frequency-

shift modulation and frequencyshift signaling.

Audio frequency-shift keying (AFSK) is a modulation technique by

which digital data is represented as changes in the frequency (pitch)

of an audio tone, yielding an encoded signal suitable for transmission

via radio or telephone. Normally, the transmitted audio alternates

between two tones: one, the "mark", represents a binary one; the


other, the "space", represents a binary zero. AFSK differs from

regular frequency-shift keying in that the modulation is performed at

baseband frequencies. In radio applications, the AFSK-modulated

signal is normally used to modulate an RF carrier (using a

conventional technique, such as AM, FM or ACSSB(R)(LM Mode(R))

for transmission. AFSK is not generally used for high-speed data

communications, as it is less efficient than other modulation modes.

In addition to its simplicity, however, AFSK has the advantage that

encoded signals will pass through AC-coupled links, including most

equipment originally designed to carry music or speech. [2,3,5,12]

2.1.3 Phase shift keying

For binary PSK (BPSK)

S0(t) = A cos (ùt) represents binary “0”

S1(t) = A cos (ùt + ð) represents binary “1”

For M-ary PSK, M different phases are required, and every n (where

M=2n )

bits of the binary bit stream are coded as one signal that is

transmitted as

A sin (ùt + .j)

Where,

j=1,...,M.

2.1.4 Quadrature Phase Shift Keying

If we define four signals, each with a phase shift differing by 900 then

we have quadrature phase shift keying (QPSK).


The input binary bit stream {dk}, dk = 0,1,2,..... arrives at the

modulator input at a rate 1/T bits/sec and is separated into two data

streams dI (t) and dQ (t) containing odd and even bits respectively.

dI(t) = d0, d2, d4 ,...

dQ(t) = d1, d3, d5 , ...

A convenient orthogonal realisation of a QPSK waveform , s(t) is

achieved by amplitude modulating the in-phase and quadrature data

streams onto the cosine and sine functions of a carrier wave as

follows:

Using trigonometric identities this can also be written as

Figure 2.1.4.1 Even and Odd data Stream


The pulse stream dI(t) modulates the cosine function with an

amplitude of ±ƒn1. This is equivalent to shifting the phase of the

cosine function by 0 or ð; consequently this produces a BPSK

waveform. Similarly the pulse stream dQ(t) modulates the sine

function, yielding a BPSK waveform orthogonal to the cosine function.

The summation of these two orthogonal waveforms is the QPSK

waveform.

The values of .(t) = 0, -(ð/2), ð/2, ð represent the four possible

combinations of aI (t) and aQ (t). Each of the four possible phases of

carriers represents two bits of data. Thus there are two bits per

symbol. Since the symbol rate for QPSK is half the bit rate, twice as

much data can be carried in the same amount of channel bandwidth

as compared to BPSK. This is possible because the two signals I and

Q are orthogonal to each other and can be transmitted without

interfering with each other.

In QPSK the carrier phase can change only once every 2T secs. If

from one T interval to the next one, neither bit stream changes sign,

the carrier phase remains unchanged. If one component aI(t) or aQ

(t) changes sign, a phase change of ð/2 occurs. However if both

components change sign then a phase shift of ð occurs.


Figure 2.1.4.2 QPSK Waveform

If a QPSK modulated signal undergoes filtering to reduce the spectral

side lobes, the resulting waveform will no longer have a constant

envelop and in fact, the occasional 180o shifts in phase will cause the

envelope to go to zero momentarily.

2.1.5 Offset Quadrature Phase Shift Keying

If the two bit streams I and Q are offset by a 1/2 bit interval, then the

amplitude fluctuations are minimized since the phase never changes

by 180o. This modulation scheme, Offset Quadrature Phase shift

Keying (OQPSK) is obtained from QPSK by delaying the odd bit

stream by half a bit interval with respect to the even bit stream.


Thus the range of phase transitions is 0o and 90o (the possibility of a

phase shift of 180o is eliminated) and occurs twice as often, but with

half the intensity of the QPSK. While amplitude fluctuations still occur

in the transmitter and receiver they have smaller magnitude. The bit

error rate for QPSK and OQPSK are the same as for BPSK.

Figure 2.1.5 OQPSK Waveform

When an OQPSK signal undergoes band limiting, the resulting

intersymbol interference causes the envelop to droop slightly to the

region of ±ƒn90o phase transition, but since the phase transitions of

180o have been avoided in OQPSK, the envelop will never go to zero

as it does in QPSK.


