Analysis of BER Performance in Presence of Nonlinear Distortion
Due to PD-HPA in Downlink DS-CDMA Signals
Abstract
A predistorter-high power ampli fier (PD-HPA) pair has become a common practice in wireless
communication to compensate for nonlinear distortion due to HPA. However, the PD-HPA pair
still produces severe signal distortion when the input signal exceeds the PD-HPA’s saturation
level. The effects of such distortion on bit error rate (BER) degradation in downlink direct
sequence-code division multiple access signals (DS-CDMA) are analyzed. We establish which
signal characteristics at the HPA input are the factors contributing to BER. Assuming that the
baseband CDMA signal is characterized as a complex Gaussian process, we develop analytic
expressions for the BER and the contributing factors to BER.
Index Terms—CDMA, nonlinear distortion, pre-distortion.
1. Introduction
Downlink direct sequence-code division multiple ac-cess (DS-CDMA) signals typically exhibit
large dynamic range since they represent the sum of signals of many users. Unfortunately, when
passed through a high power amplifier (HPA), this large dynamic range results in distortion for
components falling in the highly nonlinear regions of the HPA, which degrades the system bit
error rate (BER).
A common parameter for characterizing the dynamic range of a signal is the signal peak-toaverage power ratio (PAR). PAR is often used as an indicator to how much harm the signal will
suffer due to HPA nonlinearity, and also allows the system designer to determine the required
amount of input back-off (IBO) to reduce nonlinear distortion effects. While PAR has its use, a
signal’s dynamic range in relation to an HPA only captures only one feature of the signal’s
interplay with the HPA.
2. Objective
In this paper, an analytical description of the effects of HPA nonlinearities on the performance of
a CDMA systems has been presented, for both synchronous (orthogonal) and asynchronous
CDMA. It has been shown that, in a broad range of cases, the nonlinear distortion in the decision
variables at the receiver can be modeled by means of a complex scale factor and an additive
uncorrelated Gaussian noise: its variance and the scale factor have been evaluated analytically.
Nonlinear distortion noise is usually smaller than MAI in asynchronous systems. This model,
whose accuracy has been checked by means of simulation, has allowed an easy analytical
evaluation of the TD for some classes of HPA models.
3. Proposed scheme
In order to evaluate the system performance, in this section a statistical model for the decision
variable , given by , is developed by taking into account the effects of the nonlinear channel.
Having in mind the similarities between the multichannel CDMA signal and the multicarrier
OFDM signal, both obtained with the superposition of many elementary signals (multiplied by
the spreading sequence in the first case and by the sequence of samples of a sine wave in the
latter case), we try to extend the theoretical model proposed in [8] for OFDM systems to CDMA
systems. More precisely, we want to apply the extended Bussgang’s theorem to a CDMA signal
provided that it can be modeled as a Gaussian signal. This approach is justified by considering
that the signal at the input of the nonlinear block includes the sum of contributions which are
uncorrelated and have the same statistics. If is sufficiently large, should become a complex
Gaussian (nonstationary) random process as a consequence of the Central Limit Theorem. Of
course, we should be careful when we want to extend this approach to a CDMA signal having its
components with different power levels.
4. Software and hardware requirements

Operating system
:
Windows XP/7.

Coding Language
:
MATLAB

Tool
:
MATLAB R 2012
System requirements:
Hardware requirements:

System
:
Pentium IV 2.4 GHz.

Hard Disk
:
40 GB.

Floppy Drive
:
1.44 Mb.

Monitor
:
15 VGA Colour.

Mouse
:
Logitech.

Ram
:
512 Mb.
5. Conclusion
In this letter, we studied how nonlinear distortion due to PDHPA affects BER degradation for
transmitted downlink DSCDMA signals. We established analytically how the threshold
exceeding rate RE and the variance of the clipped portion of the signal σ2c contribute to BER
degradation. The motivation of this work is to provide system designers/operators with efficient
tools that provide potential insight into the interactions between CDMA signals and the nonlinear
PD-HPA, leading to better understanding of the impact of the PD-HPA on system BER.
References
[1] A. Conti, D. Dardari, and V. Tralli, “An analytical framework for CDMA systems with a
nonlinear amplifier and AWGN,” IEEE Trans. Commun., vol. 50, no. 7, pp. 1110–1120, July
2002.
[2] J. Proakis, Digital Communications, 4th ed. McGraw-Hill, 2000.
[3] R. Dinis and A. Palhau, “A class of signal-processing schemes for reducing the envelope
fluctuations of CDMA signals,” IEEE Trans. Commun., vol. 53, no. 5, pp. 882–889, May 2005.
[4] L. Rugini, P. Banelli, and S. Cacopardi, “Theoretical analysis and performance of the
decorrelating detector for DS-CDMA signals in nonlinear channels,” IEEE Trans. Wireless
Commun., vol. 3, no. 2, pp. 367–372, Mar. 2004.
[5] P. Banelli and S. Cacopardi, “Theoretical analysis and performance of OFDM signals in
nonlinear AWGN channels,” IEEE Trans. Commun., vol. 48, no. 3, pp. 430–441, Mar. 2000.