Beam phase modulation for improved synthetic aperture detection and estimation

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First Claim
1. A synthetic aperture system comprising:
 array elements (110) configured to transmit energy and receive energy;
a transmitter coupled with said array elements (110) wherein said transmitter comprisesa second transmit multiplier (113) coupled with said array elements (110);
a transmit complex factor (115) coupled with said second transmit multiplier (113);
a first transmit multiplier (112) coupled with said second transmit multiplier (113);
a transmit complex shading weight (114) coupled with said first transmit multiplier (112);
a signal generator (111) comprising an output that is coupled with said first transmit multiplier (112) wherein said output is multiplied by said transmit complex shading weight (114) with said first transmit multiplier (112) which is further multiplied by said transmit complex factor (115) with said second transmit multiplier (113) which results in said transmit energy at said array elements (110);
a receiver coupled with said array elements (110) wherein said receiver comprisesa first receive multiplier (117) coupled with said array elements (110);
a receive complex factor (115) coupled with said first receive multiplier (117);
a second receive multiplier (118) coupled with said first receive multiplier (117);
a receive complex shading weight (116) coupled with said second receive multiplier (118);
a sum operator (119) coupled with said second receive multiplier (118) wherein said receive energy from said array elements (110) is multiplied by said receive complex factor (115) with said first receive multiplier (117) which is further multiplied by said receive complex shading weight (116) with said second receive multiplier (118) and summed with said sum operator (119);
wherein said transmit complex shading weight (114) and said receive complex shading weight (116) are configured to nonlinear phase variation as an observer moves across the transmit energy in one or more direction and wherein said nonlinear phase variation is independent of element phase shifts utilized to steer a beam and independent of phase corrections necessitated by a nonhomogeneous propagation environment.
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Abstract
Phase modulated beam patterns are substituted for the constantphase versions that have been used in prior synthetic aperture systems. Relative movement between a radar/sonar/ultrasound platform and a point target causes a sequence of echoes from the point target to be phase and amplitude modulated by the beam pattern, as well as by the usual quadratic phase variation caused by range changes. Azimuth, range rate, and azimuth rate estimation, as well as detection in clutter, are substantially improved by appropriate beam pattern phase modulation, which is applied to the transmitter and/or receiver beam patterns. Phase modulated beam patterns are synthesized with array element weighting functions that are designed for high ambiguity function peaktosidelobe level, reduction of unwanted ambiguity ridge lines, and adequate spatial sampling. Two dimensional beam pattern phase modulation is useful when the relative motion between a transmitreceive array and multiple targets has both azimuth and elevation components.
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5 Claims
 1. A synthetic aperture system comprising:
array elements (110) configured to transmit energy and receive energy; a transmitter coupled with said array elements (110) wherein said transmitter comprises a second transmit multiplier (113) coupled with said array elements (110); a transmit complex factor (115) coupled with said second transmit multiplier (113); a first transmit multiplier (112) coupled with said second transmit multiplier (113); a transmit complex shading weight (114) coupled with said first transmit multiplier (112); a signal generator (111) comprising an output that is coupled with said first transmit multiplier (112) wherein said output is multiplied by said transmit complex shading weight (114) with said first transmit multiplier (112) which is further multiplied by said transmit complex factor (115) with said second transmit multiplier (113) which results in said transmit energy at said array elements (110); a receiver coupled with said array elements (110) wherein said receiver comprises a first receive multiplier (117) coupled with said array elements (110); a receive complex factor (115) coupled with said first receive multiplier (117); a second receive multiplier (118) coupled with said first receive multiplier (117); a receive complex shading weight (116) coupled with said second receive multiplier (118); a sum operator (119) coupled with said second receive multiplier (118) wherein said receive energy from said array elements (110) is multiplied by said receive complex factor (115) with said first receive multiplier (117) which is further multiplied by said receive complex shading weight (116) with said second receive multiplier (118) and summed with said sum operator (119); wherein said transmit complex shading weight (114) and said receive complex shading weight (116) are configured to nonlinear phase variation as an observer moves across the transmit energy in one or more direction and wherein said nonlinear phase variation is independent of element phase shifts utilized to steer a beam and independent of phase corrections necessitated by a nonhomogeneous propagation environment.  View Dependent Claims (2, 3, 4, 5)
1 Specification
Research for this invention was supported by the U.S. Government via STTR Phase II Contract N6833506C0044. The patent rights clause in that contract is Federal Acquisition Regulation (FAR) clause 52.22711, “Patent Rights—Retention by the Contractor (Short Form).” This clause states that the contractor (Chirp Corporation, which employs the inventor) may retain the entire right, title, and interest throughout the world to each subject invention. However, the Federal Government shall have a nonexclusive, nontransferable, irrevocable, paidup license to practice or have practiced for or on behalf of the United States the subject invention throughout the world.
Not Applicable
Not Applicable
The purpose of the invention is to improve stripmap synthetic aperture radar/sonar (SAR/SAS) and inverse synthetic aperture radar/sonar/ultrasound (ISAR/ISAS) via better clutter rejection, velocity parameter estimation (range rate and azimuth rate), and azimuth position estimation. The invention also is applicable to target movement in three dimensions relative to a radar/sonar/ultrasound array. In this case, the invention improves estimates of range rate, azimuth rate, elevation rate, azimuth position, and elevation position. Applications are to maritime and ground surveillance SAR containing moving objects, missile defense radar (ISAR), sonar mine hunting (SAS), and noninvasive Doppler ultrasound (ISAS) for fluid velocity measurement in two dimensions (parallel and perpendicular to the vessel).
