Communication Between Earth and Mars



7.1 Antenna Sizing and Communication Issues

J. Darcey Kuhn

Nomenclature

erfc = complementary error function

f = specified frequency, km

r = range, GHz

Eb = energy-per-bit, dB

Gt = gain of transmitting antenna, dBi

Gr = gain of receiving antenna, dBi

Lt = loss from transmitting, dB

No = noise-power-density, dBW/Hz

Pt = transmitted power, dBW

Tb = bit period

7.1.1 Introduction

The communication system supports the transmission of high and low data rate video, voice data, science data, engineering telemetry, and commands for transmission to and from Earth.1 We employ digital modulation to send commands and to receive data from both the Earth Return Vehicle (ERV) and the Habitation Module (Hab). Due to the long communication delays, and periods of communication "blackouts" and “whiteouts” high data rate transmissions are necessary to support advanced operations for deep space missions.

The purpose of the link analysis budget is to determine whether the transmitter/receiver system provides sufficient signal to noise ratio to achieve an acceptable bit error rate. The budget analysis calculates values such as the effective isotropic radiated power, communication losses, bit error rate, antenna gain, and other information relative to sizing a high and low gain antenna. Before trying to size an antenna, we first must verify our capabilities and calculations with a current example of a link budget analysis. Once all the data, equations, and calculations match the sample analysis and we understand them completely, we can then apply the same process to our mission and make the necessary changes in the data and parameters.

7.1.2 Link Budget Analysis

Purpose

The link analysis, and its output, the link budget, consists of the calculations and tabulation of the useful signal power and the interfering noise power available at the receiver. The link budget is a balance sheet of gains and losses; it outlines the detailed distribution of transmission and reception resources, noise sources, signal attenuators, and effects of processes throughout the link (Tables 7.1.1 – 7.1.4). Some of the budget parameters are statistical (e.g., allowances for the fading of signals due to space loss); the budget system is therefore a technique for evaluating the communication system performance. There is only one “channel” of data on both the uplink and downlink. A number of signals in binary digital form can be transmitted through a common channel by interleaving the pulses in time; this is referred to as time-division multiplexing (TDM). On the downlink, we make use of TDM to send both engineering data and science data (i.e., camera picture bits) in the same data stream.

The primary purpose of a link analysis is to determine the actual system operating performance and to establish that the error probability associated with that point is less than or equal to the system requirement. A link margin or safety factor tells us whether the system meets the requirements comfortably, marginally, or not at all. The link budget can help predict equipment weight, size, prime power requirements, and technical risk.

Decibels

The decibel is nothing more than an expression of the ratio between two signals. The signals might be voltages, currents, or power levels. When we turn values into the form of decibel notation, the logarithms of the ratios are used rather than the straight arithmetical ratios. The log of the ratios makes it possible to replace multiplication and division calculations with addition and subtraction. Decibel notation is frequently seen in specifications for the gain of radio antennas. Gain relative to isotropic (dBi) employs an isotropic radiator, which is a spherical source of radio frequency energy that radiates equally well in all directions.

Effective Isotropic Radiated Power (EIRP)

The term effective isotropic radiated power (EIRP) is derived from the word isotropic, which means omnidirectional. EIRP denotes the power levels that would be received at any location if an antenna were radiating equally in all directions. No real antenna can radiate this way therefore the isotropic radiator is hypothetical. It does, however, provide a very useful theoretical standard against which real antennas can be compared. Being hypothetical it can be made 100 percent efficient, meaning that it radiates all the power fed into it (Eq. 7.1.1).

Prad = Pt (7.1.1)

The product of the power we transmit, Pt, and the gain of the transmitting antenna, Gt, divided by the transmitting loss, Lt, produces the effective isotropic radiated power (Eq. 7.1.2). An example, of a conversion of the EIRP to decibels is also given below.

EIRP = Pt*Gt / Lt [W]

In decibels: EIRP = 10*log(Pt) + 10*log(Gt) – 10*log(Lt) [dBW] (7.1.2)

Transmission Losses

The EIRP may be thought of as the power input to one end of the transmission link, and the problem is to find the power at the other end.2 Some losses are constant while other losses must be estimated from statistical data, or weather conditions can be taken into consideration, especially rainfall. The losses we capture in the link budget analysis for clear-sky conditions are transmitter circuit loss, fade allowance, coverage loss and the free space loss; the largest loss in the budget.

