Retro-Reflection is defined as a process in which an incident signal is reflected back to the point of origin. In the Radio Frequency (RF) community, Retro-Reflective systems capture the incident RF signal energy and blindly re-transmit this signal. Radar Cross-Eye is one example of a Retro-Reflective System. The term blindly means that no source location or bearing angle information is required. Thus eliminating the need for a complex or expensive passive Direction Finding (DF) system to obtain the incident signal Angle of Arrival (AOA) or Direction of Arrival, and to compute a set of weights that would be used to transmit a copy of the signal back towards the incident signal direction (path). For most Retro-Reflection systems, the output weight vector or steering vector is simply the complex conjugate of the incident signal steering vector. Therefore, one only needs to obtain a course estimate for the incident signal steering vector to construct the conjugate re-transmit steering vector. This can be accomplished simply by collecting a few (array vector) signal samples, and processing them to obtain an estimate of the incident signal steering vector. No further directional processing is then required, and computing the conjugate of the incident signal steering vector is thus trivial.
In patent application Ser. No. 15/934,563 the Inventor describes a technology and methodology to rotate near field and far field wave fronts, such that the effective transmitted wave front at a point or region in space is not propagating in a direction orthogonal to the direction of travel. This technology is termed “Wave Mechanics” (WM). An RF (or acoustic) array is used to produce a set of transmitted signals, such when these signals constructively and destructively interfere in the far field, the effective wave front is rotated such that in-phase crests and troughs of the wave impinge on target in a pre-determined and calculated direction, that is not orthogonal to the natural expanding path of the wave front.
The “Single Ship” WM model is defined as when all antennas in the array are co-located on a single ship, platform, or compact system. The primary issue with co-location of all antennas within a small area is that the effective size or width of the wave mechanics resultant (width of the expanding wave front in the far field) becomes narrower as the desired rotation angle is increased and as range is increased. In fact, the effective width of this wave field is approximately on the order of the size of the transmit array itself.
In Provisional Patent Application 62/872,446, the Inventor describes a narrowband solution to the Single Ship problem, to combine Wave Mechanics with Retro-Reflection. Thus, the implementation takes in the narrowband Far Field emitted signal via numerous “Single Ship” antennas (e.g. the array), processes the narrowband signal and Retro-Reflectively re-transmits the signal back out, with the Wave Mechanics rotation mechanism injected into the array weights. The Wave Mechanics implementation of this results in a pre-determined wavefront rotation, as well as much higher received power (at the original emitter), as compared to Cross-Eye that does not generate a controlled rotated wave and requires much higher transmitter power levels. In applying this method, we can overcome the error of the limited Wave Mechanics (Single Ship) wavefront width or corridor.
For the narrowband Single Ship solution, it can be shown that for the very Far Field, that the Electric Field value at the designated points tend to be highly similar in value, independent of the chosen weights. In Ray Theory, this would be discussed as the highly ill-conditioned state where the various Rays tend to be almost perfectly parallel to one another. For single ship solutions, however, for example a large aircraft solution, where sub-arrays can be installed at the wing ends, there is likely sufficient angle differences, within processing error margin, to enable far field rotations with operationally effective rotation angles, from a single ship.
This issue can be overcome by generating two or more sub-arrays, that are spaced roughly 2 percent or the range or greater (dual ship or multi-ship models). When this is done, the width of the wave field is literally on the order of the range itself. However, the cost is in the requirement of two or more independent systems, that are also coherently synchronized.
However, the desire for a wideband signal single ship solution, with large range, on the order or 100 to 500 nautical miles (nmiles) or greater is still highly desired for much smaller platforms, including fighter jets and even small Unmanned Aerial Vehicles (UAVs). The problem is how to accurately and cost effectively project the Wave Mechanics phenomenon at great range, but also to such a small width.
The Inventor's solution is to combine Wave Mechanics with Retro-Reflection, with the full wideband signal spectrum broken up into Discrete Fourier Transform (DFT) frequency binning. Each frequency bin is then treated as an independent narrowband signal model, and the weight vector for each bin is solved for. Finally, all the different and independent frequency weights are Inverse Fourier Transformed (IDFT) back to the time domain, resulting in a time domain signal already weighted. Thus, the implementation takes in the Far Field emitted wideband signal via numerous “Single Ship” antennas (e.g. the array), processes the wideband signal and Retro-Reflectively re-transmits the wideband signal back out, with the Wave Mechanics rotation mechanism injected into the array weights. The Wave Mechanics implementation of this results in a pre-determined wavefront rotation across the full wide band frequency range, as well as much higher received power (at the original emitter), as compared to Cross-Eye that does not generate a controlled rotated wave and requires much higher transmitter power levels. In applying this method, we can overcome the error of the limited Wave Mechanics (Single Ship) wavefront width or corridor.
This Wideband Retro-Reflective WM solution requires no estimation or computation of the incident signal Angle of Arrival (AOA), and is effectively blind.