2.2 GAUSSIAN MINIMUM SHIFT KEYING BASICS

Prior to discussing GMSK in detail we need to review MSK, from

which GMSK is derived. Minimum Shift Keying (MSK) is derived from

OQPSK by replacing the rectangular pulse in amplitude with a half-

cycle sinusoidal pulse. The MSK signal is defined as:


Figure 2.2.1 – Representation of MSK signal

The MSK modulation makes the phase change linear and limited to

±ƒn(ð/2) over a bit interval T. This enables MSK to provide a

significant improvement over QPSK. Because of the effect of the

linear phase change, the power spectral density has low side lobes

that help to control adjacent-channel interference. However the main

lobe becomes wider than the quadrature shift keying.

MSK is a continuous phase modulation scheme where the modulated

carrier contains no phase discontinuities and frequency changes

occur at the carrier zero crossings. MSK is unique due to the

relationship between the frequency of a logical zero and one: the

difference between the frequency of a logical zero and a logical one


is always equal to half the data rate. In other words, the modulation

index is 0.5 for MSK, and is defined as

For example, a 1200 bit per second baseband MSK data signal could

be composed of 1200 Hz and 1800 Hz frequencies for a logical one

and zero respectively.

Baseband MSK, as shown in Figure 2.2.2, is a robust means of

transmitting data in wireless systems where the data rate is relatively

low compared to the channel BW. MX-COM devices such as the

MX429 and MX469 are single chip solutions for baseband MSK

systems, incorporating modulation and demodulation circuitry on a

single chip.


Figure 2.2.2 1200 baud MSK data signal a) NRZ data ,b)MSK

signal

An alternative method for generating MSK modulation can be realized

by directly injecting NRZ data into a frequency modulator with its

modulation index set for 0.5 (see Figure 2.2.3). This approach is

essentially equivalent to baseband MSK. However, in the direct

approach the VCO is part of the RF/IF section, whereas in baseband

MSK the voltage to frequency conversion takes place at baseband.

Figure 2.2.3 Direct MSK Modulation


The fundamental problem with MSK is that the spectrum is not

compact enough to realize data rates approaching the RF channel

BW. A plot of the spectrum for MSK reveals sidelobes extending well

above the data rate. For wireless data transmission systems which

require more efficient use of the RF channel BW, it is necessary to

reduce the energy of the MSK upper sidelobes. Earlier we stated that

a straightforward means of reducing this energy is lowpass filtering

the data stream prior to presenting it to the modulator (pre-modulation

filtering).

The pre-modulation lowpass filter must have a narrow BW with a

sharp cutoff frequency and very little overshoot in its impulse

response. This is where the Gaussian filter characteristic comes in. It

has an impulse response characterized by a classical Gaussian

distribution (bell shaped curve), as shown in Figure 2.2.4. Notice the

absence of overshoot or ringing.


Figure 2.2.4 Gaussian Filter impulse response for BT=0.3 ,0.5

Figure 2.2.4 depicts the impulse response of a Gaussian filter for BT

= 0.3 and 0.5. BT is related to the filter’s - 3dB BW and data rate by

Hence, for a data rate of 9.6 kbps and a BT of 0.3, the filter’s -3dB

cutoff frequency is 2880Hz. Still referring to Figure 2.2.4, notice that a

bit is spread over approximately 3 bit periods for BT=0.3 and two bit

periods for BT=0.5. This gives rise to a phenomenon called inter-

symbol interference (ISI). For BT=0.3 adjacent symbols or bits will

interfere with each other more than for BT=0.5. GMSK with BT=0.5 is

equivalent to MSK. In other words, MSK does not intentionally


introduce ISI. Greater ISI allows the spectrum to be more compact,

making demodulation more difficult. Hence, spectral compactness is

the primary trade-off in going from MSK to Gaussian premodulation

filtered MSK.

Figure 2.2.5 displays the normalized spectral densities for MSK and

GMSK. Notice the reduced sidelobe energy for GMSK. Ultimately,

this means channel spacing can be tighter for GMSK when compared

to MSK for the same adjacent channel interference.

Figure 2.2.5 Spectral density for MSK and GMSK


2.3 PERFORMANCE MEASUREMENTS

The performance of a GMSK modem is generally quantified by

measurement of the signal-to-noise ratio (SNR) versus BER. SNR is

related to Eb/N0 by


2.4 BER MEASUREMENT

In digital communications systems, transmitter, channel and receiver

imperfections corrupt an ideal digital communications signal so that

the digital information is corrupted. Bit error rate (BER) provides a

fundamental measure of system performance in digital

communications systems. For ideal assessment of system

performance, it is desirable to estimate BER in real-time. If accurate

BER estimation can be done in real-time, various techniques can be

employed to combat the sources of bit errors and thus minimize the

BER. This, of course, translates into benefits such as better quality of

service (QOS), greater capacity, and/or less power requirements.

