X-Band Downlink Link Budget: 600 km SSO to Ground Station¶
Demonstration of the missiontools Link class for RF link budget analysis.
Scenario
600 km sun-synchronous orbit (LTAN 10:30), nadir-pointing
X-band downlink at 8 250 MHz, 60 Mbps
Ground station: Kiruna Space Centre, Sweden (67.9°N, 21.0°E)
Modulation: QPSK, rate-3/4 turbo FEC — required Eb/N₀ = 7.0 dB
Availability target: 99.9 % (ITU-R P.618 atmospheric attenuation applied)
[1]:
import warnings
import numpy as np
import matplotlib.pyplot as plt
from missiontools import Spacecraft, GroundStation, Link
from missiontools.comm import SymmetricAntenna
from missiontools.attitude import AttitudeLaw
from missiontools.orbit.propagation import propagate_analytical
from missiontools.orbit.frames import geodetic_to_ecef, eci_to_ecef
import itur
1. Link Parameters¶
[2]:
# Waveform / link parameters
FREQ_HZ = 8.25e9 # centre frequency (Hz) — ITU-R EO downlink band
DATA_RATE = 60e6 # data rate (bit/s)
TX_POWER_W = 8.0 # transmit power (W) — solid-state PA, X-band
TX_POWER_DBW = 10 * np.log10(TX_POWER_W)
DISH_DIAM = 3.7 # receive dish diameter (m) — Kiruna tracking station
DISH_EFF = 0.6 # dish aperture efficiency
T_SYS_K = 100.0 # system noise temperature (K) — subarctic + cryogenic LNA
REQ_EB_N0 = 7.0 # required Eb/N0 (dB) — QPSK + rate-3/4 FEC, BER = 10⁻⁷
IMPL_LOSS = 2.0 # implementation loss (dB)
print(f"Frequency : {FREQ_HZ/1e9:.4f} GHz")
print(f"Data rate : {DATA_RATE/1e6:.0f} Mbps (10·log₁₀(Rb) = {10*np.log10(DATA_RATE):.1f} dB)")
print(f"TX power : {TX_POWER_W:.0f} W ({TX_POWER_DBW:.1f} dBW)")
print(f"RX dish : {DISH_DIAM:.1f} m (η = {DISH_EFF}, T_sys = {T_SYS_K:.0f} K)")
print(f"Required Eb/N0 : {REQ_EB_N0:.1f} dB")
print(f"Impl. loss : {IMPL_LOSS:.1f} dB")
Frequency : 8.2500 GHz
Data rate : 60 Mbps (10·log₁₀(Rb) = 77.8 dB)
TX power : 8 W (9.0 dBW)
RX dish : 3.7 m (η = 0.6, T_sys = 100 K)
Required Eb/N0 : 7.0 dB
Impl. loss : 2.0 dB
2. Spacecraft, Ground Station and Antennas¶
The transmit antenna is a shaped Earth-coverage beam mounted along the spacecraft nadir axis (body-z). The gain pattern is designed to remain high across the full Earth disk visible from 600 km (half-angle ≈ 66°) and roll off sharply beyond it.
The receive antenna is a 3.7 m parabolic reflector modelled with SymmetricAntenna.from_parabolic (uniformly illuminated aperture, η = 0.6). The dish tracks the spacecraft via AttitudeLaw.track, so it is always on boresight and receive gain equals the peak value at every timestep. The system G/T is derived from the dish peak gain and the assumed system noise temperature.
[3]:
EPOCH = np.datetime64('2025-06-21T00:00:00', 'us') # June solstice
# Spacecraft
sc = Spacecraft.sunsync(altitude_km=600.0, node_solar_time='10:30', epoch=EPOCH)
sc.attitude_law = AttitudeLaw.nadir()
# TX antenna — Earth coverage beam, nadir-mounted (body-z)
tx_angles = np.array([ 0, 30, 55, 65, 70, 80, 90], dtype=float) # off-boresight (°)
tx_gains = np.array([ 12, 12, 11, 9, 4, -3, -10], dtype=float) # gain (dBi)
tx = SymmetricAntenna(tx_angles, tx_gains, body_vector=[0, 0, 1])
sc.add_antenna(tx)
# Ground station: Kiruna Space Centre, Sweden
gs = GroundStation(lat=67.86, lon=20.97, alt=390)
# RX: 3.7 m parabolic dish, tracking the spacecraft
rx = SymmetricAntenna.from_parabolic(DISH_DIAM, FREQ_HZ, eff=DISH_EFF,
attitude_law=AttitudeLaw.track(sc))
gs.add_antenna(rx)
# G/T derived from dish peak gain and system noise temperature
G_T_DB_K = rx.peak_gain_dbi - 10.0 * np.log10(T_SYS_K)
alt_km = (sc.a - 6_371_000) / 1e3
print(f"Orbit : {alt_km:.0f} km SSO, i = {np.degrees(sc.i):.2f}°, LTAN 10:30")
print(f"Ground station : Kiruna ({gs.lat}°N, {gs.lon}°E, {gs.alt} m a.s.l.)")
