Embodiments of the present disclosure are directed to using a time-modulated array (TMA) to obtain space-frequency diversity beamforming to significantly enhance target interrogation under noise-limited and clutter-limited conditions. The target may be biological or non-biological in composition.
A TMA system is characterized by time-modulating each array element of a transducer array to produce simultaneous beam steering, where each beam is associated with a different carrier frequency. The inherent physics is appropriate for either electro-magnetic or acoustic transmissions [1], but the remainder of this disclosure will be primarily directed to acoustical applications.
After the effectiveness of sonar and radar systems were demonstrated in WWII, the next three decades saw improvements in the temporal and spatial properties of the acoustic and electromagnetic waves in their respective propagation media: the oceans and the atmospheric strata. From 1945 to 1975, considerable advances and innovation were made in space-time radar signal processing by applying time-frequency domain techniques in electronic scanning of antenna systems. In the meantime, the U.S. Navy's research efforts concentrated on characterizing the multi-modal acoustic properties of ocean behavior and applying radar and astronomy processing techniques to sonar [1-3].
The following is a brief review of significant research papers in the fields of both radar and sonar on the related art of TMAs.
One of the early outstanding researchers in the field was Shelkunoff [4], who in 1941 presented a general method of antenna analysis based on Maxwell's equations and circuit theory principles. Shelkunoff's method improved the understanding of the transmission process and facilitated the computation of the input impedance of antennas of arbitrary shape. In 1943, Schelkunoff [5] presented a mathematical method that influenced space-time diversity methods proposed in the 1960s: Shnitkin [6], Shanks [7]. Kummer et al [8], Davies and McCartney [9], and Johnson [10]. These advancements are specifically relevant to the use of TMAs, which is characterized by applying modulation and coding techniques to beam steering of transmit and receive beams, and by obtaining ultra-low sidelobes to minimize off-axis interference.
Shnitkin (1960-1961) presented a survey of electronically scanned antennae comprised of beam switching, phase shifting, and frequency scanning. Electronic scanning replaced the repositioning of large and heavy antennae by mechanical means, which required large moments of inertia and caused structural stresses that produced antenna distortion and deterioration of radiation patterns. A technical approach was introduced, primarily to receiving systems, to circumvent the need for high speed, high accuracy RF phase shifters that considered frequency conversion phasing schemes.
Shanks (1959-1961) enhanced the concept of a time-modulated antenna by recognizing that amplitude modulating the transmitting carrier plane wave with a Fourier spatial-temporal series generated a time-varying radiation pattern. Time-multiplexing the element signals produces a frequency-multiplexed beam signal that can be used for beam steering. This is a consequence of the Fourier transform relationship between the array aperture and the far-field pattern space. Control of the modulation frequency, duty cycle, pulse repetition rate, as well as other modulation parameters with respect to the array geometry, supports the potential of the TMA concept to achieve specific operational objectives in real environments.
It was now no longer necessary to control the phase between elements for sidelobe control as presented by Shnitkin. Instead, simple on-off element switching in a progressive manner could be employed for both transmit and receive arrays. Kummer et al (1962) applied this switching technique to a receiving antenna array to produce a −50 dB Chebyshev sidelobe level from a normal uniform −13 dB static distribution for a linear array.
Electronically beam scanned arrays were initially applied almost exclusively to linear or rectangular planar arrays. Davies and McCartney (1965) showed that these principles could also be applied to convex geometries, such as circular and cylindrical arrays. Finally, following Shanks, Johnson (1968) applied time and frequency multiplexing to linear and ring receiving arrays.
During the 1960s, considerable research was conducted by the U.S. Department of Defense, most notably the now-defunct U.S. Navy Underwater Sound Laboratory in New London, Conn. System architecture became more complex, and performance assessment required new metrics in computing the reverberation masking level. In 1968, Cole and Hanrahan [11] extended the reverberation index (RI), introduced in 1948 by Eyring et al [12], as a measure of the discrimination against reverberation (clutter) associated with single transmitter and receiver acoustic power intensity patterns. The RI was used to optimize multiple transmissions and high search rates for multi-acoustic mode operation, such as shallow-water, surface-duct, convergence zone and bottom-bounce propagation in deep water [15]. In this period , the focus was also in the area of nonlinear acoustics, most notably by Westerfelt [13; 1963], who investigated the area of interacting primary frequencies generated by an array referred to as an active parametric array.
