Telemetry System

Description

The Telemetry System governs all communication links between Transmitter and Receiver components across the simulation. It automatically creates and manages DataLinkMessage objects that represent the communication channels between compatible antenna pairs on different spacecraft, ground stations, or other entities. The system performs comprehensive link budget calculations each simulation step, computing signal power, noise power, interference, channel capacity, and bit error rates for every active link.

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Example Use Cases

• Mission Communication Analysis: Evaluate uplink and downlink performance throughout a mission timeline.
• Constellation Design: Assess inter-satellite link availability and data throughput for distributed architectures.
• Interference Studies: Analyse the impact of jamming or co-channel interference on communication reliability.
• Ground Network Planning: Optimise ground station placement and scheduling based on link availability windows.

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Module Implementation

The telemetry system operates as a centralised manager for all communication components. It maintains separate lists of transmitters and receivers, automatically creating bidirectional links between compatible pairs when antennas are added to the simulation.

Link Creation

When an antenna is added to the simulation, the telemetry system evaluates all existing antennas of the opposite type (transmitters for a new receiver, receivers for a new transmitter) and creates links where:

1. Transmission Types Match: Both antennas must use the same transmission type (Radio or Optical)
2. Different Root Objects: The antennas must belong to different root objects (e.g., different spacecraft)

Each link is represented by a DataLinkMessage that stores all computed link parameters and is accessible from both the transmitter and receiver.

Update Sequence

At each simulation step, the telemetry system performs calculations in two phases:

Phase 1 - Transmitter Processing: For each enabled transmitter:

1. Process queued data packets
2. For each link to a receiver:
   • Calculate distance and Doppler shift
   • Determine celestial access (line-of-sight past planets)
   • Calculate connection fraction, pointing losses, and space loss
   • Compute signal power and noise power
   • Calculate baseline signal-to-noise ratio

Phase 2 - Receiver Processing: For each enabled receiver:

1. Accumulate interference from all transmitting links
2. For each connected link:
   • Calculate effective signal-to-noise ratio including interference
   • Compute channel capacity, energy per bit to noise ratio, and bit error rate
   • Determine effective transmission rate
3. Process received data packets

Doppler Shift

When enabled on a receiver, the telemetry system calculates the Doppler-shifted frequency based on the relative velocity between transmitter and receiver:

$$f_r=f_t\left(1+\frac{\Delta v}{c}\right)$$

where:

• $f_r$ is the received frequency [Hz]
• $f_t$ is the transmitted frequency [Hz]
• $\Delta v$ is the relative velocity (positive for closing) [m/s]
• $c$ is the speed of light [m/s]

The relative velocity is computed from the rate of change of distance:

$$\Delta v=-\frac{d_n-d_{n-1}}{\Delta t}$$

Connection Fraction

The connection fraction determines how well the transmitted signal falls within the receiver’s passband:

$$f_c=\{\begin{array}{ll}1.0& \text{if }{f}_r-\frac{B_r}{2}\le f_t\le f_r+\frac{B_r}{2}\\ 0.0& \text{otherwise}\end{array}$$

where $f_r$ is the receiver centre frequency and $B_r$ is the receiver bandwidth.

Free Space Path Loss

The space loss represents signal attenuation due to geometric spreading of the electromagnetic wave:

$$L_s=-10{\log }_{10}{\left(\frac{c}{4\pi df}\right)}^2$$

where:

• $L_s$ is the space loss [dB] (stored as positive value)
• $d$ is the distance between antennas [m]
• $f$ is the transmission frequency [Hz]
• $c$ is the speed of light [m/s]

This follows SMAD equation 13-23a, inverted to store loss as a positive decibel value.

Pointing Loss

The pointing loss accounts for antenna misalignment. For each antenna, the off-axis angle to the target is calculated:

$$\theta ={\cos }^{-1}\left(\hat{\mathbf{d}}\cdot \hat{\mathbf{u}}\right)$$

where $\hat{\mathbf{d}}$ is the direction to the target and $\hat{\mathbf{u}}$ is the antenna boresight direction.

The pointing loss is then determined by either:

• Fixed Mode: A constant configured value
• Lookup Mode: Interpolation from a loaded electromagnetic pattern table

The total pointing loss is the sum of transmitter and receiver contributions:

$$L_p=L_{p,tx}+L_{p,rx}$$

Signal Power

The received signal power is calculated using the link budget equation:

$$P_r=P_t-L_{line}+G_t-L_{p,tx}-L_s-L_{atm}+G_r-L_{p,rx}$$

where (all in dB or dBm):

• $P_t$ is the transmitter power
• $L_{line}$ is the transmitter line loss
• $G_t$ is the transmitter antenna gain
• $L_{p,tx}$ is the transmitter pointing loss
• $L_s$ is the free space path loss
• $L_{atm}$ is the atmospheric loss
• $G_r$ is the receiver antenna gain
• $L_{p,rx}$ is the receiver pointing loss

For multi-band transmitters (e.g., Jamming Transmitter), the signal power is multiplied by the number of bands within the receiver’s frequency range.

Noise Power

The thermal noise power is calculated from the system noise temperature:

$$P_n=k_B\cdot B\cdot T_{sys}$$

where:

• $k_B=1.380649\times 10^{-23}$ J/K is Boltzmann’s constant
• $B$ is the receiver bandwidth [Hz]
• $T_{sys}$ is the system noise temperature [K]

Interference Power

Interference from other transmitting links is accumulated using a Gaussian roll-off model:

$$P_{int}=\sum _{j\ne i}{P}_{r,j}\cdot \Gamma (f_i,f_j,B_r)$$

where the interference factor $\Gamma$ is:

$$\Gamma (f_i,f_j,B)=\exp \left(-\frac{(f_i-f_j{)}^2}{2{\sigma }^2}\right)$$

with $\sigma =B/4$ chosen so that interference falls to approximately 5% at the bandwidth edge.

