É TIC A
3. Niveles de ejercicio del liderazgo ético
Ideally the satellite would process measurements and continuously derive the surface
roughness measurement directly on-board. However as the inversion procedure has not been validated, it is vital that a GNSS-R instrument has the flexibility to process the signal in a number of ways. The most flexible approach would be to downlink the raw intermediate frequency (IF) samples. Continuously recording raw IF 2 bit samples and storing on the satellite from nadir and zenith front ends, at a sample rate of 16 MHz, would accumulate around 6000 Gb (bits) per day, a data-rate that is incompatible with small satellites or hosted payloads. The TDS-1 platform is capable of downlinking about 700 Gb per day (assuming one ground station and 650 km altitude).
Some form of on-board processing is required to reduce the data rate. One intermediate product is the DDM which records the spread of the signal in time delay and Doppler shift caused by the rough surface scattering. This product has been used to retrieve surface
parameters in studies through curve fitting a scattering model to the DDM shape for example the work by [Clarizia, Gommenginger, et al. 2009]. There are other promising methods, of surface roughness measurement which the SGR-ReSI would support, such as Stare
processing (Section 4.6), however the DDM provides a commonly understood product and will be the focus here. Also Stare processing results can be derived from the DDM, but not vice versa.
There are a number of stages of processing in-between the raw samples, creating the DDM and deriving from it the surface measurements (Figure 5.3). The process can be a split between satellite and ground to provide a suitable trade-off between flexibility and data-rate.
A retransmission or 'bent-pipe' approach would retransmit the signals at point (A) and would require constant ground-station contact. SSTL's first GNSS-R experiment on UK-DMC digitally stored samples and downlinked at point (B), which limited the experiment to short data captures. Radio Occultation GNSS receivers typically downlink the product at stage (C) [Loiselet, Stricker, et al. 2000].
Figure 5.3 Processing chain for producing surface measurement from DDM of reflected signal.
By downlinking incoherent DDMs to the ground at point (D), a significant reduction in data rate occurs. Some of the flexibility in processing is lost, but significant flexibility remains for different approaches to the scattering model inversion (E) if this is performed on the ground.
5.2.1. Comparison With a Navigation Receiver “Cold Search”
It is insightful to compare the DDM in GNSS-R to the search space in a navigation receiver, so that existing techniques can be evaluated. Before tracking GNSS signals a navigation receiver must firstly search through code delay and carrier frequency to acquire these signals hidden in the noise. The size of the search space depends on the GNSS code length, chipping rate, the user velocity and the receiver clock uncertainty. The frequency search range for a ground based receiver is based primarily on the range of receiver velocities; while the code search space is carried out typically at 0.5 chip steps to limit the maximum loss associated with misalignment to –3 dB. The frequency search is ±10 kHz in steps of 500 Hz [Borre, Akos, et al. 2006], limiting the misalignment loss to a further –3 dB.
This leads to a search space of 1023 · 2 ∙ (20 × 103)/500 = 81,840 combinations or delay
‘pixels’ if considered as a DDM.
The correlation output formed in the navigation receiver’s acquisition stage is immediately discarded as the peak provides the location of the signal to initialise the tracking of the signal.
Accordingly the pixels can be searched serially, in parallel or a combination of blocks depending on the hardware available for processing. For GNSS reflectometry, it is the recording of the values in this search space that is desired, and therefore all the pixels are required to be recorded simultaneously.
The delay-Doppler map of the reflection is analogous to the GNSS acquisition search space.
It is assumed that the reflection specular point is at a known pseudo-range and carrier frequency, so the signal is already ‘found’ in this signal space. However the term ‘search space’ is still used to help show the analogy to the GNSS acquisition problem. The spread of the signal from the reflection is determined by the physical size of the scattering zone on the surface, the geometry of the transmitter, receiver and their velocities. Additionally the link-budget determines how far from the specular point a signal will have sufficient SNR for detection.
The range of delays and Doppler that would be expected from the surface could be determined from a surface scattering model combined with link-budget calculations.
However it is not clear that the current models have been effective at predicting the absolute power levels so the approach will be taken to use information derived from the results of the UK-DMC experimental GNSS-R receiver. The parameters of the UK-DMC GNSS-R
experiment are described in Section 3.2. Through all the measurements taken the antenna was
kept pointing away from nadir by 10 degrees. This means that the reflections had largely the same delay and Doppler characteristic shape with a Doppler frequency spread of around 10 kHz and a spread in delay up to about 30 μs. The DDM in Figure 5.4 is typical of the reflections processed from UK-DMC. This spread is considerably less than the search space for navigation receiver acquisition but considerable greater than that used in signal tracking.
