Agilent AN 1335

HPSK Spreading for 3GApplication Note

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In mobile communications, batterylife is one of the most important char-acteristics of the handset, and the effi-ciency of the handset power amplifieris key to maximizing battery life. Ampli-fiers are typically most efficient whenthey operate close to their saturationlevel. Therefore, mobile station ampli-fiers should ideally be designed so thatthe average power level of the signalis as close as possible to this saturationlevel.

This works well for 2G (Second Gen-eration) modulation formats, such asOQPSK (Offset Quadrature Phase ShiftKeying) or GMSK (Gaussian MinimumShift Keying). OQPSK avoids symboltransitions through zero, which reducesthe peak-to-average power ratio of thesignal. GMSK is a constant-amplitudemodulation format, so peak-to-averagepower ratio is not an issue. For theseformats, the headroom required in theamplifier to prevent compression ofthe signal and interference with theadjacent frequency channels is small(or, in the case of GMSK, nonexistent).Thus, the amplifier can operate moreefficiently.

However, in 3G (Third Generation)spread-spectrum systems, such as W-CDMA (3GPP) and cdma2000(3GPP2)1, the handset can transmitmultiple channels at different ampli-tude levels. Modulation schemes suchas OQPSK or GMSK do not preventzero-crossings for multiple channelsand are no longer suitable. There is aneed for a modulation format or aspreading technique that can accom-modate multiple channels at differentpower levels while producing signalswith low peak-to-average power ratios.

HPSK (Hybrid Phase Shift Keying), alsoknown as OCQPSK (Orthogonal Com-plex Quadrature Phase Shift Keying),has been proposed as the spreadingtechnique for W-CDMA and cdma2000.HPSK is a complex spreading schemethat is very different from the modu-lation formats commonly used untilnow. The objective of this applicationnote is to provide an overview of HPSKand explain how to start makingmodulation quality measurements onthe reverse link (uplink) of 3Gspread-spectrum systems.

This application note starts with thebasic structure of the reverse link(uplink) for W-CDMA and cdma2000with no scrambling, and explains thetransition through complex scram-bling to HPSK. The block diagramsshown are generic block diagrams forHPSK that are not particular to eitherW-CDMA or cdma2000.

The application note then describes:

• Why complex scrambling is usedand how it works

• Why HPSK is used and how it works

Finally, the application note showshow to measure modulation qualityon the reverse link of 3G systemswith existing instruments.

Introduction

Contents

3 1. Basic structure of the reverse link(uplink) of 3G systems

4 2. Complex scrambling4 How does complex scrambling work?6 Review: Why is complex scrambling

required?

7 3. HPSK7 How does HPSK work?9 Primary PN function

10 Secondary PN function11 Final HPSK spreading (scrambling)

function12 What is the benefit of HPSK?12 Review: What is HPSK?

13 4. Modulation quality measurements forthe reverse link of W-CDMA andcdma2000 systems

15 5. Summary

16 6. Glossary

17 7. References

1. Throughout this application note, W-CDMA refers tothe 3GPP (Third Generation Partnership Project) pro-posal for a 3G system, and cdma2000 refers to the3GPP2 (Third Generation Partnership Project 2) proposal.Both of these proposals are currently under develop-ment. Therefore, the information in this applicationnote is subject to change.

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Unlike 2G systems, in 3G systems,such as W-CDMA and cdma2000, themobile station can transmit morethan one channel. The different chan-nels are used for control purposes orto send voice and/or high-speed data.

For example, for W-CDMA the basicuplink signal comprises one Dedi-cated Physical Data CHannel(DPDCH) and one Dedicated PhysicalControl CHannel (DPCCH). TheDPCCH carries control information,such as an embedded Pilot thatallows for synchronous detection. TheDPDCH carries voice or data. Option-ally, more DPDCHs may be added tosupport higher data rates.

In the case of cdma2000, the mobiletransmits a Reverse Pilot (R-Pilot)channel to allow the base station toperform synchronous detection. Addi-tional channels, such as the ReverseFundamental CHannel (R-FCH) andReverse Supplemental CHannels (R-SCHs) are used to send voice andhigh-speed data, respectively.