In synthetic aperture processors, echoes are coherently pulse compressed (replica correlated or matched filtered) on reception and used to form inphase and quadrature components. These components specify the magnitude and phase of a complexvalued echo range sample. A sequence of such components from multiple signalecho pairs comprise a phase history corresponding to the range variation (measured in wavelengths) associated with relative motion between the radar/sonar platform and each point target.
If point targets at different azimuth locations do not move except for relative platform motion, then their phase histories are azimuthdisplaced versions of a predictable phase history, and they can be separated by azimuth compression if the phase history bandwidth B is sufficiently large (C. E. Cook and M. Bernfeld, Radar Signals, Academic Press, New York, 1967). If various point targets have different range rates, however, they may not be separable even if B is large. This lack of resolution can occur if range rate and azimuth displacement can compensate for one another. For example, range rate causes a displacement in frequency. If a phase history lies on a long tilted line in the timefrequency plane, a frequency displacement can be compensated by a time shift. A phase history time shift is equivalent to an azimuth shift. A tilted line in the timefrequency plane corresponds to linear frequency modulation (linear FM) and quadratic phase modulation. Quadratically phase modulated (linear FM) phase histories experience degraded rangerate/azimuth resolution with ambiguous receiver outputs, such that objects with nonzero range rate appear at the wrong azimuth.
Azimuth compression often utilizes frequency domain matched filtering to correlate the data phase history with reference phase histories. An unknown range rate causes a Doppler shift, which can be hypothesized by a frequency domain shift of a predicted (reference) phase history. Predicted phase histories are correlated with the data phase history for estimation/detection. Range rate estimation accuracy and resolution capability is proportional to the duration T of the phase histories in the absence of ambiguities and error coupling, such as those that occur with linear FM (Cook and Bernfeld, op. cit.).
Azimuth rate in the direction of assumed relative platform motion increases the rate at which the beam pattern sweeps across a target, and causes time compression of phase histories; azimuth rate in the opposite direction causes time dilation. Time scaling (compression/dilation) can be included as an additional parameter hypothesis in the azimuth compression process. The effect of nonzero range rate on a wideband radar/sonar waveform also is represented by time scaling. Estimation accuracy of compression/dilation increases with waveform timebandwidth product (R. A. Altes and E. L. Titlebaum, “Bat signals as optimally Doppler tolerant waveforms,” J. Acous. Soc. Am. Vol. 48, 1970, pp. 10141020). Azimuth rate estimation accuracy thus is proportional to the timebandwidth product (TB) of the phase histories, unless ambiguity effects limit estimation and resolution capability.
For the smooth, low timebandwidth product beam patterns that comprise prior art, the phase history caused by relative target/platform motion in broadside stripmap SAR is closely approximated by a quadratic phase function, corresponding to linear FM. The azimuth compression process is then subject to the well known rangeDoppler error coupling phenomenon for linear FM, such that the receiver response to ambiguous pairs of erroneous azimuth displacements and range rates is nearly as large as the receiver response to the correctly hypothesized azimuth and range rate. This error coupling is manifested as a ridge in the phase history azimuth/rangerate ambiguity function, and it severely degrades estimation/detection performance in a cluttered environment relative to a receiver with an ideal (thumbtack) ambiguity function. Linear FM also is relatively insensitive to azimuth rate (compression/dilation), compared to other waveforms or phase histories with the same TB product (R. A. Altes, “Optimum waveforms for sonar velocity discrimination,” Proc. of the IEEE vol. 39, 1971, pp. 16151617).
In the absence of error coupling, azimuth resolution improves as SAR/SAS beam width is increased, since phase history bandwidth is increased. Increased beam width also increases the phase history timebandwidth product, resulting in improved azimuth rate resolution. Increased beam width and phase history duration, however, cause extension of the tilted line representation of linear FM in the timefrequency plane, with consequent extension and flattening of the linear FM ambiguity function ridge line. These effects signify an increase in the effect of unknown range rate on azimuth estimation error. A tradeoff thus occurs, such that beam widening improves azimuth rate estimation but degrades azimuth and range rate estimation because of linear FM error coupling. Target detection in Dopplerdistributed clutter also tends to be degraded when the FM ridge line is extended via beam widening. Synthetic aperture processors that use beams with no phase modulation are geometrically constrained to operate with quadratic phase histories (linear FM) for azimuth compression, despite the drawbacks and tradeoffs associated with such modulation. This constrained operation constitutes the prior art.
The invention is to replace a conventional beam pattern (without nonlinear phase modulation) with a beam pattern that has nonlinear phase modulation or phase coding. Such a beam pattern is obtained by phase modulating the aperture shading function, which broadens the beam as well as imparting the desired phase modulation to the beam pattern. As the beam is swept past a point target in a SAR/SAS application (or a point target moves through the beam in ISAR/ISAS), beam coding/modulation adds beaminduced phase variation to the quadratic phase that is associated with range variation. The added beaminduced phase is controlled by the system designer rather than by geometry.
