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