Although the names and frame struc-ture of the channels are currently dif-ferent for W-CDMA and cdma2000, thebasic block diagrams of the reverselinks (uplinks) are very similar. Theblock diagrams used in this applica-tion note do not exactly correspondto W-CDMA or cdma2000. They aregeneric block diagrams that explainthe evolution of the 3G reverse linkstructure from basic complex scram-bling to HPSK.

For both W-CDMA and cdma2000, thechannels are I/Q multiplexed. In thecase of transmitting only two chan-nels, one of the channels (DPDCH orR-Pilot) is applied to the I path andthe other channel (DPCCH or R-FCH)is applied to the Q path. Additionalhigh data rate channels are combinedalternatively on the I or Q paths.Each channel is spread by a differentorthogonal code.

The different channels can be at dif-ferent power levels. If, as shown inFigure 1, no other spreading or

scrambling is applied, the I and Q sig-nals are directly filtered and appliedto the I/Q modulator. In that scheme,channels with different power levelsresult in different amplitudes for I andQ, which can produce strange constel-lations. For example, in the case ofonly two channels, unequal powerlevels result in a rectangular 4-QAMconstellation. In general, equal distri-bution of powers between the axes isdesired, especially at the receiver.Equal powers allow for symmetrybetween the I and the Q paths.

1. Basic structure of the reverse link (uplink) of 3G systems

Figure 1. Basic reverse channel structure of 3G systems (W-CDMA and cdma2000)without scrambling

OtherChannels

DPCCH orR-FCH

Otherchannels

DPDCHorR-Pilot

Walsh/ OVSF Generator

GainScale

GainScale

to basebandfilter

to basebandfilter

I chip

Q chip

Walsh/ OVSFGenerator

Walsh/ OVSFGenerator

GainScale

GainScale

Walsh/ OVSFGenerator

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In the reverse link of cdmaOne systems,both the I and Q signals are scrambledwith a PN (Pseudo-Noise) sequenceprior to modulation. PN sequencesfrom different users are uncorrelatedto each other, which allows the basestation to recover the signal from theappropriate user with minimum inter-ference from others.

Instead of traditional scrambling,complex scrambling has been proposedfor the reverse link (uplink) of bothW-CDMA and cdma2000 systems. Inaddition to providing differentiationamong users, complex scramblingfixes the unequal distribution of pow-ers by continuously rotating the con-stellation and thereby distributing thepower evenly between the axes. Thus,the receiver does not have to deal withdifferent power loads for the I and Qpaths.

Figure 2 shows a block diagram of the reverse link (uplink) with basiccomplex scrambling. After complexscrambling, the resulting I and Q base-band signals are filtered and used tomodulate the carrier.

How does complex scramblingwork?Figure 3 shows the block diagram forcomplex scrambling. Mathematically,complex scrambling performs the mul-tiplication of two complex signals: thecomplex data signal, which has alreadybeen spread into chips (Ichip + jQchip)and the complex scrambling signal (IS + jQS). To verify this, derive theexpression for the final I and Q sig-nals by following the block diagram:

1. I = Ichip. IS – Qchip

. QS

2. Q = Ichip. QS + Qchip

. IS

The data signal, scrambling signal,and resulting baseband signal are notreally complex signals. However, theresulting I and Q signals are later I/Qmodulated, so they can be expressedas complex signals:

3. I + jQ = (Ichip. IS – Qchip

. QS) + j(Ichip

. QS + Qchip. IS)

= (Ichip + jQchip) . (IS + jQS)

= Achip. As

. e j(φchip + φs )

where: Achip and e jφchip are the ampli-tude and the phase of the Ichip + jQchip

signal; As and e jφs are the amplitudeand the phase of the IS +jQS signal;

Therefore, the amplitude (A) of theresulting I + jQ signal is the productof the amplitudes of both signals. Itsphase (φ) is the sum of their phases.

2. Complex scrambling

Figure 2. Basic reverse channel structure of 3G systems (W-CDMA and cdma2000) withbasic complex scrambling

Figure 3. Complex scrambling block diagram

OtherChannels

DPCCH orR-FCH

Otherchannels

DPDCHorR-Pilot

GainScale

GainScale

GainScale

to basebandfilter

to basebandfilter

I chip

Q chip

ComplexScrambling

+

+

+

-

Q

I

I S Q S

Walsh/ OVSFGenerator

GainScale

Walsh/ OVSFGenerator

Walsh/ OVSFGenerator

Walsh/ OVSFGenerator

ComplexScrambling

+

+

+

-

Q

I

I S Q S

I chip

Q chip

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The rest of this application note willrefer to the original complex data sig-nal spread into chips as the chip sig-nal and to its I and Q components asIchip and Qchip, respectively. The result-ing complex signal will be referred toas the final signal and its I and Qcomponents simply as I and Q,respectively.

