Links Budget

Antenna Gain

where

G = Antenna gain (dB)
D = Antenna diameter (m). In calculation of transmit antenna gain and receive antenna gain, Dt and Dr are used to represent transmit antenna diameter and receive antenna diameter respectively.
lambda = Wavelength of RF carrier (m); lamda = C/f, where C (m/s) is the speed of light (300,000,000 m/s)
f = frequency of carrier (Hz)
eta = Antenna efficiency (Assumed to be 0.6)

Efficient Isotropic Radiation Power

EIRP = Pt + Gt

where

EIRP = Efficient Isotropic Radiation Power (dBw)
Pt = Transmitter output power (dBw)
Gt = Transmit antenna gain (dB)

Free Space Path Loss

where

L = Free space loss (dB)
R = The distance between transmitter and receiver (m) (the distance between the Earth and the Moon is 384,000,000 m)
lambda = Wavelength of RF carrier (m)

System Noise Temperature

where

Tsys = System noise temperature (K)
Ta = Antenna noise temperature referred to input of low noise amplifier (K, assumed to be 40 K conservatively)
Tlna = Low noise amplifier noise temperature (K)

Station Figure of Merit

where

G/T = Station figure of merit (dB/K)
Gr = Receive antenna gain (dB)
Tsys = System noise temperature (K)

Carrier to Noise Density Ratio

where

C/No = Carrier (C) to noise density ratio (dB·Hz)
EIRP = Efficient Isotropic Radiation Power (dBw)
L = Free space loss (dB) 
G/T = Station figure of merit (dB/K)
k = Boltzmann constant (1.38E-23 J/K), 10logk = -228.6

Energy of Bit to Noise Density Ratio

For a typical QPSK modulated channel, the Eb/No required to achieve a 10E-9 of BER (Bit Error Rate) is 14dB. Allowing a 5dB margin for atmospheric effects, the total required Eb/No is 19dB.

Required Average Carrier to Average Noise Ratio

 

where

C/N = Required average carrier to average noise ratio (dB)
Eb/No = Energy of bit (Eb) to noise density (No) ratio (dB)
r = Data rate (bps)
B = Measured noise bandwidth (Hz, Assumed to r/2 here)

Margin of the Link

where

M = Margin of the link (dB)
C/No = Carrier (C) to noise density (No) ratio (dB·Hz)
B = Measured noise bandwidth (Hz, Assumed to be r/2 here)
C/N (dB) = Required average carrier to average noise ratio

The Earth-Moon Links Budget

It is listed in Table A-1. No cable loss is assumed. All traffic is assumed to be digital with QPSK modulation.

Feasibility Analysis

Trade-off between Antenna Diameter and Transmit Power

It is obvious that the rover, lander and Media Vehicle should have small size and light mass to reduce launching cost. If the antenna diameter is reduced, transmit power should be increased to guarantee the overall link margin. The relations among antenna diameter, transmit power and link margin are shown in Figure A-1 and Figure A-2.

Telecommunication Coverage Analysis

Coverage on the Earth Surface

In order to cover always half the Earth from the Moon, the antenna beam width should be more than 1.91 deg. The following formula is used to calculate half-power beam width.

where

theta = The half-power beamwidth of the antenna (deg.)
N = 70 for a dish antenna
lambda = Operational wavelength (m)
D = Antenna diameter (m)
For K-band (f = 24.5 GHz), if theta = 2 deg., D = 0.42 m. For X-band (f = 8.5 GHz), if theta =2 deg., D = 1.2 m.

From the calculation of links budget, the antenna diameter of the rovers is 0.15 m, the antenna diameter of the lander and the Media Vehicle is 0.35 m. So 100% coverage on half of the Earth's surface is achieved. But the antennas of rovers, lander and Media Vehicle must be always pointed to the Earth.

Tracking Coverage

The following conditions are known.

• DSN1: Longitude = 335.5 deg., Latitude = 40.0 deg., Height = 70.0 m
   
• DSN2: Longitude = 149.0 deg., Latitude = -35.0 deg., Height = 70.0 m
   
• DSN3: Longitude = 243.0 deg., Latitude = 35.0 deg., Height = 70.0 m
   
• Moon orbit data in Earth center system

  STK 4.0 software is used for the calculation. Azimuth and elevation mask of DSN stations to the Moon. Figures A-3 to A-5 show the azimuth and elevation mask of DSN stations to the Moon on July 1, 2004. The minimum tracking elevation of each DSN 70-meter station is 10 deg.

Availability Analysis

The following conditions are assumed.

• MTBF (Mean Time Between Failures) of each DSN station K-band channel is 3000 hrs. 
• MTBF of each DSN station X-band channel is 3000 hrs. 
• MTBF of each rover, the lander, the Media Vehicle elecommunication equipment is 2000 hrs. 
• MTTR (Mean Time To Restore) of the telecommunication system (MTTRs) is 0.5 hrs. 

where

R(t) = The reliability of a system over t
t = The working time of the system

So, over 14 days the reliability of K-band channel (Rk), X-band channel (Rx), rover communications equipment (Rr), lander communications equipment (Rl), Media Vehicle communications equipment (Rm) are as follows.

The reliability of telecommunications system (Rs) is:

The MTBF of the telecommunications system (MTBFs) is:

The availability of the telecommunications system (As) is:

Links Design

Table B-3 presents the design of the Earth-Moon links for the 10 rovers, the lander and the Media Vehicle.

Design Parameters	Each Rover		Lander & Media Vehicle			DSN Stations
	TV 1	TT&C 1		TV 2	TT&C 2		TV 1	TV 2 + TT&C 2	TT&C 1
Tx Power	5 w	5 w		35 w	35 w		__	__	3000 w x12
Tx Antenna Diameter	0.15 m	0.15 m		0.35 m	0.35 m		__	__	70 m
Tx Frequency Band	K-band	K-band		X-band	X-band		__	__	K-band
Tx Data Rate	2 Mbps	100 kbps		34 Mbps	100 kbps		__	__	2 Mbps
LNA Noise Temp.	__	60 K		__	60 K		60 K	40 K	60 K
Rx Antenna Diameter	__	0.15 m		__	0.35 m		70 m	70 m	70 m
Rx Frequency Band	__	K-band		__	K-band		K-band	X-band	K-band
Rx Data Rate	__	2 Mbps		__	2 Mbps		2 MHz x 10	34Mbpsx2 +100kbpsx2	100 kbps x 10

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