An appropriate beam phase modulation function removes the constraints that have been imposed by linear FM phase histories. In a broadside stripmap SAR, appropriate beam phase modulation dramatically reduces rangerate/azimuth coupling error, greatly improves resolution and detection/estimation performance in clutter, significantly reduces estimation errors for joint estimation of azimuth, range rate, and azimuth rate, and eliminates the tradeoffs associated with conventional SAR beam width variation when phase histories have quadratic phase variation. For three dimensional operation, similar advantages apply to estimates of azimuth, elevation, azimuth rate, elevation rate, and range rate, provided that a two dimensional beam pattern is coded/modulated in azimuth and elevation so as to reduce ambiguities.
Applications include discrimination of small objects from sea clutter in maritime stripmap SAR and discrimination of moving vehicles from stationary roadside objects in ground mapping stripmap SAR. Comparison of SAR ground maps obtained at two different times can be used to identify new roadside objects. The invention enables accurate, noninvasive ISAS measurement of range, azimuth, range rate, and azimuth rate, thus creating informative representations of fluid flow parallel and orthogonal to a vessel'"'"'s length, as a function of distance from the vessel wall.
The invention improves synthetic aperture performance by appropriate nonlinear phase modulation or phase coding of the beam patterns that are used for transmission and/or reception. Beam pattern phase modulation is accomplished by nonlinear phase modulation of the shading (element weighting) function in a phased array. Prior art uses a smooth, symmetric array shading function with no phase modulation aside from element phase shifts that are applied for beam steering. The invention can use a conventional shading function (as in prior art) as the magnitude of a complexvalued array weighting function that incorporates nonlinear phase modulation.
Nonlinear phase modulation broadens the beam, but does not necessarily reduce the ratio of peak beam amplitude to the largest grating lobe in the broadened beam pattern. In fact, an appropriate phase modulation function causes a significant increase in the beam peaktosidelobe ratio defined by the largest beam pattern amplitude divided by the maximum grating lobe amplitude. The energy within the main lobe of the beam divided by the total beam energy is unaffected by appropriate nonlinear phase modulation. This energy ratio is relevant to SAR performance (R. O. Harger, Synthetic Aperture Radar Systems, Academic Press, New York, 1970).
Relative motion of platform and target causes the beam pattern to be swept across the target. The amplitude variation of the resulting phase history function is determined by the beam pattern magnitude. For a broadside beam with no phase modulation (prior art), the phase variation of the phase history function depends strictly on range changes (measured in wavelengths) over multiple pulseecho pairs. For broadside stripmap SAR (and Doppler ultrasound ISAS with the beam orthogonal to the direction of fluid motion), the phase histories exhibit quadratic phase modulation or linear frequency modulation (linear FM). Linear FM is associated with undesirable rangerate/azimuth ambiguities. Azimuth rate measurements also are relatively inaccurate.
For a broadside beam with nonlinear phase coding/modulation, relative motion of platform and target again causes the beam to be swept across the target, but the phase history depends upon amplitude and phase variations of the beam pattern as well as upon range changes. Beam pattern phase variation can be designed to suppress undesirable ambiguities, improve the accuracy of range rate and azimuth rate measurements, and improve signaltoclutter ratio. All the advantages of azimuth phase history compression are retained, provided that appropriate reference functions are used in the receiver.
Aside from ambiguity suppression, another advantage of beam coding/modulation is that a comparatively large phased array antenna can be used to produce a wide beam pattern by phase modulating the array element weighting (shading) function. For targets with known range rate, wide synthetic aperture beam patterns are desirable for broadside stripmaps (and for ISAS with a beam that is orthogonal to the motion vector of the target environment) because the duration, bandwidth, and timebandwidth product of an observed phase history is increased, yielding better resolution in azimuth, range rate, and azimuth rate. For targets/clutter with unknown range rates and with no beam phase modulation, beam widening is counterproductive because the ridge length of the linear FM azimuth/rangerate ambiguity function is increased, signifying worse azimuth/rangerate estimation performance than with a narrow beam. This problem is avoided by using appropriate beam phase modulation. Appropriate phase modulation/coding of a phased array shading function reduces the error of azimuth, range rate, and azimuth rate estimates by beam widening as well as by ambiguity suppression.
An alternative method for widening the beam pattern is to reduce aperture/array size in the direction of relative motion between the array and the target environment. Array size reduction, however, reduces the efficiency of a given phased array, and linear FM phase histories with their undesirable ambiguities are still present because no phase modulation is imposed by the beam pattern. For a large phased array, another alternative is to use a narrow spotlight (without nonlinear beam phase modulation), and to observe the same area over multiple pulseecho pairs via beam steering (W. G. Carrara, R. S. Goodman, and R. M. Majewski, Spotlight Synthetic Aperture Radar, Artech House, Norwood, Mass., 1995). Beam coding/modulation, however, provides greater area coverage rate than a spotlight, while suppressing azimuth/rangerate ambiguities.