print(f"TX antenna : peak {tx.gains_dbi[0]:.0f} dBi, body-z (nadir boresight)")
print(f"RX antenna : {DISH_DIAM:.1f} m parabolic (η = {DISH_EFF}), "
f"peak {rx.peak_gain_dbi:.1f} dBi, tracking SC")
print(f"RX G/T : {G_T_DB_K:.1f} dB/K (T_sys = {T_SYS_K:.0f} K)")
# Link
link = Link(
tx=tx, rx=rx,
tx_power_dbw=TX_POWER_DBW,
frequency_hz=FREQ_HZ,
data_rate_bps=DATA_RATE,
rx_gt_db_k=G_T_DB_K,
required_eb_n0_db=REQ_EB_N0,
implementation_loss_db=IMPL_LOSS,
use_p618=True,
)
Orbit : 607 km SSO, i = 97.79°, LTAN 10:30
Ground station : Kiruna (67.86°N, 20.97°E, 390 m a.s.l.)
TX antenna : peak 12 dBi, body-z (nadir boresight)
RX antenna : 3.7 m parabolic (η = 0.6), peak 47.9 dBi, tracking SC
RX G/T : 27.9 dB/K (T_sys = 100 K)
[4]:
# Earth disk half-angle from 600 km altitude
R_E = 6_371_000.0
H = sc.a - R_E
disk_half_deg = np.degrees(np.arcsin(R_E / (sc.a))) # nadir angle at horizon
el5_nadir = np.degrees(np.arcsin(R_E * np.cos(np.radians(5)) / sc.a)) # nadir @ 5° el
angles_fine = np.linspace(0, 90, 400)
gains_fine = np.interp(angles_fine, tx.angles_deg, tx.gains_dbi)
fig, ax = plt.subplots(figsize=(7, 4))
ax.plot(angles_fine, gains_fine, linewidth=2, color='tab:blue', label='TX pattern')
ax.axvline(disk_half_deg, color='grey', linestyle='--', linewidth=1.0,
label=f'Earth horizon ({disk_half_deg:.1f}°)')
ax.axvline(el5_nadir, color='tab:red', linestyle='--', linewidth=1.0,
label=f'5° elevation target ({el5_nadir:.1f}° off nadir)')
ax.set_xlabel('Off-boresight (off-nadir) angle (°)')
ax.set_ylabel('Gain (dBi)')
ax.set_title('Spacecraft TX antenna — Earth coverage pattern')
ax.legend(loc='lower left')
ax.set_xlim(0, 90)
ax.grid(True, alpha=0.3)
plt.tight_layout()
plt.show()
g_at_5deg = float(np.interp(el5_nadir, tx.angles_deg, tx.gains_dbi))
print(f"Gain at 5° elevation ({el5_nadir:.1f}° off nadir): {g_at_5deg:.1f} dBi")
Gain at 5° elevation (65.4° off nadir): 8.6 dBi
[5]:
_lam = 299_792_458.0 / FREQ_HZ
# –3 dB half-beamwidth: [2J₁(u)/u]² = 0.5 at u ≈ 1.616
hpbw_half_deg = np.degrees(np.arcsin(min(1.0, 1.616 * _lam / (np.pi * DISH_DIAM))))
# First null: J₁ = 0 at u = 3.8317 → sin(θ) = 1.22 λ/D
theta_null_deg = np.degrees(np.arcsin(min(1.0, 1.22 * _lam / DISH_DIAM)))
angles_rx_fine = np.linspace(0.0, 5.0, 3000) # zoom to main lobe + first few sidelobes
gains_rx_fine = np.interp(angles_rx_fine, rx.angles_deg, rx.gains_dbi)
fig, ax = plt.subplots(figsize=(8, 4))
ax.plot(angles_rx_fine, gains_rx_fine - rx.peak_gain_dbi,
linewidth=1.5, color='tab:green', label='Normalised pattern')
ax.axvline(hpbw_half_deg, color='tab:orange', linestyle='--', linewidth=1.0,
label=f'–3 dB half-beamwidth ({hpbw_half_deg:.3f}°)')
ax.axvline(theta_null_deg, color='tab:red', linestyle=':', linewidth=1.0,
label=f'First null ({theta_null_deg:.3f}°)')
ax.axhline(-3, color='grey', linestyle='--', linewidth=0.8, alpha=0.5)
ax.axhline(-13.3, color='grey', linestyle=':', linewidth=0.8, alpha=0.5,
