7.4.1 Assumptions and Calculations

The method in Larson and Wertz [3, pp. 523-537] is used to calculate the link budget for the HGA and LGA. All of the figures referenced in this section are from Reference [3].

The following are input parameters in the calculation: frequency, transmitter power, transmitter line loss, transmit antenna beamwidth, transmit antenna pointing offset, propagation path length, propagation and polarization loss, receive antenna diameter, receive pointing error, system noise temperature, data rate, bit error rate, and implementation loss. The frequency, receive antenna diameter, and receive antenna pointing error are restricted by DSN requirements. The transmitter power, transmit line loss, transmit antenna beamwidth, transmit antenna pointing offset, propagation path length, and data rate are set by the mission requirements. The propagation and polarization loss is assumed to be similar to the loss associated with a 2.2 GHz transmitter frequency according to Figure 13-10. According to Table 13-9, a system noise temperature is estimated between the values associated with the frequencies between 20 and 60 GHz. The bit error rate was estimated using a BPSK (Binary phase shift keying) Reed-Solomon modulation and coding scheme according to Table 13-11. Therefore, according to Figure 13-9, the required received energy-per-bit to noise-density, Req. E_b/N_o, was found according to the selected value of bit error rate. The implementation loss was estimated using the sample link budget in Reference [3].

The rest of the data on the link budget is calculated using equations in Reference [3] and inputs given in the previous paragraph. The items to be calculated include: transmit antenna diameter, peak transmit antenna gain, transmit antenna pointing loss, transmit antenna gain, equivalent isotropic radiated power (EIRP), space loss, peak receive antenna gain, receive antenna beamwidth, receive antenna pointing loss, receive antenna gain, received energy-per-bit to noise-density E_b/N_o, carrier-to-noise density ratio, and margin. The transmit antenna diameter, D_t, is calculated using

$$D_t = \frac{21}{f\theta}$$ (4)

where D_t is in meters, f is the frequency in GHz and q is the half-power beamwidth, in degrees, for a circular antenna. The equation used for peak transmit antenna gain, G_pt, is

$$G_{pt} = -159.59 + 20\log D_t + 20\log f + 10\log\eta$$ (5)

Here, G_pt has the units of dB, f is in Hz, and D_t is in meters. The variable h, antenna efficiency, is assumed to be 0.55. The transmit antenna pointing loss, L_pt, is calculated using

$$L_{pt} = -12\frac{e_t}{\theta^2}$$ (6)

L_pt has the units dB, e_t is the transmit antenna pointing offset, and q is the half-power beamwidth in degrees. Transmit antenna gain (dB) is the sum of the peak transmit antenna gain and transmit antenna pointing loss. The equivalent isotropic radiated power (dBW) is the sum of transmitter power (dBW), transmitter line loss, and transmit antenna gain. Space loss, L_s, is calculated as follows:

$$L_s = 147.55-20\log S-20\log f$$ (7)

where S is the propagation path length in meters and f is the frequency is Hz. The peak receive antenna gain is calculated the same way the peak transmit antenna gain was calculated. Since the receive antenna diameter is a input parameter, the diameter of DSN antennas, the receive antenna beamwidth, $\theta_r$, must be calculated in the following way:

$$\theta_r = \frac{21}{fD_r}$$ (8)

Here, f is the frequency in GHz and D_r is the antenna diameter in meters. The receive antenna pointing loss is calculated the same way the transmit antenna pointing loss is calculated. The receive antenna gain is the sum of the peak receive antenna gain and the receive antenna pointing loss. The received energy-per-bit to noise-density, E_b/N_o, is calculated by:

$$\frac{E_b}{N_o} = P+L_l+G_t+L_s+L_a+G_r+228.6-10\log T_s-10\log R$$ (9)

Here, P is the transmitter power (dBW), L_l is the transmitter line loss (dB), G_t is the transmit antenna gain (dB), L_s is the space loss (dB), L_a is the propagation and polarization loss (dB), G_r is the receive antenna gain (dB), T_s is the system noise temperature (K), and R is the data rate (bps). The carrier-to-noise density ratio (dB-Hz) is calculated using

$$\frac{C}{N_o} = (EIRP)+L_s+L_a+G_r/T_s+228.6$$ (10)

All variables are explained above except for EIRP, which is the equivalent isotropic radiated power (dBW). Margin (dB) is the last variable to calculate. The margin is found by subtracting the required E_b/N_o from the C/N_o and then adding the implementation loss. For Project Asterius a margin between 1 and 2 dB was desired.