For rangeazimuth mapping in broadside stripmap SAR, nonlinear phase modulation is applied to a phased array element weighting (aperture shading) function in the azimuth direction. This modulation affects the azimuth width and phase variation of the beam pattern, but does not necessarily affect elevation variation. For three dimensional mapping (e.g., for ISAR monitoring of multiple targets with different crossrange trajectories), nonlinear phase modulation is applied to the phased array in two dimensions to induce different azimuth and elevation dependent phase variations of the beam pattern. The azimuth and elevation phase modulation functions are designed to reduce ambiguities (error coupling) between estimates of azimuth rate, elevation rate, range rate, azimuth position, and elevation position.
The invention is to replace beam patterns with no phase variation in synthetic aperture systems (prior art) with beam patterns that have appropriate nonlinear phase modulation (or phase coding). Appropriate phase modulation/coding improves estimation/detection performance for broadside stripmap synthetic aperture radar (SAR) and for other synthetic aperture processors (squint stripmap SAR, SAS, ISAR, and ISAS). The ISAS application includes coherent processing of multiple echoes in Doppler ultrasound. Phase modulated beam patterns can provide significant improvements in estimation/detection performance, as expressed by ambiguity function properties, lower bounds on estimation errors, and signaltoclutter ratio.
Appropriate phase coding/modulation of the combined transmitreceive beam pattern is accomplished by coding/modulation of the phase of an array shading (element weighting) function for transmit and/or receive arrays. For situations where the motion between the target environment and the array platform involves significant changes in elevation as well as azimuth, beam pattern phase variations are applied in both azimuth and elevation, and are chosen to reduce confusion between estimates of azimuth, elevation, azimuth rate, elevation rate, and range rate.
Phase histories are formed from inphase and quadrature (I,Q) samples at the output of a coherent signalecho correlator or matched filter for each echo in a sequence of pulseecho pairs.
For suitable beam coding/modulation, the receiver becomes much less ambiguous with respect to joint range rate and azimuth estimates, and much more sensitive to azimuth rate. Because of this increased sensitivity, the receiver must generate extra range rate and azimuth rate parameter hypotheses in order to assure that all possible targets can be detected. The payoff is better resolution of desired objects from clutter (with correspondingly better detection performance) and more accurate estimation of position and velocity parameters.
For appropriate beam phase coding in elevation as well as azimuth, accurate simultaneous estimation of range, range rate, azimuth, azimuth rate, elevation, and elevation rate becomes possible. Beam coding in elevation generally is not applicable to broadside stripmap SAR, but is important for applications in which targets can move in elevation as well as azimuth relative to the radar/sonar platform.
For nonzero azimuth rate (target motion parallel to the path 105 in
For estimation of azimuth (phase history time shift), lower bounds on resolution bin size and the standard deviation of the time shift estimate are inversely proportional to the bandwidth of the observed phase history. For range rate (phase history frequency shift) estimation, lower bounds on resolution bin size and the standard deviation of the frequency shift estimate are inversely proportional to phase history time width (duration). For cross range rate (compression/dilation) estimation, the lower bounds are inversely proportional to the timebandwidth product of the observed phase history (Cook and Bernfeld, op. cit.; Altes and Titlebaum, op. cit.; Altes, op. cit.).
Nonlinear phase modulation of an array shading function broadens the beam width, and a point target that moves across the beam along path 105 in
For a given complex beam pattern, broadside stripmap phase histories can be predicted from hypothesized azimuth, azimuthrate, range, and rangerate parameters. These predictions can be tested with an estimation/detection process that correlates predicted (reference) phase histories with the data phase history. For multiple point targets at different azimuths, the correlation process is conveniently implemented with a frequency domain matched filter: The Fourier transform of the data phase history is multiplied by the conjugate of the Fourier transform of the hypothesized phase history, and the resulting product is inverse Fourier transformed.
The receiver response to hypothesized azimuth, azimuthrate, and rangerate parameters can be represented by a generalized ambiguity function that depends on the three parameters. The central peak amplitude of the ambiguity function represents the receiver response corresponding to correct parameter hypotheses. Other ambiguity function samples correspond to various combinations of the hypothesized parameters. Sidelobes are local ambiguity function maxima that are not at the central peak. A ridge sometimes is formed by a set of ambiguous parameter combinations that lie on a line through the peak. For energy normalized phase histories, an ideal ambiguity function has unit amplitude at the central peak and low amplitude elsewhere (low sidelobe and ridge levels).
Hann function (halfwave, cosinesquared) phase modulation of an array shading function with Hann function amplitude imparts high timebandwidth product phase histories to point targets in broadside stripmap SAR. These phase histories result in a sharp central peak and uniformly low sidelobe levels of the azimuth/rangerate/azimuthrate ambiguity function, relative to no phase modulation and to other phase modulation functions that have been applied to the Hann array shading function. For example, a Hann shading function magnitude that is modulated by a hat function phase variation (linear decrease in phase from the array center to the edges) is unacceptable because the center of the resulting beam pattern is completely suppressed, yielding poor ambiguity properties despite a large timebandwidth product. Conversely, Hann shading function magnitude that is phase modulated by a parabolic phase function (quadratic decrease in phase from the array center to the edges) is unacceptable because the beam pattern center is accentuated; the beam edges are attenuated by a smooth, Gaussianshaped function that reduces the timebandwidth product of phase histories and provides relatively poor ridge suppression of the ambiguity function in the azimuth/rangerate plane.