Experimental sonar research in the 1970s focused on understanding the limitations of reverberation in multi-modal operation and assessing the application of coding principles to beam-forming. Among the many fine contributors in this period are Vogliss [14], Winder [15], and Haykin [16].
The basic principles of receive beam scanning using matrix formulation were developed by Vogliss, who discussed limitations such as the scanning speed, the number of modulating frequencies in Part 1 [1971], and the design flexibility in Part 2 [1972].
A general overview of the state-of-the-art in sonar system technology was presented by Winder [1975] that reviewed the various acoustic transmission and signal processing technologies commonly employed and the major associated operational considerations, such as the cross-beam reverberation build-up and the incurred blind zone re scanning time.
Haykin (1976) expanded on the multiple-beam sampler architecture of Johnson by employing a structure similar to the Fast Fourier transform to reduce the hardware, resulting in greater reduction in circuit complexity as the number of elements increases.
For the past 60 years, the TMA concept primarily addressed the architecture of receiving arrays, primarily due to the advancements in FFT processing and micro-minimization. The real value of TMA is on transmit, where beams can be directed and optimized in multi-mode transmissions to maximize the signal-to-masking noise ratio on receive, utilizing frequency to spatially-decouple the clutter or reverberation on receive and to significantly simplify the receiver architecture by employing high resolution FFT spectral algorithms, for both radar and sonar applications. The concept of spatial decoupling is to convert coherent summation to incoherent summation, that is, being linear on the basis of energy, such as white noise, instead of being linear on the basis of amplitude.
It is thus desirable to provide TMA design to be efficient and functional within specific operational transmit constraints of real applications utilizing arrays of various geometry such as linear, convex, planar and parametric.
It is also desirable to provide real-time operational TMA systems that consider transmit design constraints such as interbeam interference within the transmitting bandwidth, bearing-doppler ambiguity, and spectra leakage interference from outside the passband.
In addition, it is desirable to provide real-time operational TMA systems that consider design constraints such as the power amplifier source level and peak power rating in transmit, and the cross-beam reverberation or clutter masking level in receive.
Embodiments of the present disclosure are directed to using a time-modulated array (TMA) to obtain space-frequency diversity beamforming to significantly enhance target interrogation under noise-limited and clutter-limited conditions. The target may be biological or non-biological in composition. Depending on the application, real-time operational TMA systems consider design constraints such as interbeam interference within the transmitting bandwidth, bearing-doppler ambiguity, spectra leakage interference from outside the passband, power amplifier transmit source level, and peak power rating in transmit and cross-beam reverberation or clutter masking level in receive. These system design requirements were not considered in previous research on multi-beamforming systems.
According to an embodiment of the disclosure, there is provided method for generating a spatial distribution of acoustic transmitting frequencies by a time modulated array (TMA) of transducers that permit simultaneous multiple beam steering, including generating, by a tapped delay line, a plurality of pulsed sampling signals, wherein each pulsed sampling signal includes a series of frequency harmonics and successive signals of the plurality of pulsed sampling signals are separated by a predetermined delay time, mixing each of the plurality of pulsed sampling signals with a time-limited information signal wherein a plurality of mixer output signals is generated, bandpass filtering each of the plurality of mixer output signals, and generating a first plurality of simultaneous TMS beams from the plurality of filtered and weighted output signals by driving a plurality of acoustic transducers in a spatial array of acoustic transducers. Each beam of the first plurality of simultaneous beams is associated with one of a plurality of transmitting carrier frequencies, and the first plurality of simultaneous beams are subject to design constraints that control a bearing target doppler ambiguity, a uniform response in bearing, out-of-band spectra leakage interference, peak power level, and cross-beam reverberation. A secondary plurality of beams is formed that includes a plurality of different primary carrier frequencies that intersect the first plurality of simultaneous TMA beams in a far-field and based on nonlinear properties of a propagation medium, and a parametric sonar array is produced. Multiple echo frequencies are received and processed by a spectrum analyzer, where each spectral component of the multiple echo frequencies corresponds to a unique spatial bearing.
According to a further embodiment of the disclosure, the method includes producing a spectral component with a phase slope that corresponds to a particular beam steering angle by time-modulating each array element in a spatial array.
