Localization and Handover in Satellite Systems

In a terrestrial network handover means the user moved. Here it usually does not. The program makes the point with arithmetic: the satellite's point on the ground runs at 6.65 kilometres every second, while a car on a motorway adds 0.0278 kilometres a second. The user's own movement is a rounding error. Everything that follows is caused by the network moving.

Intra-satellite handover

A satellite's footprint is not one cell. It is divided into spot beams, each a narrow beam from the satellite's antenna, and each beam is a cell in the sense the terrestrial world means: its own frequencies or codes, reused in beams far enough away.

The beams are fixed to the satellite, so they sweep across the ground with it. The program computes how fast. With the whole footprint as one cell a user is inside it for 624.8 seconds. Divide it into 16 beams and each is about 1,039 km across, crossed in 156.2 seconds. Into 48 beams and each is about 600 km across, crossed in 90.2 seconds. Into 96 and it is 63.8 seconds.

So a user sitting perfectly still in a chair is handed from beam to beam about every minute and a half. That is intra-satellite handover, and it is the most frequent thing the system does. It is also the easiest: the same satellite is involved throughout, so the decision and the switch are made on board.

Inter-satellite handover

Eventually the satellite sets. From [LEO and MEO], a satellite at 780 km passing straight overhead is above ten degrees for 10.4 minutes, and the program adds what happens when the pass is not overhead: 9.1 minutes for a user half way to the edge of the swath, and only 4.6 minutes near the edge. Ten minutes is the best case, not the usual one.

At that point the call must move to the next satellite, which is inter-satellite handover. If the constellation has links between its satellites the call may also have to be rerouted across the grid of [Routing in Satellite Systems], so the path changes as well as the radio link.

Gateway handover

A third kind has no counterpart on the ground at all. The user's satellite has not set and the radio link is perfect, but the gateway that connects that satellite to the fixed network is itself passing out of the satellite's footprint, because a gateway is just another point on the ground and leaves the footprint at the same rate a user does: at best 10.4 minutes.

The call must then be moved to another gateway while the radio link stays exactly as it was. The user notices nothing. This is gateway handover, and it exists because in a satellite system the connection to the fixed network is itself made over a radio link that comes and goes.

Inter-system handover

The last kind is between the satellite system and a terrestrial one, for a dual-mode handset that can use either.

The program shows which way the preference runs, and why it is not a close call. At 1,600 MHz, reaching the satellite at 780 km costs 154.4 dB. Reaching a mast at the edge of a 10 km cell costs 116.5 dB, a 3 km cell 106.1 dB, and a 500 m cell 90.5 dB. The terrestrial link is 38 to 64 dB cheaper, which is a factor of between six thousand and two and a half million.

So a dual-mode handset uses the ground network wherever there is one, and falls back to the satellite only where there is not. Handover to the satellite happens when the terrestrial signal is lost, and back the moment it returns. Satellite capacity is scarce and expensive, and this is how it is saved for the places that have no alternative.

A ten minute call

Put the four together for a caller sitting still, as the program does. With 48 beams a satellite: about 6.7 beam handovers and 1.0 satellite handovers in ten minutes, plus a gateway handover if the gateway happens to be leaving, plus an inter-system handover if the caller walks indoors near a mast.

Roughly eight handovers in a ten minute call, none of them because anyone moved. A terrestrial network doing that would be considered broken. Here it is normal, and the entire design of the signalling, the registers and the routing exists to make it invisible.

Handover, computed

# Handover in a low constellation: how often, of which kind, and why.
import math

GM, R, C = 3.986004418e14, 6378137.0, 299792458.0
ALT = 780e3
r = R + ALT
ELEV = 10.0

T = 2 * math.pi * math.sqrt(r ** 3 / GM)
v_orbit = math.sqrt(GM / r)
v_track = v_orbit * R / r                    # the sub-satellite point's speed on the ground
gamma = math.acos(R / r * math.cos(math.radians(ELEV))) - math.radians(ELEV)
foot_km = gamma * R / 1000                   # footprint radius on the ground

print("The satellite, and the patch of ground it owns:")
print("  period %.1f min, orbital speed %.0f m/s" % (T / 60, v_orbit))
print("  its point on the ground runs at %.0f m/s, which is %.2f km every second"
      % (v_track, v_track / 1000))
print("  at a %.0f degree minimum elevation the footprint reaches %.0f km from that point"
      % (ELEV, foot_km))

