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ACPR Prediction Of CDMA Systems Through Statistical Behavioural Modelling Of Power Amplifiers With Memory

Tracey S. L. Goh, Roger D. Pollard

School of Electronic and Electrical Engineering, University Of Leeds, Leeds LS2 9JT, UK

. .

Absarer - Behavioural modda for power ampllfien (PA) have traWondIy been dweloped b u d on conventional AM-AM and AM-PM curva from o n e tone measnrementa, wbkb dhcounts the praence of memory In the aptem However, PI d g d bandwidth Increases In ipread spectrum ryrtemr, memory effects become more severe. Tbeae effects mult tiom.tbe frequency reapom of mateblng networks, nonlinar cnpadtnnca of the molirton and the reaponre ofthe b iu network&

Multi-atage blgh power nmpllRtrr require more ,accurate bebavioural modeh to provide a better ,dadption of. memory effecta and blgbly nonlinear cbuncterlrtlu tbau memorylar modeh baaed on dngletone trnnafer characterbth Tbia la achleved using measured twwtone transfer cblrrcterlstio of the ?nupUtndc and pbaie oftbe fundnmcntul, IMJ and IMS. componenb, wbicb hnr blghly nonlinear componenta that r e p m e t the ampURer I dgnUlcant memory.

A atatlrtlcd technique la then appued wmeb dowr accurate, fut . .nd diiclent p d c t l o n of the ad]acent channel power ratio (ACPR) of the eommnniutloo ryltem without tlmbconaumlng, tlme-domaln .Imnhtions.

Index ‘ T e r n - Communicatwn system M ~ e c U ~ , CDMA, behavioural d e l

1. INTRODUCTION 2 . ,.

_ * In cellular i d ,personal communication systems

(PCS), ACPR is the preferred linearity’figure in characterising nonlinear distortion of a nonlinearities &vice to evaluate.its effects on RF

. . system performance. ACPR is defined as the power m the main channel divided by the power in lower and upper adjacent channels usually in a specified

, .bandwidth at a specific off* fmm the hand edge.

In ,the IS-95 standard, the nonliearity control regulation is specified by the out-of-band b w e r

emission levels. The PA generates eo-channel and adjacent channel interference due to intermodulation (IMD) and sidehand,regrowth. The adjacent channel interference levels increase through the generation of out-of-hand components by the nonlinear amplifier chain and with the increase in traosmilter power causing spectral regrowth.

n u s , the need for linearity is one oithe principal drivers in the design of modern power amplifiers (PA). Signals such as CW. classical FM and GMSK have constant envelop& (amplitudes) and therefore more resilient to nonliiearities. , L-inear amplification is critical when the signal contains both amplitude and phase modulation and non- constant envelopes (Fig.1) such as in ‘modern shaped-pulse data modulation (QAM, QPSK) and multiple carriers (OFDM, WCDMA).

The proposed method considep the nonlinear. transformation of the input autocorrelation h,ction using statistical properties of a complex Gaussian random variable to develop a simple expmsion for the autocorrelation of the output si@. This leads to an output spectrum approximate fmm which ACPR can be determined [1,2]. However, by using readily available AM-AM and AM-PM measured data (one-tone transfer characteristics), PA nonlinearity is assumed to be memoryless.

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Thus the purpose of this paper is to present

an accurate way to predict ACPR at the output of a nonlinear amplifier represented by a behavioural model based on two-tone characterisation with phase information which incorporates a better description of memory effects.

a statistical technique that yields an analytical expression for the autocorrelation function of the output signal as a function of the statistics of the quadrature input signal transfonned by a hehpioural model of the amplifier.

The behavioural model is derived using AM-AM and AM-PM data but unlike conventional behavioural models, which use AM-AM and AM- PM effects extracted from one-tone complex gain measurements swept over input power, the model here is based on two-tone transfer characteristics.

One-tone transfer characteristics cannot properly describe the nonlinearity of high power amplifiers because they do not model thq memory behaviour.. A power amplifier with memory effects will have an output signal determined by the real time input signal and previous input signals. Memory effects result in IM asymmetry and IMD variation caused by thermpl time constants of high power amplifiers.