This chapter outlines techniques for performing real-time BER

estimation.

System providers need techniques to approximate real-time BER

estimation, without having to resort to brute-force counting methods.

Because of the dynamic, often unpredictable, nature of the wireless

channel, a priori (deductive) techniques (e.g., where the channel is

assumed before demodulation) are not very useful and are

unreliable .A posteriori (inductive) estimation techniques (e.g., where

knowledge of signal impairments is acquired after the signal is

demodulated) are preferable because they assume no prior

knowledge of the channel.

BER can be measured by counting the number of errors that occur

within a given sequence of bits. This method becomes impractical for


small BERs of interest. For example, one would have to transmit a

known training sequence of 10,000 bits and receive one error out of

that known sequence to calculate a very crude BER=10-4 (and the

variance of the estimator would still be quite high). BERs on the order

of 10-6 or 10-7 require training sequences of 1,000,000 or

10,000,000 bits, respectively.

Measured BER based on one error is unreliable, since BER is a

random variable with some probability density function (pdf). For

more accurate BER estimates, the BER pdf should be taken into

account. Even for known data, received communications signals are

random processes (since the channel conditions are random), and

thus, BER is a random variable. In a binary system, the decision

statistic is that quantity (usually a sample) by which a decision is

made at the receiver as to whether a +1 or a -1 (i.e., zero) was sent.

BER measurement is an important factor in selection of any particular

modulation technique .In next chapter the mathematical

implementation of GMSK is given and error measurement is done.


CHAPTER-3

MATHEMATICAL IMPLEMENTATION

OF GMSK


MATHEMATICAL IMPLEMENTATION OF GMSK

The baseband signal is generated by first transforming the zero/one

encoded bits into -1/+1 encoded bits. This -1/+1 signal is then filtered

in such a way that the "boxcar" shaped +1/-1 pulses are transformed

into Gaussian-shaped signals. The baseband signal is then

modulated using frequency modulation, producing a complete GMSK

signal. If the Gaussian shapes do not overlap, then the modulation

form is called 1-GMSK. If the slots overlap 50% (½), the modulation is

called 2-GMSK, and so on.

3.1 GMSK TRANSMITED SIGNAL

A GMSK transmitter can be implemented by a Gaussian

premodulation low pass filter and FM modulator, where the GMSK

signal is produced by applying the NRZ data stream of unity

amplitude to the Gaussian filter whose response is


Bb is the 3 dB bandwidth of a low pass filter having a Gaussian

shaped spectrum, T is the bit period, and is the normalized

bandwidth. The resulting signal is multiplied by 2ðhf, where hf is the

GMSK modulation index, and applied to a voltage control oscillator

(VCO).

Figure 3.1.1 Direct FM modulator

However, the GMSK baseband signals in our simulation is produced

by a phase modulator where the binary symbol sequence Ik, either 1

or -1, is processed by the phase constructor prior to a quadrature

phase modulator.

Figure 3.1.2 Production of FM via phase modulation


The carrier phase which contains information of the GMSK signal with

normalised modulation bandwidth of Bn=0.5 can be expressed as:

where Ik is the sequence of bipolar source bits and Ö(t) is the phase

shape with the following definitions:

The phase of the GMSK signal in the nthbit interval can be

rearranged as


where è(t,I)is the correlative state vector that depends on the two

most recent bits and èn is the accumulated phase of all the previous

bits that have passed through the phase constructor and it is referred

to as the phase state.

The term Ö(t) is obtained by convolving a ramp of width one bit

period and height ð/2 ( an MSK ramp ) by a Gaussian function whose

response is shown by Equation 1, hence the name Gaussian MSK.

3.2 DEMONSTRATION OF MODULATION

To demonstrate the modulation, we are using the following randomly

chosen binary data stream. (This data stream repeats after 12 bits.)

{1,1,-1,1,1,-1,-1,1,-1,1,-1,-1, 1,1,-1,1,1,-1,-1,1,-1,1,-1,-1,............}.

The beginning of this data stream can be represented graphically by

the following figure.

Figure 3.2.1 Data stream


As the data passes through the filter it is shaped and ISI (inter symbol

interference) is introduced since more than one bit is passing through

the filter at any one time. For BN = 0.5, since the bits are spread over

two bit periods, the second bit enters the filter as the first is half way

through, the third enters as the first leaves etc....The first few

Gaussian shaped pulses are represented graphically in the following

figure.