Figure 5.4 A UK-DMC reflection processed using the software receiver. Colour scale is chosen to provide a measure of reflection detectability. Processing as described in Section 4.1.
5.2.2. Sampling Resolution
Without a full and finalised retrieval technique to go from DDM to an estimate of the Earth surface roughness, the most appropriate way to determine the required sampling intervals for delay and Doppler is to consider the properties of the ambiguity function.
Over-sampling of the ambiguity function wastes computational effort for no gain in information, whereas under-sampling will produce gaps where signal power and therefore information is lost. From the shape of the GPS C/A code ambiguity function which is shown in Figure 2.6, the maximum losses can be calculated for the ambiguity function and have been listed in Table 5.1 for Doppler and Table 5.2 for delay.
Table 5.1 Maximum loss with different sampling resolutions in Doppler dimension
Frequency Spacing
[Specific case 𝑻𝒄𝒐𝒉 = 1 ms]
Power Loss (dB) 2/𝑇𝑐𝑜ℎ = [2000 Hz] -inf. (due to null) 1/(𝑇𝑐𝑜ℎ) = [1000 Hz] -3.9
1/(2𝑇𝑐𝑜ℎ) = [500 Hz] -0.9 1/(4𝑇𝑐𝑜ℎ) = [250 Hz] -0.2
Table 5.2 Maximum loss with different sampling resolutions in delay dimension
Delay Spacing
[Specific case 𝑻𝒄 = 978 ns]
Power Loss (dB)
1 𝑇𝑐 = [978 ns] -6.0
1/2 𝑇𝑐 = [489 ns] -2.5
1/4 𝑇𝑐 = [244 ns] -1.15
1/8 𝑇𝑐 = [122 ns] -0.6
By choosing frequency and delay resolutions of 1/(2𝑇𝑐𝑜ℎ) and 1/4 𝑇𝑐 respectively, the DDM will be sampled sufficiently that it will be within 2 dB of a continuous representation of the DDM. Alternatively, choosing improved resolutions of 1/(4𝑇𝑐𝑜ℎ) and 1/8 𝑇𝑐, the DDM will be sampled sufficiently to be within 1 dB of the continuous DDM. The smoothing effect of the ACF leads to diminishing returns when improving the DDM sampling resolution, with very closely spaced samples being highly correlated.
The summary of the comparison between GNSS navigation and reflectometry requirements is shown in Table 5.3. The required DDM resolution has been specified for a maximum
sampling induced power error of 1 dB. This value is thought to be suitable, but it is expected that different inversion techniques will have different sensitivity to the sampling resolution.
The specifications of the reflectometry processor are considerably different to that of the navigation receiver, both in the search space, the resolution and most significantly in the requirement for the full DDM result to be calculated continuously at the rate of 1/𝑇𝑐𝑜ℎ. The sampling frequency is taken to be 𝑓𝑠=16.367 MHz as this provides sufficient Nyquist bandwidth for an anti-aliasing filter with wide transition band and low group delay variation;
additionally this is a commonly supported frequency among RF front-end chip-sets.
Table 5.3 Reflectometry DDM processor requirements compared to navigation cold search.
Navigation cold-search Reflectometry
Delay Range 1023 chips 30 chips
Delay Resolution 0.5 chips 0.125 chips
Number of delay pixels 2048 240
Doppler Range 80 kHz (for orbiting receiver) 10 kHz Doppler Resolution 50 Hz to 500 Hz depending
on coherent integration
Under 1 minute typical Continuous, 1 ms Number of simultaneous
PRNs
1 4 (From Section 3.6)
With a chosen DDM sampling resolution the requirements for the capacity of the satellite downlink rate can be determined for each reflectometry channel. By generating 1 second integration DDMs of the ocean once a second, with resolution 240 x 40 pixels, and 10 bit quantisation per pixel, then a 96 Kibit/s data stream is produced, or 8.3 Gb per day per reflection. The DDM is effectively a picture, which could be compressed, or only parts selected for downlink, so this is not necessarily the minimum rate, but gives an upper bound of what needs to be supported per reflection channel.