According to a further embodiment of the disclosure, the spatial beamformer comprises two sub-beamformers, wherein one or both are TMA beamformers, whose output intersects in a specific region in the far-field with one or more common maximum response axes (MRAs).
According to a further embodiment of the disclosure, the spatial array is an N-point element linear array with constant element spacing d and a time-varying far-field pressure for a monochromatic signal is given as:
wherein θ is a pointing angle, which is a direction of maximum response for a particular beam associated with a harmonic number, ap are weighting coefficients for each harmonic p, Wm is a complex weighting for each element m, fr is a reference frequency, fs is a fundamental harmonic frequency, fo is a transmit frequency, p ranges from a first harmonic Po to a last harmonic Pc, c is the speed of sound, and ϵ is +1 or −1 depending on whether a sum or difference frequency band is retained.
According to a further embodiment of the disclosure, the method includes choosing a total delay time τ equal to a sampling period, Nτ=1/fs, wherein τ=−d sin(θ)/c, and the pointing angle θ is a function of the harmonic parameters (p) and (fs), the center frequency fc=fr+ϵfo, and the array parameters (N) and (d).
According to a further embodiment of the disclosure, the design constraints include a sampling frequency fs that is at least: fs=FD+6/T, wherein fD is the maximum doppler and T is the signal pulselength.
According to a further embodiment of the disclosure, the design constraints include a design constraint that controls out-of-band spectra leakage interference that is 2f≥(Pc−Po)fs, wherein (fs) is a sampling frequency that includes spreading due to source, target and receiver speeds.
According to a further embodiment of the disclosure, the pointing angle θp=sin−1[2πp/(Nkpd)], wherein kp is a harmonic dependent wave-number that equals 2π(fr+ϵfo+pfs)/c.
According to a further embodiment of the disclosure, when the information signal is s(t) has a complex Fourier spectrum S(f′), the time-varying far-field pressure is expressed by:
According to a further embodiment of the disclosure, the total peak power required for M tonals is (2M2Prms), wherein Prms is an rms power per tonal required for a specified source level.
According to a further embodiment of the disclosure, a transmit source level of the TMA SLTMA for the linear array with a constant input electrical power is equal to transmit source level of the linear array SLLIN reduced by the number of frequency coded beams according to SLTMA=SLLIN−10 log M, wherein SLTMA=20 log rms pressure on the MRA.
According to a further embodiment of the disclosure, the spatial array is an N-point element circular array with constant angular element spacing ζ, and a time-varying far-field pressure for an arbitrary signal with complex Fourier spectrum S(f′) is given as: p(θ,t)=Σpap∫df′S(f′){ΣmWmexp(−j2π[(fp(R/c)(cos(θ−mç)−cos(θ)+pm/N))])}×exp(j2πfpt), wherein θ is a pointing angle, which is a direction of maximum response for a particular beam associated with a harmonic number, ap are weighting coefficients for each harmonic p, Wm is a complex weighting for each element m, fP=(f′+fr+ϵfo+pfs) where fr is a reference frequency, fs is a fundamental harmonic frequency, fo is a transmit frequency, p ranges from a first harmonic Po to a last harmonic Pc, R is the radius of the circular array, c is the speed of sound, and ϵ is +1 or −1 depending on whether a sum or difference frequency band is retained.
According to a further embodiment of the disclosure, the method includes additional phase weightings that enhance spatial filtering, wherein each element is phased back-to-a-line or to a circular arc for maximum echo-to-noise ratio.
According to a further embodiment of the disclosure, the method includes selecting frequencies that decrease the coherence of the spatially interacting beams that transmit major lobes wherein one or more of a cross-beam masking clutter or a reverberation level is reduced.
According to a further embodiment of the disclosure, the spatial array is a planar array of N1-point elements with an inter-element d1-spacing in a first direction and N2-point elements with an inter-element d2-spacing in a second direction that is excited by complex signal s(t)=2u(t)cos ωot u(t) that represents a low-frequency amplitude modulation u(t) with carrier frequency ωo and whose complex Fourier spectrum is S(ω′)=U(ω′+ωo)+U(ω′−ωo), wherein a time-varying far-field pressure for an arbitrary signal with complex Fourier spectrum S(f′) is given as:
where α and β are the direction cosines of a far-field observation point with respect to the 1-direction and 2-direction, respectively, ω12=ωr
According to a further embodiment of the disclosure, the spatial array further comprises a dual beamformer that generates a set of collinear first difference primary frequencies, wherein the first beamformer includes a set of beams of a multi-element TMA array and a second beamformer produces a wide-beam that encompasses all major TMA transmission lobes for deep depth underwater applications, wherein a source level of the wide beam is equal to a peak source level of the TMA array.
