An Analysis of the Distortion Effects of Nonlinear Amplifiers on CDMA Signals

Abstract

This paper 1,2 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. The paper derives a closed-form expression for the output signal power, the output signal power-todistortion power spectral density ratio as a function of the input signal power back-off, 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 R T 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 ). Alternatively at 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.

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

“…The property that the various distortion terms are uncorrelated has also been verified by simulations as shown in [15]. Thus the cross-spectral density terms are zero and the power spectral density (PSD) of the sum is the sum of the PSDs of the individual distortion terms, i.e., 31d(f) 12 (9) ]P(f) 16 3Aq f (8) where Pq(f) denotes the PSD of the individual terms c1(t).c2(t).c3(t) in the summation in (6).…”

“…In [15] the result for (Ps/Nod) has been obtained by considering only the first-and third-degree terms in the expansion (2) applicable to the case when the amplifier operates under a relatively large output back-off. In this paper the analysis is expanded to the case when an arbitrary number of terms in (2) may need to be considered as is the case when the amplifier is operated under a relatively small output back-off.…”

“…It has also been shown that even for the case of square-root raised cosine filtered case both the signal and distortion terms have the same power spectral densities. These spectral densities have been obtained by simulations in [15] for the case of 1 Mcps code chip rate and are approximately equal to -58 dBW/Hz at f equal to zero. For any other chip rate equal to Rem measured in Mcps, the spectral density is simply normalized by R,m.…”

“…Although inclusion of many higher-order terms makes the analysis somewhat tedious, the final result is in relatively simple form, as is shown in the paper. It may be noted that in the IM (intermodulation) noise analysis of the FDMA signal, generally only third-order terms and at times fifth-order terms are considered adequate in the analysis [12][13][14][15][16]. In the present application, however, due to the need for operating the amplifier at relatively low back-off, terms on the order of forty are required to provide accurate results in that region of operation.…”

“…In an earlier paper by the author [15], for illustration of the methodology, only the first-and third-degree terms are considered in the expansion. These terms are enough if the amplifier is operated with sufficiently large output back-off.…”