Signal-to-Noise Ratio

The baseline SNR excludes interference:

$${\text{SNR}}_{base}=10{\log }_{10}\left(\frac{P_r}{P_n}\right)$$

The effective SNR includes interference:

$${\text{SNR}}_{eff}=10{\log }_{10}\left(\frac{P_r}{P_n+P_{int}}\right)$$

Both are clamped to a minimum of 0 dB (linear ratio of 1).

Channel Capacity

The theoretical maximum data rate is calculated using the Shannon-Hartley theorem:

$$C=B{\log }_2\left(1+10^{{\text{SNR}}_{eff}/10}\right)$$

where $C$ is the channel capacity [bps] and $B$ is the bandwidth [Hz].

Energy per Bit to Noise Ratio

The $E_b/N_0$ normalises the SNR by the spectral efficiency:

$$\frac{E_b}{N_0}={\text{SNR}}_{eff}+10{\log }_{10}\left(\frac{B}{R_b}\right)$$

where $R_b$ is the transmission bit rate [bps].

Bit Error Rate

The bit error rate is calculated based on the modulation scheme. For each modulation type, the BER is a function of $E_b/N_0$:

Modulation	BER Formula
BPSK	$\frac{1}{2}\text{erfc}\left(\sqrt{E_b/N_0}\right)$
QPSK	$\frac{1}{2}\text{erfc}\left(\sqrt{E_b/N_0}\right)$
BFSK	$\frac{1}{2}\text{erfc}\left(\sqrt{E_b/N_0\cdot 0.5}\right)$
8-PSK	$\frac{1}{3}\text{erfc}\left(\sqrt{E_b/N_0}\sin (\pi /8)\right)$
16-QAM	$\frac{3}{8}\text{erfc}\left(\sqrt{0.1\cdot E_b/N_0}\right)$
64-QAM	$\frac{7}{24}\text{erfc}\left(\sqrt{E_b/N_0/21}\right)$

The complementary error function is approximated using the Horner’s method (Abramowitz and Stegun 7.1.26):

$$\text{erfc}(x)\approx t\cdot \exp \left(-x^2+\sum _{k=0}^9{a}_k{t}^k\right)$$

where $t=1/(1+0.5|x|)$.

BER is clamped to the range $[0,0.5]$, where 0.5 represents random noise (no signal).

Transmission Rate

The effective transmission rate is the minimum of the transmitter bit rate and channel capacity:

$$R=\min (R_{b,tx},C)$$

If the effective SNR falls below the receiver sensitivity threshold, the transmission rate is set to zero.

Celestial Access

Line-of-sight occlusion by celestial bodies is computed using ray-sphere intersection. For each planet in the Solar System, the system tests whether the line segment between transmitter and receiver intersects the planetary sphere:

Given:

• ${\mathbf{p}}_1$ = receiver position
• ${\mathbf{p}}_2$ = transmitter position
• $\mathbf{s}$ = planet center
• $r$ = planet radius

The intersection is found by solving the quadratic:

$$a{t}^2+bt+c=0$$

where:

• $a=\mathbf{d}\cdot \mathbf{d}$
• $b=2(\mathbf{d}\cdot {\mathbf{p}}_1)-\mathbf{d}\cdot \mathbf{s}$
• $c=|\mathbf{s}{|}^2+|{\mathbf{p}}_1{|}^2-2(\mathbf{s}\cdot {\mathbf{p}}_1)-r^2$
• $\mathbf{d}={\mathbf{p}}_2-{\mathbf{p}}_1$

If the discriminant $b^2-4ac\ge 0$ and both roots $t_1,t_2\in [0,1]$, the link is occluded.

Pass Tracking

The telemetry system tracks communication passes for each link:

• Passes: Incremented each time a link transitions from disconnected to connected
• Current Pass Time: Duration of the current pass, reset on new connection
• Total Pass Time: Cumulative time across all passes
• Current Data: Data transferred in current pass [Mb]
• Total Data: Cumulative data transferred [Mb]

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Assumptions/Limitations

• Links are only created between antennas on different root objects; intra-spacecraft communication is not modelled.
• The system assumes far-field propagation; near-field effects are not considered.
• Atmospheric loss must be provided externally; the system does not compute atmospheric attenuation.
• The connection fraction uses a rectangular passband model; real filter responses may differ.
• Interference calculations assume all signals are independent; coherent interference is not modelled.
• The celestial access calculation models planets as perfect spheres; terrain and atmospheric refraction are not considered.
• Polarization mismatch losses are not explicitly computed.
• The system processes transmitters and receivers in parallel; race conditions are avoided by careful data structure design.
• Multi-path propagation effects are not modelled.
• The BER calculation assumes ideal matched filtering and synchronization.

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References

[1] Wertz, J.R. and Larson, W.J. “Space Mission Analysis and Design (SMAD).” 3rd ed. Microcosm Press and Kluwer Academic Publishers, 1999.

[2] Sklar, B. “Digital Communications: Fundamentals and Applications.” 2nd ed. Prentice Hall, 2001.

[3] Abramowitz, M. and Stegun, I.A. “Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables.” Dover Publications, 1964.

[4] Shannon, C.E. “A Mathematical Theory of Communication.” Bell System Technical Journal, Vol. 27, 1948.