Free Space Loss

The attenuation between two isentropic antennas separated by a distance r, at a specified frequency f, is known as the free space loss (FSL) (Eq. 7.1.3). There is a decrease in the electric field strength, and thus in signal strength (power density or flux density), as a function of distance. For a satellite communications link, the space loss is the largest single loss in the system from the spreading of the signal in space. The possibility of absorption, reflection, refraction, and diffraction can modify the free space transmission. It is a loss in the sense that all radiated energy is not focused on the intended receiving antenna.

FSL=32.4+20*log(r)+20*log(f) (7.1.3)

Signal-to-noise Ratio Degradation

A fundamental requirement for satisfactory satellite communications is the maintenance of a sufficient signal-to-noise ratio (SNR). 3 The SNR is a measure of audio signal power relative to noise power at the output of a satellite receiver. The SNR can degrade in two ways: (1) through the decrease of the desired signal power, and (2) through the increase of noise power, or the increase of interfering signal power.

For a digital system, the demodulator must contain one or more threshold detectors, which allocate to each received symbol one of the permitted values. If the symbol is correctly identified, the noise has no effect whatsoever. However, sometimes the noise voltage is large enough to cause the receiver output to lie on the wrong side of the threshold and so result in an error in interpretation. The probability of error in any one bit, known as bit error rate, depends on the product of the received signal power and the length of the bit interval.

Bit Error Rate (BER)

The performance of a digital system is generally measured in terms of the bit error rate (BER), and it is a function of the energy-per-bit to noise-power-density ratio Eb/No [dB]. We calculate the energy per bit Eb by multiplying the average received power Pr and the bit period Tb (Eq. 7.1.4):

Eb = Pr*Tb (7.1.4)

The probability of the detector making an error as a result of the noise is given by (Eq. 7.1.5):

Pe = ½ erfc*[pic] (7.1.5)

where the erfc value can be found in tabular or graphical form in mathematical tables. For typical transmission systems the BER may lie on in the range of 10-3 – 10-9. For our mission we establish a bit error rate of approximately 10-5, therefore the required Eb/No would be 10 dB as seen in the link budget analysis. The bit error rate can be significantly improved by the use of encoding techniques, which permit error detection and correction.

Transmitter and Receiver Antenna Gains

The antenna parameter that relates the power output (or input) to that of an isotropic radiator as a purely geometric ratio is the antenna directivity or directive gain. The importance of using highly directional antennas is that they provide signal power gain.

For a paraboloidal antenna the isotropic gain is given by (Eq. 7.1.6):

G = η*(10.472*f*D)2 (7.1.6)

Where f is the carrier frequency in gigahertz, D is the reflector diameter in meters, and the η is the aperture efficiency. For our mission link budget the value of 0.55 is the aperture efficiency

The 34m HEF transmitter antenna gain can range from 65 to 67.1 dBi, and the gain the antenna receives lies between 75.2 and 80 dBi. Table 7.1.1 – 7.1.2 shows that we met the design requirements of the DSN in our link budget calculation.

Deep Space Network

In order to receive the faint signal transmissions sent at Mars from the ERV and Habitation Module, we utilize the gigantic tracking antennas of the Deep Space Network (DSN). The NASA DSN is an international network of antennas that supports interplanetary spacecraft missions and radio and radar astronomy observations for the exploration of the solar system and the universe (Figure 7.1.1). The DSN currently consists of three deep-space communications facilities placed approximately 120 degrees apart around the world: at Goldstone, in California’s Mojave Desert; near Madrid, Spain; and near Canberra, Australia. This strategic placement permits constant observation of spacecraft as the Earth rotates.4

Missions that have an altitude above the Earth of greater than, or equal to, 2.0E6 km are put into Category B of the DSN. This limits the bandwidths available (C, Ka, X, S) as well as dish size and location for DSN.

The DSN 34m High Efficiency (HEF) Subnetwork antenna in the USA, Australia, or Spain is the ground communication we chose to communicate to and from the Mars. The reason being that there is a large demand for the 70m antennas from DSN, and our mission requires that communication is readily available. The 34m HEF antennas can uplink at frequencies ranging from 7145 to 7190 MHz and receive downlinks from 8400 to 8500 MHz. The transmit power from the antennas ranges from 20-200 kW. For our mission we chose the maximum power possible to help ensure its success, though lower levels of power are most likely for communication.

