Frequency Diverse Array Radars - IEEE Xplore
Frequency Diverse Array Radars Paul Antonik and Michael C. Wicks
Hugh D. Griffiths and Christopher J. Baker
U.S. Air Force Research Laboratory Rome, NY, USA
University College London London, UK
Abstract— This paper presents a generalized structure for a frequency diverse array radar. In its simplest form, the frequency diverse array applies a linear phase progression across the aperture. This linear phase progression induces an electronic beam scan, as in a conventional phased array. When an additional linear frequency shift is applied across the elements, a new term is generated which results in a scan angle that varies with range in the far-field. This provides more flexible beam scan options, as well as providing resistance to point interference such as multipath. More general implementations provide greater degrees of freedom for spacetime-frequency-phase-polarization control, permitting novel concepts for simultaneous multi-mission operation, such as performing synthetic aperture radar and ground moving target indication at the same time.
I.
Figure 1. An element-to-element frequency offset is applied to the radiated waveforms.
INTRODUCTION Now consider the case where the waveforms radiated from each element are not identical. In [1], the authors discussed a range-dependent beamformer. In that case, the frequency of the waveform radiated from each element was incremented by a small amount (∆f) from element-toelement. This is illustrated in Figure 1.
In a traditional phased array composed of ideal isotropic radiators, all of the waveforms radiated from each of the radiating elements are identical. If all radiated signals are continuous wave signals with identical phase, the antenna beam will point at broadside, or orthogonal to the face of the aperture. The signals that impinge on a far field target at an angle θ with respect to broadside direction will be identical, except for a phase shift due to a path length difference for each element. The phase shift between adjacent elements due to path length difference is:
ψ
=
2π d
λ
sin (θ ) ,
The phase difference between adjacent elements in the range-dependent beamformer was then shown to be:
∆ψ
(1)
where: d is the spacing between elements, θ is the direction of a point in space with respect to boresight, and λ is the transmitted wavelength.
=
2 π f 1 d sin (θ ) − c 2 π ∆f d sin (θ ) . + c
2 π R 1 ∆f c
(2 )
The first term in (2) is simply the conventional phase shift due to path length difference due to look angle θ. The new terms in (2) due to frequency diversity are −
2 π R 1 ∆f and c
2 π ∆f d sin (θ ) . The first term is range and frequency c offset dependent, while the second term is dependent on the
0-7803-9497-6/06/$20.00 © 2006 IEEE.
215
scan angle and frequency offset. The first new term is important because it shows that for a frequency diverse array the apparent scan angle of the antenna now depends on range.
II.
The phase shift of (2) causes the beam to focus at some apparent angle θ’: f 1 sin (θ ) − f
θ ′ = arcsin
R 1 ∆f fd
+
∆f sin (θ ) . f
(3)
GENERALIZED FREQUENCY DIVERSE ARRAY
The analysis of the range-dependent beamformer assumed that all radiated signals were CW and identical, except for a small frequency offset across elements. In general, the waveforms applied to each channel in Figure 1 can be different. Let the waveform radiated from antenna i on pulse j be Wi, j . In the case of the range-dependent beamformer, each Wi, j has a frequency and an initial
. Notice that the apparent scan angle is generally dominated by the second term of the argument for targets in the far field. To simplify, let the
phase. Separating the frequency and phase components, let
nominal scan angle (θ) be zero, indicating that the beam is not intentionally scanned by means of a linear phase progression across the array, and also let the element spacing be λ/2. Then the apparent scan angle can be written as: 2 R 1 ∆f θ ′ = arcsin (4) . c
where: W i, j has frequency diversity but no phase diversity, and constant frequency for any element, and φi, j contains phase information.
Wi, j
= φ i, j ⊗ W 0 i, j
(5)
,
0
A variety of schemes may be employed to select all
φi, j .
For the range-dependent beamformer, a linear phase algorithm may be used. But flexibility in the selection of φi, j also allows the insertion of message signals, or the
For example, let ∆f = 350 Hz. Near the face of the antenna (R1 = 0), θ’ = 0 º. This indicates that the beam focuses in the broadside direction, as would be expected for the case of no linear phase progression. However, at R1 = 200 km, θ’ = 27.8 º. Figures 2 and 3 shows patterns in range and angle for frequency offsets of 0 and 350 Hz.
creation of waveforms which perform multiple functions at the same time [2]. Alternative coding schemes may include: • • • • •
Random PSK M-ary PSK Costas Orthogonal Frequency (OFDM) Genetic Algorithms
Division
Multiplex
However, not all phase weights will be sufficient; Constraints must be placed on the selection of φi, j to ensure stable beam patterns. Further extensions provide more degrees-of-freedom, resulting in greater control over beam and waveform shaping. Figure 4 provides a model for the generalized frequency diverse array. In the case of the range-dependent beamformer, all Wi are CW signals with a frequency offset
Figure 2. Beam pattern without frequency offset applied.
