Digital Modulation Techniques in Mobile Communications

Digital Modulation Techniques inMobile CommunicationsFahredd'n Sadikoglu 1

Digital Modulation TechniqueSender DestinationMessageMessageModulationChannel DemodulationFahredd'n Sadikoglu 2

Modulation Techniques• Modulation is the process of encoding information from amessage source in a manner suitable for transmition.• The ultimate goal of a modulation technique is to transport themessage signal through a radio channel with the best possiblequality while occupying the least amount of radio spectrum.SenderMessage Modulation ChannelD(t)C(t)=A COS (wt+Φ)Fahredd'n Sadikoglu 3

• Modulation may be done by varying the amplitude,phase, or frequency of a high frequency carrier inaccordance with the amplitude of the messagesignal.C(t)=A COS (wt+Φ)ASK FSK PSK

Amplitude Shift Keying (ASK)- Pulse shaping can be employed to remove spectralspreading.- ASK demonstrates poor performance, as it is heavilyaffected by noise and interference.

Frequency Shift Keying (FSK)- Bandwidth occupancy of FSK is dependant on the spacing of thetwo symbols. A frequency spacing of 0.5 times the symbol periodis typically used.- FSK can be expanded to a M-ary scheme, employing multiplefrequencies as different states.-

Phase Shift Keying (PSK)- Binary Phase Shift Keying (BPSK) demonstrates better performancethan ASK and FSK.- PSK can be expanded to a M-ary scheme, employing multiple phasesand amplitudes as different states.- Filtering can be employed to avoid spectral spreading.

PSK & DPSKFahredd'n Sadikoglu 8

Multi-PhaseBinary Phase ShiftKeying (BPSK)1: φ 1 (t)= p(t) cos(ω c t)••0: φ 0 (t)= p(t)cos(ω c t+π)M-ary PSK⎛ 2π⎞pk() t = p()t cos⎜ωct+k⎟⎝ M ⎠xxxxxxImImxxxxReReFahredd'n Sadikoglu 9

QPSK* Quadrature Phase Shift Keying is effectively two independentBPSK systems (I and Q), and therefore exhibits the sameperformance but twice the bandwidth efficiency.* Quadrature Phase Shift Keying can be filtered using raisedcosine filters to achieve excellent out of band suppression.* Large envelope variations occur during phase transitions, thusrequiring linear amplification.

Quadrature Phase-Shift Keying(QPSK)Constellation diagram for •QPSK with Gray coding.Each adjacent symbol onlydiffers by one bit.QPSK can encode two bits •per symbol, shown in thediagram with Gray coding tominimize the BER twice therate of BPSK.QPSK may be used either todouble the data ratecompared to a BPSK systemwhile maintaining thebandwidth of the signal orto maintain the data-rate ofBPSK but halve thebandwidth needed.•Fahredd'n Sadikoglu 11

• Constellation diagram for QPSKwith Gray coding. Each adjacentsymbol only differs by one bit.• QPSK can encode two bits persymbol, shown in the diagramwith Gray coding to minimize theBER twice the rate of BPSK.• QPSK may be used either todouble the data rate comparedto a BPSK system whilemaintaining the bandwidth of thesignal or to maintain the datarateof BPSK but halve thebandwidth needed.

QPSKModeled as two BPSK systems inparallel•Imx0 1 1 1 0 0 1 0Serial toParallelConverterR b1 1 0 0R b /20 1 0 1xR b /2cos ω c t90xT s =2 T b-+ BPF•xxxReFahredd'n Sadikoglu 13

• The binary data that is conveyed by this waveform is: 1 1 0 0 0 1 1 0.• The odd bits, highlighted here, contribute to the in-phase component:1 1 0 0 0 1 1 0. The even bits, highlighted here, contribute to thequadrature-phase component: 1 1 0 0 0 1 1 0 .• In the timing diagram for QPSK. The binary data stream is shownbeneath the time axis. The two signal components with their bitassignments are shown the top and the total, combined signal at thebottom. Note the abrupt changes in phase at some of the bit-periodboundaries which are not satisfied.

QPSK TYPESFahredd'n Sadikoglu 15

QPSKFahredd'n Sadikoglu 16

Fahredd'n Sadikoglu 17

Offset QPSK (OQPSK)Ideally amplitude of QPSK signal isconstantIf pulses are shaped, then constantenvelope is lost and phase shift of πradians causes waveform to go to zerobrieflyCan only use less efficient linear amplifiersOQPSK or Staggered QPSKWaveforms are shifted by ½ bitFahredd'n Sadikoglu 18

OQPSKBit transitions occur every T b sec •Limited to changes of +/- π/2 •Smaller envelope variations •-TT3T5T7T9T02T 4T6TFahredd'n Sadikoglu 19

Offset Quadrature Phase-ShiftKeying (OQPSK)• Offset quadrature phase-shift keying OQPSK is a variant of PhaseShift Keying modulation using 4 different values of the phase totransmit. It is sometimes called Staggered quadrature phase shiftkeying SQPSK .• OQPSK limits the phase-jumps that occur at symbol boundaries to nomore than 90° and reduces the effects on the amplitude of the signaldue to any low-pass filtering.