High Gain Antenna

The high gain antenna (HGA) is necessary to support all communication links for the mission to Mars. According to our calculations the HGA weighs approximately 500 kg and has a fully deployed diameter of 3.35 m. One HGA attaches to the ERV that orbits Mars and the other connects to the Habitation module.

The antennas are stowed in the ERV and Hab and deploy after launch and retract into the spacecraft before landing. Each HGA sits on the end of a 2.13 m long boom that attaches to two rotating joints, called gimbals, which hold the antenna to the boom (see Figure 7.1.2). The gimbals allow the antenna to automatically track and point at the Earth during transit.

[pic]

The link budget analysis shows the HGA receives data at a frequency of 7.2 GHz on the C-band frequency. The HGA also transmits on the X-band frequency at 8.5 GHz (Table 7.1.1 – 7.1.2) the distance of 401300000 km from Earth to Mars.

The analysis uses the maximum transmission power of the DSN at 200 kW for uplinks, and the power for downlinks (30kW) during transit comes from the fully charged solar panels. The maximum` is most likely not be necessary but we wanted to test the limits of the HGA. As a design reference we refer to the communication data given from the space shuttle. To sustain the voice link, command link, and real-time video the DSN transmits data to the HGA at a high data rate of 128 kbps. The HGA is capable of communicating back to Earth at a maximum data rate of 25 MHz. The space shuttle’s forward link consists of two air-to-ground voice streams at 32 kbps and 8kps of command and 16 kbps of synchronization. In addition, the space shuttle’s return link includes digital data (real-time or playback) from 2 Mbps to 50 Mbps.

Table 7.1.1 Uplink from 34m HEF Subnetwork to High Gain Antenna

|  |Link Budget |Nomenclature |

|Uplink Distance from Earth to Mars, km |401300000.00 |r |

|Frequency, GHz |7.20 |f |

|Transmit Power, dBW |53.01 |Pt |

|Transmitter Antenna Gain, dBi |65.58 |Gt |

|Terminal EIRP, dBW |116.59 |EIRP |

|Received Isotropic Power, dBW |-175.03 | |

|Received Signal Power, dBW |-131.58 |Pr |

|Receiver Antenna Gain, dBi |45.45 |Gr |

|System G/Tos, dB-K |9.35 |Gr/Tos |

|Received Pr/No, dB-Hz |60.92 |(Pr/No)r |

|Received Eb/No, dB |19.85 |(Eb/No)r |

|Margin, dB |8.35 |M |

Table 7.1.2 Downlink to 34m HEF Subnetwork from High Gain Antenna

|  |Link Budget |Nomenclature |

|Uplink Distance from Earth to Mars, km |401300000.00 |r |

|Frequency, GHz |8.50 |f |

|Transmit Power, dBW |44.77 |Pt |

|Transmitter Antenna Gain, dBi |46.89 |Gt |

|Terminal EIRP, dBW |89.66 |EIRP |

|Received Isotropic Power, dBW |-209.39 | |

|Received Signal Power, dBW |-127.29 |Pr |

|Received Antenna Gain, dBi |78.10 |Gr |

|System G/Tos, dB-K |64.96 |Gr/Tos |

|Received Pr/No, dB-Hz |88.17 |(Pr/No)r |

|Received Eb/No, dB |14.19 |(Eb/No)r |

|Margin, dB |2.69 |M |

Low Gain Antenna

With the link budget analysis we designed a low gain antenna (LGA) that supports command and voice communication. There are two LGAs on both the Hab module and the Earth Return Vehicle (ERV). We took the concept that the Galileo project follows and placed a LGA in the center of the HGA for both vehicles. On the ERV the second antenna attaches to the Crew Transfer Vehicle (CTV), to support communication when landing on Earth. The CTV LGA can also communicate with the high and low gain antennas on the ERV that orbit around Mars. There are two LGAs for redundancy in the design of the mission to Mars in case the HGA were to fail. These antennas are capable of supporting the rest of the mission to ensure its success.

The DSN is capable of transmitting to the LGA at a frequency of 10 GHz (X-band) with a maximum power of 200 kW. The downlink from the LGA occurs at 8 GHz (X-band) and employs a power of 800 W (Table 7.1.3 – 7.1.4).

