## 1 Satellite Constellations with Zenith Propagation Paths at Any Site  
Among satellite constellations, the GeoSurf constellations are a good choice for future worldwide internet infrastructure because they share most of the advantages of current GEO (geostationary), MEO (medium Earth orbit) and LEO (low Earth orbit) satellite constellations without suffering most of their drawbacks because they emulate the geostationary orbit with zenith paths in sites located at any latitude [1]. In [2], we have compared the tropospheric attenuation of GeoSurf zenith paths with the paths of GEO, MEO and LEO satellites. In [3], we have assessed how the annual average probability distribution \(P(A)\) of exceeding a given rain attenuation \(A\) (dB) depends on the carrier frequency \(f_{c}\) (GHz) in the GeoSurf paths at sites in different climatic regions. All these studies refer to narrow-band channels, i.e., channels with negligible linear (amplitude and phase) distortions. In [4], we have estimated the slowly time-varying transfer function and linear distortions that are likely found in ultra-wideband radio links in GeoSurf constellations working at millimeter wavelengths. As a practical example, the bandwidth considered was 10 GHz wide, centered at 80 GHz (W-Band), because we think it might be used in future worldwide internet radio links using spread spectrum modulation and code division multiple access (CDMA) [5, 6, 7, 8, 9, 10] with BPSK and QPSK modulation, once high-frequency large wideband technology--now developed at lower frequencies [11]--will also be available at W-band. CDMA can provide a large processing gain and can be designed without considering issues related to frequency and access coordination which, together with the advantages of the GeoSurf constellations mentioned in Reference [1], can be an effective choice to provide high bit rates to users. The literature on what today is defined as \"wideband\" communication does not refer to rain attenuation or to the ultra-wideband radio links studied here but instead refers only to radio links in clear-sky conditions (mainly multipath), both for terrestrial and satellite systems [5; 12; 13; 14; 15; 16]; therefore, we discuss these topics further, following work carried out by [4; 17]. Following our previous study [4], the purpose of this paper is to assess--with simulations using onsite rain rate time series and the synthetic storm technique (SST) [18]--the interference due to amplitude and phase distortions produced by rain attenuation in the ultra-wideband communication systems mentioned above and designed for using double sideband-suppressed carrier (DSB-SC) modulation in both quadrature channels (QPSK). We assume that the total signal-to-noise ratio (SNR) of the Gaussian channel is greater than the minimum required to guarantee a bit error probability smaller than the maximum value tolerated by users. Under this hypothesis, we estimate how the in-band attenuation and phase delay affect the baseband digital signal. We evaluate the sampler output of a direct channel (e.g., the cosine channel, inter-symbol interference, ISI) and the quadrature interference (QI) coming from the orthogonal channel (the sine channel, referred to also as the quadrature channel). For illustrating the characteristics of the interference, we report the results concerning radio links simulated at Spino d'Adda (Italy), Madrid (Spain) and Tampa (Florida), which are sites in different climatic regions (Table 1). We have considered these specific sites because the rain rate time series \(R(t)\) (mm/h)--averaged in 1 min intervals--have been continuously recorded onsite for several years, which is a sufficiently long period to provide reliable experimental results when SST is applied. The rain fade in GeoSurf radio links is independent of the particular GeoSurf design (e.g., altitude and number of satellites) because all paths to/from a satellite of the constellation are always locally vertical (zenith).