antenna related aspects
DESCRIPTION
Antenna related aspects mti radarTRANSCRIPT
Chapter 8
Antenna related aspects
8.1 Introduction
In this chapter some antenna specific aspects are discussed. Chapter 6 dealt in somedetail with spatial transforms to reduce the signal vector space in the spatial dimension.Some specific properties of linear arrays were identified. It was shown how to useidentical subarrays to reduce the number of antenna channels in order to reduce thenumber of degrees of freedom of the space-time processor. The concept of overlappingsubarrays led directly to the concept of symmetric auxiliary channels (Figure 6.8).Planar array configurations for near-optimum space-time MTI processing were derived(Figure 6.18). In this chapter we try to find out how these or similar techniques can beapplied to realistic (also non-linear) antenna arrays.
While in the previous chapters all results were based on linear arrays, in this chapterwe consider array configurations which have more aptitude to practical applications. Inparticular the MTI capability of circular planar arrays as used for example in aircraftnose radar will be analysed. Different subarray configurations will be compared. Forinstance, random subarrays have been implemented in the ELRA ground-based phasedarray radar system (SANDER [445]).
Other geometries such as randomly spaced arrays, conformal arrays and planarhorizontal array antennas will be discussed as well. Moreover, we will considerantennas with a realistic number of sensors. Most of the results presented in earlierchapters are based on a linear array with 24 elements which is not a realistic number.The antennas used in the following will have 480 or 1204 elements.
Tapering the array aperture is an important point of interest. It is desirable tocontrol the antenna sidelobes. In this context the question arises of how far space-time processing may increase the sidelobe level. We further analyse the synthesisof difference patterns at subarray level and the effect of space-time filtering on thesidelobes.
The second aspect is the fact that aperture tapering attenuates the sidelobe clutterspectrum. We will discuss the question of how far tapering can lead to simplifiedprocessing. In essence we compare space-time adaptive processing with conventional
MTI processing (beamformer + temporal clutter filter).
8.2 Non-linear array configurations
All the previous results have been based on a very special kind of antenna array: lineararrays with equidistant sensor spacing. There are several good reasons to consider thisarray type. First it is the simplest array configuration which appears to be suitable forfundamental research. Secondly, as has been shown in Chapter 6, linear (or rectangularplanar) arrays have certain benign properties which lead to near-optimum processorschemes operating at very low computational expense, thus making real-time operationpossible.
A special class of planar arrays was already addressed in Figure 6.18. Thesesubarray configurations were particularly optimised for airborne MTI processing inthat subgrouping is done only in the horizontal. However, MTI is normally not the onlyfunction of an array antenna so that other functions, in particular jammer suppression,will dictate the kind of subarray. Since jammers may be located in all three dimensions(different from clutter) the subgrouping will be done in such a way that there will alsobe vertical degrees of freedom.1 Such array configurations will be discussed in somedetail in the following. In Chapter 15 we will show that vertical degrees of freedomcan be used to mitigate ambiguous clutter returns.
8.2.1 Circular planar arrays
Circular planar arrays play an important role particularly in aircraft nose radars, forexample in the concept of the AMSAR radar (ALBAREL et al [12], GRUENER et al[178]).
The number of elements is typically about one to several thousand. In the followingnumerical analysis we assume an array with 1204 elements. Some results on STAPwith circular forward looking antenna have been reported by KLEMM [258, 259].
Obviously it does not make sense to design the optimum adaptive processoraccording to (4.1) and Figure 4.1. One ends up with covariance matrices of dimension6000 x 6000 which is of no use for practical applications and even causes trouble forsimulation on a general-purpose computer.
8.2.1.1 Space-time processor with aperture tapering
A block diagram of the space-time processor used in this analysis is shown in Figure8.4. The N sensor outputs are followed by taper coefficients and phase shifters forbeamforming. Tapering of the receive array may be required to maintain low sidelobesof the directivity pattern. No tapering is normally applied in the transmit path of theradar in order not to lose signal energy.
In the next stage K subarrays are formed whose beams are steered altogether inthe same direction. The subarray outputs are normalised in such a way that the whitenoise level is the same for all subarrays. This is necessary because the inverse of the
1 Aspects of manufacturing may have an impact on subarray forming as well.
clutter covariance matrix in the adaptive processor tries to normalise all outputs downto uniform noise levels. This, however, would just negate the tapering which is anundesirable effect (NICKEL [377]).
After the noise normalisation we find the inverse of the space-time covariancematrix or the space-time adaptive FIR filter according to (7.11). The followingnumerical results are based on a space-time FIR filter with temporal filter length L = 5.
The clutter filter is followed by some additional coefficients for forming sum ordifference patterns. Before entering the secondary beamformer the signals have tobe weighted again with the inverse noise normalisation factors to compensate for thenormalisation applied to the subarray outputs before adaptive processing. The outputsignal of the secondary beamformer is then fed into a Doppler filter bank according to(1.12) which in turn is connected with a detection and indication device.
The whole processing chain can be described by a linear transform as in (6.1) and(6.10). The received space-time signal vector at subarray level is given by
(8.1)
Figure 8.1: Irregular subarrays
is the space-time transform. The spatial subvectors of the received space-time signalvector are first multiplied with taper weights, phase coefficients and normalisationfactors so that the spatial transform at subarray level becomes
(8.3)
(8.2)
where
Figure 8.2: Checkerboard subarrays
where
(8.4)
describes the subarray forming. A t is an N x N diagonal matrix containing the TVtaper weights and the beamsteering phase coefficients. A n i s a K x K diagonal matrixcontaining the subarray normalisation coefficients. The normalisation coefficients aregiven by
(8.5)
Figure 8.3: Dartboard subarrays
Figure 8.4: The subarray FIR filter processor with tapered antenna array
where iVsa is the number of antenna elements of the k-th subarray while w i is thetaper weight associated with the i-th antenna element. This normalisation provides aconstant receiver noise power at all subarray outputs.