For simplicity, a signal with only twochannels (one in the I path and theother one in the Q data paths) is usedto explain this concept in the I/Qplane (see Figure 4).

In the case of two channels with thesame amplitude (same amplitude forIchip and Qchip), the chip signal mapsonto a QPSK constellation. Thescrambling signal also maps onto aQPSK constellation (since the scram-bling IS and QS signals have values of1 or -1).

In the case of two channels with dif-ferent amplitudes, the chip signalmaps onto a rectangular 4-QAM con-stellation. The scrambling signal stillcorresponds to a QPSK constellation.

What is the final constellation for thetwo cases in Figure 4?

Figures 5a through 5d illustrate whathappens for a single chip point in theoriginal QPSK constellation (Case 1).The original chip signal is the samefor all the figures (from 5a to 5d) andthe scrambling signal is different. Theamplitude of the final signal is theproduct of the amplitudes of the chipand scrambling signals. The phase ofthe scrambling signal is added to thephase of the original chip signal (45°).Any point from the original QPSK chipconstellation is rotated by 45°, -45°,135°, or -135°, depending on the valuesfor IS and QS at that time. For example,in Figure 5a, the phase of the scram-bling signal is +45°, so 45° is addedto the phase of the original chip point.

Figure 5a. Scrambling signal at +45°

Figure 5b. Scrambling signal at -45°

I+jQ

1,1

1,-1

-1,1

-1,-1

Ichip +jQchip IS+jQS

1,1

1,-1

-1,1

-1,-1

?

?

Case 1:two channelsat equalamplitude

Case 2:two channelsat differentamplitude

Figure 4. What is the result of complex scrambling the chip and scrambling signals forthese two cases?

1,1

45˚

1,1

45˚

0,2+45˚

2

45˚

Ichip +jQ chip IS+jQ S I+ jQCase 1: two channels at equal amplitude

2 2

1,1

45˚

1,-1

2

2

-45˚

2

45˚

-45˚

2,0

Ichip +jQchip IS+jQS I+jQ

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Therefore, in the case of two channelswith equal amplitudes (QPSK constel-lation) all the points of the final con-stellation lie on top of the I or Q axis.The result is a QPSK constellationaligned with the I/Q axes (rotated 45°from the original constellation).

In the case of two channels withunequal amplitudes, the amplitude ofthe resulting constellation is also con-stant, as shown in Figure 6. The chippoints from the original 4-QAM con-stellation are rotated by 45°, -45°, 135°,or -135°, since the scrambling signalstill corresponds to a QPSK constella-tion. However, the final constellationhas eight points distributed around acircle, since the phases for the chippoints in the original constellation are different from 45°, -45°, 135°,and -135°. The angular distribution of the points is determined by the relative amplitudes of the two chan-nels (Ichip and Qchip). Figure 6 showsthe resulting constellations for thesetwo cases.

Review: Why is complex scram-bling required?In W-CDMA and cdma2000, themobile phone can transmit multipleI/Q multiplexed channels at differentpower levels. In addition to providingdifferentiation among users, complexscrambling distributes the powerevenly between the I and Q axes.

Figure 5c. Scrambling signal at +135°

Figure 5d. Scrambling signal at -135°

Figure 6. Complex scrambling distributes the power evenly between the I and Q axes

-1,11,1

45˚2

2 +135 ˚

-2,0

+135˚

2

45˚

Ichip +jQchip IS+jQS I+jQ

-1,-1

Ichip +jQchip IS+jQS I+jQ

1,1

45˚2

2 -135 ˚

2

45˚

0,-2 -135˚

1,1

1,-1

-1,1

-1,-1

Ichip +jQchip IS+jQS I+jQ

1,1

1,-1

-1,1

-1,-1

Case 1:two channelsat equalamplitude

Case 2:two channelsat differentamplitude

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2G systems commonly use modula-tion formats that limit transitionsthrough zero in the reverse link(uplink). For example, cdmaOne usesOQPSK (Offset Quadrature PhaseShift Keying). This reduces the peak-to-average power ratio of the signal,which allows for a more efficientamplifier, maximizing battery life.