Figure 3.2.2 Shaped pulses representing the data stream

These individual shaped pulses are then added together to give a

function which is represented graphically in the following figure. This

is the function denoted by b(t).


Figure 3.2.3 Function B(t)

This function, b(t), is then integrated, with respect to t (time) from t to ,

to give the function c(t) as shown in the second figure. This function

c(t) is represented graphically below.

Figure 3.2.4 Function C(t)


Once we have the function c(t), we take Sine and Cosine functions of

it to produce the I and Q-baseband signals. Taking the Cosine of c(t)

produces the I-baseband signal I(t) i.e. I(t) = Cos[ c(t) ].

This function I(t) is represented graphically below.

Figure 3.2.5 I-baseband signa


Taking the Sine of c(t) produces the Q-baseband signal Q(t) i.e.

Q(t) = Sin[ c(t) ].

Figure 3.2.6 Q-baseband signal

These two functions I(t) and Q(t) are then passed through the I/Q

modulator which leads to the output signal m(t) which can be written

as m(t) = Sin(2ïfc t) I(t) + Cos(2ïfct) Q(t), where, fc is the carrier

frequency used as the oscillator in the second figure The GMSK

signal m(t) is represented

Figure 3.2.1 GMSK modulated signal


CHAPTER-4

SIMULATION OF

GMSK


4.1 SIMULATION


4.2 BERNOULLI BINARY GENERATOR

The Bernoulli Binary Generator block generates random binary

numbers using a Bernoulli distribution. The Bernoulli distribution with

parameter p produces zero with probability p and one with probability

1-p. The Bernoulli distribution has mean value 1-p and variance p(1-

p). The Probability of a zero parameter specifies p, and can be any

real number between zero and one.

Probability of a zero:-The probability with which a zero output

occurs.

Initial seed:-The initial seed value for the random number generator.

The seed can be either a vector of the same length as the Probability

of a zero parameter, or a scalar.

Sample time:-The period of each sample-based vector or each row

of frame-based matrix.


Frame-based outputs:-Determines whether the output is frame-

based or sample-based. This box is active only if Interpret vector

parameters as 1-D are unchecked.

Samples per frame:-The number of samples in each column of a

framebased output signal. This field is active only if Frame-based

outputs are checked. Interpret vector parameters as 1-D.If this box is

checked, then the output is a one-dimensional signal. Otherwise, the

output is a twodimensional signal. This box is active only if Frame-

based outputs are unchecked.

4.3 GMSK MODULATOR BASEBAND

The GMSK Modulator Baseband block modulates using the

Gaussian minimum shift keying method. The output is a baseband

representation of the modulated signal. The BT product parameter

represents bandwidth multiplied by time. This parameter is a

nonnegative scalar. It is used to reduce the bandwidth at the expense

of increased intersymbol interference. The Pulse length parameter

measures the length of the Gaussian pulse shape, in symbol

intervals. For the exact definitions of the pulse shape, see the work

by Anderson, Aulin, and Sundberg among the references listed

below. The Symbol prehistory parameter is a scalar or vector that

specifies the data symbols used before the start of the simulation, in

reverse chronological order. If it is a vector, then its length must be

one less than the Pulse length parameter. In this block, a symbol of


1 causes a phase shift of ð/2 radians. The Phase offset parameter is

the initial phase of the output waveform, measured in radians.

Input type:-Indicates whether the input consists of bipolar or binary

values.

BT product:-The product of bandwidth and time.

Pulse length (symbol intervals):-The length of the frequency pulse

shape.

Symbol prehistory:-The data symbols used before the start of the

simulation, in reverse chronological order.

Phase offset (rad):-The initial phase of the output waveform.

Samples per symbol:-The number of output samples that the block

produces for each integer or bit in the input


CHAPTER-5

RESULTS


RESULTS

5.1 BERNOULLI BINARY GENERATOR :-

The Bernoulli Binary Generator is used to generate random data bit

required as input to the simulation model.

In this generator

+1 is denoted for 1 and,

-1 is denoted for 0

Figure 5.1.1:- Output of Bernoulli Binary Generator

5.2 GMSK MODULATOR:-

The output of Bernoulli Binary Generator is applied to the input of

GMSK modulator, which first converts binary data train to the

Gaussian shaped train by passing through the Gaussian filter which


is shown in figure 5.2.1. This Gaussian shaped train is the input to the

modulator section. The output modulated signal is shown in figure

5.2.2.