As in Chapters 5 and 6 the vector quantities of clutter, noise, target signal andreceived echoes become
and the clutter covariance matrix is
where T is defined by (8.2), (8.4) and (8.3).The total processor in the transformed domain then becomes
(8.6)
(8.7)
(8.8)
sensors
taper weights
phase shifters
subarrays
subarraynormalisation
inverse of K x L space-time covariance matrixor K x L space-time adaptive FIR filter
D: difference weights^S: unity weights
compensation fornormalisation
secondarybeamformer
M - L + 1 point Doppler filter bank
detectormax
f
IF[C
lB]
Figure 8.5: Improvement factor for irregular subarray configuration (<p L = 0°): o notapering; * Taylor weighting and subarray normalisation
where A " 1 compensates for the subarray normalisation and s T is the transformedsignal replica including a Doppler filter and the transformed (or secondary)beamformer. In practice the Doppler filter will be replaced by a Doppler filter bankwhich is followed by a detection device.
The improvement factor becomes according to (1.55),
(8.9)
This processor has been analysed by the author [258] with respect to directivitypatterns, especially for low sidelobe design. As any space-time processor has bydefinition spatial dimension some impact of the clutter rejection on the resultingdirectivity patterns can be expected. It has been shown in [258] that thanks to thesubarray normalisation almost no effect on the sidelobe level can be noticed. Even forthe difference patterns formed at subarray level relatively good sidelobe behaviour wasachieved.
For the subsequent numerical evaluation a 40 dB Taylor weighting has beenused. For Taylor array pattern synthesis for circular arrays see TAYLOR [487] andM AlLLOUX [331, pp. 157 - 160]. The Bayliss synthesis for creating difference patternswith low sidelobes is given in BAYLISS [35] and MAILLOUX [331, pp. 160-162].
F
IF[C
lB]
Figure 8.6: Improvement factor for checkerboard subarray configuration ( ^ L = 0°): Ono tapering; * Taylor weighting and subarray normalisation
8.2.1.2 Clutter rejection performance
In Figures 8.5, 8.6 and 8.7 improvement factor curves are presented for the threedifferent subarray configurations shown in Figures 8.1 (irregular subarrays),2 8.2(checkerboard), and 8.3 (dartboard). The upper curves show the improvement factorin SCNR for the case that no tapering was applied. The arrays were assumed to bein the forward looking orientation, with look angle y> = 0°. For clutter filtering thespace-time FIR filter as described in Chapter 7 was used.
First of all we notice the clutter notch which appears at nearly F = 0.5. The readeris reminded that the PRF is chosen so that the maximum clutter Doppler frequency issampled at the Nyquist rate. The maximum clutter Doppler frequency occurs in theforward looking direction (cp — 0°). The slight deviation from F = 0.5 is due to theelevation of the radar (see Table 2.1).
The upper curves (no tapering, i.e., Wi=I in Figure 8.4) coincide well with thetheoretical optimum. There are no losses as in the case of linear arrays and disjointsubarray processing; compare with (6.3) and (6.4). The IF curves are quite independentof the subarray forming.
The lower IF curves show the case of 40 dB Taylor weighting. In the pass bandsome 2 dB losses have to be taken into account. This tapering loss is the penaltyfor achieving low sidelobes. Also, the clutter notch is slightly broadened whichdegrades the detectability of slow targets. Notice that the checkerboard subarray
2This subarray structure has been optimised so that the sidelobes of a difference beam formed at subarraylevel are minimised (NICKEL [377]).
F
IF[C
lB]
Figure 8.7: Improvement factor for dartboard subarray configuration (ip L = 0°): o notapering; * Taylor weighting and subarray normalisation
antenna performs worst. This has to do with the regular subarray structure which hasa tendency for high grating sidelobes. However, for reasons of manufacturing thisantenna might be particularly attractive for practical use.
8.2.1.3 Impact of clutter rejection on beampatterns
Now let us find out how the processor shown in Figure 8.4 performs in terms of antennadirectivity patterns. First we have to answer the fundamental question: why do weneed low sidelobes after adaptive clutter rejection? We can assume that jamminghas been cancelled, either by an additional spatial anti-jamming pre-filter or by thespace-time filter simultaneously with the clutter. Wu R. et al. [566] have developed atechnique for controlling the sidelobes of an array in the presence of adaptive jammercancellation.
Clutter is by nature strongly heterogeneous. When adapting a clutter rejection filtera certain amount of data is needed to estimate the covariance matrix, for example byaveraging space-time clutter echo dyadics. Such averaging can basically be done inthe time or range dimension or both. In both cases data are averaged that stem fromdifferent locations on the ground and, due to the heterogeneous nature of the clutterbackground, have different clutter statistics. The resulting clutter rejection filter istherefore matched only to the average clutter and might not be able to suppress strongclutter discretes.3 To cope with this effect low sidelobes are desirable.
3 Projection type processors circumvent the problems of dynamic range of clutter echoes because they
F
dB
Figure 8.8: Irregular subarrays, no tapering ( ^ L = 0°): O azimuth beampattern, noclutter rejection; * azimuth beampattern after space-time processing
There is another interesting aspect of aperture tapering. The reduction of antennasidelobes results in attenuation of sidelobe clutter Doppler frequencies. This might leadto simplified clutter rejection architectures. We will discuss this question in Section 8.3.
Figures 8.8,8.9 and 8.10, show three different modes of operation of this processor.The antenna directivity pattern is in general calculated as
(8.10)
where b(ip) is a beamformer vector (or the spatial part of the target signal replica),while b(<^o) plays the role of a source located at angle (po.
The directivity pattern of the processor shown in Figure 8.4 is accordingly
(8.11)
where K n is the upper left (spatial) submatrix of Q^ 1 .It should be noted that (8.11) represents the directivity pattern before Doppler
filtering. After Doppler filtering the directivity pattern becomes
(8.12)
which means that basically the antenna pattern varies with Doppler. For simplicity weuse (8.11) in the following analysis. However, some deviations from the results shownbelow can be expected if Doppler filtering is included in the consideration.
form a clutter notch that ideally is an exact null, see the remarks in Chapter 15.
<P
dB
Figure 8.9: Irregular subarrays, Taylor weighting, no subarray normalisation ( ^ L -0°): o azimuth beampattern, no clutter rejection; * azimuth beampattern after space-time processing, white noise case; x azimuth beampattern after space-time clutterrejection
Figure 8.8 shows the beampatterns for an array after Figure 8.1 (irregularsubarrays). No tapering has been applied. Therefore, the maximum sidelobe of thebeampattern without processing (circles) is about —18 dB. As can be noticed fromthe second curve (asterisks) additional space-time clutter suppression leads to someincrease of the sidelobes and slight broadening of the main beam. Also, the nulls in thebeampattern are flattened out.