According to a further embodiment of the disclosure, the set of collinear first difference primary frequencies {Δfi} is defined as {Δfi}=|{WideBeam}−{TMAi}|abs={16 kHz}−{12.17 kHz, 13.00 kHz, 13.83 kHz, 14.68 kHz}={3.83 kHz, 3.0 kHz, 2.17 kHz, 1.34 kHz}.
According to a further embodiment of the disclosure, the collinear first difference frequencies include transmission spectra whose echoes are input to a spectrum analyzer.
According to a further embodiment of the disclosure, the collinear first difference frequencies for the parametric array maintain a high efficiency in the demodulation process, wherein the frequency down-ratio is 3-to-10.
According to a further embodiment of the disclosure, the method includes filtering each of the plurality of mixer output signals wherein one of a sum-frequency sideband or a difference frequency sideband is filtered from each of the plurality of mixer output signals.
According to a further embodiment of the disclosure, the le method includes complex weighting each of the plurality of mixer output signals.
According to a further embodiment of the disclosure, the bandpass filtering is one of a sum frequency band pass filtering or a difference frequency bandpass filtering:
According to a further embodiment of the disclosure, the different primary carrier frequencies of the plurality of different primary carrier frequencies are one of lower primary carrier frequencies or higher primary carrier frequencies.
According to another embodiment of the disclosure, there is provided an acoustic space-frequency diversity system that includes a tapped delay line includes a plurality of taps that generate a plurality of pulsed sampling signals, wherein each tap generates one of the plurality of pulsed sampling signals, each pulsed sampling signal includes a series of frequency harmonics, and successive signals of the plurality of pulsed sampling signals are separated by a predetermined delay time; a plurality of mixers, wherein each mixer of the plurality of mixers combines one of the plurality of pulsed sampling signals with an a time limited information signal to generate one of a plurality of mixer output signals: and a spatial array of transducer elements, where each transducer element of the spatial array of transducer elements receives one of the plurality of mixer output signals. The spatial array of transducer elements generates from the plurality of mixer output signals a plurality of simultaneous beams where each beam of the plurality of simultaneous beams is associated with one of a plurality of carrier frequencies, where the plurality of simultaneous beams are subject to design constraints that control a bearing-target doppler ambiguity, a uniform response in bearing, out-of-band spectra leakage interference, peak power level, and cross-beam reverberation upon receive.
According to a further embodiment of the disclosure, the spatial array of transducer elements includes 3-rectangular elements that generate simultaneous endosteal and periosteal bone healing beam patterns, wherein each rectangular element measures 25 mm×3.4 mm with an inter-element spacing of 3.5 mm.
According to a further embodiment of the disclosure, the system includes a set of bandpass filters, wherein each bandpass filter of the plurality of bandpass filters receives one of the plurality of mixer output signals and filters one of a sum-frequency side lobe or a difference frequency side lobe from the one of the plurality of mixer output signals.
Embodiments of the disclosure are directed to a unique acoustic space-frequency diversity system that includes a time modulated array that generates a spatial distribution of transmitting frequencies that permit simultaneous multiple beam steering, where each beam is associated with a different carrier frequency. Each transmit beam can be steered to a different spatial direction in either the vertical or horizontal plane for maximum acoustic coverage and signal-to-masking ratio. The multiple transmitted frequencies can be received with a single omnidirectional piezoelectric hydrophone whose output is processed with a high-resolution fast Fourier transform (FFT) receiver, where each spectral component corresponds to a unique spatial bearing. Thus, by coding the spatial acoustic field in frequency, the receiver architecture complexity is minimized and most of the cross-beam clutter or reverberation masking level in the receiver display output can be significantly reduced.
Embodiments of the disclosure refine the frequency encoding procedure in the TMA beamforming process of operational systems to address the issues given above.