Figure 5.2.1:- Output of Gaussian Filter

Figure 5.2.2:- GMSK Modulated Signal


CHAPTER-6

APPLICATION OF GMSK


6.1 APPLICATION OF GMSK in GSM

In digital communication, Gaussian minimum shift keying or GMSK

is a continuous-phase frequency-shift keying modulation scheme. It is

similar to standard minimum-shift keying (MSK); however the digital

data stream is first shaped with a Gaussian filter before being applied

to a frequency modulator. This has the advantage of reducing

sideband power, which in turn reduces out-of-band interference

between signal carriers in adjacent frequency channels. However, the

Gaussian filter increases the modulation memory in the system and

causes intersymbol interference, making it more difficult to

discriminate between different transmitted data values and requiring

more complex channel equalization algorithms such as an adaptive

equalizer at the receiver.

GMSK is most notably used in the Global System for Mobile

Communications (GSM).

Global System for Mobile communications (GSM: originally from

Groupe Spécial Mobile) is the most popular standard for mobile

phones in the world. Its promoter, the GSM Association, estimates

that 82% of the global mobile market uses the standard [1]. GSM is

used by over 2 billion people across more than 212 countries and

territories.[2][3] Its ubiquity makes international roaming very common

between mobile phone operators, enabling subscribers to use their

phones in many parts of the world. GSM differs from its predecessors

in that both signaling and speech channels are digital call quality, and


http://en.wikipedia.org/wiki/Digital_call_quality

http://en.wikipedia.org/wiki/Mobile_phone_operator

http://en.wikipedia.org/wiki/Roaming

http://en.wikipedia.org/wiki/#_note-2


http://en.wikipedia.org/wiki/1000000000_(number)


http://en.wikipedia.org/wiki/GSM_Association

http://en.wikipedia.org/wiki/Mobile_phone

http://en.wikipedia.org/wiki/Mobile_phone

http://en.wikipedia.org/wiki/Global_System_for_Mobile_Communications

http://en.wikipedia.org/wiki/Global_System_for_Mobile_Communications

http://en.wikipedia.org/wiki/Adaptive_equalizer

http://en.wikipedia.org/wiki/Adaptive_equalizer

http://en.wikipedia.org/wiki/Intersymbol_interference

http://en.wikipedia.org/wiki/Sideband

http://en.wikipedia.org/wiki/Gaussian_function

http://en.wikipedia.org/wiki/Minimum-shift_keying

http://en.wikipedia.org/wiki/Modulation

http://en.wikipedia.org/wiki/Frequency-shift_keying

http://en.wikipedia.org/wiki/Digital_communication

so is considered a second generation (2G) mobile phone system.

This has also meant that data communication were built into the

system using the 3rd Generation Partnership Project (3GPP).

The GSM logo is used to identify compatible handsets and

equipment The key advantage of GSM systems to consumers has

been better voice quality and low-cost alternatives to making calls,

such as the Short message service (SMS, also called "text

messaging"). The advantage for network operators has been the

ease of deploying equipment from any vendors that implement the

standard.[4] Like other cellular standards, GSM allows network

operators to offer roaming services so that subscribers can use their

phones on GSM networks all over the world.

Newer versions of the standard were backward-compatible with the

original GSM phones. For example, Release '97 of the standard

added packet data capabilities, by means of General Packet Radio

Service (GPRS). Release '99 introduced higher speed data

transmission using Enhanced Data Rates for GSM Evolution (EDGE).


http://en.wikipedia.org/wiki/Enhanced_Data_Rates_for_GSM_Evolution

http://en.wikipedia.org/wiki/General_Packet_Radio_Service

http://en.wikipedia.org/wiki/General_Packet_Radio_Service

http://en.wikipedia.org/wiki/3GPP#Standards


http://en.wikipedia.org/wiki/Short_message_service

http://en.wikipedia.org/wiki/3GPP

http://en.wikipedia.org/wiki/2G

6.2 APPLICATION OF GMSK IN AEROSPACE

Using bandwidth-efficient modulation, communication satellites

can transmit signals through a smaller frequency band. The

Aerospace Corporation's research into one such technique has

yielded tangible benefits for the military's protected

communication satellites.

The recent proliferation of terrestrial and space-based

communication systems has given rise to an increasingly critical

problem—the lack of available frequency spectrum. One tool that

satellite system designers can use to maximize the use of

available spectrum is bandwidth-efficient modulation. This

technique can enhance bandwidth efficiency while retaining

reasonable power efficiency and implementation complexity.

Because of the wide applicability of bandwidth-efficient

modulation to most new satellite systems, The Aerospace

Corporation has performed extensive research in this area. One

recent application can be found in the Advanced Extremely High

Frequency (AEHF) program.