Figure 8.9 shows the same situation as before but with 40 dB Taylor weighting andwithout subarray normalisation. We notice first of all a broadening of the main lobewhich is a natural consequence of the tapering. In a way the taper function reduces theeffective aperture size.
It can be noticed that in the circled curve (no clutter rejection) all sidelobes of theantenna are suppressed below 40 dB. When space-time adaptive processing is applied,either for white receiver noise only (*), or for clutter rejection (x), the effect of taperingis negated so that the sidelobe come up on the same level as in Figure 8.8. The adaptiveprocessor has the property of normalising the subarray outputs in such a way thatthe white noise power is uniform in all channels. Therefore the effect of tapering iscancelled.
In Figure 8.10 we finally show the effect of additional subarray outputnormalisation. As can be seen the sidelobe level is well below 40 dB, for both cases(with and without clutter rejection). It can be noticed that there is little effect of theclutter rejection filter on the resulting beam pattern.
9
dB
Figure 8.10: Irregular subarrays, Taylor weighting with subarray normalisation (<p L =0°): * azimuth beampattern, no clutter rejection; x azimuth beampattern after space-time clutter rejection
It can be seen from Figures 8.11 and 8.12 that similar beampatterns are obtained forthe checkerboard and dartboard subarray configurations. The beampattern is obviouslyquite independent of the kind of subarray formation.
8.2.1.4 Difference pattern generation at subarray level
Difference patterns are the basis of monopulse techniques (SKOLNIK [468, Chapter18]). Monopulse techniques are used for location of detected targets with highaccuracy, i.e., accuracy beyond the beamwidth determined by the antenna aperture.Monopulse techniques play a major role in tracking radar.
There are many possibilities of forming difference patterns. One prominentexample is the Bayliss weighting, see BAYLISS [35] and MAILLOUX [331, p. 160].
The monopulse angle estimator is activated only if a target has been detected. Inorder to save radar operation time it is desirable to use the same data as obtained alreadyfor detection by the sum beam. Therefore, the Bayliss weighting cannot be applieddirectly to the sensor outputs. Instead we have to use data which have been gatheredby use of a tapered antenna array at the subarray outputs. The difference weighting atthe subarray outputs is approximately (NICKEL [377])
(8.13)
<P
where g is the vector of Bayliss coefficients at the sensor level while g s a includes the
dB
Figure 8.11: Checkerboard subarrays, Taylor weighting with subarray normalisation(ipL — 0°): * azimuth beampattern, no clutter rejection; x azimuth beampattern afterspace-time clutter rejection
transformed Bayliss coefficients at the subarray level. The subarray transform T sa wasdefined in (8.4).
Figures 8.13-8.16 show some numerical examples for difference pattern synthesiswith the irregular subarray structure given by Figure 8.1. In Figure 8.13 the case ofBayliss weighted sensor outputs can be seen, however without subarray normalisation.
As can be seen the sidelobe level is below 40 dB if no adaptive processing is applied(o). The effect of adaptive processing, either against white noise (x) or clutter (*), isdramatic. Obviously the adaptive processor compensates for the Bayliss weighting(except for the null in look direction) so that the sidelobes come up tremendously. Thesame effect was observed for the Taylor weighting applied to sum pattern synthesisin Figure 8.9. Including subarray normalisation according to (8.5) keeps the sidelobelevel below 40 dB (Figure 8.14).
In Figure 8.15 the difference pattern was formed at the subarray level using thetransformed Bayliss weighting according to (8.13). No subarray normalisation wasused. As can be seen one sidelobe is at — 24 dB, the others are below 30 dB.
As a result we find that additional subarray normalisation gives only very littlefurther reduction of the sidelobe level (Figure 8.16). In Figures 8.17 and 8.18 thedifference patterns of the checkerboard and dartboard arrays are calculated for the sameconditions as in Figure 8.16. In particular, the checkerboard array tends to produce ahigh sidelobe level. It should be noted that the irregular structure shown in Figure 8.1has been optimised to achieve low sidelobe levels (NICKEL [377]).
<P
dB
Figure 8.12: Dartboard subarrays, Taylor weighting with subarray normalisation (ip L =0°): * azimuth beampattern, no clutter rejection; x azimuth beampattern after space-time clutter rejection
8.2.1.5 Reduction of the number of subarrays
So far we considered circular apertures partitioned into 32 subarrays. The number32 looks fairly high for the purpose of clutter rejection only. This high numberof channels might be required when clutter suppression has to be carried out underjamming conditions (see Chapter 11).
In the following we try to reduce the number of output channels by combiningseveral of the subarrays into one. For the look direction we assumed <p L = 45°. Recallthat at this angle the clutter returns are Doppler broadband while in the flight direction(<£>L = 0°) clutter echoes are narrowband.4 Therefore, clutter rejection at (^L = 45° isa more difficult task than in the flight direction.
Consider for example Figure 8.19a. It shows the 32 subarrays of the checkerboardarray which was presented in Figure 8.2. The other three pictures in Figure 8.19 showdifferent ways of combining the square subarrays into larger ones.
Figure 8.20 shows the corresponding IF curves. As can be seen the cluttersuppression performance is only slightly degraded if the number of subarrays isreduced (c and d). With K — 6 channels reasonable clutter rejection is still obtained.
In Figure 8.21 we combine subarrays of the dartboard array so as to cut down thenumber of subarrays to K = 4, 8 or 16. In Figure 8.22 we find that for only foursubarrays (case b in Figure 8.21) the adaptive filter does not perform sufficiently well
4Notice that the IF curves in Figures 8.5, 8.6 and 8.7 have been calculated for the forward look direction(<£>L = 0°) because the associated beampatterns have been calculated for broadside steering.