First, the geometry of the linear, convex and planar arrays are presented in a series of signal representations that are clearly defined. Conducting these functional operations results in the general expression for the instantaneous spatial-temporal pressure field producing simultaneous beams as a function of frequency.
Second, in practical TMA operation, the spatial distribution of the beams will depend upon the constraints of finite pulselength, finite array bandwidth, element directivity pattern, and target doppler. These, in turn, will impact on the following engineering and operational considerations:
Interbeam interference will result in a nonuniform signal response on the maximum response axes (MRA's) of a preformed beam (PFB) receiver. For efficient detection capability at all bearings, the spatial distribution of the maximum response axis should be (almost) constant, i.e., the separation frequency (fs) should be sufficiently large so that the sidelobes of each sinc function do not seriously overlap the adjacent sinc function, as expressed in EQ. (6), below.
Bearing-doppler ambiguity is a consideration in those applications characterized by target and/or platform motion. Since normal TMA operation codes the spatial distribution of beams in frequency, if the frequency separation between beams is insufficient, a moving target at a given bearing may produce a doppler shifted echo frequency that lies within the frequency band assigned to an adjacent beam. Although the detection capability of sonar will not be meaningfully affected, the target will appear on the display at an erroneous bearing. This is referred to as a “bearing-doppler ambiguity” and must be eliminated to permit accurate target localization and tracking. Thus, in practice, the harmonic separation will have to be much greater than that indicated above to avoid bearing-doppler ambiguity due to the combined effects of target and sonar platform motion.
For a moving source, target, and receiver, the frequency of the echo pulse (fe) is given by (Horton),
f
e
=f
p[(c−vt)(c−vr)]/[(c−vs)(c−vt′)]
where fp the transmitted frequency at the source, (c) is the velocity of the sound wave moving away from the source, (c−vx) is the relative velocity of the sound wave removing source, (c−vt) is the relative velocity of the transmitted pulse at the target, (c−vt′) is the relative velocity of the sound wave reflected from the moving target, and (c−vr) is the relative velocity of the sound wave at the moving receiver.
The total maximum doppler (fD) incurred is determined by computing the range of (fe-fp) for the spread of source and receiver speeds and opening and closing target speeds. If it is assumed that vt=vt′ and vr=−vs, (vt, vr)/c1, and c=4920 feet/sec, then the doppler shift fD is
f
D
=|f
e
−f
p|max=0.7fp|vs−vt|max (in Hz).
Combining previous results, the separation frequency fs required to eliminate bearing-doppler ambiguity and provide reasonably uniform responses in bearing is
f
s
=f
D+6T′=0.7fp|vs−vt|max+6/(pulselength).
Spectra (out-of-band) interference leakage can be reduced to insignificant levels (less than 50 dB re MRA) by judicious selection of the separation or sampling frequency fs and information frequency fo and the number of beams, namely, that
2f≥(Pc−Po)fs
where Pc and Po are integers that denote the last and first harmonics, respectively, (Pc−Po) is the number of beams, (fs) is determined from the equation above, which includes the spreading due to source, target and receiver speeds.
It has been shown that interbeam interference and bearing-doppler ambiguity can be eliminated by increasing the sampling sufficiently to cover the total doppler spread, including both platform and target. However, for a given piezoceramic element design, as the sampling frequency increases, the number of allowable frequency diversity beams decreases. Also, the information frequency fo must increase in accordance with the equation above, to avoid out-of-band leakage interference.
Third, the transmit source level (SLLIN) on a maximum response axis (MRA) for a linear array with N elements with constant input electrical power will be reduced by the number of frequency coded beams, so that the transmit source level for the TMA is
SLTMA=SLLIN−10 log M=[7.16+10 log PeN+10 log Eff+DI]−10 log M
where the reference (for sonar operation) is to 1 microbar at a distance of 1 yard from the face of the transducer element, (Pe) is the electrical power input per element, (Eff) is the transmitting frequency, (DI) is the directivity index of the transducer array, (M) is the number of beams formed, and each element contributes to the source level simultaneously. In an embodiment, SL=20 log rms pressure on the MRA.
It is important to see how the number of beams impacts on the peak power rating of the power amplifier. For the case of M harmonics of peak amplitude (A), when the tonals are in phase and add coherently, the peak amplitude will be (MA) at the fundamental period (1/fs). This implies that if the rms power per tonal required to give a specified source level is Prms, then the total peak power required for (M) tonals is (2M2Prms). The design complexity and cost of the power amplifiers will increase with the number of tonals or TMA beams, i.e., whether it is a narrowband or wideband system.