With Gaussian minimum shift keying, the rectangular pulses

representing input bits are converted into Gaussian shaped pulses.

The resulting carrier signal is smooth in phase, and therefore requires

less bandwidth to transmit. The configuration shown here uses a

bandwidth–bit-time product of 1/5.


A successor to Milstar I and II, the AEHF program will form the

basis of the military's next-generation protected communication

system. Specifications called for a tenfold increase in capacity

over the current Milstar system; however, early studies clearly

indicated that the new downlink requirements could not be met

within the existing frequency allocation simply by extending the

Milstar design. The MILSATCOM (Military Satellite

Communications) Joint Program Office at the Air Force Space

and Missile Systems Center asked Aerospace to help investigate

alternative signaling methods that would use the allotted

bandwidth more efficiently.

6.2.1 Phase-Shift Modulation

Aerospace researchers began by characterizing traditional binary

phase-shift keying and quarternary phase-shift keying—two

commonly employed satellite signal-transmission techniques—in

light of the new capacity requirements. Milstar currently uses

differential phase-shift keying for its downlink. This method is

similar to binary phase-shift keying and exhibits the same power

spectral density, a measure of the distribution of signal power

versus frequency.


Systems that transmit multiple signals within a given bandwidth

have several options for sharing frequency resources. One

technique, called frequency-division multiple access, assigns a

carrier or channel to each signal, centered at a unique

transmission frequency. Designers typically want to space these

channels as closely as possible to increase the system capacity,

but as the spacing gets too close, the power spectra start to

overlap, and power from one channel spills into another. This

phenomenon, known as adjacent channel interference, increases

the probability of transmission errors, also known as the bit-error

rate (see sidebar, Performance Measures for Digital

Communication Systems).


http://www.aero.org/publications/crosslink/winter2002/03_sidebar1.html


The power spectral density for Gaussian minimum shift keying is

much more compact than that of differential phase-shift keying and

does not exhibit the same pronounced sidelobes. In this example, the

bandwidth–bit-time product is 1/6.


Gaussian minimum shift keying waveforms with varying bandwidth–

bit-time products are compared with binary and differential phase-

shift keying. As the bandwidth–bit-time product decreases, the

waveform spectra grows narrower.


The power spectral density of both binary and quarternary phase-

shift keying is fairly broad, and when channels are packed

together too tightly, the adjacent channel interference can be

severe. In the case of the AEHF program, the channels would

have to be spaced far apart to avoid large degradations from such

interference. Researchers discovered that they simply could not fit

enough channels within the allocated downlink frequency to meet

the capacity requirement using standard binary, differential, or

quarternary phase-shift keying. Other, more advanced modulation

techniques would have to be found.

6.2.2 Gaussian Minimum Shift Keying

Aerospace had been studying a modulation technique known as

Gaussian minimum shift keying for potential application in the Air

Force Satellite Control Network and recognized that it might be a

good candidate for the AEHF program.


Gaussian minimum shift keying is a form of continuous phase

modulation, a technique that achieves smooth phase transitions

between signal states, thereby reducing bandwidth requirements

(see sidebar, Modulation Basics). With Gaussian minimum shift

keying, input bits with rectangular (+1, -1) representation are

converted to Gaussian (bell-shaped) pulses by a Gaussian filter

before further smoothing by a frequency modulator. Also, in most

cases, the Gaussian pulse is allowed to last longer than one bit

time—the amount of time a binary 1 is in the "on" position.

Consequently, the pulses overlap, giving rise to a phenomenon

known as intersymbol interference. The extent of this overlap is

determined by the product of the bandwidth of the Gaussian filter

and the data-bit duration; the smaller the bandwidth–bit-time

product, the more the data bits or pulses overlap.



Measured data showing growth of sidelobes in the power spectral

density of offset quarternary phase-shift keying. The pink curve

indicates performance through a standard (linear) amplifier, while the

green curve shows the poorer performance though a saturated

(nonlinear) amplifier.


The resulting carrier signal is very smooth in phase—particularly

in comparison to waveforms generated through standard binary or

quarternary phase-shift keying. This is important because signals

with smooth phase transitions require less bandwidth to transmit.