However, in complex scrambling, ifrandom PN signals are assigned to IS

and QS, transitions from any point toany point in the final constellationare possible. This results in a highpeak-to-average ratio when comparedto existent 2G formats for the reverselink. Figure 7 shows the constellationdiagrams of an OQPSK signal and aQPSK signal with basic complexscrambling. The spreading techniquethat uses basic complex scramblingand PN signals for IS and QS is knownas Pseudo-Noise Complex QuadraturePhase Shift Keying (PNCQPSK).

3G systems use Hybrid Phase ShiftKeying (HPSK), also known asOrthogonal Complex QuadraturePhase Shift Keying (OCQPSK), toreduce the peak-to-average powerratio of the signal. HPSK is a varia-tion of basic complex scrambling thateliminates zero-crossings for everysecond chip point. It accomplishesthis by using a specific repeatingsequence (or function) as the scram-bling signal and by choosing specificorthogonal codes to spread the differ-ent channels.

How does HPSK work?Basically, HPSK uses complex scram-bling with a fixed repeating functionas the scrambling signal. This func-tion is known as the Walsh rotator,and it is defined as W0 = {1,1} for IS,and W1 = {1, -1} for QS.

Figure 8 illustrates what happens inthe I/Q plane. In this case, two con-secutive chip points fall at the sameplace on the I/Q plane. The repeatingWalsh rotator sequence (IS = W0 = {1,1};QS = W1 = {1,-1}) is used as the scram-bling signal. For two consecutive iden-tical chip points, the first one is rotatedby +45°, and the second one by -45°,which ensures that they will be 90°apart in the final constellation andthe transition between them does notgo through zero.

This technique assumes pairs of con-secutive identical chips. This can beachieved by using only even-numberedWalsh functions to spread the datafrom the different channels. Even-numbered Walsh functions consist of pairs of identical bits. For example,for a Walsh code length of 8 bits: W0 ={1,1,1,1,1,1,1,1}, W2 = {1,1,-1,-1,1,1,-1,-1},and so forth. Therefore, using onlyeven-numbered Walsh functions tospread the different channels ensuresthat the chip signal consists of pairsof identical consecutive chips.

3. HPSK

45˚

1,1

45˚

1st+45˚

45˚

Ichip +jQchip IS+jQS=W0+ jW1 ={1,1} + j{1,-1}

I+jQ

1,-1

-45˚

1st 2nd 1st

2nd

-45˚

2nd.

Figure 8. Complex rotator rotates first and second chip points by +45° and -45°, respectively

QPSK with BASICCOMPLEX SCRAMBLING

OQPSK

(a) (b)

Figure 7. Constellation of (a) an OQPSK signal versus (b) a QPSK signal with basic complexscrambling (Agilent Technologies E4406A VSA series transmitter tester screen displays)

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Figure 9 shows a generic block dia-gram where the Walsh rotator is usedas the scrambling signal. To simplifythe diagram, only two channels at thesame amplitude are transmitted. Theorthogonal functions chosen in thiscase to spread each one of the chan-nels are 8-bit Walsh codes 0 and 2,respectively. For example, if the datasignal is ID = 1 and QD = -1, the chipsignal is Ichip = 1,1,1,1,1,1,1,1 and Qchip

= -1,-1,1,1,-1,-1,1,1. The constellationof this signal consist of the complexpoints Ichip + jQchip = {1 – j1, 1 – j1, 1 +j1, 1 + j1, 1 – j1, 1 – j1, 1 + j1, 1 + j1}.Therefore, the chip signal consists ofpairs of identical consecutive points.Each pair is multiplied with the scram-bling signal formed by the Walsh rota-tor IS + jQS = W0 + jW1 ={1 + j1, 1 – j1}.Therefore, the first point in the pairis phase shifted by +45°, and the sec-ond one by -45°, which ensures thatthey will be 90° apart in the finalconstellation.

In the real system, the length of theorthogonal code for each channeldepends on that channel’s data rate.

