Rover calculations link budget
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Rover/Lander Link Budget
Since the rover and lander will both be close to the surface, we need to use a propagation model that takes interference into account. The path loss can be approximately expressed in dB as:
Lpath_dB = Lfs + Lmp + Lsh
Lfs - Free-space path loss Lmp - Loss due to destructive multipath interference Lsh - Loss due to shadowing (in our case, rocks and terrain)[1] Lfs is simplest, with a closed-form solution: Lfs = 20 log(4 pi f d / c) d=distance between TX and RX antennas f=frequency in Hz c=speed of light
For 2.4 GHz (assuming 802.11 or similar radio link), and 500m (GLXP target), that works out to 94 dB. For 1000m, it is 100 dB.
Lmp is difficult to calculate directly, even if the exact geometry is known. In this case, it isn't, so we must treat the losses statistically. According to Siwiak, and supported by Goldsmith [2], the statistics of multipath fading are Rayleigh. In our case, since the line-of-sight path will often be present, Rician statistics are more appropriate. However, in order to treat the various components separately as we are, we should neglect the line-of-sight path and assume a Rayleigh distribution. The nulls due to multipath can be 30-40 dB, but interference can also be constructive. Ultimately, the mean of the Rayleigh distribution is 0 and the variance depends on a parameter that is generally determined empirically. For this reason, in many approximations the multipath fading term is replaced with a lognormal approximation with a standard deviation of 7.5 dB.
Lsh represents "slow fading" nulls created by shadowing of the radio signal by obstacles. It is also generally determined empirically, and expressed as a probabilistic estimate of the expected value, also lognormally distributed. Since it is not possible in our case to empirically determine the statistics, I propose that values derived for terrestrial urban environments provide a good model, since the scale of the rocks and terrain features compared to the rover are comparable to medium sized building to an automobile or portable radio. Standard deviation values derived for urban environments range from 4 to 14 dB.
Since the expression for total path loss contains random variables, it is necessary to select a reliability factor less than 100% to arrive at a solution, and the number of standard deviations of the random variables adjusted based on a z-factor calculation. For example, 95% reliable communication requires 1.645 standard deviations, while 99% reliability requires 2.326 standard deviations. To be more rigorous, since the random variables are uncorrelated, we should use their RMS sum in the calculation.
To approximate, however, we can use the individual standard deviations, and for 95% probability of successful communication out to 500m our expression becomes:
Lpath_dB = 94 + 7.5(1.645) + 14(1.645) = 129.3675 dB
Antenna Diversity
The multipath loss treatment above assumes a narrowband communication channel. For wideband (such as Wi-Fi), the losses will be much less. They can be further mitigated by the use of antenna diversity, such as that employed in 802.11n (known as "MIMO" for "Multiple-In, Multiple-Out".) This will also boost the antenna gain (up to 6 dB for 2 antennas). The tradeoffs, of course, are complexity, cost, launch mass, etc.
Antenna gain improvement is reduced by non-orthogonal antenna placement. Since perfect orthogonality is difficult to achieve in practice, actual gain from multiple antennas will be less than the theoretical ideal. Similarly, the reduction in fading losses (or fading resistance) depends on the physical and electrical distance between the antennas, which is often not ideal due to practical considerations. But, for an idea of the benefit, the Lmp term can be set to zero. The budget calculation above then improves to 117.03 dB.
Using the Link Budget
The IEEE 802.11 standard [3] mandates receiver sensitivity of -80 dBm for 1 Mb/s. Including fading and assuming antenna gains of 2dBi for transmit and 8dBi for receive, for the case without fading:
117 - (8+2) -80 = 27 dBm (1W is 30 dbm), so your 1W TX can support 1 Mb/s, with margin.
Interference
Interference from unwanted external signals must be accounted for, although it is not generally part of the link budget. There are two major types of interfering signals: 1) Out-of-band interference: High levels of out-of-band interference may damage the sensitive receiver hardware. They should be controlled with an external filter (such as a SAW) just after the antenna. The losses associated with these types of filters are small, 0.5 - 1 dB. 2) In-band interference: Unwanted signals in the receiver band cannot be easily separated from the desired signals. Therefore, it is modeled as an impact to the minimum detectable signal or receiver sensitivity. One potential issue for Wi-Fi is that the standard calls for a Clear Channel Assessment (CCA) prior to transmitting. If the receiver detects an energy level on the channel greater than -65 dBm (per the standard), the unit will not transmit a packet. If the ambient noise is greater than that, the Wi-Fi link will be useless because it will never transmit.
Coverage Computations and Maps
The SPLAT! program was used to compute a coverage map assuming 1 m high transmit antenna and 0.02 m high receive antenna for a section of the lunar surface in the Descarte Highlands near the landing site of Apollo 16. A Line-of-site path loss analysis and a Longley-Rice coverage analysis were performed in a single run. Redacted text output follows (full version here):
--==[ SPLAT! v1.2.3 Path Analysis ]==-- ------------------------------------------------------------------------- Transmitter site: lander Site location: 7.0128 South / 345.6536 West (-7° 0' 46" S / 345° 39' 12" W) Antenna height: 1.00 meters AGL / 1.00 meters AMSL Antenna height above average terrain: 68.61 meters Distance to rover: 1.46 kilometers ------------------------------------------------------------------------- Receiver site: rover Site location: 7.0061 South / 345.6650 West (-7° 0' 22" S / 345° 39' 54" W) Antenna height: 0.02 meters AGL / 0.02 meters AMSL Antenna height above average terrain: 365.19 meters ------------------------------------------------------------------------- Longley-Rice path calculation parameters used in this analysis: Earth's Dielectric Constant: 13.000 Earth's Conductivity: 0.002 Siemens/meter Frequency: 2400.000 MHz Polarization: 1 (Vertical) Transmitter ERP: 1.0 Watts ------------------------------------------------------------------------- Summary for the link between lander and rover: Free space path loss: 103.35 dB Longley-Rice path loss: 146.81 dB Attenuation due to effects of terrain: 43.46 dB Total path loss including lander antenna pattern: 147.27 dB Field strength at rover: 27.60 dBuV/meter Voltage produced by a terminated 50 ohm 0 dBd gain antenna: 0.39 uV Voltage produced by a terminated 75 ohm 0 dBd gain antenna: 0.48 uV -------------------------------------------------------------------------
The graphical output data from SPLAT! can be imported into Google Earth and examined there. Here are some screen images of how the Descarte Highlands analysis looked.
References:
- ↑ Siwiak, K. Radiowave Propagation and Antennas for Personal Communications ) http://www.amazon.com/gp/product/159693073X/ref=s9_simb_gw_xi_s2_p14_t1?pf_rd_m=ATVPDKIKX0DER&pf_rd_s=center-2&pf_rd_r=1FCY6WG7FT783PMD7R82&pf_rd_t=101&pf_rd_p=470938631&pf_rd_i=507846
- ↑ Goldsmith, A. "Design and Performance of High-Speed Communication Systems over Time-Varying Radio Channels" http://wsl.stanford.edu/Publications/Andrea/thesis.pdf
- ↑ IEEE 802 Working Group, "IEEE 802.11-2007 IEEE Standard for Information technology-Telecommunications and information exchange between systems-Local and metropolitan area networks-Specific requirements - Part 11: Wireless LAN Medium Access Control (MAC) and Physical Layer (PHY) Specifications," http://standards.ieee.org/getieee802/802.11.html