OPSKFahredd'n Sadikoglu 21

QPSK vs. OQPSKFahredd'n Sadikoglu 22

QPSK & OQPSK0 1 1 1 0 0 0 1(-1, 1)(a q, a i)(1, 1)cos ωtsinωt(-1, -1)(1, -1)Fahredd'n Sadikoglu 23

Disadvantages of OQPSK(1) OQPSK introduces a delay of half a symbol into thedemodulation process. In other words, using OQPSKincreases the temporal efficiency of normal QPSK.The reason is that the in phase and quadrature phasecomponents of the OQPSK cannot be simultaneouslyzero. Hence, the range of the fluctuations in thesignal is smaller.(2) An additional disadvantage is that the quiescientpower is nonzero, which may be a design issue indevices targeted for low power applications.

π/4-QPSKDual constellation diagram for π/4-QPSK. Thisshows the two separate constellations withidentical Gray coding but rotated by 45° withrespect to each other.This final variant of QPSK uses two identicalconstellations which are rotated by 45° (π / 4radians, hence the name) with respect to oneanother. Usually, either the even or odd databits are used to select points from one of theconstellations and the other bits select pointsfrom the other constellation. This also reducesthe phase-shifts from a maximum of 180°, butonly to a maximum of 135° and so theamplitude fluctuations of π / 4–QPSK arebetween OQPSK and non-offset QPSK.Fahredd'n Sadikoglu 25

QPSKOQPSKπ/4-QPSKFahredd'n Sadikoglu 26

Minimum Shift Keying (MSK)• It is a special type of continuous phasefrequencyshift keying (CPFSK).• The peak frequency deviation is equal to 1/4the bit rate.• MSK has a modulation index of 0.5 .KMSK=2 ∆F / RbFahredd'n Sadikoglu 27

● The name Minimum Shift Keying (MSK) implies the minimumfrequency separation that allows orthogonal detection as two FSKsignals VH(t) & VL(t).T∫ VH(t)VL(t)dt =0●0MSK is a spectrally efficient modulation scheme and is particularlyattractive for use in mobile communication systems because of itspossesses properties such as :● constant envelope.● Spectral efficiency.● Good BER performance.● Self-synchronizing capability.

MSKMSK uses changes in phase to represent 0's and 1's, but unlike most otherkeying, the pulse sent to represent a 0 or a 1, not only depends on whatinformation is being sent, but what was previously sent. The pulse used inMSK is the following:Fahredd'n Sadikoglu 29

● Right from the equation we can see that θ(t) depends not only from the symbol beingsent (from the change in the sign), but it can be seen that is also depends on θ(0) whichmeans that the pulse also depends on what was previously sent. To see how this workslet's work through an example. Assume the data being sent is 111010000, then thephase of the signal would fluctuate as seen in the figure below.

● If it assumed that h = 1/2, then the figure simplifies. The phase can now go up ordown by increments of pi/2, and the values at which the phase can be (at integerintervals of Tb) are {-pi/2, 0, pi/2, pi}. The above example now changes to the graphbelow. The figure illustrates one feature of MSK that may not be obvious, when a largenumber of the same symbol is transmitted, the phase does not go to infinity, but rotatesaround 0 phase.

• An MSK signal can be thought of as a specialform of OQPSK where the baseband rectangularpulses are replaced with half-sinusoidal pulses.N-1 N-1SMSK(t)=∑ ‏+‏fctחmIi(t)p(t-2iTb)cos2‎ ∑ ‏.‏fctחmQi(t)p(t-2iTb-Tb)sin2‎i=0 i=0whereP(t) =cos(חt/2Tb) 0

MSK better than QPSKEven though the derivation of MSK was produced by analyzing the changes inphase, MSK is actually a form of frequency-shift-keying (FSK) with(where f1 and f2 are the frequencies used for the pulses). MSK produces anFSK with the minimum difference between the frequencies of the two FSKsignals such that the signals do not interfere with each other. MSKproduces a power spectrum density that falls off much faster compared to thespectrum of QPSK. While QPSK falls off at the inverse square of the frequency,MSK falls off at the inverse fourth power of the frequency. Thus MSK canoperate in a smaller bandwidth compared to QPSK.Fahredd'n Sadikoglu 33