The novelty is using a captured estimate of the incident steering vector, and using each weight to construct the Rf matrix for each frequency bin, and for a given desired rotation angle. The Rf matrix, on for each bin, is then used to compute a set of transmit weights, also one set of weight for each bin, and Inverse FFT the resultant to obtain the time domain weights that will produce the rotation angle, with an unknown incident signal angle.
First, we review the Narrowband Retro-Reflective Wave Mechanics technique:
a
m
=G
m(θ)exp−j·(m-1)·k·d·sin(θ
Where:
Gm(θ)=the antenna voltage of the mth antenna, in the θ direction
K=wave number=2π/λ
d=sensor to sensor spacing, assumed equal in this model.
θi=Incident signal direction of arrival, to the line normal to the array.
This mth component of the steering vector can also be represented as a function of frequency or simply an electrical phase:
Where:
ω=radial frequency, and
c=speed of light, and
ϕm=phase of the mth antenna, relative to a common reference phase
For this simplistic model, the sensor to sensor spacing(s) are equal.
Assume also, for this simplified model, that the antenna gains are equivalent from sensor to sensor, such that:
G
m(θi)=G(θi) for all m=1,2, . . . ,M.
Therefore, the Array Factor, for the received signal, can be expressed as:
And the Array factor for the reverse transmitted signal can be expressed as:
Where
Bm=the output signal for antenna m
Therefore, to coherently sum in the far field, in the same direction as the receive signal,
B
m
=G(θi)·exp+j·(m-1)·k·d·sin(θ
Therefore, for this coherent summation, θi=θo
Note that the incident phase and the output phases are related by:
ϕo=−ϕi=−ϕo=conjugate(ϕo)
Or that the two phases are simply conjugates of one another. Thus a Retro-Reflective output signal is simply steered with the conjugate of the incident signal steering vector.
The diagram in
Again, it should be noted that the following example is only using M=3 sources and N=M=3 Far-Field points. However, this method can be utilized for any M and N.
This steering vector is easily obtained with the collection of a few data samples (array snapshots), especially for relatively high SNR signals.
A simple narrowband Retro-Reflective signal can therefore be produced by transmitting the incident signal, s(t), back with steering weights of conjugate [a(θi)].
We are interested in generating a Retro-Reflective Wave Mechanics signal, that would be transmitted from each of the three source antennas. Furthermore, we would want this to be a blind function, that would not require Directing Finding or determination of the Incident Signal Direction, θi. One of the benefits of this approach is that the computation of the required weights, and injection of these weights into a transmitted Retro-Reflective signal could occur in microseconds, with the DSP architecture developing into a custom FPGA module.
Recall that the narrowband form of the Wave Mechanics solution, for M transmit antennas and N Far-Field points, is:
Where each rnm in the matrix is simply the distance from a Far Field point n, to the source antenna m.
The more compact form of this expression is:
Where for rnm large, then rnm≈r.
Neglecting the 1/r term as a constant, this can be represented as:
R
xx
h=V
The key is to estimate the rnm components, in a blind fashion, for a desired Wave rotation angle of β.
Note that in [00059] that N=M has been used. However, in general, Rxx can be a N×M matrix, and V would then be a N×1 vector.
The primary approximation to use in the development, is to assume that for a given source spacing d, or Far Field point separation λ/2, that the y-component of the effective distance will be much much larger than the x-component. In general, the Far Field point separation will be less than or equal to λ/2 to reduce spatial aliasing.
For example, the distance from source antenna #1 to Far-Field Point #1 can be estimated as:
r
11=√{square root over ([d·sin(θi)+R+(λ/2)·sin(β)]2+[d−λ/2]2)}
We can see that when R>>d−λ/2 that:
r
11
≈d·sin(θi)+R+(λ/2)·sin(β)
Using similar reasoning, we can observe that:
r
12≈0+R+(λ/2)·sin(β)
r
13
≈d·sin(θi)+R+(λ/2)·sin(β)
Therefore, the first row of the narrowband implementation of Rxx would be:
Which is an M×1 vector. Notice the transpose “T”.
It should be noted that for [00053], the first antenna is selected as the reference antenna, where-as in [00077], the middle antenna is selected as the reference antenna. Additionally, in [00077], the first column of delays (complex exponentials) have already been conjugated to produce beamformed transmit outputs, aligned with the incident signal. Thus, it should be noted that the left side column of complex exponentials in [00077] can be easily computed from [00053]. The right side column, which includes the complex exponentials in rotation angle, are easily computed from the known incident signal wavelength, λ, as well as the desired rotation angle, β.
Therefore, another means to implement this would simply be to conjugate the terms in [00053], and use them directly in [00077] for the left side column.
