On the statistical properties of the capacity of sparse multipath fading channels

Most existing works in wireless communications assume rich scattering. However, there is growing experimental evidence that physical wireless channels can exhibit a sparse structure. By assuming an asymmetric Doppler power spectral density (PSD), we can model and simulate sparse channels by using a finite sum of weighted complex harmonic functions, also called sum of cisoids (SOC). In this paper, we focus on the analysis of the statistical properties of the instantaneous capacity of sparse SOC-based multipath fading channels under line-of-sight (LOS) conditions. The probability density function (PDF), the cumulative distribution function (CDF), the level-crossing rate (LCR), and the average duration of fades (ADF) of the channel capacity are studied. The asymptotic behavior of the capacity is also investigated by providing an approximate solution to the distribution of the outage intervals for low capacity thresholds. Our study shows that the capacity of mobile radio channels behaves in sparse scattering environments completely different from what is known from previous studies assuming rich scattering. However, on average and on specific conditions, the channel capacity behaves like that of the reference (Rayleigh/Rice) model which assumes rich scattering. Finally, the validity of the analytical expressions is checked by computer simulations.