Relevant ambiguity functions correspond to combined transmitreceived beam patterns. The transmission beam pattern (radiation pattern) is obtained by applying samples of the complexvalued weighting (shading) function p_{trans}(x,y) to the transmitter phased array elements, along with phase shifts for beam steering. This complex weighting process is illustrated in
During transmission, the shading and beam steering operations at each element are implemented by two multiplications, performed respectively by multipliers 112 and 113 in
During reception, the beam steering and shading operations at each element are again represented by two multiplications, performed respectively with two multipliers 117 and 118 in
For a planar array with element m,n located at x_{m},y_{n}, the complexvalued radiation pattern at a point on a sphere of radius r_{0 }with the center point of the sphere at the array center is
where θ and φ are shown in
Δr(x_{m},y_{n})=[(x_{m}−x_{0})^{2}+(y_{n}−y_{0})^{2}+z_{0}^{2}]^{1/2}−r_{0} (2)
For the coordinate system in
x_{0}=r_{0 }sin θ cos φ,y_{0}=r_{0 }sin θ sin φ,z_{0}=r_{0 }cos θ. (3)
The transmission array weighting function p_{trans}(x_{m},y_{n}) in Equation (1) is denoted by 114 in
If the same array weighting function and steering vector are applied during both transmission and reception, then
p_{rec}(x,y)=p_{trans}(x,y) (4)
where p_{rec}(x,y) is denoted by 116 in
P_{TR}(θ,φ)=[P_{trans}(θ,φ)]^{2}. (5)
When Equation (4) is true, the transmit/receive beam pattern is obtained from the radiation pattern in Equation (1) by squaring the radiation pattern magnitude and doubling the radiation pattern phase shift at each point where the beam pattern is evaluated.
For the SAR embodiment described here, the twodimensional transmission weighting function 114 is separable:
p_{trans}(x,y)=p_{trans,az}(x)p_{trans,el}(y). (6)
p_{trans,az}(x)=cos^{2}[πx/(2dM)]exp{jγ cos^{2}[πx/(2dM)]},−dM≦x≦dM. (7)
The magnitude of p_{trans,az}(x) is a Hann weighting defined over 2M+1 azimuth (x) locations in the phased array 109 with uniform element spacing d. Since the elements at x=±dM have zero weight, they are not utilized; the number of functional element locations in the azimuth dimension of the phased array is 2M−1. The element spacing d should be less than or equal to onehalf wavelength (λ/2) for adequate spatial sampling. For a shading function that corresponds to prior art, the modulation factor γ equals zero, and the shading function in Equation (7) is realvalued.
p_{trans,el}(y)=cos^{2}[πy/(2dN)],−dN≦y≦dN, (8)
and
For the SAR embodiment presented here, the same array element weights (and the same array) are used for reception weights 116 as well as for transmission weights 114 in
The transmit/receive beam pattern as a function of azimuth for γ=0 is illustrated in
When nonlinear phase modulation is applied to the array shading function in the azimuth direction, an example of the resulting beam pattern as a function of azimuth is illustrated in
Ambiguity functions are obtained from the beam patterns and from the geometry in
 R_{0}≡the smallest range between the platform (transmitreceive array location) and the target, which occurs at time t=t_{0 }and at broadside azimuth (θ=0 φ=0)
 v_{paz}≡platform velocity (relative motion between transmit/receive array and target environment) along the path 105 shown in
FIGS. 1 and 2  v_{tr}≡range rate, the target velocity component (measured relative to the platform) that is orthogonal to the path 105 in
FIGS. 1 and 2 .  v_{taz}≡target azimuth rate that is not included in the platform velocity
 t_{0}≡time when the target is at broadside azimuth; estimation of target azimuth is equivalent to estimation of t_{0 }
 t≡time measured relative to the time when the target is at broadside azimuth; t−t_{0}≦T_{obs}/2
 T_{obs}≡phase history observation time≈B_{10dB}R_{0}/v_{paz }
 B_{10dB}≡beam width [radians] determined by the interval between the points where the beam pattern drops to onetenth of its maximum value.
The timevarying range between a point target and the center of the transmitreceive array is
Assuming that v_{tr}(t−t_{0})≦v_{tr}T_{obs}/2<<R_{0},
R(tt_{0},v_{tr},v_{taz})≅R_{0}+v_{tr}(t−t_{0})+[(v_{paz}+v_{az})^{2}/2R_{0}](t−t_{0}) (10)
For a signal center frequency with wavelength λ, the range dependent phase shift for twoway propagation is
φ_{range}(tt_{0},v_{tr},v_{taz})=(4π/λ)R(tt_{0},v_{r},v_{taz}). (11)
This phase shift function has a linear component (4π/λ)v_{tr}(t−t_{0}) corresponding to a frequency shift of the corresponding phase history, and a quadratic component (4π/λ)[(v_{paz}+v_{taz})^{2}/(2R_{0})](t−t_{0})^{2 }that depends on platform velocity and crossrange velocity.