<P
dB
Figure 8.13: Irregular subarrays, Bayliss weighting, no subarray normalisation (ipi, —0°): o azimuth difference pattern, no clutter rejection; x azimuth difference patternafter space-time processing, white noise case; * azimuth difference pattern after space-time clutter rejection
(* curve). Notice that we reduced the number of degrees of freedom down to K — 4.In the horizontal dimension we have practically only two degrees of freedom. As theflight direction is horizontal the effective number of degrees of freedom is reduceddown to two which is obviously too small, particularly in view of the fact that the twosubarrays are not equal and, hence, produce different clutter spectra. Some losses canbe noticed even for eight subarrays. These may be mitigated, however, by applyinga larger filter length, of course at the expense of higher computational load. In theexamples shown we used L — 5.
Even for an irregular subarray structure (Figures 8.23 and 8.24), forming of asmaller number of subarrays (in this example K-I) has no significant detrimentaleffect on the clutter rejection performance.
We should keep in mind (see the considerations in Section 6.1.3) that optimumperformance was obtained for uniform overlapping subarrays in the case of a lineararray, Accordingly, optimum planar arrays were proposed in Figure 8.20. While thecheckerboard array still has some similarity with a linear array the dartboard and theirregular configuration have no relation to a linear array.
It should further be noted that the losses in SNIR exhibited by Figures 8.20, 8.22and 8.24 may be mitigated by increasing the temporal filter length L. In all shownexamples L = 5 was chosen (according to the list of standard parameters in Chapter 2,p. 63).
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Figure 8.14: Irregular subarrays, Bayliss weighting with subarray normalisation ( ^ L =0°): x azimuth difference pattern after space-time processing, white noise case; *azimuth difference pattern after space-time clutter rejection
8.2.1.6 T^-A-processing
In the following we come briefly back to E-A-processing already addressed in Section6.3.2. This techniques uses two channels only as a spatial basis, a sum beam and adifference beam, which both are available in many commercial radar antennas. Recallthat WANG H. et al. [515] have found that this technique may be a cheap solutionfor space-time clutter rejection.5 Examples for linear arrays have been presented inSection 6.3.2. In the following we apply the same technique to a circular planar array.
E-A-processing can be described by a spatial transform as given by (6.33). Thefirst column denotes the coefficients of the sum beamformer while the second columnincludes the weights of a difference beam. This spatial transform has to be insertedinto (6.1), in order to obtain a space-time notation.
In the following examples the temporal filter length has been assumed to be L = 2which is the minimum possible filter length. In this way the space-time FIR filteraccording to (7.11) will have only four coefficients.
Figure 8.25 shows the performance of E-A-processing for a sidelooking circularplanar array (look directions 90° and 45°). It can be noticed that the performanceis quite poor if no additional tapering is applied (Figure 8.25a and 8.25c). Taperingalleviated the space-time processing task considerably as can be seen from Figures8.25b and 8.25d.
5 The authors used MCARM data which have been generated by a linear sidelooking array.
<P
dB
Figure 8.15: Irregular subarrays, transformed Bayliss weighting at subarray level, nosubarray normalisation (</?L = 0°): x azimuth difference pattern after space-timeprocessing, white noise case; * azimuth difference pattern after space-time clutterrejection
Similar results for a forward looking array are shown in Figure 8.26 (look directions0° and 45°). For look direction 0° we have the Doppler narrowband case because inthe flight direction the isodops are run fairly tangential through the azimuth-range cells.Therefore, each cell contains only one Doppler frequency. As can be seen from Figures8.26a and 8.26b this case is easy to handle for the E-A-processor. The single clutterfrequency in the range cell leads to a narrow clutter notch, with and without tapering.
In the look direction 45° we encounter Doppler broadband clutter returns.Obviously, the S-A-processor does not cancel the clutter echoes sufficiently (Figure8.26c). As in the sidelooking case, tapering reduces the number of degrees of freedomand leads to satisfactory clutter rejection performance (Figure 8.26d). This works onlyas long as the sidelobe level of the array is of the order of magnitude of the CNR. Forlarge CNR (40 dB in Figure 8.27) severe losses at off-broadside directions occur evenwith 40 dB Taylor tapering applied (Figure 8.27d).
8.2.2 Randomly spaced arrays
In the following we consider briefly two kinds of array antennas with randomdistribution of the antenna elements. The aptitude of such antenna configurations forspace-time clutter rejection is discussed.
9
dB
Figure 8.16: Irregular subarrays, transformed Bayliss weighting at subarray level andsubarray normalisation (y?L = 0°): x azimuth difference pattern after space-timeprocessing, white noise case; * azimuth difference pattern after space-time clutterrejection
8.2.2.1 Example for planar arrays: the ELRA antenna
The ELRA system is an experimental multifunction ground-based phased array radar(GROEGER et al [176], SANDER [446, 445]). The phased array antenna is thefunctional basis for multifunction operation, which in essence means search and track.The radar includes various auxiliary functions such as MTI, jammer cancellation,sequential detection, power management, etc.
The receive antenna has a planar circular surface on which 768 sensors aredistributed in a pseudo-random fashion. The operating frequency is 2.7 GHz, thearray diameter is about 5 m. This means that the array is strongly thinned comparedwith a A/2 element raster. However, thanks to the random element distribution inboth dimensions ambiguities in either azimuth or elevation are largely suppressed.The width of the main beam is determined by the diameter of the aperture; thesidelobe level, however, is determined by the number of elements. The element densitydecreases from the center of the aperture to the edge so as to provide some densitytapering.
The array is subdivided into 48 subarrays with 16 elements each. Subarraybeamforming is formed in the RF domain. Due to the random positions of theelements all subarrays have different shapes which in turn leads to suppression ofambiguities (grating lobes, grating nulls) due to secondary beamforming (combinationof subarrays).
<P
dB
Figure 8.17: Checkerboard subarrays, transformed Bayliss weighting at subarray leveland subarray normalisation (tp L = 0°): x azimuth difference pattern after space-time processing, white noise case; * azimuth difference pattern after space-time clutterrejection
As far as space-time clutter filtering is concerned the ELRA receive array iscomparable to the irregular subarray structure in Figure 8.1. In both cases we haveirregular subarrays which all receive different clutter spectra and different clutter-to-noise ratios. Thanks to the large numbers of subarrays in both cases (32 and 48,respectively) space-time adaptive filtering can be expected to work properly. We omita numerical analysis for this type of antenna.
