Aerospace and Electronic Systems Magazine December 2017 - 46

Feature Article:

DOI. No. 10.1109/MAES.2017.170043

Estimating the Sensitivity and Linearity Requirements
of an OTH Radar Receiving System
Rod I. Barnes, WR Systems Ltd., Fairfax, VA, USA
G. Fred Earl, Riverside Research, Crystal City, VA, USA

INTRODUCTION
A desirable goal for an over-the-horizon radar (OTHR) receiver chain
is to avoid degradation of available signal to noise ratio over unused
channels within a nominated band of interest. If there is a design requirement for the receiver to perform instantaneously wideband, this
can present a significant challenge as the dynamic range of signals
within the high frequency (HF) band in the form of large broadcast
signals, by way of contrast to the very low spectral densities characterizing cosmic noise, can easily exceed the linear range of components in a typical receiver chain. In narrowband systems, this has
been handled in various ways by constraining the bandwidth impinging on sensitive downstream components, with a highly linear bandpass filter, or custom mixer and filter. Even in narrowband systems
care must be taken to ensure that the receive chain internal noise and
nonlinear products do not significantly impact at operational frequencies of interest. More recently, with the advent of direct digital receivers (DDRx) based around high speed high dynamic range analogue
to digital converters (ADCs), a desire to operate OTHR with wide
open front ends (WOFE) has emerged. In a WOFE DDRx there is no
bandpass filtering within the operational range of the receiver. The
principle is to enable multiple simultaneous functions using the large
radar receive array, e.g. the usual narrowband radar with a complementary wideband frequency management support (FMS) system [1].
This goal demands simultaneous access across the full spectrum and
therefore constrains the filtering solution and increases the technical
demand on the receiver components. As discussed in Barnes et. al. [2]
the general application of Commercial-Off-The-Shelf (COTS) DDRx
to attempt WOFE at HF will generally result in some level of system imposed performance limiting. The use of customized, dynamically adaptive front-end gain stages, including the use of equalization,
where the gain is a tailored function of frequency, can allow the receiver to approach a satisfactory WOFE solution in some applications,
e.g. the spectral environment evaluation and recording [2] receiver.
Given the difficulty of avoiding receiver imposed limitations,
it is desirable to have a means of assessing the likely performance
Authors' address: WR Systems Ltd., Head Office, 11351
Random Hills Road, Fairfax, VA 22030, United States, 22030,
E-mail: (rbarnes@wrsystems.org).
Manuscript received February 2, 2017, revised September 5,
2017, and ready for publication September 13, 2017.
Review handled by D. O'Hagan.
0885/8985/17/$26.00 © 2017 IEEE
44

of a proposed receiver given a specific mission (e.g. simultaneous full array OTHR and FMS at HF); or alternatively specifying
the receiver system requirements given the specific mission and
the tolerable level of degradation. We therefore describe below a
method of collecting the appropriate data and applying this to an
arbitrary receiver chain for these purposes.

MODEL
A model of the system of interest is shown in Figure 1. The model
starts at a measurement tap, which is a common reference point
where a spectral assessment system must independently characterize the time evolution of the external noise levels from the environment supplied by an antenna, the system internal noise levels, and
the environmental signal levels. The desire then is to propagate
these measurements from the measurement point back through any
coupling system used to extract the measurement and then along
the chain of the receiver system to the output of signal processing.
To assess the system impacts on potential signal to noise ratio,
we chose the independent physical quantities of analysis to be the
internal (system) noise voltage, vi(t), external noise voltage, ve(t),
and external signal voltage, vs(t). vs(t) can be distinguished from
ve(t) in that it is comprised of band limited signals in the spectral
domain whose peak spectral power exceeds the surrounding external noise power by some nominal threshold. More is said on these
distributions and the extraction processes later.
Let us define a wanted narrowband radar signal vr(t) that can be
centered at any frequency in the spectrum of interest. Then ideally
the RMS value of the quantity vr/(ve + vi + vs) remains unchanged
through the chain, since ideal noiseless components would provide
purely linear gain which would not alter this ratio. In practice, many
different deleterious effects are possible including a degradation in
the ratio vr/vi (internal noise limiting) and by the introduction of distortion products that alter vs by nonlinear behavior in the components.
After processing, radar measurements are made in the spectral
domain, so although we wish to analyze the system with voltage
time series, the signal to noise ratio is eventually characterized as
an estimate of the ratio of spectral powers. In a 50 ohm system, the
square of the voltages divided by 50 forms in the limit a Fourier
transform pair with the power spectral density. Hence, the achievable SNR as a function of frequency can be estimated before and
after propagation of the voltages through the system, to quantify
the degradation as a function of frequency of any of these effects.

IEEE A&E SYSTEMS MAGAZINE

DECEMBER 2017



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