HPSK limits the choice of availableorthogonal spreading codes. However,this limitation does not place a largeconstraint, because a single mobiledoes not need to support a large num-ber of traffic channels. In most cases,there are sufficient orthogonal codesto handle most channel configurationsfor both cdma2000 and W-CDMA.

In HPSK, transitions through zero areonly eliminated for pairs of consecu-tive points. Transitions across pairsmay go through zero. For example, forfour consecutive points, the transi-tion between the first and the secondpoints (or the third and the fourth)does not go through zero. However,the transition between the secondand the third point may go throughzero. The basic idea behind HPSK isto minimize zero-crossings to improve

the peak-to-average power ratio of thesignal. Figure 10 shows the constella-tions of two signals: the first onewithout HPSK spreading, and the sec-ond one with HPSK spreading. Theconstellation for HPSK shows fewerzero-crossings.

Figure 9. HPSK: Complex scrambling with Walsh rotator and even-numbered Walsh codes

+

+

+

-

W0 W1

I chip

Q chip

1 channel

W0

1 channel

W2

{1,1} {1,-1}

{1,1,1,1,1,1,1,1}

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

I

Q

Figure 10. Constellation of signal (a) without HPSK spreading and (b) with HPSK(E4406A VSA series transmitter tester displays)

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In addition to minimizing zero-cross-ings, HPSK eliminates 0° phase shifttransitions for every second chippoint. A 0° phase transition occurswhen two consecutive points are atthe same place on the final constella-tion. This causes overshooting trajec-tory, which increases the peak-to-average power ratio of the signal, asshown in Figure 11.

HPSK forces 90° transitions betweenpairs of consecutive points. This min-imizes 0° phase transitions, whichfurther reduces the peak-to-averagepower ratio of the signal.

Primary PN functionAs shown so far, HPSK uses a Walshrotator and the right choice of orthog-onal functions for the different chan-nels to minimize zero-crossings and0° transitions in the final constella-tion. This improves the peak-to-aver-age power ratio.

The real HPSK block diagram is morecomplex. After complex multiplicationwith the Walsh rotator, a primary PNspreading code PN(1) is applied to thefinal I and Q signals to allow for iden-tification of the mobile and correla-tion at the receiver. The PN(1)

sequence is the same for I and Q andit does not affect the number of 90°transitions. Figure 12 shows a blockdiagram of HPSK with the primaryPN function.

The PN(1) spreading code does notnecessarily have to be applied afterthe complex scrambling. It caninstead be directly multiplied withthe I and Q components of the scram-bling signal before the complexscrambling. The final result is thesame in both cases.

Figure 11. 0° phase shift transitions cause higher signal overshoot

peak caused by0˚ phase shift

peak caused by90˚ phase shift

Figure 12. HPSK: Complex scrambling, Walsh rotator, even-numbered Walsh codes andprimary PN sequence

+

+

+

-

W0 W1

I chip

Q chip

1 channel

W0

1 channel

W2

Q

I

PN(1)

{1,1} {1,-1}

{1,1,1,1,1,1,1,1}

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

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Figure 13 shows why the PN(1) sequencedoes not affect the number of 90° tran-sitions. The PN(1) sequence is alwaysthe same for I and Q. Therefore, avalue of PN(1) of +1 does not changethe location of the constellation point.A value of -1 inverts the location ofthe final constellation point. In thisexample, the final constellation points(after complex scrambling with theWalsh rotator and before applying thePN(1) sequence) correspond to (0,1) and(1,0). The figure shows the four possi-ble cases.

In the first case, the value of PN(1) is +1for both points. Therefore the constel-lation does not change. In the secondcase, the value of PN(1) is -1 for the firstpoint in a pair and +1 for the secondpoint. The location of the first constel-lation point changes, but the resultingconstellation points are still 90° apart.In the third case, the value of PN(1) is+1 for the first point in a pair and -1for the second point. Again, the result-ing constellation points are 90° apart.In the fourth case, the value of PN(1) is-1 for both the first and second points.The location of both constellationpoints is inverted, but the resultingconstellation points are still 90° apart.

Secondary PN functionA decimated secondary PN spread-ing code (P) is multiplied with the Q component of the Walsh rotator (W1 = {1,-1}), as shown in Figure 14.The secondary PN spreading codeminimizes Multi-Access Interference(MAI), thereby improving reception at the receiver [1].

