Q5Wireless Communication

Satellite Link Design and Received Power Expression

The link design process for a satellite communication system begins with the transmit earth station (or satellite transponder, for the downlink) power Pt and transmit antenna gain Gt, whose product PtGt is defined as the Effective Isotropically Radiated Power (EIRP) - the power that would need to be radiated by a hypothetical ideal isotropic (omnidirectional) antenna to produce the same power flux density at the receiver as the actual directional transmit antenna produces. The signal then propagates across the very large distance separating the earth station and satellite (roughly 36,000 km for a geostationary link), experiencing free-space path loss Lp = (4pid/lambda)^2, which is by far the dominant loss term in any satellite link budget given the enormous distances involved, along with additional atmospheric and other propagation losses La (rain attenuation, atmospheric gas absorption, antenna pointing loss, and polarization mismatch loss, all of which become more significant at higher frequency bands such as Ku-band and Ka-band).

At the receiving end (the satellite transponder for an uplink, or the receiving earth station for a downlink), the receive antenna gain Gr collects a fraction of the incident power flux density proportional to the antenna's effective aperture area, yielding the received power Pr = (EIRP x Gr)/(Lp x La), or equivalently in logarithmic (dB) form, Pr(dBW) = EIRP(dBW) - Lp(dB) - La(dB) + Gr(dB). The complete satellite link design process computes this received power for both the uplink (earth station to satellite) and downlink (satellite to earth station) legs separately, and combines them (typically via a combined carrier-to-noise ratio calculation accounting for both uplink and downlink noise contributions, since the satellite transponder itself adds thermal noise on the uplink that is then relayed and further degraded by downlink noise) to determine the overall end-to-end link performance, expressed as the overall carrier-to-noise ratio (C/N) or equivalently energy-per-bit-to-noise-density ratio (Eb/N0) available to the demodulator, which must exceed the minimum threshold required for the chosen modulation and coding scheme to achieve the target bit error rate with an adequate margin to accommodate expected fading (particularly rain fade at higher frequency bands) over the required link availability percentage.

Definitions

• Coverage angle: the half-angle of the cone, measured from the satellite, within which the satellite's antenna beam illuminates the earth's surface (its 'footprint'), or equivalently the angular region on the earth's surface (measured from the sub-satellite point, as seen from the center of the earth) within which the satellite remains visible above a specified minimum elevation angle - a larger coverage angle corresponds to a wider-beam antenna illuminating a larger footprint area on the ground, at the cost of reduced power flux density (and hence reduced received signal strength) delivered to any single point within that larger footprint.
• Slant range: the straight-line (line-of-sight) distance between an earth station and the satellite, as opposed to the satellite's altitude (measured perpendicular to the earth's surface) - the slant range depends on both the satellite's altitude and the earth station's elevation angle to the satellite, being minimum when the earth station is located directly beneath the satellite (elevation angle of 90 degrees) and increasing as the earth station's elevation angle to the satellite decreases toward the horizon.
• Orbital period: the time required for a satellite to complete one full revolution around the earth in its orbit, determined entirely by the satellite's orbital altitude (semi-major axis) via Kepler's third law - for a geostationary orbit at approximately 35,786 km altitude, the orbital period equals almost exactly one sidereal day (23 hours, 56 minutes), which is precisely the condition that allows a geostationary satellite to appear stationary relative to a fixed point on the rotating earth.
• Orbital velocity: the linear (tangential) speed at which a satellite travels along its circular orbital path, which decreases as orbital altitude increases (following an inverse-square-root relationship with orbital radius derived from balancing gravitational and centripetal forces) - low earth orbit (LEO) satellites, orbiting at only a few hundred kilometers altitude, travel at roughly 7.5 km/s and complete an orbit in about 90 minutes, whereas a geostationary satellite at 35,786 km altitude travels at a much slower orbital velocity of approximately 3.07 km/s, completing its single orbit over the full ~24 hour period matching the earth's own rotation.

The satellite link design process described above is typically carried out separately for the uplink (earth station to satellite) and downlink (satellite to earth station) legs of the overall path, since each leg has its own distinct EIRP, path loss, and receive antenna gain/noise-temperature parameters - the uplink is characterized by a comparatively powerful, large earth-station transmitter and a much smaller, power-limited satellite receive antenna and low-noise-amplifier, while the downlink is characterized by a power-limited satellite transponder transmitter and a comparatively large, sensitive earth-station receive antenna, reflecting the very different size, power, and cost constraints applicable to space-segment versus ground-segment equipment.

Understanding the distinction between coverage angle, slant range, orbital period, and orbital velocity is essential for satellite system planning: coverage angle and the resulting footprint size determine how many earth stations or how large a geographic service area a single satellite can serve, slant range directly determines both the free-space path loss (via the received-power formula derived above) and the one-way propagation delay experienced by the link (a significant consideration for geostationary satellite links, whose slant range of roughly 36,000 km produces a propagation delay of about 120 ms one-way, noticeably affecting interactive voice or data applications), and orbital period and velocity together determine whether a satellite appears stationary (geostationary) or in continuous relative motion (non-geostationary) as seen from any fixed point on the earth's surface, directly shaping the antenna-tracking requirements of any earth station communicating with it.

The propagation delay consideration mentioned above is particularly significant for interactive applications: a round-trip delay of roughly 240 ms for a single geostationary satellite hop (and potentially double that, approaching 500 ms, if a call must traverse two such hops) is large enough to be noticeably perceptible in voice conversation and can meaningfully affect the responsiveness of interactive data applications, which is one of the key reasons non-geostationary constellations (MEO and LEO, offering much shorter slant range and hence much lower propagation delay, at the cost of requiring many more satellites for continuous coverage) have become increasingly attractive for latency-sensitive broadband and communication services in recent years.