label='First sidelobe level (–13.3 dB)')
ax.set_xlabel('Off-boresight angle (°)')
ax.set_ylabel('Gain relative to peak (dB)')
ax.set_title(f'GS RX antenna — {DISH_DIAM:.1f} m parabolic reflector, '
f'{FREQ_HZ/1e9:.3f} GHz (peak {rx.peak_gain_dbi:.1f} dBi)')
ax.legend(fontsize=8, loc='lower left')
ax.set_xlim(0, 5)
ax.set_ylim(-50, 2)
ax.grid(True, alpha=0.3)
plt.tight_layout()
plt.show()
print(f"Peak gain : {rx.peak_gain_dbi:.1f} dBi")
print(f"HPBW : {2*hpbw_half_deg:.3f}°")
print(f"First null : {theta_null_deg:.3f}°")
print(f"G/T : {G_T_DB_K:.1f} dB/K (T_sys = {T_SYS_K:.0f} K)")
Peak gain : 47.9 dBi
HPBW : 0.579°
First null : 0.687°
G/T : 27.9 dB/K (T_sys = 100 K)
3. Contact Windows¶
[6]:
t_start = EPOCH
t_end = EPOCH + np.timedelta64(1, 'D')
passes = gs.access(sc, t_start, t_end, el_min=5.0, max_step=np.timedelta64(30, 's'))
print(f"Passes above 5° elevation in 24 h: {len(passes)}")
def _max_el(sc, gs, aos, los, npts=20):
"""Approximate peak elevation during a pass."""
ts = aos + np.arange(npts) * ((los - aos) / (npts - 1))
r_eci, _ = propagate_analytical(ts, **sc.keplerian_params, propagator_type=sc.propagator_type)
r_ecef = eci_to_ecef(r_eci, ts)
r_gs = geodetic_to_ecef(np.radians(gs.lat), np.radians(gs.lon), gs.alt)
delta = r_ecef - r_gs
rng = np.linalg.norm(delta, axis=1)
lat_r, lon_r = np.radians(gs.lat), np.radians(gs.lon)
up = np.array([np.cos(lat_r)*np.cos(lon_r), np.cos(lat_r)*np.sin(lon_r), np.sin(lat_r)])
return float(np.degrees(np.arcsin(np.einsum('ij,j->i', delta, up) / rng)).max())
max_els = [_max_el(sc, gs, *p) for p in passes]
for i, ((a, l), me) in enumerate(zip(passes, max_els)):
dur = (l - a) / np.timedelta64(1, 'm')
mark = ' ◀ selected' if i == int(np.argmax(max_els)) else ''
print(f" Pass {i+1:>2}: AOS {str(a)[:19]}Z dur {dur:4.1f} min max el {me:4.1f}°{mark}")
best = int(np.argmax(max_els))
aos, los = passes[best]
Passes above 5° elevation in 24 h: 11
Pass 1: AOS 2025-06-21T01:12:56Z dur 10.5 min max el 76.7°
Pass 2: AOS 2025-06-21T02:48:44Z dur 9.8 min max el 33.1°
Pass 3: AOS 2025-06-21T04:24:16Z dur 8.2 min max el 16.8°
Pass 4: AOS 2025-06-21T05:59:06Z dur 7.2 min max el 12.9°
Pass 5: AOS 2025-06-21T07:33:00Z dur 8.0 min max el 16.2°
Pass 6: AOS 2025-06-21T09:06:52Z dur 9.7 min max el 30.8°
Pass 7: AOS 2025-06-21T10:41:48Z dur 10.5 min max el 79.5° ◀ selected
Pass 8: AOS 2025-06-21T12:18:31Z dur 9.5 min max el 26.0°
Pass 9: AOS 2025-06-21T13:58:09Z dur 4.6 min max el 7.4°
Pass 10: AOS 2025-06-21T22:12:23Z dur 5.5 min max el 8.7°
Pass 11: AOS 2025-06-21T23:47:22Z dur 9.7 min max el 29.2°
4. Link Margin During the Pass¶
Link margin is computed at 30-second intervals using Link.link_margin(), which applies free-space path loss, the spacecraft transmit antenna pattern (gain vs. nadir angle), and ITU-R P.618 atmospheric attenuation. Points where the Earth blocks the line of sight are returned as NaN.