If v_{taz }is in the same direction as v_{paz }(positive v_{taz}), the phase history is compressed in time, with a corresponding increase in the linear FM chirp rate associated with the quadratic phase variation. Conversely, if v_{taz }is in the opposite direction from v_{paz }(negative v_{taz}), the phase history is dilated in time, with a corresponding decrease in the linear FM chirp rate associated with the quadratic phase variation.
The timevarying azimuth angle between a point target and the center of the transmitreceive array is
Again assuming that v_{tr}(t−t_{0})≦v_{tr}T_{obs}/2<<R_{0},
θ(tt_{0},v_{tr},v_{azz})≈tan^{−1}{[(v_{paz}+v_{taz})/R_{0}]t}. (13)
For a combined transmitreceive beam pattern P_{TR}(θ,φ), the beaminduced timedependent echo variation is P_{TR}[θ(tt_{0},v_{tr},v_{taz}), φ], where θ(tt_{0},v_{tr},v_{taz})], is given by Equation (13). The beaminduced phase modulation is
φ_{beam}(tt_{0},v_{tr},v_{taz})=tan^{−1}{imag{P_{TR}[θ(tt_{0},v_{tr},v_{taz}),φ]}/real{P_{TR}[θ(tt_{0},v_{tr},v_{taz}),φ]}} (15)
and the beaminduced amplitude modulation is P_{TR}[θ(tt_{0},v_{tr},v_{taz}),φ].
The complete phase history function (including amplitude variation) for the point target is
h_{az}(tt_{0},v_{tr},v_{taz})=P_{TR}[θ(tt_{0},v_{tr},v_{taz}),φ]exp{j[φ_{rang}(tt_{0},v_{tr},v_{taz})+φ_{beam}(tt_{0},v_{tr},v_{taz})]}. (16)
Broadside stripmap SAR ambiguity functions are obtained by correlation of an energy normalized data phase history h_{az}(t0,0,0) with a sequence of energy normalized reference (hypothesized) phase histories h_{az}(tt_{0},v_{tr},v_{taz}) for different to values (azimuth≡v_{paz}t_{0}), range rates v_{tr }and target azimuth rates v_{taz}:
A frequency domain implementation of the inner product in Equation (17) takes advantage of the fact that v_{tr }is associated with a frequency shift, and that different t_{0 }values are easily hypothesized by computing the inverse Fourier transform of the frequency domain product of the Fourier transform of the data phase history and the conjugated Fourier transform of a reference (hypothesized) phase history.
The generalized ambiguity function in Equation (17) represents the response of an estimator/detector receiver that is optimum for additive white, Gaussian noise, when the phase histories for specified t_{0}, v_{tr}, v_{taz }are known except for a constant phase shift, and the additive noise power is zero. The ambiguity function can be constructed from the delaydependent outputs of a bank of matched filters, where each filter impulse response is a conjugated, timereversed phase history corresponding to a different v_{tr}, v_{taz }pair.
A receiver for SAR data from a phase modulated beam pattern is implemented as in Equation (17) with the noisefree point target phase history replaced by the data phase history:
Estimator/detector receiver response for hypothesized parameters
where h_{az,ref}(tt_{0},v_{tr},v_{taz}) in Equation (18) equals h_{az}(tt_{0},v_{tr},v_{taz}) in Equation (16). The receiver in Equation (18) implements a generalized datareference cross ambiguity function. When a data phase history is not energy normalized and the reference phase histories are energy normalized, the output of the estimator/detector is proportional to the squared amplitude of the data phase history and is thus an estimate of relative target strength. In this case, the outputs of the estimator/detector in equation (18) for various hypothesized ranges, azimuths, range rates, and azimuth rates comprise a map of target strength as a function of the four variables range, azimuth, range rate, and azimuth rate. This map is a generalized synthetic aperture image, which conventionally represents target strength as a function of range and azimuth.
Improved detection performance in clutter is associated with increased signaltoclutter ratio (SCR). The “signal” in the SCR calculation is the expected receiver response to a point target in the absence of noise and clutter, and is represented by the ambiguity function amplitude with perfect parameter hypotheses, at the origin of the ambiguity function coordinates. The “clutter” in the SCR calculation is the expected receiver response to clutter, and is represented by the three dimensional integral of the product of the ambiguity function and the clutter distribution in azimuth/rangerate/azimuthrate space.
For maritime radar, a model for the sea clutter distribution is shown in
SCR has been calculated using the three dimensional ambiguity functions represented by
For a broadside stripmap maritime SAR that uses the array weighting function in Equations (7) and (8), SCR becomes larger as the modulation factor γ increases, as indicated by
The phase change between array elements is the frequency in radians per meter multiplied by the element spacing d in meters per element:
Phase change per element=−[πγ/(2M)] sin [πx/(dM)],−dM≦x≦dM. (20)
The maximum absolute phase change per element in the azimuth (x) direction is
For adequate spatial sampling, the maximum phase change between elements should be less than or equal to π radians, which implies that
γ≦2M=no. of functional array element rows (in the azimuth direction)+1 (22)
where functional array element rows have nonzero element weighting function magnitude.