8.2.2.2 Volume arrays
The crow's nest antenna6 (WILDEN and ENDER [549]) is a spherical aperture randomly
filled with horizontal ring dipoles. This kind of array has the property of 360°azimuthal coverage. In contrast to spherical conformal antennas all array elementscontribute to the beamforming process for all look directions.
This kind of array has a natural density tapering because the sphere is thicker inthe middle than at the outer edges. The positions of the elements have been chosen atrandom, however under the constraint that no spacing between neighbouring elementsmust be smaller than half a wavelength. This random spacing is to provide a constantbeampattern independent of the look angle. The problem of space-time processing with
6In fact, this antenna looks like a crow's nest in a tree. A 'crow's nest' is also a lookout platform on topof the mast of a sailing boat from where an overview of 360P is possible.
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Figure 8.18: Dartboard subarrays, transformed Bayliss weighting at subarray leveland subarray normalisation ((^L = 0°): x azimuth difference pattern after space-time processing, white noise case; * azimuth difference pattern after space-time clutterrejection
such an array has been addressed by KLEMM [247].For space-time clutter rejection only the ^-coordinate of the individual sensor
positions is relevant because this is the flight direction (see Figure 2.1). Figure 8.28ashows schematically a projection of the sensor positions of a randomly spaced volumearray in the xz-plane.
The upper curve in Figure 8.30 shows the gain curve for a fully adaptive space-time FIR filter. The number of elements was chosen to be TV = 480. The temporaldimension was limited7 to L = 2.
As can be seen a reasonable performance is basically possible with such exoticantenna. The question now is how to reduce the signal subspace in such a way that thiskind of antenna could be used in practical systems.
For this purpose let us come back to the considerations on subarrays made inChapter 6. We stated that a prerequisite for efficient reduction of the number ofchannels through forming subarrays is that all subarrays are identical. Only then dothey have identical beampatterns and, therefore, receive all the same clutter spectrum.This is the condition under which the number of antenna channels can strongly bereduced without significant losses in clutter rejection.
To illustrate this in the case of the crow's nest antenna we subdivide the sphericalarray into subarrays in various ways and calculated the improvement factor (see Figure
7Larger values of L would have exceeded the capacity of the computer used for the analysis.
<P
a. b.
d.c.
Figure 8.19: Subarray combination based on checkerboard structure: a. 32 squaresubarrays; b. 6 columns; c. 12 subarrays; d. 18 subarrays
8.29). For curve a the sphere has been subdivided into eight octants as is requiredfor monopulse with a spherical antenna anyway. For curve b the sphere has been cutinto five slices, each with identical numbers of sensors. Therefore, the thickness of thesubarrays (extension in the flight direction) is different. In curve c five slices of equalthickness have been formed. Finally, curve d shows overlapping subarrays in the flightdirection.
All four concepts have one property in common: The shapes of the individualsubarrays are different. This means that the subarray beam shapes are different sothat the received clutter Doppler spectra are different. Therefore the spectra of clutterechoes between different subarray outputs are decorrelated. No near-optimum clutterrejection performance can be expected. In fact, the four IF curves in Figure 8.29indicate quite bad performance.
We have to look for some way to achieve identical subarrays. One possible solutionmay be found by modifying the antenna array according to Figure 8.28. Each ofthe sensors is replaced by a sensor doublet. The doublets are arranged in the flightdirection. Now we have two identical arrays displaced by a certain distance in theflight direction. After beamforming for both subarrays in the same look direction weare left with two channels only which both receive the same clutter spectrum. There isjust a phase difference due to the displacement of the subarrays.
IF[C
lB]
Figure 8.20: Number of subarrays (checkerboard, FL, </?L = 45°): o 32 squaresubarrays; * 6 columns; +12 subarrays; x 18 subarrays
The lower curve (*) in Figure 8.30 shows the improvement factor for the doubletsensor array. Since the temporal dimension of the clutter FIR filter was chosen to beL — 2 the total number of space-time filter coefficients is only KL — 4 which isthe absolute possible minimum! There are some losses close to the clutter Dopplerfrequency in the look direction, however, we notice that this curves approximates theoptimum (upper) curve quite well. Replacing the doublet sensors by triplets yields evenfurther improvement (x).
8.2.3 Conformal arrays
Conformal antenna arrays will play a major role in future air- and spaceborne radarsystems. The advantage of conformal arrays is that the hull of an air or space vehiclecan be used as the supporting construction.
THOMPSON and PASALA [491] analysed linear arrays with a curved geometry.They found that the number of degrees of freedom increases due to the curvature, andthat clutter suppression is degraded.
8.2.3.1 Cylindrical arrays
A lot of air vehicles have a cylindrical shape with the cylinder axis coinciding with theflight direction. We are not talking necessarily about circular cylinders. By 'cylinder'we mean any surface whose yz-dimensions are constant with the flight direction x
F
a. b.
c. d.
Figure 8.21: Subarray combination based on dartboard structure: a. 32 subarrays; b. 4subarrays; c. 8 subarrays; d. 16 subarrays
(for the coordinates see Figure 2.1). There are a lot of air vehicles such as airplanes,missiles, RPVs, etc., which have a cylindrical shape (or parts of which are cylindrical).
For all kinds of cylindrical antenna arrays all the considerations that have beenmade in Chapter 6 for linear or rectangular arrays are valid. That means, formation ofidentical subarrays or the implementation of symmetric auxiliary sensor configurationsafter Figure 6.12 is straightforward. Notice that a rectangular planar array as shown inFigure 6.18b is a special case of a cylindrical array. Cylindrical conformal arrays arefavourable for side- and downlooking air- and spaceborne MTI radar.
8.2.3.2 Forward looking conformal arrays
With conformal array technology forward looking radar antennas can be designedwhich have a sidelooking capability as well. They might even be able to look to the rearto a certain extent, which means an azimuthal coverage of more than 180 °. The MTIcapability will be based on a similar principle as proposed for the crow's nest antenna.Instead of designing doublet or triplet sensors several identical tracks of sensors haveto be arranged one below the other.