[7]:
STEP = np.timedelta64(30, 's')
n_pts = int((los - aos) / STEP) + 1
t_pass = aos + np.arange(n_pts) * STEP
# Compute link margin (P.618 loop — takes a few seconds)
with warnings.catch_warnings():
warnings.simplefilter('ignore')
margin = link.link_margin(t_pass, availability_pct=99.9)
# Elevation angle at each timestep
r_sc_eci, _ = propagate_analytical(t_pass, **sc.keplerian_params, propagator_type=sc.propagator_type)
r_sc_ecef = eci_to_ecef(r_sc_eci, t_pass)
r_gs_ecef = geodetic_to_ecef(np.radians(gs.lat), np.radians(gs.lon), gs.alt)
delta_ecef = r_sc_ecef - r_gs_ecef
rng_m = np.linalg.norm(delta_ecef, axis=1)
lat_r, lon_r = np.radians(gs.lat), np.radians(gs.lon)
up_hat = np.array([np.cos(lat_r)*np.cos(lon_r), np.cos(lat_r)*np.sin(lon_r), np.sin(lat_r)])
el_deg = np.degrees(np.arcsin(np.einsum('ij,j->i', delta_ecef, up_hat) / rng_m))
t_min = (t_pass - t_pass[0]).astype('int64') / 60e6 # minutes since AOS
ok = ~np.isnan(margin) # unobstructed timesteps
# ── dual-axis plot ──
fig, ax1 = plt.subplots(figsize=(10, 5))
ax2 = ax1.twinx()
ax2.fill_between(t_min[ok], el_deg[ok], alpha=0.12, color='tab:blue')
ax2.plot(t_min[ok], el_deg[ok], color='tab:blue', linewidth=1.2, label='Elevation')
ax2.set_ylabel('Elevation (°)', color='tab:blue')
ax2.tick_params(axis='y', labelcolor='tab:blue')
ax2.set_ylim(0, el_deg[ok].max() * 1.2)
ax1.plot(t_min[ok], margin[ok], color='tab:orange', linewidth=2.0, label='Link margin')
ax1.axhline(0, color='tab:red', linestyle='--', linewidth=1.0, alpha=0.8, label='Closure threshold (0 dB)')
ax1.axhline(3, color='tab:green', linestyle=':', linewidth=1.2, alpha=0.9, label='Design target (3 dB)')
ax1.set_xlabel('Time since AOS (min)')
ax1.set_ylabel('Link margin (dB)', color='tab:orange')
ax1.tick_params(axis='y', labelcolor='tab:orange')
h1, l1 = ax1.get_legend_handles_labels()
h2, l2 = ax2.get_legend_handles_labels()
ax1.legend(h1 + h2, l1 + l2, loc='upper right', fontsize=9)
ax1.set_title(f'X-band downlink — {str(aos)[:19]}Z | Kiruna | 99.9% availability')
ax1.set_xlim(0, t_min[ok].max())
ax1.grid(True, alpha=0.3)
plt.tight_layout()
plt.show()
print(f"Pass statistics (P.618 @ 99.9% availability, 8.25 GHz):")
print(f" Min margin : {margin[ok].min():+.1f} dB at el = {el_deg[ok][np.nanargmin(margin[ok])]:4.1f}° (AOS/LOS)")
print(f" Max margin : {margin[ok].max():+.1f} dB at el = {el_deg[ok][np.nanargmax(margin[ok])]:4.1f}° (max elevation)")
Pass statistics (P.618 @ 99.9% availability, 8.25 GHz):
Min margin : +6.0 dB at el = 5.1° (AOS/LOS)
Max margin : +23.8 dB at el = 80.5° (max elevation)
5. Margin vs Elevation¶
Plotting margin against elevation angle shows how the link budget varies as the satellite rises and sets. The colour indicates time since AOS.
