Communication - Calculations
Constants| Parameter | Description | Value | Units | | c | speed of light | 2.99792458e+8 | meters/second | | k | Boltzmann's Constant
| 1.3806503e-23 | meters2*kg/(s2*K) | | f | frequency of choice | 60e+9 | Hz | | λ | wavelength | 5e-3 | meters |
Coding and Modulation
| Parameter | Description | Value | Calculation | | rdr | raw data rate
| 1 bit/sec
| Arbitrary selection.
| | cdr | coded data rate
| 2 bits/sec
| Implementing a turbo code (1/2). rdr*2 = cdr
| | bps | bits per symbol
| 2 bits/sym
| Using QPSK, bps = 2.
| | Ts | symbol period
| 1 symbol/sec
| bps/cdr | | rolloff | roll off for raised cosine pulse
| 0.5 | Arbitrary Selection
| | BW | bandwidth | 1.5 Hz
| 1/Ts*(1+rolloff) | | SNR | Signal to Noise
| 2dB | Arbitrary selection + overhead. 1dB is the minimum according to study
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Link Budget| Parameter | Description | Value | Calculation/Discription | | dsd | satellite dish diameter
| 25m | Arbitrary selection. Parabolic dishes in space are on the order of 22m today.
| | dds | "deep space" diameter
| 70m | Diameter of the largest dish in the NASA Deep Space network.
| | ηsd | Efficiency of satellite
| 0.75 | Arbitrary selection. This is a realistic approximation.
| | ηds | Efficiency of "deep space"
| 0.94 | Actual figure provided by NASA.
| | Gsd | Gain of satellite dish
| 83.65 dBW
| Gds = 10*log10(ηsd*(π*25/λ)2) | | Gds | Gain of "deep space"
| 91.62 dBW | Gds = 10*log10(ηds*(π*70/λ)2) | | Tsys | total system temperature | 31K | T=3K (space) + 28K (LNAs) | Pn
| noise power
| -211.92 dBW
| Pn = k*Tsys*BW
| Pr
| received power
| -209.92 dBW
| Pr = Pn + SNR
| Pt
| transmit power
| 20dBW | Arbitrary selection. Realistic approximation.
| Rds
| reach of "deep space" dish
| 7.64837 ly
| Rds=10^((Pt+Gsd+Gds+20*log10(λ/(4*π))-Pr )/20)
| | Rsd | reach of satellite dish
| 3.05805 ly
| Rsd=10^((Pt+Gsd+Gsd+20*log10(λ/(4*π))-Pr)/20)
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