Aerospace and Electronic Systems Magazine December 2017 - 67
Frazer
In a MS-OTHR, we seek more than the single scatterer response Sr(τ, ν) shown in (12). A set of S rp (τ ,ν ) are generated according to the ionospheric propagation structure between radar and
surveillance region
{Sr1 (τ ,ν ), S r2 (τ ,ν ),..., S rP (τ ,ν )} ∈ T
(15)
where each scatterer response S rp (τ ,ν ) in T contains different ionospheric clutter contributions. Some or all members of T are then
processed to generate target detections.
The MIMO radar scheme used in the experiment comprised
transmitter antenna subarrays concurrently transmitting K different
radar waveforms (one per subarray) u(t ) = u1 (t ),..., uk (t ),..., u K (t )
of equal energy. This is the subarray-space waveform set case
where there is a one-to-one mapping between waveforms and subarrays.
Before proceeding we note that our approach requires that the
Cross-Ambiguity Function between waveforms in the waveform
set u(t)
χ u u (τ ,ν ) = ui (t )uk* (τ − t )e − j 2π f ν dt
j k
(16)
is sufficiently low
χ u u (τ ,ν ) < a for j ≠ k
(17)
j k
b N (ψ a ) ≡ [b1 (ψ a ),..., bN (ψ a )] T
(23)
the N-variate receive antenna array steering vector for the cone-angle direction-of-arrival ψa directed toward the surveillance region.
The vectors aK(ψd) and bN(ψa) are the transmit and receive
beamformers, respectively. Since the individual S ruk (τ ,ν ) in (22)
are available following signal transmission, propagation, scatter
from targets and clutter, return propagation and reception, it is possible to implement both the transmit and receive beamformer at the
receiver. Both aK(ψd) and bN(ψa) can be selected based on knowledge of the ionospheric conditions (layer heights, etc.) and can be
adjusted for each delay (or range) in Sr(τ, ν) in the domain of τ in
Sr(τ, ν). The P scatterer responses S rp (τ ,ν ) in (15) can be computed
using appropriate beamformers as
N
K
n =1
k =1
S rp (τ ,ν ) = bn (τ , hp ) ak (τ , hq ) S ruk (τ ,ν )
(24)
for a set of ionospheric layer heights hp and hq and the geometry of
the radar location and region of surveillance. Range-Doppler maps
derived from experimental data in this manner corresponding to
various S rp (τ ,ν ) are shown in Figures 17 and 20.
The waveform set used in MSR-I comprised K = 12 timestaggered LFMCW waveforms where the individual waveform set
member start-time was uniformly dispersed in time throughout the
waveform repetition interval. The choice of waveform set cardinality is based on the results reported in [24], [39].
and that the cross-scatterer response
u u
S r j k (τ ,ν ) = S (τ ,ν ) ∗ χ u j uk (τ ,ν )
(18)
is also low
u u
S r j k (τ ,ν ) < r
(19)
for j ≠ k
for some small values a and r. A more complete discussion of
these assumptions is given in [39].
The scatterer response function is a superposition of the individual waveform set member scatterer response functions including allowance for the spatial structure of the transmit array subarrays
K
S r (τ ,ν ) = ak S ruk (τ ,ν )
(20)
k =1
where the ak are complex weights with
a K (ψ d ) ≡ [a1 (ψ d ),..., aK (ψ d )]
T
(21)
the K-variate transmit antenna array manifold (steering) vector for
the cone-angle direction-of-departure ψd that will illuminate the
surveillance region.
In a MIMO radar the receiver system is also multichannel (with
N receiver channels) so that (20) can be rewritten as
N
K
n =1
k =1
S r (τ ,ν ) = bn ak S ruk (τ ,ν )
where the bk are complex weights with
DECEMBER 2017
(22)
SOUNDING SYSTEM
Ionospheric sounding receivers [49] were located on the coast at
Pt. Hedland, Eighty-Mile Beach, Broome, and at the JORN receive
site. These received oblique incidence sounder transmissions from
transmitters located at South Hedland, Curtin, and the JORN transmit site. The overall sounder network provided an on-line measurement of the state of the ionosphere for the radar-to-surveillance
region in real-time at the experiment control station at the JORN
receive site. It allowed immediate detailed understanding of the
structure of the ionosphere as part of the experiment. We note,
however, that this information is not required in the MS-OTHR
processing.
INITIAL RESULTS AND DISCUSSION
The results presented here are a representative example of modeselectivity results achieved during the MSR-I experiment. Consider the range-Doppler map in Figure 13a. This shows the radar
response Sr(τ, ν) in range (750-1,600 km) and Doppler (-1.5-1.5
Hz) for a single radar waveform and hence typical of that measured
using a classical OTHR (albeit operated at reduced power). There
is significant clutter return from land (stationary and approximately zero Doppler from 750-1,000 km range) and the moving
ocean (Bragg scatter at approximately 1,000-1,600 km and Doppler of -0.4 Hz and 0.4 Hz). There is also significant ionospheric
multimode and ionospheric Doppler shifted clutter present as well
as some weak second-order Bragg scatter from the ocean. Target
detection is severely compromised by ionospheric clutter in the
IEEE A&E SYSTEMS MAGAZINE
65
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