Generating minimum-shift keyingFahredd'n Sadikoglu 34

MSKFahredd'n Sadikoglu 35

Gaussian Minimum Shift KeyingGMSKEven though MSK's power spectrum density falls quite fast, it does not fall fastenough so that interference between adjacent signals in the frequency bandcan be avoided. To take care of the problem, the original binary signal ispassed through a Gaussian shaped filter before it is modulated with MSK.Frequency Response:The principle parameter in designing an appropriate Gaussian filter is the timebandwidthproduct WTb. Please see the following figure for the frequencyresponse of different Gaussian filters. Note that MSK has a time-bandwidth productof infinity.Fahredd'n Sadikoglu 36

As can be seen from above, GMSKs power spectrum drops much quickerthan MSK's. Furthermore, as WTb is decreased, the roll-off is much quicker.

Time-Domain Response:Since lower time-bandwidth products produce a faster power-spectrum roll-off,why not have a very small time-bandwidth product. It happens that with lowertime-bandwidth products the pulse is spread over a longer time, which cancause intersymbol interference.Therefore as a compromise between spectral efficiency and time-domainperformance, an intermediate time-bandwidth product must be chosen.





The figure shows the 16-bit NRZ (Non-Return-to-Zero)sequence (-1,-1,-1,+1,+1,-1,+1,+1,+1,+1,-1,+1,-1,+1,-1,-1)and the corresponding phase trajectory of MSK (left) andGMSK (right) signals. The phase increment per symbol isfor the MSK signal.

The figure shows the in phase I (real) and quadrature Q (imaginary)components of the MSK (left) and GMSK (right) corresponding base bandequivalent signals.

• The figure shows the MSK and GMSK modulatedsignals for two different symbols.• Notice the slight difference of frequency between themodulated signal of symbol (-1) and symbol (1). Thisshows the FM nature of MSK and GMSK signals.

The reliability of a data message produced by a GMSKsystem is highly dependent on the following:(1) Receiver thermal noise: this is produced partly by the receiveantenna and mostly by the radio receiver.(2) Channel fading: this is caused by the multipath propagationnature of the radio channel.(3) Band limiting: This is mostly associated with the receiver Iffrequency and phase characteristics(4) DC drifts: may be caused by a number of factors such astemperature variations, asymmetry of the frequency response ofthe receiver, frequency drifts of the receiver local oscillator.

(5)Frequency offset:* This refers to the receiver carrier frequency drift relativeto the frequency transmitted caused by the finite stabilityof all the frequency sources in the receiver. The shift is alsocaused partly by Doppler shifts, which result due to therelative transmitter/receiver motion.* The frequency offset causes the received IF signal to beoff-center with respect to the IF filter response, and thiscause more signal distortion.* The frequency offset also results in a proportional DCcomponent at the discriminator output.

(6)Timing errors:- The timing reference causes the sampling instants to be offset fromthe center of the transmit eye.- As GMSK is a filtered version of MSK, this introduces another variablethat can be used to describe the exact nature of the GMSKmodulation.- This variable is referred to as the BT, where B is the 3dB point of theGaussian filter, and T is the bit duration. Therefore a BT of infinitywould relate to MSK.- The smaller the BT the smaller the spectral density however thiscomes at a trade off of increased inter-symbol interference.- This is because by smoothing the edges of the bit pulses they begin tooverlap each other. The greater the smoothing, the greater theoverlapping, until eventually individual bits may be undetectable.

How to implement a GMSK modulator?Fahredd'n Sadikoglu 49

How to implement a GMSK demodulator?Fahredd'n Sadikoglu 50

GSM Modulation SpecificationsIn the GSM standard, Gaussian Minimum Shift Keying with a time-bandwidthproduct of 0.3 was chosen as a compromise between spectral efficiency andintersymbol interference. With this value of WTb, 99% of the power spectrum iswithin a bandwidth of 250 kHz, and since GSM spectrum is divided into 200kHz channels for multiple access, there is very little interference between thechannels. The speed at which GSM can transmit at, with WTb=0.3, is 271 kb/s.(It cannot go faster, since that would cause intersymbol interference).Fahredd'n Sadikoglu 51

References[5] S. Haykin, Communication Systems, 4th Edition, New York: John Wiley & Sons, Inc., 2001, pp. 387-399.[6] J.G. Sempere, "An overview of the GSM system by Javier Gozalvez Sempere," [Online document],April 1998, Availablehttp://www.comms.eee.strath.ac.uk/~gozalvez/gsm/gsm.htmlhttp://en.wikipedia.org/wiki/Phase-shift_keyingFahredd'n Sadikoglu 52

Digital Modulation Techniques in Mobile Communications

You also want an ePaper? Increase the reach of your titles

Delete template?

Save as template?