P is a decimated version of the realchip rate sequence PN(2). For example,for a decimation factor of two, P holdsits value for two chip time periods,which effectively makes its rate halfthe chip rate. P randomizes the direc-tion of the phase rotation while keep-ing the phase difference of 90° betweenpairs of consecutive final points.

Figure 13. Effect of primary PN sequence

PN1(1) =-1

1st90 ˚

1st

I+ jQ

2nd.

90 ˚

Case 1PN (1) PN (1)=1,1

2nd.

Case 2

PN (1) =-1,1

90˚

Case 4

PN(1) =-1,-1

90 ˚

PN1(1) =-1

1st

2nd.

PN2(1) =-1

I+jQCase 3=1,-1

1st

2nd.PN2

(1) =-1

+

+

+

-

W0 W1

I chip

Q chip

1 channel

W0

1 channel

W2

Q

I

PN(1)

{1,1} {1,-1}

{1,1,1,1,1,1,1,1}

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

PN(2)Pdecimate

Figure 14. HPSK: Complex scrambling, Walsh rotator, even-numberedWalsh codes and primary and secondary PN sequences

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Figure 15 illustrates the effect of P inthe final constellation. In the firstcase, P = 1. Therefore, the Q compo-nent of the scrambling signal is W1 ={1,-1}. The first chip point is rotatedby +45°, and the second by -45°. Inthe second case, P = -1. Therefore, theQ component of the scrambling signalis now {-1,1}. The first chip point isrotated by -45° and the second by+45°. This still avoids zero-crossingsand 0° transitions between these twochip points.

Final HPSK spreading (scram-bling) functionWhen PN(1) and P are included, thetotal spreading (or scrambling) func-tion for HPSK is:

4. IS + jQS = PN(1) 3 (W0 + jP 3 W1)

where: W0 = {1,1}; and W1 = {1,-1}.

Since W0 = {1,1}, this function can beremoved from the equation. The

function can then be expressed as:

5. IS + jQS = PN(1) + jPN(1) 3 P 3 W1

where: W0 = {1,1}; and W1 = {1,-1}.

W-CDMA and cdma2000 may imple-ment this function in different ways.Figure 16 shows the W-CDMA imple-mentation as it is currently (9/99)being proposed.

In W-CDMA, Orthogonal VariableSpreading Functions (OVSFs) areused instead of Walsh codes. TheDPCCH is always spread with a 256-bitcode 0 (C256,0), which corresponds to{1,1,1,1,1,1...}, so it does not need tobe implemented in the block diagram.When a single traffic channel is trans-mitted, the OVSF code for that chan-nel depends on its data rate. BecauseOVSF 0 = W0 = {1,1}, this section ofthe Walsh (or OVSF) rotator does notneed to be implemented in the blockdiagram.

1st

2nd.

2nd.

1st

I + jQ

Case 1: P=1

Case 2: P=-1

45˚

1,1

45˚

Ichip + jQ chipIS+ jQ S=W0+ jPxW 1 ={1,1}+ jPx {1,-1}

1,-1

-45˚

1st 2nd 1st

2nd

1,1

45˚

1,-1

-45˚

2nd

1st

Figure 15. The decimated secondary PN sequence (P) randomizes the direction of the rotation

DPCCH

DPDCH

OVSF Generator

GainScale

GainScale

to basebandfilter

to basebandfilter

ComplexScrambling

+

+

+

-

OVSF 2Generator

1,-1

Deciby 2

225

Scramble CodeGenerator

3840 kcps

3840 kcps

Q

I

PN(1)

PN(2)P

Figure 16. Proposed uplink structure for W-CDMA (3GPP)

12

A 225 gold code generator is used toobtain the two pseudorandomsequences. The generator uses twosets of shift registers to generate thegold codes.

Figure 17 shows the block diagramfor the reverse link of a cdma2000Spread Rate 3 (SR3) system with theR-Pilot and a traffic channel.

In cdma2000, the Pilot is not spreadwith any Walsh code, which corre-sponds to Walsh code 0, {1,1,1,1,1,1...}.The fundamental traffic channel isalways spread with Walsh 16 code 4,{1,1,1,1,-1,-1,-1,-1,1,1,1,1,-1,-1,-1,-1}.The PN(1) is formed by applying auser’s 42-bit code mask to the origi-nal cdmaOne 42-bit long code, andscrambling the result against thecdmaOne I short code. P is created by delaying the long code by one chip,scrambling it with original cdmaOneQ short code, and decimating by afactor of two.