According to an embodiment, simultaneous multiple beam frequency steering can be obtained by producing controlled frequency-varying phase shifts between adjacent transducer elements. A basic TMA acoustic system depicting the technique for a general array, in broad terms, can be considered to be comprised of the signal generator, which is an informational signal, the TMA beamformer, which includes a pulsed sampling signal, a tapped delay line, mixers, bandpass filters, and complex weightings, a power amplifier, considered normalized to 1 watt, and a transducer array.
For a linear array, the formulation of a instantaneous pressure field p(θ, t) is based on
Referring to
E
s(t)=ΣP
where j=√{square root over (−1)}, (fr) is a reference frequency, (fs) is the fundamental harmonic or separation frequency, and Po and Pc are integers denoting the first and last harmonics, respectively. The weighting coefficients, ap, are included for generality. The fundamental frequency is chosen to satisfy the requirements of total doppler spread, including target and platform motion, and the effects of finite signal pulselength. The reference frequency is chosen to facilitate subsequent filtering operations. The total number of harmonics is (Pc−Po+1). If the time is referenced to tap m+1, the sampling signal output by the mth-tap is given by
m
E
s(t)=ΣP
where (τ) is the delay between successive taps. Each mEs(t) is then mixed or time-modulated by a mixer 204 with a time-limited information signal, s(t) 203, of the form
s(t)=pT(t)cos(2πfo), (3)
where fo is the transmit frequency pT(t) is a rectangular envelope of pulselength 2T defined by:
whose Fourier transform is
The output of the mth-mixer is
Taking the Fourier transform of Em(t), the sum and difference spectra are
It may be seen that the effect of a finite pulse length is to introduce a sin(x)/x (sinc function) amplitude distribution for each harmonic. Considering transmitting in the sum-frequency band, the lobes of the first sin(x)/x term in the curly brackets establish the degree of interbeam interference. The lobes of the second term reflect the spectra leakage interference from outside the passband. By applying the condition, 2fo>(Pc+Po)fs, spectra leakage will be minimal.
After filtering by bandpass filters 205, which filter one of the lobes in the curly bracket term of EQ. (6), the resultant signal waveform may be weighted by the shading coefficient Wm 206 prior to driving the mth-array element and is given by
Ê
m(t)≈WmpT(t)Σpap{exp(j2π[(fr+ϵf0+pfs)t−m(fr+pfs)τ])}, (7)
where the index ϵ is +1 or −1 depending on whether the sum or difference frequency band, respectively, is retained. Note that the weighting by the complex shading coefficient Wm 206 is optional and can be eliminated in other embodiments. Exemplary, non-limiting complex shading coefficients have unit magnitude and 0 phase. The approximation is due to the time-limited nature of the information signal. In the monochromatic case, T→∞, and the approximation can be replaced by an equality. EQ. (7) may be further simplified by letting (frτ) be an integral number of cycles, i.e., frτ=q, where q is any integer and assuming T→∞,
Ê
m(t)=WmΣpa p{exp(j2π[(fr+ϵf0+pfs)t−mpfsτ])}. (8)
Continuing with
The attenuation will be less with more realizable filter characteristics. In actuality, the signal does not end abruptly at t=2T, but continues to decay, eventually reaching a steady-state of zero amplitude. With the property of reciprocity between conjugate Fourier domains, a broadband filter will produce a more rapid decay than a narrowband filter. Finally, a primary difference is clearly shown by comparing EQS. (1) and (8): each spectral component has a phase slope defined by the harmonic number. It will be shown below that when Êm(t) is applied to a TMA planar array of spatial elements, every harmonic number—and thus, each spectral component—corresponds to a particular beam steering angle.
If each signal Êm(t) is applied to the mth-transducer element of the linear array 207, the time-varying sound pressure at an arbitrary point in the far-field is the vector sum of the signals {Êm(t)}, considering relative propagation time delays, The far-field TMA sound pressure p(θ, t) in the direction θ, where θ is the angle of the line to the far-field observation point 208 with respect to an array normal 209, may then be expressed as
p(θ,t)=ΣmÊ(t−mτ), (9)
referred to the m=1 element where τ=−d sin(θ)/c and c is the velocity of sound.
