The wave spectrum of the fluctuations in a plasma can be determined by first measuring the cross-power density spectrum and then performing a spatial Fourier transform. The feasibility of using this method to measure the fluctuations in the ionosphere by placing a cross-power spectrum analyzer on an orbiting satellite is assessed by determining the integration time required to make the measurement. The theory considers in particular spherical probes biased into the electron saturation region. The method consists in assuming an equilibrium plasma wave spectrum, from which the power spectrum directed to each spherical probe and the available power at the amplifier input are determined. Using statistical theory, this information is used to determine the integration time needed to measure the cross-power spectral density at the output terminals of the cross-power spectrum analyzer to a specified accuracy. For typical experimental conditions the integration times are found to increase from 0.1 to 1000 s as the probe spacing increases from 2 to 10 Debye wavelengths for ion wave frequencies. For electron plasma wave frequencies the corresponding increase is from 10 to 104 s.