On the other hand, this very smooth phase makes the receiver's

job much harder. With Gaussian minimum shift keying, there are

no well-defined phase transitions to detect for bit synchronization,

and the energy from each bit is mixed with the energy from

several other bits. The transmitter output looks nothing like the

data input, and on the receiver side, a special demodulator of

increased complexity is needed to extract the data bits. For the

receiver to achieve a given bit-error rate, the transmitter must

generate more power to overcome the receiver noise in the

presence of the intersymbol interference. In other words, the

Gaussian minimum shift keying waveform is usually less power-

efficient than more traditional waveforms such as binary phase-

shift keying and requires a more complex receiver, but this

potential reduction in power efficiency and increase in receiver

complexity could be rewarded with a very significant

enhancement of bandwidth efficiency. So, with Gaussian

minimum shift keying, there is a trade-off between bandwidth

efficiency and power efficiency.

Gaussian minimum shift keying is not new—the technique has

been used extensively in Europe for cell-phone applications with a

bandwidth–bit-time product of 0.3. But system designs using very

small bandwidth–bit-time products such as 1/5 or 1/8 are new—


and challenging. Aerospace became interested in these smaller

bandwidth–bit-time products because of their narrow bandwidth

occupancy and the rapid roll-off of their power spectra. These two

factors strongly influence the ability to pack many different

channels into a limited amount of bandwidth. The Gaussian

minimum shift keying waveform exhibits a steep power spectrum

and therefore coexists well with adjacent channels in a frequency-

division multiple-access system.

The resulting carrier signal is very smooth in phase—particularly

in comparison to waveforms generated through standard binary or

quarternary phase-shift keying. This is important because signals

with smooth phase transitions require less bandwidth to transmit.

On the other hand, this very smooth phase makes the receiver's

job much harder. With Gaussian minimum shift keying, there are

no well-defined phase transitions to detect for bit synchronization,

and the energy from each bit is mixed with the energy from

several other bits. The transmitter output looks nothing like the

data input, and on the receiver side, a special demodulator of

increased complexity is needed to extract the data bits. For the

receiver to achieve a given bit-error rate, the transmitter must

generate more power to overcome the receiver noise in the

presence of the intersymbol interference. In other words, the

Gaussian minimum shift keying waveform is usually less power-

efficient than more traditional waveforms such as binary phase-

shift keying and requires a more complex receiver, but this

potential reduction in power efficiency and increase in receiver


complexity could be rewarded with a very significant

enhancement of bandwidth efficiency. So, with Gaussian

minimum shift keying, there is a trade-off between bandwidth

efficiency and power efficiency.

Gaussian minimum shift keying is not new—the technique has

been used extensively in Europe for cell-phone applications with a

bandwidth–bit-time product of 0.3. But system designs using very

small bandwidth–bit-time products such as 1/5 or 1/8 are new—

and challenging. Aerospace became interested in these smaller

bandwidth–bit-time products because of their narrow bandwidth

occupancy and the rapid roll-off of their power spectra. These two

factors strongly influence the ability to pack many different

channels into a limited amount of bandwidth. The Gaussian

minimum shift keying waveform exhibits a steep power spectrum

and therefore coexists well with adjacent channels in a frequency-

division multiple-access system.


This graph shows the measured power spectral density for Gaussian

minimum shift keying when passed though a standard (linear) and

saturated (nonlinear) power amplifier. Even in scenarios involving

saturated amplifiers, the technique does not give rise to significant

sidelobes. In this example, the bandwidth–bit-time product is 0.125,

and the data rate is 1 megabit per second.


CHAPTER-7

CONCLUSION


CONCLUSION

This project has presented a partial simulating model of GMSK with

its identical real life conditions. The variations in the performance of

signal at various stages and under various circumstances (such as

with and without noise, multipath fading etc) is drawn on separate out

blocks. These results help comparing GMSK model with all other

known schemes BPSK (which was previously used widely ) at

BT=0.3 has BER of about 0.251, but from this model the BER of

GMSK has found to be about 0.530 under same conditions when

differentially encoded method was used.

But using OQPSK method shows the same performance as BPSK.

Spectrum utilization is an very importance factor since in wireless

communication the spectrums to be allocated is limited. GMSK

introduces use of Gaussian filter for prefiltering which compresses the

width and removes unwanted side lobes. Thus it also reduces power

requirements.

Overall we can conclude that GMSK is an intelligent compromise

between spectrum utilization, power requirement and the BER

performance. Thus GMSK is widely used in modern communication

systems.