Carrying out the summation utilizing EQ. (8), the output of the linear multi-element transducer array 207 is
where it can be seen that each beam in the summation is associated with one of the carrier frequencies.
To improve the visualization and understanding of the TMA process, the above derivation of the beam pattern distribution expressed in EQ. (10) assumes a long signal pulse length to approximate the monochromatic case and negligible spectra leakage.
For an information signal s(t) with complex Fourier spectrum S(f′), the far-field time-varying pressure for a monochromatic signal given in equation (10) is weighted by the spectrum to give:
where the total delay time Nτ is chosen to be equal to the sampling period, Nτ=1/fs.
In a variation of the linear array according to an embodiment, the TMA beamformer for the linear array of N-equi-spaced transducer elements depicted in
The sum of EQ. (10) may be recognized as the beam pattern for a linear array of frequency (fr+ϵfo+pfs) pointing in the direction
θp=sin−1[2πpfsτ]/(kpd)] (12)
where θp is a pointing angle, which is a direction of maximum response for a particular beam associated with a harmonic number, (kp) is the harmonic dependent wave-number,
k
p=2π/λp=2π(fr+ϵfo+pfs)/c. (13)
By choosing the total delay time equal to the sampling period, Nτ=1/fs, the pointing angle θp is a function of the harmonic parameters (p) and (fs), the center frequency (fr+ϵfo), and the array parameters (N) and (d); EQ. (12) simplifies to
θp=sin−1[2πp/(Nkpd)]. (14)
For a given array geometry and fixed values of (fr, fo, fs), the range of (p) allowable in a TMA design according to an embodiment are those which satisfy the inequality,
[2πp/(Nkpd)]abs≤1. (15)
According to an embodiment, the number of acceptable beams determines the spatial coverage and the required bandwidth of the transmitting system. Due to practical constraints of transducer bandwidth and the operational requirement that the harmonic beams have uniform beamwidth and sidelobe structure, the number of harmonics is TMA beamforming will be less than that permitted by EQ. (15).
EQ. (15) expresses how the acoustic (or E/M) system parameters define the directions to which the beams are simultaneously steered. As the number of elements or element spacing increases, the MRAs of the harmonic beams will move closer to one another. For a fixed element spacing, increasing the center frequency (zeroth harmonic) will result in a narrower 3 dB beamwidth. This implies that as the separation frequency increases, the beamwidths will become narrower for positive harmonics and wider for negative harmonics, the latter accompanied with steering angles that diverge more widely from the zeroth harmonic. For separation frequencies much smaller than the center frequency, the harmonic wave-number will be practically constant, producing a symmetric distribution. If [2πp/(Nkpd)]abs1, then the beam steering angles will be multiples of [2πp/(Nkpd)]abs. If it is desired to steer a particular harmonic in a given direction, say θp*, it can be done by defining the delay time τp* such that
τp*=kpd sin θp*/(2πpfs). (16)
where fP=(f′+fr+ϵfo+pfs). The term in the square brackets is the conventional beam pattern steered to a direction defined by the harmonic number of the sampling signal. Note that the direction of each component beam cannot be determined directly, since the quantity in the exponent is not in general zero for all (m) when (θ) corresponds to the MRA of a particular beam. Also, each harmonic represents a beam smeared out slightly due to the finite bandwidth of the signal s(t). As for linear arrays, this, as well as interbeam interference, is minimized for signals having long pulselengths.
According to an embodiment, additional phase weightings can be introduced to phase each element back-to-a-line or to a circular arc. This will act as a spatial filter to maximize the signal-to-noise ratio. Let this phasing circle 312 pass through the apex, A 313 of the circular transducer array 307, and be perpendicular to the symmetry axis. The phase weighting will be:
exp[−j2π(fp/c)[R(1−cos α)−ρ(1−cos β)], (18)
where (α) is the angular location of the mth-element with respect to the symmetry axis, (ρ) is the radius of the phasing circle, and β=sin−1(R/ρ)sin α. Note that (ρ)(R), the radius of the circular transducer array, so that the center 310 of the phasing circle is behind the tapped delay line 302. The circular TMA formulation is completely characterized by EQS. (17) and (18).