[8]:
fig, ax = plt.subplots(figsize=(8, 5))
sc_pl = ax.scatter(el_deg[ok], margin[ok], c=t_min[ok], cmap='plasma', s=35, zorder=3)
ax.axhline(0, color='tab:red', linestyle='--', linewidth=1.0, alpha=0.8, label='0 dB closure')
ax.axhline(3, color='tab:green', linestyle=':', linewidth=1.2, alpha=0.9, label='3 dB target')
ax.set_xlabel('Elevation angle (°)')
ax.set_ylabel('Link margin (dB)')
ax.set_title('Link margin vs elevation angle — coloured by time since AOS')
cb = plt.colorbar(sc_pl, ax=ax)
cb.set_label('Time since AOS (min)')
ax.legend(fontsize=9)
ax.grid(True, alpha=0.3)
plt.tight_layout()
plt.show()
6. Link Budget Summary¶
The table below shows the complete link budget at a set of reference elevation angles, computed analytically from geometry. The off-nadir angle is derived from the slant-range geometry; P.618 attenuation is evaluated with ITU-R P.618 at 99.9% availability.
[9]:
_C = 299_792_458.0
_R_E = 6_371_000.0
_H = sc.a - _R_E
_K = 10 * np.log10(1.380649e-23) # Boltzmann constant in dBW/K/Hz ≈ −228.6
print("Link budget — 8.25 GHz | 60 Mbps | 99.9% availability | Kiruna")
print(f"TX: {TX_POWER_W:.0f} W ({TX_POWER_DBW:.1f} dBW) | "
f"G/T: {G_T_DB_K:.1f} dB/K | Req Eb/N0: {REQ_EB_N0:.1f} dB | "
f"Impl. loss: {IMPL_LOSS:.1f} dB")
print()
hdr = (f" {'El':>3} {'Off-nadir':>9} {'G_tx':>5} {'Range':>7} "
f"{'FSPL':>7} {'EIRP':>7} {'Eb/N0':>6} {'P618':>5} {'Margin':>7}")
print(hdr)
print('─' * len(hdr))
for el_v in [5, 10, 20, 30, 45, 60, 90]:
el = np.radians(el_v)
rng = -_R_E*np.sin(el) + np.sqrt(_R_E**2*np.sin(el)**2 + _H**2 + 2*_R_E*_H)
alpha = np.degrees(np.arcsin(_R_E * np.cos(el) / (_R_E + _H)))
g_tx = float(np.interp(alpha, tx.angles_deg, tx.gains_dbi))
fspl = 20 * np.log10(4 * np.pi * rng * FREQ_HZ / _C)
eirp = TX_POWER_DBW + g_tx
c_n0 = eirp - fspl + G_T_DB_K - _K
eb_n0 = c_n0 - 10 * np.log10(DATA_RATE)
with warnings.catch_warnings():
warnings.simplefilter('ignore')
a618 = itur.atmospheric_attenuation_slant_path(
gs.lat, gs.lon, FREQ_HZ / 1e9, el_v, 0.1, D=0)
p618 = float(np.asarray(a618.value if hasattr(a618, 'value') else a618))
mrg = eb_n0 - REQ_EB_N0 - IMPL_LOSS - p618
flag = ' ◀ design point' if el_v == 5 else ''
print(f" {el_v:>3}° {alpha:>8.1f}° {g_tx:>5.1f} {rng/1e3:>6.0f}km "
f"{fspl:>7.1f} {eirp:>7.1f} {eb_n0:>6.1f} {p618:>5.2f} {mrg:>+7.1f}{flag}")
print('─' * len(hdr))
print(f" {'':>3} {'(°)':>8} {'(dBi)':>5} {'':>7} "
f"{'(dB)':>7} {'(dBW)':>7} {'(dB)':>6} {'(dB)':>5} {'(dB)':>7}")
Link budget — 8.25 GHz | 60 Mbps | 99.9% availability | Kiruna
TX: 8 W (9.0 dBW) | G/T: 27.9 dB/K | Req Eb/N0: 7.0 dB | Impl. loss: 2.0 dB
El Off-nadir G_tx Range FSPL EIRP Eb/N0 P618 Margin
──────────────────────────────────────────────────────────────────────────
5° 65.4° 8.6 2345km 178.2 17.6 18.1 3.20 +5.9 ◀ design point
10° 64.0° 9.2 1948km 176.6 18.2 20.4 1.59 +9.8
20° 59.1° 10.2 1406km 173.7 19.2 24.2 0.80 +14.4
30° 52.2° 11.1 1087km 171.5 20.1 27.3 0.54 +17.8
45° 40.2° 11.6 824km 169.1 20.6 30.2 0.38 +20.8
60° 27.2° 12.0 691km 167.6 21.0 32.2 0.31 +22.8
90° 0.0° 12.0 607km 166.4 21.0 33.3 0.27 +24.0
──────────────────────────────────────────────────────────────────────────
(°) (dBi) (dB) (dBW) (dB) (dB) (dB)