The principle can be seen in Figure 8.31. As seen from the top or from below thereare three parabolic tracks which denote the sensor trajectories. Notice that they are
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Figure 8.22: Number of subarrays (dartboard, FL, (/?L = 45°): o 32 subarrays; * 4subarrays; + 8 subarrays; x 16 subarrays
displaced by a certain distance in the flight direction (Figure 8.31a). In practice theseparabolas (or similar trajectories, depending on the aircraft shape) will be installedone below the other as can be seen in Figure 8.31b. All sensors belonging to onetrajectory will be combined by a beamformer network. As a result we obtain in thegiven example three channels which all have the same beam pattern and, hence, thesame clutter spectrum. This is, as carried out before, the prerequisite for successfulclutter suppression at low computational expense.
8.2.4 Horizontal planar arrays
The properties of horizontal planar arrays operating in a down-look mode have beendiscussed by KLEMM [243]. Such an array may be mounted under the fuselage of anair vehicle in the x?/-plane (for definition see Figure 2.1) and may be scanned over 360 °in azimuth. Because of the vertical sensor directivity pattern this array will, however,operate properly only at depression angles larger than about 30 °.
It has been stated in Chapter 3, p. 114, that the DPCA effect8 makes use of theplatform motion in that spatial decorrelation due to travel delays of incoming wavescan be compensated for. This decorrelation effect appears only in wideband radarsystems. Since this effect is based on the platform velocity it works normally only forsidelooking linear or planar arrays.
8DPCA (displaced phase center antenna, see Section 3.2.2) means that each of the sensors of asidelooking line array assumes the position (or, more correctly the clutter phase) of its predecessor afterone PRI.
F
a. b.
Figure 8.23: Subarray combination based on irregular structure: a. 32 subarrays; b. 7subarrays
If the array has an extension in the ^-direction the DPCA effect can be exploitedto compensate for lateral velocity components as may occur due to wind drift, inparticular with weather clutter. In addition, for broadband radar the lateral motionenables the processor to compensate for bandwidth-induced spatial decorrelationeffects.
8.2.5 Circular ring arrays
The use of STAP with a circular ring array has been analysed by Z ATM AN [577], seeFigure 8.32, BELL et al [36], and FUHRMANN and RIEKEN [137]. This antenna is apart of the UESA project (UHF Electronically Scanned Array). 60 antenna elementsare distributed on a circle. 20 adjacent elements out of 60 will be excited so as to enable360° azimuthal coverage. All the cited work is centred about the UESA program (UHFElectronically Scanned Array) sponsored by ONR, USA. The antenna will be mountedon an aircraft and may replace in the future mechanically rotating devices like theAWACS antenna.
ZATMAN has demonstrated that optimum STAP works well with a circular array.Some problems which we identified earlier already in the context of forward lookingarrays can degrade the performance of the circular array as well:
• The clutter Doppler is range dependent as for forward looking arrays. Thismay lead to shortage of training data at short range and range dependent cluttersuppression.
• The system bandwidth leads to broadening of the clutter notch which causesdegradation in slow target detection.
• The clutter rank is slightly higher than for a comparable linear array which leadsto a slight widening of the clutter notch and a slight SNIR loss outside the clutterDoppler area.
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Figure 8.24: Number of subarrays (irregular subarrays, FL, cp L = 45°): o 32 subarrays;* 7 subarrays
• Post-Doppler STAP techniques have proven to operate sufficiently well even forthe circular antenna.
• According to [577] pre-Doppler techniques show significant degradation.
The last statement on pre-Doppler processing is questionable. We achieved goodresults for the circular planar forward looking array which also has a geometry quitedifferent from a uniform linear array.
8.3 STAP and conventional MTI processing
8.3.1 Introduction
The worldwide enthusiasm about STAP should not make us forget that under certainconditions conventional MTI processing (beamforming and temporal adaptive clutterrejection) may be sufficient, especially in conjunction with tapering of the antennaaperture. One prominent example is the high PRF mode of an airborne radar wheremost targets of interest are faster than the maximum clutter speed. In this case a simplehigh-pass filter can be sufficient for clutter suppression.
It should noted that in most of the literature on space-time adaptive processingknown to the author a comparison between space-time and simple temporal adaptiveprocessing (beamforming, tapering, adaptive temporal filtering) is missing. In manypapers different space-time architectures are compared among each other, but the
F
Figure 8.25: S-A processing for circular antenna (SL, L = 2, CNR = 20 dB):a. <£>L = 90°, no tapering; b. if ̂ — 90°, tapering; c. <̂ L = 45°, no tapering; d.<̂L = 45°, tapering;
comparison with conventional one-dimensional processing is not done. In some casesthe numerical results achieved with space-time processing are quite poor so that simpletemporal processing may compete with space-time processing. This may come trueparticularly for large antennas with narrow beam and low sidelobes. The enthusiasmabout STAP should not make us overlook simple standard solutions.
Figure 8.33 shows such a conventional temporal processor. In the sequel all resultsobtained with the space-time processor will be compared with this conventional one-dimensional processor.
In the following numerical evaluation several problems are to be discussed:
• What is the effect of aperture tapering on the clutter rejection performance?
• Do we need space-time adaptive processing when tapering is applied?
• What is the dependence on the look direction?
In the following we consider mainly forward looking arrays (aperture in the cross-flightdirection). Similar results can be obtained for sidelooking arrays.
c. d.
b.a.
Figure 8.26: S-A processing for a circular antenna (FL, L = 2, CNR = 20 dB):a. (^L = 0°, no tapering; b. (^L — 0°, tapering; c. y?L — 45°, no tapering;d. Lpi, — 45°, tapering;
8.3.2 Linear arrays
Let us first compare the optimum processor (Chapter 4), the space-time FIR filterprocessor (7.11), Figure 8.4, and also the conventional MTI according to Figure 8.33,for the case of a linear array. Figures 8.34-8.36 show the IF for a linear array.
In Figure 8.34 the upper curve has been calculated for the optimum processor. Notapering was applied. The look direction is 45 °. The clutter notch appears at the clutterDoppler frequency in the look direction. It should be noted that the area around theclutter notch relates to slow targets and is therefore of special importance.
It can be recognised that the optimum curve is quite well approximated by thespace-time adaptive processor according to Figure 8.4. Beamforming plus temporaladaptive filtering leads to severe losses in the neighbourhood of the Doppler frequencyin the look direction. That means a severe degradation of slow target detection.