applied from element-to-element. For SAR, the Wi are wideband waveforms. Each antenna element is represented by a two-dimensional (time and space) impulse response, which allows the incorporation of antenna effects such as mutual coupling. Phase control is applied to each spatial channel in the form of a true time delay, although this reduces to a phase shift in the narrowband case. Even the spacing of the spatial channels is flexible. In the
Figure 3. Range-dependent beam pattern with 350 Hz frequency offset
216
conventional array, channels are uniformly spaced; this is not necessarily the case for airborne and distributed array applications. A hardware implementation of the frequency diverse array is shown in Figure 5. Flexible control over frequency, phase, and amplitude is provided by the waveform control subsystem. Figure 6 illustrates a dynamic allocation of spatial channels for a moving platform. A subarray or array is formed from a subset of the full aperture. At time t1, waveforms Wi, j
Figure 6. Frequency diverse array with dynamic allocation of spatial elements
are applied in time and space across the sub-aperture to accomplish one or more missions (e.g., SAR or
SAR/GMTI). A new set of Wi, j is computed and applied at time t2 and beyond. In this way, Wi, j are transmitted with variation in space, fast time, slow time, and frequency. The use of this formulation for multi-mission operation is discussed in a companion paper [3] . III.
SUMMARY
This paper has extended the range-dependent beamformer into a generalized frequency diverse array. The frequency diverse array provides greater control over modulation and beam synthesis when compared to the conventional phased array. Moreover, the generalized structure of the frequency diverse array provides many more degrees of freedom than the conventional array. Combined with new advances in signal processing , the frequency diverse array can enable a range dependent beamfomer for flexible beam scan options, and also for the mitigation of point interference such as multipath. The generalized frequency diverse array also provides new modes for radar, including synthetic aperture radar simultaneous with moving target indication.
Figure 4. Generalized model of a frequency diverse array
REFERENCES [1]
[2]
[3]
Figure 5. Hardware implementation of the frequency diverse array
217
P. Antonik, M.C. Wicks, H.D. Griffiths, C.J. Baker, “Range Dependent Beamforming”, 2006 International Waveform Diversity and Design Conference, 22-27 Jan 2006. P. Antonik, H. Griffiths, D.D. Weiner, M.C. Wicks, Novel Diverse Waveforms, In-House Technical Report, AFRL-SN-RS-TR-2001-52, June 20. P. Antonik, M.C. Wicks, H.D. Griffiths, C. J. Baker, “Multi-Mission Multi-Mode Waveform Diversity”, Proc. 2006 IEEE Radar Conference, Verona, NY, 24-27 April 2006.
Hugh D. Griffiths and Christopher J. Baker
U.S. Air Force Research Laboratory Rome, NY, USA
University College London London, UK
Abstract— This paper presents a generalized structure for a frequency diverse array radar. In its simplest form, the frequency diverse array applies a linear phase progression across the aperture. This linear phase progression induces an electronic beam scan, as in a conventional phased array. When an additional linear frequency shift is applied across the elements, a new term is generated which results in a scan angle that varies with range in the far-field. This provides more flexible beam scan options, as well as providing resistance to point interference such as multipath. More general implementations provide greater degrees of freedom for spacetime-frequency-phase-polarization control, permitting novel concepts for simultaneous multi-mission operation, such as performing synthetic aperture radar and ground moving target indication at the same time.
I.
Figure 1. An element-to-element frequency offset is applied to the radiated waveforms.
INTRODUCTION Now consider the case where the waveforms radiated from each element are not identical. In [1], the authors discussed a range-dependent beamformer. In that case, the frequency of the waveform radiated from each element was incremented by a small amount (∆f) from element-toelement. This is illustrated in Figure 1.
In a traditional phased array composed of ideal isotropic radiators, all of the waveforms radiated from each of the radiating elements are identical. If all radiated signals are continuous wave signals with identical phase, the antenna beam will point at broadside, or orthogonal to the face of the aperture. The signals that impinge on a far field target at an angle θ with respect to broadside direction will be identical, except for a phase shift due to a path length difference for each element. The phase shift between adjacent elements due to path length difference is:
ψ
=
2π d
λ
sin (θ ) ,
The phase difference between adjacent elements in the range-dependent beamformer was then shown to be:
∆ψ
(1)
where: d is the spacing between elements, θ is the direction of a point in space with respect to boresight, and λ is the transmitted wavelength.
=
2 π f 1 d sin (θ ) − c 2 π ∆f d sin (θ ) . + c
2 π R 1 ∆f c
(2 )
The first term in (2) is simply the conventional phase shift due to path length difference due to look angle θ. The new terms in (2) due to frequency diversity are −
2 π R 1 ∆f and c
2 π ∆f d sin (θ ) . The first term is range and frequency c offset dependent, while the second term is dependent on the
0-7803-9497-6/06/$20.00 © 2006 IEEE.
215
scan angle and frequency offset. The first new term is important because it shows that for a frequency diverse array the apparent scan angle of the antenna now depends on range.
