Theoretical derivation of the stochastic behavior of a WCDMA signal measured with a spectrum analyzer

Frequency-selective measurements with a spectrum analyzer are the most obvious means to accurately measure the power of a communication signal. In this paper, models for the spectrum analyzer and for the wideband code division multiaccess (WCDMA) signal are described. Based on these models, the analytic expressions for the probability density function (PDF) of the displayed signal have been derived for the different detection modes [sample, root mean square (rms) and positive-peak detection] of the spectrum analyzer. Based on these theoretical considerations, the dependence of the mean and standard deviation of the measured signal on the observation time of the detector has been examined, which showed a good agreement with the simulated results.