The names PN(1), PN(2), and P are notused in W-CDMA or cdma2000, buthave been added to both block dia-grams for clarification.

What is the benefit of HPSK?The probability of a zero-crossing fora regular QPSK or PNCQPSK signalwith two channels at the same ampli-tude is 1/4. For HPSK, the probabilityof a zero-crossing is limited to everyother chip point, and is thereforereduced in half (1/8). The probabilityof 0° phase shift transitions is alsoreduced from 1/4 to 1/8. All thisimproves the peak-to-average powerratio of the signal by approximately 1 to 1.5 dB. HPSK spreading is stilladvantageous when multiple channelsat different amplitudes are transmitted.

Figure 18 shows the CCDF (Comple-mentary Cumulative DistributionFunction) for two signals:

1. A signal with basic complex scrambling. This signal has been generated from acdma2000 SR1 forward link signalwith a single traffic channel (whichuses basic complex scrambling). Thefiltering has been modified tocdma2000 reverse link filtering(which, as opposed to the forwardlink, does not include an equalizationfunction).

2. A signal with HPSK spreading.This signal is a cdma2000 SR1 reverselink signal with two channels (R-Pilotand R-FCH) at the same power level.

The CCDF curve provides the distri-bution of particular peak-to-averageratios versus probability. In this case,for a probability of 0.1%, the peak-to-average ratio of the HPSK signal isabout 1 dB lower than the signal withbasic complex scrambling. Pleasenote that this plot does not provide astraight comparison between basiccomplex scrambling and HPSK. Thecoding between forward and reverselink signals is different, which mayimpact the results. However, the plotis indicative of the performance ofHPSK spreading versus basic complexscrambling.

Signals with high peak-to-average powerratio may saturate the power amplifier,causing higher interference in the adja-cent channels and a reduction of sys-tem capacity. To minimize this, theamplifier must be designed with alarger back-off, which in turn reducesamplifier efficiency. Therefore, highpeak-to-average power ratios reducebattery life, one of the critical charac-teristics of the mobile phone.

Review: What is HPSK?HPSK is a spreading technique thatuses complex scrambling with aWalsh rotator and selected orthogo-nal spreading codes for the differentchannels to minimize the peak-to-average power ratio of the signal.

Signal with BasicComplex Scrambling

Signal withHPSK spreading

Delta Marker : -1.05 dB

Figure 18. CCDF comparison between sig-nals with and without HPSK (E4406A VSAseries transmitter tester display)

R-FCH

Walsh 16Generator

R-Pilot

GainScale

GainScale

to basebandfilter

to basebandfilter

ComplexScrambling

+

-

{1,-1}

Deciby 2

1-ChipDelay

Long CodeGenerator

3686.4 kcps

3686.4 kcps

+

+ Q

I

PN(1)

PN(2)P

Walsh 2Generator

Short CodeGenerator

Short CodeGenerator

User LongCode Mask

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

Figure 17. Proposed reverse link structure for cdma2000 SR3 systems

13

As shown earlier, the reverse link(uplink) structure for W-CDMA andcdma2000 systems is very differentfrom that of 2G systems. The maindifferences are:

• Each mobile can transmit severalchannels at different power levels.

• HPSK spreading is used to limitthe peak-to-average power ratio ofthe reverse link signal.

These differences will probably affectthe way modulation quality is definedfor the reverse link. For example, somesort of code-domain power and QPSK/HPSK demodulation/de-spreading maybe necessary to provide the appropri-ate testing.

While the measurement methodologyis being defined, existing test equip-ment can be used to obtain an indica-tion of the modulation quality of thesignal. The easiest methodology is toconfigure the signal so that it mapsonto a known constellation (forinstance QPSK or 16QAM) and meas-ure uncoded EVM (before HPSK de-spreading at the receiver side).Three suggested configurations aregiven below. The screen images wereobtained using the Agilent Technolo-gies instruments shown in Figure 19.

• QPSK constellation (see Figure 20):Activate DPCCH (or R-Pilot) andone traffic channel at the samepower level.