Yang [3], reported that a more accurate behavioural model based /on two-tone characterisation with phase informatiou would be a better choice for modelling multi-stage high power amplihers. Measured two-tone data will then be fitted to the conventional m d e l of AM-AM and AM-PM distortion characteristics/

11. MODEL DESCIUPTION

A. Signal Characterisaiion

The bandwidth of a general IS-95 CDMA signal with N spread spectrum signals can be expressed as

where m.(i) is the nth baseband signal and c.(i) is the nth pseudonoise code.

The Gaussian approximation can be made for forward-link CDMA signals with large number of Walsh-coded channels transmitted at the same frequency. The spectrum of s(t) then resembles a band-limited white Gaussian stochastic process in

accordance to the law of lwgC numbers and the central limit theorem. s(i) can be expressed statistically where ac is the centre carrier frequency and 61, ( I ) is an independent identically distributed (i.i.d.) random variable uniformly distributed over [Os 2x1. s(t )= A(t)cos( w,t+@,(t))

=JZz(r)cos(w,t+~,,(t)) (2)

EQ.(2) is then analogous to the complex envelope representation of the amplitude and phase modulated carrier where A(t) and &(I) we the amplitude and phase components of the modulation.

z(r) = A(r)e/'*(') = f(r) + jJ(r) (3)

Any narrow-band RF bandpass signal and system can be represented by its baseband complex envelope and response, respectively. Thus, using bandpass nonlinearity theory [4] and Kaye s narrowband quadrature decomposition method [SI, the distorted complex envelope i( i) can be described as

(4) z(r) = G[A(r)] , I ( % ( ~ ) + + [ A ( ~ ) ] )

whereby G[A(i)] is the magnitude transfer characteristic and &4(f)] is the amplitude dependent phase shifi.

B. Behavioural Model of the Nonlinear Pawer AmpIHer.

The method in [1,2] provides insight into how nonlinearity affects the output spectrum by developing a modular approach that considers the transformation of the input statistics through the modulation scheme and the nonlinearity. .

The output power spectrum is estimated from an analytical expression for the output autocorrelation function that describes the transformation of a complex Gaussian signal when passed through a bandpass nonlinearity modelled by an odd order complex power series obtained from measured or simulated AM-AM and AM-PM characteristics of the device. Only the odd tenns are considered for a narrowband RF system as they produce intennodulation distortion in-band and adjacent

521

channel distomon. The even terms fall out of the band of interest in a narrowband RF wmunication system.

The nonlinear PA can be characterised u s q obtained AM-AM and AM-PM measurements and represented as a bandpass nonlinearity with wmplex transfer characteristic [1,2]

6 [ ~ ( t ) 1 = do+ riI f(r) + ri3 i 3 ( r )

+ris 2 ( t ) + & ,?'(t)+ ... ( 5 )

Fig.2 shows the baseband equivalent quadrature modulator cascaded with a nonlinear element. The digital quadrature modulated signal,i(r), is modelled as the quadrature addition of f(r)and j ( t ) . The mput signal is then characterised using its autocorrelation function,j=(s) (Fig 3a) derived from the time domain waveform i ( t ) whereby

i = ( r ) = a ~ ( t ) F ( t + r ) ] (6) The autocorrelation function is substituted into

the mathematical behavioural model to yeld the correlation parameters of the output signal [I ,2] as;

1-1 "odd

The output spectrum is then obtained by the Fourier Transform of the output autocorrelation (Fig.3b) in (7). The output power spectrum is the sum of the individual spechum of each term in (7) (See Fig. 4) scaled by the input power level, A, and the corresponding magnitude of the complex coefficients. Numerical integration of the output spectrum yields the ACPR.

QUADRATURE MODULATOR NONUNEAR OEVlCE

Figurc 2 Bsscband Equxvdmt Quadnturr Modulated Nonllncar Amplifier

522

In. Twc-mne T m S m CWCmmsncs ,

. . MPAsuRehwr.

The experimental setup, adopted from [3], using a vector .signal generator (Agilent ESG E4438C) to generate the two-tone tst signal, is shown in Fig. 7. The device under test @UT) is a 24dFJ gain, 2GHz broadband amplifier oIp8349B) and a Mini- Circuits ZFL-SOOLN preamplifier of frequency range 0.1 to 500 MHz and 26 dFJ gain was used as the reference PA. It acts as a reference IM generator by operating at the low centre frequency of 800 kHz so that memory effects can be neglected The fundamental, IM3 and IMS signals in the reference path will then have constant phases for all input power levels up until the gain compression point.

