INSTITUT D’ÉLECTRONIQUE ET DE … D’ÉLECTRONIQUE ET DE TÉLÉCOMMUNICATIONS DE RENNES Carrier...

INSTITUT D’ÉLECTRONIQUE ET DE TÉLÉCOMMUNICATIONS DE RENNES

Carrier per Carrier Analysis of SDR Signals Power Ratio

Christophe MOYAssociate Professor at Supélec

[email protected]:

SDRF Technical Conference,

Orlando, USA, November 2006

1UMR6164

SUPELEC - Campus de Rennes - FRANCE

SCEE team – Signal, Communication and Embedded Systems

IETR – UMR 6164

Institute of Electronics and Telecommunications of Rennes

Authors: Sidkiéta ZABREJacques PALICOTYves LOUETChristophe MOYChristian LEREAU


Ideal Software Radio

• Ideal software radio (SWR)– digitize the globality of the RF spectrum at Rx– generate all the channels of a multi-standard

BTS with a single DAC and RF amplifier at Tx

GSM DCS UMTSPCS cellular

Bluetooth

Home RF

SDRF Technical Conference’06 - November 2006 - Orlando 2

- -

82

48

49

86

98

94

88

0-9

15

92

5- 9

60

-

17

01-

17

85

18

05-

18

80

- -

18

50

19

10

19

30

19

90

-

19

20

19

80

211

02

17

0

-2

40

02

50

0

-5

15

05

72

0 frequences [MHz]

GSM

900DCS

1800

UMTS

IEEE 802.11a

Example ofa futuremini-BTSon-board atransatlantic

plane

PCS

1900

cellular

US

Home RF

WIFI : IEEE 802.11b

Hyperlan


Software Defined Radio

• Technlology constraints– ADC, DAC speed and quality – processing power of processors, FPGA… – power consumption – analog components bandwidth and linearity…


• Restricted to sub-parts of the spectrum– channels of one standard for instance

Spectrum of a multiplex of GSM CarriersSpectrum of a multiplex of GSM Carriers

925.000 925.200 925.400 925.600 925.800

… …


SDR RF signal and PR issue

• A SDR RF signal at least, and moreover a Software Radio RF signal– multi-band signal– multiplex of carriers

• Major drawback of a multiplex of carriers


• Major drawback of a multiplex of carriers– suffer from high Power Ratio (PR)– known also as the PAPR (Peak-to-Average

Power Ratio)

• Cause– non constant envelop of the signal


PR issue

• The difference between the average power and the max power is high – either under use the amplifier (input back-off)– or generate non linearities

• Non linearities1.8

2output power


• Non linearities– area 1: linear– area 2: non linear– area 3: saturation

• Signal corruption• BER degradation 0 0.5 1 1.5 2 2 .5 3 3 .5 4

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

1 2 3

input power


Facing PR issue

• PR is an old issue– 70’s on satellite communications– 80’s till now: OFDM (DVB-T, DAB, 802.11g)

• OFDM signal– a multiplex of carriers


– a multiplex of carriers– very close to SWR and SDR signal– particularly suffers from PR issue

• Idea: take advantage of solutions investigated for OFDM and apply to SDR signals


OFDM and PR

• OFDM PR definition– based on a time PR calculation– on the samples after IFFT (all generated from

a single time signal)– definition

{ }2

2

,

)(

)(

tSE

tSMaxPR mc =


{ }2,

)(tSEmc

• SDR approach– a multiplex of signals on several carriers– each generated independently from the others– a frequency approach would be more suitable– each standard one by one


Time PR vs frequency PR

• Computing the PR in the frequency domain would better fit to SDR signal – SDR signals are a set of signals at different

carriers– compute the global PR from each carrier PR


• Three questions– Is it equivalent to compute the PR in the time

and the frequency domains?– Is it correct to apply it to SDR signals?(Q1)

(Q2)

(Q3)– How to compute or approximate the PR in the frequency domain?


Carrier per carrier analysis

• Multi-standard SDR signal

( ) ( ) tfiP

p

pii

pi

i

etrtS ,2

1

,

π

∑=

=

• SDR single-standard signal made of a plurality of equidistant carriers


analogy( ) ∑−

=

=1

0

2N

k

tfi

kkeCtZ

π

( ) ( ) ( ) tppfiP

p

piiii

i

etrtS∆−+

=

∑=)1(2

1

,0,π

plurality of equidistant carriers

• OFDM signal

(Q1)


OFDM signal

ft1

OFDM symbol 1

CNsN-1CNs1CNs0

C2N-1C21C20

C1N-1C11C10

PRfr(0)

fN-1f1f0

t

f

PR

PRfr(1) PRfr(N-1)

CNsN-1CNs1CNs0

C2N-1C21C20

C1N-1C11C10

CNsN-1CNs1CNs0

C2N-1C21C20

C1N-1C11C10

PRfr(0)

fN-1f1f0

t

f

t

f

PR

PRfr(1) PRfr(N-1)


t

OFDM symbol 2

OFDM symbol NS

t2

tNs

PRNs,freqPRNs,freq

f0 fp fN-1


Demo for an OFDM signal

• PR upper-bound usuallycomputed in the timedomain: PRtemp

– on each OFDMsymbol (line) CNsN-1CNs1CNs0

C2N-1C21C20

C1N-1C11C10

PRfr(0)

fN-1f1f0

t

f

PR

PRfr(1) PRfr(N-1)

CNsN-1CNs1CNs0

C2N-1C21C20

C1N-1C11C10

CNsN-1CNs1CNs0

C2N-1C21C20

C1N-1C11C10

PRfr(0)

fN-1f1f0

t

f

t

f

PR

PRfr(1) PRfr(N-1)

PRtemp(2)

PRtemp(Ns)


PRNs,freqPRNs,freq

PRfr(0)

PRfr(p)

PRfr(N)

• New calculation of PR– frequency PR on each column: PRfr(p) then max

– then the max PRNs,freqis computed from the set of time PR

• We find the same PRNs,freq(Q2)


•10•-1

PR upper-bounding

• PR approximation in the frequency domain – probabilistic

∑

∑=

+

≤N

N

p

frP

temp

KpPRA

PR1

)(.

•10•0

•Upper bound

•Temporal PR

OFDM sig

nal


•0 •2 •4 •6 •8 •10 •12 •14•10

•-3

•10•-2

•10

– P[PRtemp>threshold](complementary cumulativedistribution fonction)

∑=

N

p

pA1

S(dB)

•Pro

b(P

ME

PR

>S

)

obtained by the new PRfreq approach

classical approach

OFDM sig

nal –

64 ca

rriers –

1000 sy

mbols

(Q3)


Example on a GSM signal

• Time PR and upper-bound– 10 GSM carriers– 1000 symbols– 20 experiments

•

7

8

9

10

Temporal PR

Upper bound

• Results


0 2 4 6 8 10 12 14 16 18 200

1

2

3

4

5

6• Results

– only 2 dB upper-bound

– perfectly followstime PR variations


Conclusion

• This new PR approach (in the frequency domain) may help in the SDR domain for – applying OFDM reduction methods to SDR

signals – for the PR evolution analysis through a


– for the PR evolution analysis through a transmission chain

• Equivalence for SDR single-standard• Perspective

– to be proven for multi-standard SDR signals


Thank you for your attention


Thank you for your attention

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