For γ=30 in Equation (22), the number of functional array element rows in the azimuth direction should be greater than or equal to 59. At Xband (λ=3 cm), an array that is L meters long in azimuth with element spacing λ/2, contains approximately 67 L element rows. If γ≦67 L+1, then γ=30 corresponds to an Xband array that is at least 43 cm long in the azimuth direction. A longer array can accommodate a larger value of γ.
A second constraint on γ pertains to permissible observation time. The phase modulated beam pattern 139 in
A third constraint on γ is that the phasemodulated beam pattern should not cause under sampling of beaminduced phase histories as a target moves through the beam. The maximum absolute value of the beaminduced phase change between echoes should be less than or equal to π radians. The maximum absolute value of the beaminduced phase change between echoes equals the maximum absolute value of the slope of the phase function 142 in
Letting PRI denote the radar pulse repetition interval, the crossrange azimuth displacement between observations equals (the radar platform velocity+azimuth rate)×PRI and the alongrange displacement between observations equals (the target range rate)×PRI. If PRI=ζR_{0}/c where ζ is a constant (usually greater than ten) and c is the propagation velocity, the argument of the arctangent function is approximately ζv_{paz}/c where v_{paz }is the radar platform velocity. The quantity v_{paz}/c is usually very small, and ζv_{paz}/c<<1. The azimuth change in radians between observations is usually very small, and the third constraint is rarely an important limitation for γ.
Appropriate beam phase modulation improves synthetic aperture resolution in azimuth, range rate and azimuth rate, and suppresses ambiguity function ridges. This improvement implies that a four dimensional output representation is relevant, i.e., a map of target strength as a function of range, azimuth, range rate, and azimuth rate. This dimensionality increase is of no concern for computer analysis of estimator/detector outputs, provided the computer has sufficient memory and processing speed. The increased dimensionality is important, however, for display of the outputs for the benefit of a human observer.
A stripmap representation that is suitable for a human observer can be obtained as follows. At a given stripmap (range, azimuth) pixel location, the most likely range rate {circumflex over (v)}_{tr }and azimuth rate {circumflex over (v)}_{taz }(conditioned on the pixel range and azimuth values) are the values of v_{tr }and v_{taz }that maximize X_{az,dataref}(t_{0}, v_{tr}, v_{taz})^{2 }in Equation (18) for the specified pixel azimuth (t_{0}) and range. The corresponding maximum value X_{ax,dataref}(t_{0},{circumflex over (v)}_{tr},{circumflex over (v)}_{taz})^{2 }is the target strength estimate at the pixel location. The maximum likelihood range rate {circumflex over (v)}_{tr }and azimuth rate {circumflex over (v)}_{taz }at the pixel location can be combined into a single velocity parameter {circumflex over (v)}=√{square root over ({circumflex over (v)}_{tr}^{2}+{circumflex over (v)}_{taz}^{2})}. In the stripmap for human observation, the target strength estimate at the pixel location is represented by pixel intensity (brightness), and the velocity estimate {circumflex over (v)} at the pixel location is represented by a pixel color code.
Such a generalized display is unnecessary if the observer specifies v_{tr }and v_{taz }values that are of interest. In this case, the four dimensional target strength map is evaluated at the specified v_{tr }and v_{taz }values, resulting in a conventional stripmap function of range and azimuth. In ultrasonic ISAS for noninvasive flow measurement in a conduit (e.g., a blood vessel), the observer may specify range (distance from the transducer array, orthogonal to the array surface) and azimuth (e.g. the zeroazimuth line orthogonal to the array), and the resulting display represents target strength at the chosen location as a function of fluid velocity components parallel and orthogonal to the conduit.
In practice, an observer often is interested in the difference between the current data image and a reference image. The reference image can represent the average clutter in the surrounding area at the observation time or a registered image of the same area that was viewed at a previous time. The difference image can be obtained by subtracting the reference image from the current image, or by subtracting log (reference image plus a small constant) from log(current image plus a small constant), which is equivalent to creating a normalized image via division of the current image by the reference image. At each range and azimuth, the display shown to the observer represents the maximum over all relevant range rates and azimuth rates of the difference image at the specified range and azimuth. If the range rate and azimuth rate of interest can be specified by the observer, then the range, azimuth map shown to the observer is the difference image evaluated at the given values of v_{tr }and v_{taz}. A nonnegative difference image is obtained by applying a nonlinear operation such as halfwave rectification (the image sample value or zero, whichever is largest), an exponentiation operation, an absolute value operation, or squaring, depending on the application.
Broadside stripmap SAR as described in Equations (1)(18) and
 v_{pr}≡range rate component of platform velocity (relative motion between the transmit/receive array and the target environment in the direction orthogonal to the azimuth, elevation plane)
 v_{pel}≡elevation component of platform velocity (relative motion between the transmit/receive array and the target environment in the elevation direction)
 v_{tel}≡target elevation rate that is not included in the platform velocity.
A combined transmitreceive phase modulated beam pattern P_{TR}(θ,φ) that is phase coded in both azimuth (φ=0) and elevation (φ=π/2) is used.