4. Modulation quality measurements for the reverse link of W-CDMA and cdma2000 systems

Figure 19. Instrument setup

ESG-D Series RF DigitalSignal Generator

E4406A VSA SeriesTransmitter Tester

OR 89441A VectorSignal Analyzer

Figure 20. EVM (uncoded) and constellation for a W-CDMA signal with two channels atthe same amplitude level (E4406A VSA series transmitter tester display)

14

• 8PSK constellation (see Figure 21):Activate DPDCH (or R-Pilot) andone traffic channel 7.65 dB below.

• 16QAM constellation (see Figure22): Activate DPCCH (or R-Pilot)and two traffic channels at thesame power level.

The uncoded EVM measurement doesnot reveal faults in the coding andspreading but provides an indicationof the quality of the baseband filter-ing, modulation, and the IF and RFsections. For example, errors in thebaseband filtering, I/Q impairments,compression at the amplifier, and LOinstability increase EVM. Most ofthese errors can be identified by ana-lyzing the different modulation dis-plays (constellation, magnitude oferror vector versus time, phase errorversus time, magnitude error versustime, and so forth). For example, again imbalance between I and Qcauses an asymmetric constellation,as shown in Figure 23.

Figure 21. EVM (uncoded) and constellation for a W-CDMA signal with two channelsthat have an amplitude difference of 7.65 dB (89441A vector signal analyzer display)

Figure 22. EVM (uncoded) and constellation for a W-CDMA signal with three channels atthe same amplitude level (89441A vector signal analyzer display)

Figure 23. EVM (uncoded) and constellation for a W-CDMA signal with an I/Q gainimpairment (E4406A VSA series transmitter tester display)

15

This application note has explainedwhy HPSK has been selected as thespreading technique for the reverselink (uplink) of 3G systems such asW-CDMA and cdma2000. The mainpoints of the application note are:

• In W-CDMA and cdma2000 sys-tems, the mobile phone can trans-mit multiple I/Q multiplexed chan-nels at different power levels.

• Complex scrambling facilitates thisby distributing the power evenlybetween the axes.

• HPSK is a variation of complexscrambling that uses a Walsh rota-tor and specific orthogonal (Walshor OVSF) spreading functions tominimize zero-crossings and 0°phase shift transitions. Thisimproves the peak-to-averagepower ratio of the signal.

• The application note shows how tostart making modulation qualitymeasurements on the reverse linkof W-CDMA and cdma2000 signalsusing existing instrumentation.

5. Summary

16

2G Second Generation

3G Third Generation

3GPP Third Generation Partnership Project

3GPP2 Third Generation Partnership Project 2

CCDF Complementary Cumulative Distribution Function

CDMA Code Domain Multiple Access

cdmaOne IS-95 standard-based CDMA system

cdma2000 cdmaOne derivative, 3G proposal

DPCCH Dedicated Physical Control CHannel

DPDCH Dedicated Physical Data CHannel

EVM Error Vector Magnitude

GMSK Gaussian Minimum Shift Keying

HPSK Hybrid Phase Shift Keying

I/Q In-Phase/Quadrature

IF Intermediate Frequency

LO Local Oscillator

MAI Multi Access Interference

OCQPSK Orthogonal Complex Quadrature Phase Shift Keying

OQPSK Offset Quadrature Phase Shift Keying

OVSF Orthogonal Variable Spreading Function

PN Pseudo-Noise

PNCQPSK Pseudo-Noise Complex Quadrature Phase Shift Keying

PSK Phase Shift Keying

QAM Quadrature Amplitude Modulation

QPSK Quadrature Phase Shift Keying

RF Radio Frequency

R-FCH Reverse Fundamental CHannel

R-Pilot Reverse Pilot

R-SCH Reverse Supplemental Channel

SR Spreading Rate

W-CDMA Wideband CDMA, 3G proposal

6. Glossary

17

[1] Proposal for Orthogonal Complex QPSK, Tdoc SMG2 UMTS 85/98.

[2] JaeRyong Shim and SeungChan Bang, Spectrally Efficient Modulationand Spreading Scheme for CDMA Systems, IEE, August 19, 1998.

[3] Comments on ACP Simulation of Nokia and BER Simulation Results onOCQPSK, Tdoc SMG2 UMTS-L1 211/98.

[4] BER Simulation Results for HPSK (OCQPSK), Tdoc SMG2 UMTS-L1225/98.

7. References

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