Table 7.1.3 Uplink to 34m HEF Subnetwork to Low Gain Antenna

|  |Link Budget |Nomenclature |

|Uplink Distance from Earth to Mars, km |401300000.00 |r |

|Frequency, GHz |10.00 |f |

|Transmit Power, dBW |53.01 |Pt |

|Transmitter Antenna Gain, dBi |68.43 |Gt |

|Terminal EIRP, dBW |119.44 |EIRP |

|Received Isotropic Power, dBW |-165.03 | |

|Received Signal Power, dBW |-135.24 |Pr |

|Receiver Antenna Gain, dBi |31.78 |Gr |

|System G/Tos, dB-K |-4.32 |Gr/Tos |

|Received Pr/No, dB-Hz |57.26 |(Pr/No)r |

|Received Eb/No, dB |13.46 |(Eb/No)r |

|Margin, dB |1.96 |M |

Table 7.1.4 Downlink from 34m HEF Subnetwork to Low Gain Antenna

| |Link Budget |Nomenclature |

|Uplink Distance from Earth to Mars, km |401300000.00 |r |

|Frequency, GHz |8.00 |f |

|Transmit Power, dBW |29.03 |Pt |

|Transmitter Antenna Gain, dBi |25.41 |Gt |

|Terminal EIRP, dBW |52.44 |EIRP |

|Received Isotropic Power, dBW |-228.93 | |

|Received Signal Power, dBW |-156.08 |Pr |

|Receiver Antenna Gain, dBi |74.85 |Gr |

|System G/Tos, dB-K |55.10 |Gr/Tos |

|Received Pr/No, dB-Hz |59.38 |(Pr/No)r |

|Received Eb/No, dB |15.58 |(Eb/No)r |

|Margin, dB |4.08 |M |

Blackout / Whiteout Dates

A communication “blackout” occurs when the sun is between Earth and Mars and no voice or data link can occur for that period of time. The maximum duration of the two blackouts that occur are nine days each (see Table 7.1.5). A “whiteout” occurs when the Earth is between the sun and Mars and too much solar radiation may make it impossible to communicate with Earth. The effect of a whiteout occurs in the range of three degrees to either side of the event. Only one whiteout occurs during the mission and it lasts eight days.

Table 7.1.5 Dates of Blackout/Whiteout during the mission

|9 November 2011 |ERV launch from Earth |

|11 September 2012 |ERV arrival in orbit around Mars |

|27 March - 05 April 2013 |Communication Blackout (Mars – Earth) |

|04 January 2014 |Hab Launch from Earth |

|26 April - 04 May 2014 |Communication whiteout (Mars – Earth) |

|14 July 2014 |Hab arrival at Mars |

|26 May - 04 June 2015 |Communication Blackout (Mars – Earth) |

|26 December 2015 |ERV launch for return to Earth |

|12 August 2016 |ERV/CTV arrival at Earth |

Cost Analysis

The cost for government projects to use the DSNs 34m HEF Subnetwork is $1,152 per hour. After launch on November 9th, 2011 the ERV reaches Mars in 172 days, we stay 590 days on the planet, and then the ERV/CTV returns to earth in 230 days. The mission duration is approximately 1000 days. During that time blackout and whiteout days must be considered, therefore the total cost for communication 24 hours a day (nominal) would be 27.5 millions dollars.

Conclusions

The link budget analysis provides specifications, analyses, and tabulations that help with the development of a communication system. We design the high and low gain antennas for the mission to Mars with the link budget. To ensure communication is available when needed a safety factor, the margin, exists in the budget. We also add a backup LGA for redundancy. All the calculations fit within the requirements of the Deep Space Network which is our ground communication during the mission.

Acknowledgements

I would like to thank Professor James Garrison for taking time to help answer all of my communication and satellite questions. He helped to support the success of this project from the aspect of communication. Equally important I want to thank Professor David Filmer for taking time out of his schedule to meet with me and review the link analysis budget.

References

1) Drake, B., “Human Exploration Technology – Goals and Requirements,” , September 1997

2) Flock, W. L., “Propagation Effects on Satellite Systems at Frequencies Below 10 GHz,” NASA Reference Publication 1108(02), 1987.

3) Roddy, D., “Satellite Communications,” 2nd ed., McGraw-Hill, New York, 1996.

4) Wolff, S., “Deep Space Network Home Page,” , March 12, 2001.

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Figure 7.1.1 NASA DSN 34m Antenna.

Figure 7.1.2 2001 Mars Odyssey HGA attached to a boom.

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