For two cross range dimensions with (v_{pr}+v_{tr})(t−t_{0})≦v_{pr}+v_{tr}T_{obs}/2<<R_{0},
θ(tt_{0},v_{tr},v_{taz})≅tan^{−1}{[(v_{paz}+v_{taz})/R_{0}]t}≡θ(t), (25)
φ(tt_{0},v_{tr},v_{tel})≡tan^{−1}{[(v_{pel}+v_{tel})/R_{0}]t}≡φ(t), (26)
and the range dependent phase shift for twoway propagation is
φ_{range}(tt_{0},v_{tr},v_{taz},v_{tel})=(4π/λ)R(tt_{0},v_{tr},v_{taz},v_{tel}). (27)
For a combined transmitreceive beam pattern P_{TR}(θ,φ), the beaminduced timedependent echo variation is P_{TR}[θ(tt_{0},v_{tr},v_{taz}), φ(tt_{0},v_{tr},v_{tel})] where θ and φ are given by Equations (25) and (26), respectively.
The beaminduced phase modulation is
φ_{beam}(tt_{0},v_{tr},v_{taz},v_{tel})=tan^{−1}{imag{P_{TR}[θ(t),φ(t)]}/real{P_{TR}[θ(t),φ(t)]}}, (28)
the beaminduced amplitude modulation is P_{TR}[θ(t),φ(t)], and the complete phase history function (including amplitude variation) for the point target is
The generalized ambiguity function corresponding to an energy normalized data phase history with t_{0}=v_{tr}=v_{taz}=v_{tel}=0 and energy normalized reference phase histories with various hypothesized values of t_{0}, v_{tr}, v_{taz}, and v_{tel }is a function of four variables:
The receiver corresponding to Equation (30) is implemented with a generalized datareference cross ambiguity function as in Equation (18):
Estimator/detector receiver response for hypothesized parameters
where h_{az,el,ref}(tt_{0},v_{tr},v_{taz},v_{tel}) in Equation (31) equals h_{az,el}(tt_{0},v_{tr},v_{taz},v_{tel}) in Equation (29). If data phase histories are not energy normalized and reference phase histories are energy normalized, estimator/detector outputs are representative of relative target strengths at the hypothesized parameter values. A map of relative target strengths at various hypothesized ranges, azimuths, elevations, range rates, azimuth rates, and elevation rates comprises a further generalization of a conventional synthetic aperture image. The added image dimensions make depictions for a human observer (without loss of information) more difficult than in the lower dimensionality case represented by
Human observation of the estimator/detector outputs is feasible if difference images are computed as in the lower dimensionality case. At a chosen range, azimuth, and elevation sample, values of v_{tr}, v_{taz}, and v_{tel }are selected to correspond with the maximum difference image value; the maximum is computed with respect to range rate, azimuth rate, and elevation rate at the chosen range, azimuth, and elevation. The resulting map of target strength difference as a function of range, azimuth, and elevation can be depicted by a sequence of azimuth, elevation plots corresponding to different range values or by a sequence of range, azimuth plots corresponding to different elevation values, depending on the application. Similar difference representations are used if v_{tr}, v_{taz}, and v_{tel }are specified by an observer.
The many possible combinations of the four variables t_{0}, v_{tr}, v_{taz}, v_{tel }increase the opportunity for high ambiguity sidelobes. One obvious example occurs when the beam pattern is separable and the component azimuth and elevation beam patterns are the same: P_{TR}(θ,0) equals P_{TR}(θ,λ/2). In this case, the phase history of a target that moves along vector v_{az }157 relative to the azimuthcoded beam pattern 158 in
p_{trans,az}(x)=p_{rec,az}(x)=cos^{2}[πx/(2dM)]exp{jγ cos^{2}[πx/(2dM)]},−dM≦x≦dM (32)
p_{trans,el}(y)=p_{rec,el}(y)=cos^{2}[πy/(2dM)]exp{−jγ cos^{2}[πy/(2dM)]},−dM≦y≦dM. (33)
The γ sign reversal is effective if the maximum value of the cross ambiguity function between the two phase histories from
Improved resolution, ambiguity reduction, and position/velocity parameter estimation (including azimuth rate and elevation rate) are obtained from appropriate phase coding/modulation of the aperture shading function. These characteristics are important for SAR detection of small targets in clutter and for ISAS characterization of flow and turbulence in fluids. In the latter case, flow in a conduit is noninvasively monitored from a stationary array with the beam centerline orthogonal to the vessel. The result is a representation of fluid velocity components parallel and orthogonal to the conduit, as a function of position inside the conduit.
A less obvious application is to resolve many different point scatterers that can be used to measure the average motion (pulsetopulse position change) of the target environment relative to the radar/sonar/ultrasound array and/or to measure delay variations caused by a nonhomogeneous propagation medium. This capability is important for position/velocity/delay error correction in applications where sensor position varies and is difficult to track to within a small fraction of a wavelength (e.g., sonar systems on underwater platforms), when the average motion of the target environment is difficult to predict (e.g., ISAS applied to ultrasonic analysis of blood flow in the heart), or when the propagation medium is nonhomogeneous. In principle, reference targets can be resolved by maximizing the receiver target response with respect to phase history hypotheses that are conditioned on various uncompensated position, motion, or delay errors. The corresponding phase history corrections are then used for detection and parameter estimation of other objects. The invention improves reference target resolution, identification, and phase history estimation by using beam pattern phase modulation to suppress ambiguities and improve estimation/detection performance.