Figure 8.35 shows the same constellation as before, however with look angle0° (looking straight forward). Now we notice that the suboptimum space-timeprocessor after Figure 8.4 yields an IF curve that coincides perfectly with the optimum.Furthermore, the conventional processor after Figure 8.33 shows a considerableimprovement in performance. In view of the fact that this processor requires very lowprocessing capacity this might be a good compromise between cost and performance.
In order to explain this behaviour let us have a look at the isodop map in Figure
a. b.
c. d.
Figure 8.27: E-A processing for a circular antenna (FL, L = 2, CNR = 40 dB):a. ^ L = 0°, no tapering; b. </?L = 0°, tapering; c. ipi, = 45°, no tapering;d. </?L = 45°, tapering;
3.1. Forward looking (0°) means looking from the center of the plot to the right inthe x-direction. Notice that here each of the hyperbolas runs perpendicular to the lookdirection so that in a certain range-azimuth cell almost no Doppler variation occurs.The processor encounters more or less one single clutter Doppler frequency only! Thisis the reason why the conventional temporal processor performs quite well. In theforward look direction clutter echoes are Doppler narrowband.
It should be noted that this narrowband effect is typical for a forward looking array.It does not occur for sidelooking arrays which normally do not look in the direction(p = 0 (endfire).
Looking under 45° (up or down in Figure 3.1) the isodops run almost in parallelwith the constant azimuth lines. Therefore, each angle-range cell contains a lot ofdifferent Doppler frequencies (high Doppler gradient). Here we encounter Dopplerbroadband clutter. This is the reason why the conventional processor curve in Figure8.34 deviates so strongly from the optimum. The response of the temporal filter isdictated by the clutter bandwidth while the space-time filter makes use of the fact thatthe clutter spectrum is just a narrow ridge in the azimuth-Doppler plane so that a narrowclutter notch is obtained regardless of the clutter bandwidth.
In Figure 8.36 Hamming tapering was applied to the array aperture. Again weconsider the case of 45° look direction. Now some tapering loss can be noticed in
a. b.
d.c.
Figure 8.28: Randomly distributed arrays: a. single sensors; b. sensor doublets
the pass band (the curves do not reach the theoretical optimum). Secondly, one cannotice that the stop band of the conventional processor is still considerable broadened.Tapering does not seem to give any advantage for clutter rejection.
8.3.3 Circular planar array
The following considerations are focused on a circular planar antenna array withoperational dimensions. The number of sensors is N = 1204, the number of echoeswas chosen to be M — 64, the number of subarrays is K — 32, the temporal filterlength is L = 5. Therefore, the dimension of the clutter covariance matrix at subarraylevel is 32 • 5 x 32 • 5 instead of 1204 • 5 x 1204 • 5 at the sensor level. The irregularsubarray configuration shown in Figure 8.1 is assumed. This antenna configuration hasalready been analysed in Section 8.2 with respect to directivity patterns. We compareagain the space-time FIR filter processor with conventional processing (beamformer +adaptive temporal filter). Calculation of the IF of the optimum processor for such alarge antenna exceeds by far the capacity of available computers.
In the subsequent calculations we concentrate on the subarray structure shown inFigure 8.1. This irregular subarray structure has been optimised so as to yield optimumsidelobe control for the difference patterns, see NICKEL [377].
8.3.3.1 No tapering
Figure 8.37 shows the improvement factor versus the normalised target Dopplerfrequency for space-time processing after Figure 8.4. The four curves have been plottedfor different azimuth angles (<pL = 0°, 20°, 40°, 60°). Figure 8.38 has been plotted forthe conventional MTI processor (beamformer + adaptive temporal filter) after Figure8.33. The parameter constellation is the same as before.
The advantage of space-time processing over time processing only is obvious.Space-time processing achieves a narrow clutter notch at the Doppler frequencyassociated with the look direction. The temporal adaptive filter shows broad areas withlow signal-to-clutter ratio which reflect the Doppler response of the antenna beam. The
b.a.
flight direction
Figure 8.29: Performance of the crow's nest antenna (subarray techniques):a. 8 octants; b. 5 slices (cut in the cross-flight plane) with equal numbers of sensors;c. 5 slices in the cross-flight plane with equal extension in the flight direction; d. 3-Doverlapping subarrays in the flight direction
width of the clutter notches depends very much on the width of the clutter spectrumwhich in turn depends on the look angle (see the above remarks). It is a maximum foripL = 60° and a minimum for </?L = 0 ° . We see from Figure 8.38 that for cpi, = 0°the performance is comparable to space-time processing (compare the clutter notches).For space-time processing the width of the clutter notches is nearly independent of thelook direction.
While the IF curves for the linear array run quite smoothly we find some slightripple for the circular array in Figure 8.37, which can be explained as follows.
The best subarray structure is given by uniform overlapping subarrays for lineararrays ([244] and Chapter 6). Only in this case do all subarrays have identicaldirectivity patterns, and the subarray displacement is A/2 which means that the Nyquistcondition for the spatial dimension is perfectly fulfilled. In this sense the irregularsubarrays of the circular antenna depicted in Figure 8.37 provide irregular spatialsampling where each 'spatial sample' has its individual clutter-to-noise ratio andindividual clutter spectrum. Therefore, clutter output signals at different subarrayshave mutual correlation losses which limits the potential of clutter rejection.
c. d.
a. b.
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Figure 8.30: MTI performance of the crow's nest antenna (N = 480; L = 2; CNR =20 dB): o optimum processing; * doublet sensor approach; x triplet sensor approach
8.3.3.2 Influence of tapering
In Figures 8.39 and 8.40, a 40 dB Taylor weighting has been applied to the circularantenna (see Figure 8.1). In Figures 8.39 and 8.40 we find the IF curves achievedby the space-time processor and the temporal filter again for the look directions^ L = 0°, 20°, 40°, 60°. We assumed CNR = 20 dB in both plots. It can be seen thattapering leads to a considerable improvement for the temporal filter. Even at the 20 °look direction (Figure 8.40) we obtain a relatively narrow clutter notch. In the forwardlooking case (^L = 0°, narrowband clutter, Figure 8.40) the temporal filter performsas well as the space-time filter. Since there is only one clutter frequency present it canbe cancelled well by the temporal filter. It should be noted that in the pass band about2 dB tapering losses have to be taken into account.
