A High-Order Analysis of the Distortion Effects of Nonlinear Amplifiers on CDMA Signals

This paper presents a direct method of analyzing the distortion effects of the power amplifier nonlinearity on the CDMA signal. In the analysis approach of the paper, the various user signals, which are composed of data-modulated Walsh codes, which are also modulated by various scrambling codes, are modeled as independent random sequences. These sequences are band limited, using square-root raised cosine filters and modulated by a carrier frequency before being input to the nonlinear power amplifier. In the analysis approach of the paper, the amplifier characteristics are approximated by a polynomial of sufficiently high degree such that over the range of input signal, the approximation error is negligible. For the region of amplifier operation of interest in this paper, terms of degree higher than forty may be needed compared to an earlier simplified analysis presented by the author wherein only cubic distortion terms have been considered. The expressions for both the output signal power and the output signal power-to-distortion power spectral density ratio are given in the form of a finite series with its coefficients being a function of the amplifier input power level, the number of codes, and the amplifier transfer characteristics. The paper also shows that the amplifier possesses a maximum capacity defined as the maximum total bit rate Rt that can be present at the amplifier input for a specified output signal power back-off and the required output bit energy to distortion power spectral density ratio (E_b/N_0d). Also for any given output back-off and user data rate, the (E_b/N_0d) ratio is a strong function of the number of codes M in the CDMA signal.