APPENDIX

Matlab Code For GMSK Modulation and Demodulation

clear all;

close all;

%*********************************

% Variable Definition

%*********************************

DRate = 1; % data rate or 1 bit in one second

M = 18; % no. of sample per bit

N = 36; % no. of bits for simulation [-18:18]

BT = 0.5; % Bandwidth*Period (cannot change )

T = 1/DRate; % data period , i.e 1 bit in one second

Ts = T/M;

k=[-18:18]; % Chen's values. More than needed;

% only introduces a little more delay

%******************************************************************

% CONSTRUCTION OF GAUSSIAN FILTER

%******************************************************************

alpha = sqrt(log(2))/(2*pi*BT);

% alpha calculated for the gaussian filter

h = exp(-(k*Ts).^2/(2*alpha^2*T^2))/(sqrt(2*pi)*alpha*T);

% Gaussian Filter Response in time domain

figure;

plot(h,'*r')

title('Response of Gaussian Filter');


xlabel( 'Sample at Ts');

ylabel( 'Normalized Magnitude');

grid;

bits = [zeros(1,36) 1 zeros(1,36) 1 zeros(1,36) -1 zeros(1,36) -1

zeros(1,36) 1

zeros(1,36) 1 zeros(1,36) 1 zeros(1,36)];

% data is randomly selected, here 1 indicates 1 and -1 indicates zero

%**************

% MODULATION

%**************

m = filter(h,1,bits);

% bits are passed through the all pole filter described by h, i.e bits are

% shaped by gaussian filter

t0=.35; % signal duration

ts=0.00135; % sampling interval

fc=200; % carrier frequency

kf=100; % Modulation index

fs=1/ts; % sampling frequency

t=[0:ts:t0]; % time vector

df=0.25; % required frequency resolution

int_m(1)=0;

for i=1:length(t)-1 % Integral of m

int_m(i+1)=int_m(i)+m(i)*ts;

end

tx_signal=cos(2*pi*fc*t+2*pi*kf*int_m);

% FM is a form of angle modulation in Which the instantaneous


%frequency of the carrier signal is varied linearly with the baseband

signal m(t),

x = cos(2*pi*fc*t);

y = sin(2*pi*fc*t);

figure;

subplot(2,1,1)

stem(bits(1:250))

title('RANDOM DATA BITS,+1 FOR ONE AND -1 FOR ZERO ');

grid;

subplot(2,1,2)

plot(m(1:250),'r')

title('GAUSSIAN SHAPED TRAIN');

xlim([0 260]);

figure;

plot(tx_signal)

title('MODULATED SIGNAL');

xlim([0 225]);


REFERENCES

1. Simon Haykin, “Communication System” ,3rd edition ,(pg-114)

2. John G. Proakis, “Digital Comunication” , 4th edition,

( pg -80,283,660,800)

3. Herbert Taub and Donald Schilling “Principles of

Communication System” ,Tata Mcgraw Hill edition,(pg-

249,286,298)

4. J. S. Chitode, “Electronic Communication”, 3rd edition, (pg-

390,406,440)

5. W.C.Y. Lee, “Cellular Mobile Communication”, 2nd edition, (pg-

463,471,480)

6. A.B. Carlson, “Communication Systems” 3rd edition, (pg-217)

7. B.P. Lathi, “Communication Systems” ,2nd edition, (pg-71,119)

8. A.V. Openheim, “Signals and System” ,4th edition, (pg-

189,378)

9. http://en.wikipedia.org/wiki/GMSK

10. http://www.answers.com/topic/continuous-phase-modulation

11. http://encarta.msn.com/encyclopedia_761569907/Radio.htm l#

461530 757

12. www.ofcom.org.uk/static/archive/ra/topics/research/topics/emc/l

inkpc p/appd.pdf -

13. www.eetkorea.com/ARTICLES/2003AUG/A/2003AUG29_

NTEK_A N.PDF

14. www.dsprelated.com/showmessage/51149/1.php

15. www.mathworks.com/matlabcentral/fileexchange/

loadFile.do?objectI d=10503&objectType=file


http://www.mathworks.com/matlabcentral/fileexchange/

http://www.eetkorea.com/ARTICLES/2003AUG/A/2003AUG29_

http://www.ofcom.org.uk/static/archive/ra/topics/research/topics/emc/l

http://encarta.msn.com/encyclopedia_761569907/Radio.htm%20l#

16. www.cholar.lib.vt.edu/theses/public/etd-59415

13972900/etd.pdf

17. www.synetcom.com/images/pdf/Spra139.pdf

18. www .etfec.oxfordjournals.org/cgi/reprint/E88-A/10/2863.pdf

19. www.hpl.hp.com/techreports/98/HPL-98-36.pdf

20. www.eecg.utoronto.ca/~tcc/DenisDalyBAScThesis.pdf

21. www.comblock.com/download/com1028.pdf

22. www.comblock.com/download/com1027.pdf

23. Matlab 7


http://www.cholar.lib.vt.edu/theses/public/etd-59415

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