Following the method of analyzing the linear array, the pulse sampling signal Es(t) is again a finite harmonic series input to the tapped delay line, similar to that in EQ. (1),
E
s
(t)=ΣP
where the subscripts 1, 2 refer to either the first or second tapped delay line, and the output at the m1-tap in the D1 direction is;
m
1
E
s
(t)=exp(j2πfr
For an information signal 303 of the form s(t)=2u(t)cos ωot, where u(t) is the low-frequency amplitude modulation, the complex Fourier spectrum can be expressed as S(ω′)=U(ω′+ωo)+U(ω′−ωo). Therefore, the output of the m1-mixer is
where the index, ϵ1, is +1 or −1 depending on whether the sum or difference frequency, respectively, is retained by the bandpass filter. The m1-mixer output, Êm
m
2
E
s
(t)=exp(j2πfr
The resultant signal is filtered again prior to driving the m1,2 array element, and is designated E′m
If each signal E′m
where α and β are the direction cosines of the far-field observation point with respect to the 1-direction and 2-direction, respectively, and ω12=ωr
cos α=(2πp1/N1)(c/d1ω12),
cos β=(2πp2/N2)(c/d2ω12). (24)
Each harmonic represents a beam smeared out slightly due to the finite bandwidth of s(t). This, as well as interbeam interference, is minimized for signals having long pulselengths.
The linear, convex, and planar TMAs described above require a special receiver to process the echo returns. This is because space has now been coded into frequency and thus requires a fine-frequency detection and tracking receiver.
There are a number of applications of TMA technology that have not been considered to date (2020), such as medical therapeutic ultrasound, acoustic microscopy, and underwater mining, exploration, and communications.
The TMA approach can promote Bone Growth Stimulation (BGS) for simultaneous endosteal and periosteal bone fracture healing which would require two different spatial beams with different steering angles as shown in
A TMA approach according to an embodiment can also be used for a Scanning Acoustic Microscope (SAM). A SAM device can provide unique information about the absorption, elastic properties, and density of tissue cells, which can improve the visualization and clinical assessment of consistent patterns of cellular malignancy.
Acoustical bio-physics estimates a maximum SAM frequency of about 4-5 GHz, producing a wavelength λ of 347 nm. However, an issue with operating at this frequency is that the usual aluminum motor-driven spatial-positional-stepping system is fabricated by an aluminum extrusion process that produces a positional error of about 1 μm (≈1 GHz). A TMA according to an embodiment can eliminate this effect by electronically producing the acoustic beams to cover the desired sector.
A TMA approach according to an embodiment can also be used for underwater communications and oceanographic mining and exploration. Accurate spatial communications in several specific bearings requires minimal sidelobe interference while mining and exploration requires special consideration of beams propagating to mineral beds at different ocean depths and bearings correlating to frequency dependent attenuation. For these applications the term bearing refers to either azimuthal or D/E (depth/elevation).
The same 9-element linear array may include a second beamformer that utilizes complex element weightings to produce the wide-beam shown in
According to an embodiment, for the parametric array in
A TMA approach according to an embodiment can be characterized by at least six (6) unique features for obtaining space-frequency , diversity beamforming for various medical applications, namely:
From the foregoing, it will be appreciated by those skilled in the art that embodiments of the present disclosure can provide an effective method and apparatus that overcomes many of the limitations associated with the mechanical stimulation of biological materials.
A TMA approach according to an embodiment can be characterized by at least eight (8) unique features for obtaining space-frequency diversity beamforming for underwater sonar applications, namely:
It will also be readily appreciated by one with ordinary skill in the art use a method and apparatus according to embodiments of the disclosure in a variety of sonar applications, such as multi-mode echo-ranging, the detection of deep moored mines, and submarine active sonar. It may also provide a multi-beam formation capability for circular and planar arrays.
Although certain exemplary embodiments of the present disclosure have been specifically described herein, it will be apparent to those skilled in the art to which embodiments of the disclosure pertain that variations and modifications of the various embodiments shown and described herein may be made without departing from the spirit and scope of this disclosure.
This application is a National Phase of PCT application PCT/US2020/062877, filed on Dec. 2, 2020, in the U.S. Receiving Office, the contents of which are herein incorporated by reference in their entirety.
Filing Document | Filing Date | Country | Kind |
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PCT/US2020/062877 | 12/2/2020 | WO |