Similarly,
r
21
≈d·sin(θi)+R+(0)·sin(β)
r
22≈0·d·sin(θ1)+R+(0)·sin(β)
r
23
≈−d·sin(θ1)+R+(0)·sin(β)
Therefore, the second row of the narrowband implementation of Rxx would be:
Finally,
r
31
≈d·sin(θi)+R−(λ/2)·sin(β)
r
32≈0·d·sin(θi)+R−(λ/2)·sin(β)
r
33
≈−d·sin(θi)+R−(λ/2)·sin(β)
Therefore, the third row of the narrowband implementation of Rxx would be:
We can now approximate the Rxx matrix as:
It should noted that from the original narrowband incident steering vector:
which has been numerically estimated, a known incident signal carrier frequency, and desired Rotation angle, β, that the narrowband Rxx matrix can be quickly and accurately computed.
Finally, we solve for the narrowband model as:
R
xx
h=V
Via a direct matrix inversion, as:
h=Rxx
−1
V
Or via the use a Genetic Algorithm.
Note that for the case of a desired rotated plane wave, that
That is, the far field desired voltage (or field) response is the same for each Far-Field point.
Wideband Mechanism for Retro-Reflective Wave Mechanics
The previous model (Provisional Patent No. 62/872,446) is likely sufficient for narrowband signals only. That is, when the bandwidth of the incident signal is much less than 1/100th of the carrier frequency.
Assume now that the incident signal is a wideband signal, s(t), that we want to replicate and conjugate, to feed into each antenna in the source array. As with the prior [narrowband signal model] method, we will want this signal to form an output, represented by:
output=h(t)·s(t)
The incident signal, s(t), can be sampled from a single antenna and separated into a collection of Frequency domain samples via conversion through a [complex] Discrete Fourier Transform (DFT). Each of the Frequency domain samples can be represented as:
Where:
n≡index of data samples (or the sample number in time)
N≡number of samples per DFT
f≡frequency index (integer), or the frequency of each [complex] DFT spectral bin.
Sampling of the signal, within each frequency bin for all the antennas, however, would result in:
Thus similar to [00053], we obtain a steering vector, a(θi, f+fc, for each frequency bin, that is both a function of the incident signal angle of arrival as well as the frequency of the bin. It should be noted that these delays will be a function of the carrier frequency, fc, thus the frequency f needs to be denoted not only as the discrete frequency of the baseband frequency bin, but also to account for any frequency shifting in the down conversion process. The steering vector for incident angle θi and carrier frequency fc can be represented for each bin, f, as:
It should be noted that the wavenumber value k, in the exponent, is now represented by:
We can now build the Wave Mechanics steering vectors for the wideband model, for each [frequency] bin, similar to the how the vectors were built in the narrowband model. That is, for each bin, f=1, 2, . . . , N, we compute the vectors:
Where β is the desired rotation angle, and fc is the carrier frequency shift. Note also, that the transposed vectors are of dimension 1×M, where “T” is the transpose operator.
We can now approximate a Rxx matrix, for each frequency bin, as:
Next, we solve for the weights vectors, hf, for each bin, using:
R
xx(θi,f+fc)hf=Vf
Note that for the case of a desired rotated plane wave, that
For all frequency bins.
That is, the far field desired voltage (or field) response is the same for each Far-Field point.
We can now solve the weights, for each [frequency] bin, f=1, 2, . . . , N, via a direct matrix inversion, as:
h
f
=R
xx(θi,f+fc)−1Vf
Or via the use a Genetic Algorithm.
We now reconstruct the desired output signal, to be fed into the RF Upconverter, as:
Notice that Wn is the Inverse DFT for the wideband signal output, fully weighted across all frequencies, which is then output to the same antennas, as [00074]. The discrete frequency response, for the time series analog signal s(t), Sf, is now multiplied at each frequency Bin by the spectral Bin weights, hf, to obtain the Inverse DFT, which is again back in the time domain. This is the output, from the Processing (FPGAs) which would be sent to the transmitter (multi-Channel) exciters.
System Implementation:
The system in
It is assumed that the signals from each of the M antennas, in the RF Downconvert path (shown on the left) are coherently frequency shifted to baseband, that RetroReflective (RR) Wave Mechanics Processor will compute an estimated wideband receive steering vectors [000125] through [000127] for each frequency bin, the wideband Rxx Matrices [000130] for each frequency bin, and finally solve for an optimal set of weights hf, for each frequency bin [000138]. These weights are then sent to the waveform generator, multiplied and form the Transmit Signal Construction stage. These digital signals are then passed through a Digital to Analog (DAC) Converter and RF upconverted (frequency shifted), and finally re-transmitted out the same antennas.
Another embodiment of the invention would include the use of RF Switches, shown in
Both embodiments function to receive the incident signal, quickly compute the received steering weights (vector), conjugate the weights, multiply by the complex rotation exponentials, and use the resulting matrix to compute a set of transmit weight, hf, used to send a rotation signal back to the original source.
The present application claims priority to the earlier filed provisional application having Ser. No. 62/872,580, and hereby incorporates subject matter of the provisional application in its entirety.