II.
The phase shift of (2) causes the beam to focus at some apparent angle θ’: f 1 sin (θ ) − f
θ ′ = arcsin
R 1 ∆f fd
+
∆f sin (θ ) . f
(3)
GENERALIZED FREQUENCY DIVERSE ARRAY
The analysis of the range-dependent beamformer assumed that all radiated signals were CW and identical, except for a small frequency offset across elements. In general, the waveforms applied to each channel in Figure 1 can be different. Let the waveform radiated from antenna i on pulse j be Wi, j . In the case of the range-dependent beamformer, each Wi, j has a frequency and an initial
. Notice that the apparent scan angle is generally dominated by the second term of the argument for targets in the far field. To simplify, let the
phase. Separating the frequency and phase components, let
nominal scan angle (θ) be zero, indicating that the beam is not intentionally scanned by means of a linear phase progression across the array, and also let the element spacing be λ/2. Then the apparent scan angle can be written as: 2 R 1 ∆f θ ′ = arcsin (4) . c
where: W i, j has frequency diversity but no phase diversity, and constant frequency for any element, and φi, j contains phase information.
Wi, j
= φ i, j ⊗ W 0 i, j
(5)
,
0
A variety of schemes may be employed to select all
φi, j .
For the range-dependent beamformer, a linear phase algorithm may be used. But flexibility in the selection of φi, j also allows the insertion of message signals, or the
For example, let ∆f = 350 Hz. Near the face of the antenna (R1 = 0), θ’ = 0 º. This indicates that the beam focuses in the broadside direction, as would be expected for the case of no linear phase progression. However, at R1 = 200 km, θ’ = 27.8 º. Figures 2 and 3 shows patterns in range and angle for frequency offsets of 0 and 350 Hz.
creation of waveforms which perform multiple functions at the same time [2]. Alternative coding schemes may include: • • • • •
Random PSK M-ary PSK Costas Orthogonal Frequency (OFDM) Genetic Algorithms
Division
Multiplex
However, not all phase weights will be sufficient; Constraints must be placed on the selection of φi, j to ensure stable beam patterns. Further extensions provide more degrees-of-freedom, resulting in greater control over beam and waveform shaping. Figure 4 provides a model for the generalized frequency diverse array. In the case of the range-dependent beamformer, all Wi are CW signals with a frequency offset
Figure 2. Beam pattern without frequency offset applied.
applied from element-to-element. For SAR, the Wi are wideband waveforms. Each antenna element is represented by a two-dimensional (time and space) impulse response, which allows the incorporation of antenna effects such as mutual coupling. Phase control is applied to each spatial channel in the form of a true time delay, although this reduces to a phase shift in the narrowband case. Even the spacing of the spatial channels is flexible. In the
Figure 3. Range-dependent beam pattern with 350 Hz frequency offset
216
conventional array, channels are uniformly spaced; this is not necessarily the case for airborne and distributed array applications. A hardware implementation of the frequency diverse array is shown in Figure 5. Flexible control over frequency, phase, and amplitude is provided by the waveform control subsystem. Figure 6 illustrates a dynamic allocation of spatial channels for a moving platform. A subarray or array is formed from a subset of the full aperture. At time t1, waveforms Wi, j
Figure 6. Frequency diverse array with dynamic allocation of spatial elements
are applied in time and space across the sub-aperture to accomplish one or more missions (e.g., SAR or
SAR/GMTI). A new set of Wi, j is computed and applied at time t2 and beyond. In this way, Wi, j are transmitted with variation in space, fast time, slow time, and frequency. The use of this formulation for multi-mission operation is discussed in a companion paper [3] . III.
SUMMARY
This paper has extended the range-dependent beamformer into a generalized frequency diverse array. The frequency diverse array provides greater control over modulation and beam synthesis when compared to the conventional phased array. Moreover, the generalized structure of the frequency diverse array provides many more degrees of freedom than the conventional array. Combined with new advances in signal processing , the frequency diverse array can enable a range dependent beamfomer for flexible beam scan options, and also for the mitigation of point interference such as multipath. The generalized frequency diverse array also provides new modes for radar, including synthetic aperture radar simultaneous with moving target indication.
Figure 4. Generalized model of a frequency diverse array
REFERENCES [1]
[2]
[3]
Figure 5. Hardware implementation of the frequency diverse array
217
P. Antonik, M.C. Wicks, H.D. Griffiths, C.J. Baker, “Range Dependent Beamforming”, 2006 International Waveform Diversity and Design Conference, 22-27 Jan 2006. P. Antonik, H. Griffiths, D.D. Weiner, M.C. Wicks, Novel Diverse Waveforms, In-House Technical Report, AFRL-SN-RS-TR-2001-52, June 20. P. Antonik, M.C. Wicks, H.D. Griffiths, C. J. Baker, “Multi-Mission Multi-Mode Waveform Diversity”, Proc. 2006 IEEE Radar Conference, Verona, NY, 24-27 April 2006.
