"Penetrating Planets Since 2004"
ECE6390 Introduction to Satellite Communications Fall, 2004
 Initial Research
 Introduction
 Project Requirements
 Neptune Facts
 Calculations
 Penetrating Probes
 Introduction
 Design
 Calculations
 Parts & Pricing
 Relay Satellite
 Introduction
 Link with Probe
    Calculations
 Link with Earth
    Calculations
 Parts & Pricing
 Conclusions
 Summary
 Total Cost
 Contact Info
 Home » Relay Satellite » Link with Earth » Calculations

Calculations

 

The associated gain of a DSN antenna is determined by, with a diameter of 34m and an efficiency η = 0.94,


FormBox[RowBox[{G, =, RowBox[{(4π(ηπR)^2)/λ^2, =, RowBox[{RowBox[{RowBox[{ ... }]}], =, RowBox[{RowBox[{8.47001, , 10^6}], =, RowBox[{69.2788,  , dB}]}]}]}]}], TraditionalForm]


Similarly, the gain of the relay satellite antenna, with a diameter of 4m and an efficiency of η = 0.85, is determined to be 50.2534 dB.

The power of the radio transmission will be about 100 W, the same as the probes.  Performing the link budget analysis, the signal power received at the Earth DSN dish is


P_receiver = P_transmitter + G_transmitter + 20 log_10(λ/(4 π r)) + G_receiver ɯ ... Box[{-, 164.672}],  , dB}],  , =,  , RowBox[{3.55531, ,  , 10^(-17), W}]}]}]}], TraditionalForm]


The bandwidth of the signal was increased to approximately 50 kHz due to the additional redundancies of the turbo coding correction.  With a T_sys = 20K, the DSN antennas will introduce a noise of


N_receiver = (k) (T_sys) (B)  FormBox[RowBox[{      &nbs ... {RowBox[{2.07099, , 10^(-17), W}], =, RowBox[{RowBox[{-, 166.838}], dB}]}]}]}], TraditionalForm]


The Carrier to Noise ratio can then be determined by


FormBox[RowBox[{(C/N) _dB, =, RowBox[{RowBox[{10,  , RowBox[{log_10, (, RowBox[{RowBox[{(, Row ... [{(, RowBox[{2.07099, , 10^(-17)}], )}]}], )}]}], =, RowBox[{2.347,  , dB}]}]}], TraditionalForm]

 

In any digital link it is important to determine the BER.  The total C/N ratio received at NASA's Deep Space Network was 2.347 dB.  If this signal contained no error correction, the BER would be


FormBox[RowBox[{BER_BPSK, =, RowBox[{RowBox[{Q, (, RowBox[{RowBox[{(, RowBox[{2, RowBox[{(, Ro ... 347, /, 10}]}], )}]}], )}], ^, (1/2)}], )}], =, RowBox[{3.1944, , 10^(-2)}]}]}], TraditionalForm]


With such a low carrier to noise ratio, approximately 1 in every 32 bits would be lost.  However, error correction was used, which essentially yields in a BER of 0; from Figure 2 in Section Penetrating Probes » Design, the BER for a rate 1/2 turbo code is extremely low for any C/N above 1 dB.  A rate 1/3 turbo code was used, resulting in more coding gain; therefore, an error-free communications channel can be assumed.

 

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William W
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