The two-tone input signal is.chbsen with a 100 kHz separation with IMD transient response in mind [3]. A vector modulator, which comprises a variable attenuator and phase shifter, is used to adjust the amplitude and phase of the fundamental, IM3 and IM5 components kom the DUT to cancel the signals at the output of the combiner. The phase change from the adjustment is obtained from the phase of measured by the network analyser. The relative amplitudes of the fundamental, IM3 and IMS signals are measured on the spectrum analyser. The sequence is repeated with increasing input power until the PA is driven deep into saturation.

IV. SIMULATIONS . ,. ' . . , . . .

Least-squares fitting using MATLAB is employed to extract the complex coefficients in the nonlinearity model (5). The measured and modelled amplitude and .phase characteristics for the fundamental, IM3 and IMS components are in excellent agreement as shown in Figs. 8 - 10. The coefficients obtained from the transfer characteristics are then substituted into (7) to evaluate' an IS-95 CDMA simal. Long random

output spec!m from the nonlinear PA is obtained from (7) through FFT. It is obvious from Fig.5 that the 3d, 5' and 7' order components contribute largely to spectral regrowth.

ACPR,,, for the CDMA signal in this experiment is -39dB for the respective input and output power spectrum levels in Fig.6. It is defined as the ratio of the adjacent channel power in a 30 kHz resolution bandwidth measured at an 885 kHz offset from the channel centre frequency. swept over the lower adjacent channel to the total power in the main channel bandwidth of ' 1.23 MHz.

. . . . . . . . . .

Fr.q".ncy("* , . Figwe 5: CDMA Output Fundamntpl and Higher order Spccm

sequences of 2" bits were usedin the sinhation to obtain a good estimate of the autocorrelation. The

I Figwe 7 Orpmirncntpl Setup for Two-Tone MePSwemat

d =I I

Figure 9 Measured and Modelled IM3 Amblihldc and Phase

a, . . . . . . . I

Figure IO: Measured and Modelled IMS Amplihldo and Phasc

V. CONCLUSIONS

A two-tone transfer characteristic measurement combined with a statistical behavioural modelling method provides for the speed and efficiency needed for system level simulation and without having to assume a memoryless or quasi- memoryless nonlinearity. The statistical method provides mathematical insight into the transformation of input signal statistics whereby an appropriate behavioural model helps to qhantify PA nonlinear effects. This in turn serves to provide useful knowledge for appropriate linearisation schemes and optimum design of RF power amplifiers.

ACKhOWEffiMENT / The authors thank Youngoo Yang, Roland

Clarke, John Rule and Eamonn Gilmartin for their support, helpful comments, and assistyce in making the measurements.

REFERENCES

[I] K. G. Gard, H. M. Gutierrez, and MI B. Steer, "Chatacterizatiou of spectral regrowth in microwave amplifiers based on the nonlinear transformation of a complex Gaussian process," IEEE Trans. Microwave Theory Techniques, vol. 47, no. 7, pp.1059-lb69, July 1999.

[2] K. G. Gard, M. E. Steer and L. E. Larson, "Generalised Autocorrelation Analysis of Spectral Regrowth from Bandpass Nonlinear Circuits", 2001 IEEE MTT-S Int. Microwave amp. Dig.,vol.l, pp.9-12,2001.

[33 Y. Yang, J. Yi, 3. Nam, B. Kim and M. Park, "Measurement of two-tone transfer characteristics of high-power amplifiers, " IEEE Tyans. on Microwave Theory and Techniques, vol. 49, no. 3 , pp.568-571, March 2001.

141 N. M. Blachman, " Band-pass nonlinearities," IEEE Pans. Information Theory, vol. IO, pp. 162- 164, Apr. 1964.

[5] A. R. b y e and D. A. George, "Analysis and compensation of bandpass nonlinearities for communications," IEEE Trans. Communications, vol. 20, pp. 965-972, Oct. 1972.