Aerospace and Electronic Systems Magazine December 2017 - 49

Barnes and Earl
RBW or 3 dB above the undithered quantization noise level, Figure 5.
The behavior of a dithering signal in suppressing ADC distortion,
which had a peak spur level close to -150 dBW is a well-known property [4], [5] and the same behavior is confirmed in our model.
All the ADC modelling so far has been for an ideal ADC transfer function. A nonideal transfer function can be modelled and
has been shown to increase distortion products. Clearly, in order
to evaluate the effect of departures from ideal ADC transfer functions, specific data defining the nature and magnitude of the departures is required. At this stage the quantification of these departures
has not been attempted and applied to this model.
To bring these noise and distortion products into the model, we
have chosen to use manufacturer data on the ADC chip itself. An
example of the data readily available is shown below in Figure 6
for the case of the LTC 2217 produced by Linear Technologies.
From the right panel it can be seen that the spurious-free dynamic
range (SFDR) in this case holds up to about 90 to 100 dB when the
largest signals are within 40 dB of full scale deflection (FSD) and
dither is applied. The nature of the spurs can be seen in the two tone
test. Of particular importance is the "continuum" of spurs that are
seen often about 10 dB below the quoted SFDR, which would be
corrupting over the full band. In the model, we have as input, the
maximum signal levels at the ADC relative to FSD, after the application of the frontend attenuation is determined, and can use these along
with the predicted SFDR to predict what level the corrupting level of
spurs will sit in any particular run. We therefore treat ADC nonlinear
distortion as a broadband effect occurring at the modelled level.
The remaining components in the model are digital down conversion (channel selection and decimation) and the signal processing
chain. The digital down-conversion is treated as ideal, in the model,
since current field-programmable gate array capabilities have proven they allow processing with sufficient dynamic range and speed
to retain pristine linearity simultaneously with real time processing.
In application to OTHR, correlation (range) and Doppler processing are typical stages encountered early post digitization. It is
generally found that external noise and system internal noise, as
opposed to weak interference or Electromagnetic Interference, do
not range or Doppler form and so the effect of these processing
steps is to reduce the noise resolution bandwidth in the usual spectral processing manner. This is accounted for in the model.
Depending on the nature of signals (linear and nonlinear generated) these signals will generally not range form but may Doppler
form if repetitive. For frequency-modulated continuous waveform
(FMCW) waveform often used in OTHR, this could mean a suppression in level anywhere from ∼20 dB to ∼40 dB for standard
waveforms (e.g. bandwidth 10 kHz, waveform repetition frequency of 50 Hz, coherent integration time of 2.56 s). No attempt to
treat every signal based on actual processing has been made. At
this stage the model uses a middling 30 dB approximation to the
suppression of nonlinear components.
The application of array processing (beamforming) to the model is difficult since the long term capture of wideband data across
OTHR arrays remains a formidable task due to the volumes of data
involved. Although it is known that external noise is generally directional, no attempt to capture this has been done in this model
and 0 dB gain is attributed to the beamforming stage on both exDECEMBER 2017

Figure 6.

Manufacturer quoted data on the performance of the LTC 2217 in two
tone test (left) and SFDR vs. input level (right) (courtesy of Linear
Technologies data sheet).

ternal and internal noise. Similarly, little data is available on beamforming of nonlinear components. It is known that the phase relationship of nonlinear components will be disrupted and therefore
the beamformed direction will be randomized to some extent, and
it seems appropriate to treat the behavior as an average gain across
an ensemble of nonlinear products based on the percentage of operationally used beamspace against the total possible beamspace.
For this reason partial beamformer gain in this manner, is applied
to the non-linear voltages in beamformer processing.
Once the output voltages through the entire chain are achieved,
comparison of the various propagated components can be performed
to see what if anything has been corrupted by the receive and processing systems. The ideal performance reference can be achieved
by application of the net linear gain on the external noise. In the
spectral domain this is just the original external noise spectral density with the addition of a constant logarithmic shift to put it in the
final range-Doppler-beam resolution cell. We can then compare this
ideal with similarly propagated versions of the nonlinear signals
and internal noise, with the appropriate scaling applied to each of
these separately. Comparison is carried out in the spectral domain
in a nominal resolution bandwidth, and any increase above some
minimum threshold in the power spectral density over the ideal, can
now be attributed to internal noise limiting and non-linear products.

INPUT VOLTAGE DATA
To supply the voltage time series required for the analysis, a measure of the internal and external noise and all HF signals must be
achieved independently. To measure the internal noise of a single
element system the input can be terminated at the antenna output
with its characteristic impedance, often 50 ohms. The internal
noise may not be precisely accurate measured this way, because
the antenna impedance is not 50 ohms at all frequencies, however

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Table of Contents for the Digital Edition of Aerospace and Electronic Systems Magazine December 2017