# 1. Intra-satellite handover. The footprint is not one cell: it is divided
#    into spot beams, and a user crosses them one after another.
print()
print("Inside one satellite: crossing its spot beams")
area = math.pi * (foot_km * 1000) ** 2
for beams in (1, 16, 48, 96):
    cell_area = area / beams
    cell_r = math.sqrt(cell_area / math.pi)
    cross_s = 2 * cell_r / v_track
    print("  %3d %-6s each covers %8.0f km2, about %4.0f km across, crossed in %5.1f s"
          % (beams, "beam:" if beams == 1 else "beams:", cell_area / 1e6,
             2 * cell_r / 1000, cross_s))
print("  the beams are fixed to the satellite, so they sweep the ground with it: a user")
print("  standing still is handed from beam to beam, and that is intra-satellite handover.")

# 2. Inter-satellite handover. The satellite itself sets.
print()
print("Between satellites: how long one is usable")
best = T * (2 * math.degrees(gamma) / 360.0)
print("  passing straight overhead, it is above %.0f degrees for %.1f min" % (ELEV, best / 60))
for offset_frac, label in ((0.0, "straight overhead"), (0.5, "half way to the edge"),
                           (0.9, "near the edge of the swath")):
    off = gamma * offset_frac                     # how far off the track the user stands
    half = math.acos(math.cos(gamma) / math.cos(off))
    print("  %-26s usable for %4.1f min" % (label, T * (2 * math.degrees(half) / 360.0) / 60))
print("  a pass that is not overhead is shorter, so the figure above is the best case.")

# 3. What a ten minute call actually costs in handovers.
print()
print("A ten minute call, standing perfectly still:")
CALL_MIN = 10.0
for beams in (16, 48, 96):
    cell_r = math.sqrt(area / beams / math.pi)
    cross_min = (2 * cell_r / v_track) / 60
    print("  with %2d beams a satellite: about %4.1f beam handovers and %.1f satellite handovers"
          % (beams, CALL_MIN / cross_min, CALL_MIN / (best / 60)))
print("  none of them because the caller moved. A car at 100 km/h adds %.4f km/s to a"
      % (100 / 3600.0))
print("  ground track already running at %.2f km/s, which changes almost nothing."
      % (v_track / 1000))

# 4. Gateway handover. The gateway must stay in view of the same satellite.
print()
print("Gateway handover: how long one ground station stays with one satellite")
print("  a gateway enters the footprint and leaves it at the same rate as any point:")
print("  at best %.1f min, the same figure as a user's pass" % (best / 60))
print("  so a call held on one satellite may still have to be moved to another gateway,")
print("  and the user notices nothing: the radio link has not changed at all.")

# 5. Inter-system handover, and why it is preferred in one direction.
print()
print("Inter-system handover: satellite against terrestrial, at 1600 MHz")
def fsl(f_mhz, d_km):
    return 32.44 + 20 * math.log10(f_mhz) + 20 * math.log10(d_km)
sat_db = fsl(1600, ALT / 1000)
for cell_km in (0.5, 3.0, 10.0):
    print("  a terrestrial cell of %4.1f km costs %5.1f dB, against %5.1f dB to the satellite"
          % (cell_km, fsl(1600, cell_km), sat_db))
print("  the terrestrial link is %.0f to %.0f dB cheaper, so a dual-mode handset uses the"
      % (sat_db - fsl(1600, 10.0), sat_db - fsl(1600, 0.5)))
print("  ground network wherever there is one, and the satellite only when there is not.")

# 6. Where the network has to look to find a user.
print()
print("Finding a user: what the registers have to hold")
sats = 66
print("  the home register holds, as on the ground, the user's subscription and where to ask")
print("  the visitor register holds the users currently being served")
print("  a third register is needed that the ground network has no use for: the current")
print("  position of all %d satellites, and which one is serving each user" % sats)
print("  it must be updated every time a user is handed on, which the program above puts at")
print("  once every %.1f min per user in a call, and more often between beams" % (best / 60))

Distinctions

What it does not mean

Handover here does not mean the user moved. Almost none of it is caused by the user; the beams and the satellites sweep past a stationary caller.

A spot beam is not a smaller satellite. It is one beam of one satellite's antenna, and a beam handover is handled entirely on board.

Gateway handover does not interrupt the radio link. The link to the satellite is untouched; only the ground station and the path beyond it change.

Inter-system handover is not symmetric. Terrestrial is preferred in both directions, because it is tens of decibels cheaper and its capacity is not scarce.

The satellite register is not the visitor register under another name. The visitor register says which users are here; the satellite register says where the moving equipment is and which piece of it currently reaches each user.

Frequent handover is not a fault. It is the unavoidable consequence of putting the base station in an orbit that crosses the sky in ten minutes.

Quick revision

• Registers: home (subscription and where to ask), visitor (users served here now), and a satellite user mapping register holding the satellites' current positions and each user's serving satellite. The third exists because the base stations move.
• Calling: home register gives the gateway, the satellite register gives the satellite and its position, the call goes up, across if there are links, and down.
• Four handovers: intra-satellite (beam to beam), inter-satellite (satellite sets), gateway (ground station leaves the footprint), inter-system (satellite to terrestrial and back).
• Rates: ground track 6.65 km/s; with 48 beams a cell is about 600 km across and crossed in 90.2 s; a satellite lasts 10.4 min overhead, 9.1 half way out, 4.6 near the edge; a gateway also 10.4 min.
• A 10 minute call: about 6.7 beam handovers and 1.0 satellite handovers, none caused by the caller.
• Inter-system preference: satellite 154.4 dB against 116.5 dB for a 10 km cell and 90.5 dB for a 500 m cell, so terrestrial is 38 to 64 dB cheaper and is always preferred.
• A car adds 0.0278 km/s to a footprint moving at 6.65 km/s: the user's speed is irrelevant.

Test yourself

1. Why does a satellite system need a register that a terrestrial mobile network does not? Because a terrestrial network's base stations are fixed, so knowing which cell serves a user is enough to know how to reach them, and the answer stays true. In a satellite system the base stations are in orbit at over seven kilometres a second, so knowing which satellite serves a user is useless without also knowing where that satellite is at this moment, and both facts change every few minutes. The system therefore keeps a register of the current positions of all the satellites and of which satellite is serving each user, in addition to the home and visitor registers.

2. How is a call delivered to a satellite user? The call arrives for the number and reaches the user's home location register, which holds the subscription and a pointer to the gateway currently serving that user. That gateway consults the register of satellite positions and serving satellites to find which satellite has the user now and where it is, and the call is then routed up to that satellite, across the constellation if it has links between its satellites, and down to the terminal.

3. Name and explain the four handovers. Intra-satellite handover moves the call from one spot beam of a satellite to the next, because the beams are fixed to the satellite and sweep across the ground with it. Inter-satellite handover moves the call to the next satellite when the current one sets. Gateway handover moves the connection to a different ground station because the gateway has left the satellite's footprint, while the radio link to the user is untouched. Inter-system handover moves the call between the satellite network and a terrestrial one, in either direction, as terrestrial coverage is lost or regained.

4. Why does a stationary user hand over so often? Because the movement that matters is the network's, not the user's. The satellite's point on the ground travels at 6.65 kilometres every second, so with 48 spot beams a cell about 600 kilometres across is crossed in 90.2 seconds, and the satellite itself is usable for at most 10.4 minutes. A car on a motorway adds 0.0278 kilometres a second to that, which changes nothing. A ten minute call from an armchair therefore takes about 6.7 beam handovers and one satellite handover.

5. What is gateway handover, and why has it no terrestrial counterpart? It is moving a call from one ground station to another because the ground station has passed out of the serving satellite's footprint, even though the user's radio link is unchanged and perfectly good. It has no terrestrial counterpart because on the ground the base station's connection to the fixed network is a cable that does not move. In a satellite system that connection is itself a radio link to a point on a turning earth, and a gateway leaves the footprint at the same rate a user does, at best every 10.4 minutes.

6. In inter-system handover, which network is preferred, and why? The terrestrial network, in both directions. At 1,600 MHz a satellite at 780 kilometres costs 154.4 dB of free space loss, while a mast at the edge of a ten kilometre cell costs 116.5 dB and one at the edge of a 500 metre cell costs 90.5 dB, so the terrestrial link is between 38 and 64 dB cheaper, a factor of thousands to millions. The handset therefore uses the ground network wherever one exists and falls back to the satellite only where none does, which also saves scarce and expensive satellite capacity for the places that have no alternative.