For higher clutter-to-noise ratio (40 dB in Figure 8.41) the losses encountered byconventional processing are significant. Except for ^ L = 0° space-time processing issuperior to temporal processing. In the forward look direction the temporal filter againperforms perfectly.
It should be noted that all space-time curves with tapered aperture run quitesmoothly, which is an indication that tapering cuts down the number of degrees offreedom (or eigenvalues of Q) by reducing the sidelobe level.
F
Figure 8.31: Parabolic trajectories of a forward looking array: a. top view, b. side view
8.3.3.3 Effect of temporal filter length
Earlier results with linear arrays (Figure 7.10) have shown that the clutter suppressionperformance is almost independent of the temporal filter length L. The reason for thisbehaviour is that with a linear array all subarrays can be made identical so that thedirectivity patterns of all subarrays are identical. Under such conditions the clutterDoppler spectra of the subarray outputs are identical so that clutter cancellation simplybe done by mutual delay and subtraction.
If the subarrays are different the directivity patterns and, hence, the clutter spectra atthe subarray outputs are different. Then clutter cancellation requires additional spectralshaping before delay and subtraction. This spectral shaping can be done by the space-time filter if a sufficient number of temporal degrees of freedom L is available.
Compare Figure 8.42 with Figure 8.43. Figure 8.42 has been calculated forL = 2 taps while in Figure 8.42 L = 6 was assumed. We notice that the adaptivespace-time FIR filter shows some improvement due to increased filter length whilefor conventional processing (beamformer + adaptive temporal filter) no advantage isachieved by increasing the filter length.
8.3.3.4 Effect of PRF
In most of the numerical calculations we assumed that the PRF was chosen to bethe Nyquist frequency of the clutter bandwidth. Therefore, the Doppler response wasunambiguous between F = - 0 . 5 . . . 0 . 5 . In low PRF and medium PRF modes the PRFmay be chosen so that the clutter spectrum is undersampled in the time dimension.This causes ambiguities within the clutter bandwidth, see for example Figures 3.20and 3.21. The following results are based on the irregular subarray structure shown inFigure 8.1.
In Figure 8.45 the effect of the choice of the PRF is demonstrated. The upper curvesshow the space-time FIR filter results, while the lower curves have been calculatedfor the beamformer + adaptive temporal FIR filter. It can be seen that for Nyquistsampling (subplot a) we find only one clutter notch within the clutter bandwidth whilefor decreasing PRF (subplots b-d) the number of ambiguous clutter notches increases.
The clutter notches cause 'blind' velocities as usual in MTI systems. Theseambiguous blind velocities result in degradation in target detection within the clutter
sensor trajectoriesa. b.
aircraft nose
flight direction
excited elements
idle elements
Figure 8.32: Scheme of 60-element circular ring array, with 20 elements excited
band. However, as can be seen particularly from Figure 8.45d the 'clutter resolution'(width of the clutter notch) of the space-time filter is much higher than that of theconventional beamformer. Therefore, regardless of the losses at the blind velocities,the space-time filter is clearly superior to one-dimensional processing. The advantageof space-time processing shown by Figure 8.45 is impressive.
8.3.4 Volume array
For completeness we compare the space-time and the conventional temporal processoralso for the case of the crow's nest antenna. As can be seen from Figure 8.44,the conventional MTI processor fails completely. It behaves similar to the subarraytechniques which were briefly addressed in Figure 8.29.
8.4 Summary
While all the results obtained in the previous chapters were based on linear arrays,in this chapter we focus on alternative antenna array configurations which are moreadapted to practical requirements. The findings of this chapter can be summarised asfollows
1. Circular planar antenna arrays will play a major role in future aircraft noseradars. It turns out that circular antennas exhibit favourable properties with
sensors
taper weights
phase shifters
L point adaptive temporal FIR filter
M point Doppler filter bank
detectormax
f
Figure 8.33: Beamformer and temporal clutter filter cascaded
respect to space-time adaptive clutter cancellation. In detail the following resultswere obtained:
• Space-time adaptive processing can be used with sideways or forwardlooking circular planar antennas.
• For large antennas the optimum processor is of no practical use due tocomputational complexity.
• The suboptimum STAP processor based on a subarray structure anda space-time FIR filter reaches almost optimum clutter rejectionperformance. In this context it should be noted that the circular shape ofthe antenna provides some horizontal tapering.
• Tapering results in slight tapering losses but may improve the performanceof the conventional beamformer/temporal adaptive filter processor,especially in the vicinity of the clutter notch.
• In the broadside direction of the array (flight axis) clutter echoes arenarrowband so that the conventional processor may be satisfactory.
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Figure 8.34: Performance of a linear array without tapering (<£>L = 45°, CNR = 20dB, FL): x optimum processing; o space-time adaptive FIR filter; * non-adaptivebeamformer + adaptive temporal filter
• The clutter bandwidth increases with the off-broadside look direction sothat the performance of the temporal filter is considerably degraded whilethe space-time processor exhibits the same performance as in the broadsidedirection. However, tapering mitigates the effect of the clutter bandwidthat moderate CNR values.
• In the case of high CNR values (40 dB), only the space-time processoryields sufficient clutter rejection.
• If additional broadband jammers are present the conventional processorfails because there is no temporal correlation that could be exploited.
2. Space-time adaptive clutter rejection can be performed with conformal arrays aslong as they are cylindral and equispaced in the flight direction.
3. Other conformal array configurations are possible, for instance ellipse-like arraysat the nose of an aircraft (see Fig. 8.31).
4. A volume array like the crow's nest antenna cannot be subdivided into subarraysso that satisfactory space-time clutter rejection is achieved. One way ofsuboptimum processing may be a configuration with sensor doublets or tripletsinstead of single sensors. However, this will probably involve problems ofpractical implementation.
5. If the PRF is chosen below the Nyquist rate of the clutter bandwidth ambiguousclutter notches (blind velocities) occur. However, space-time processing is
F
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Figure 8.35: Performance of a linear array without tapering (<PL = 0 ° , CNR = 20dB, FL): x optimum processing; o space-time adaptive FIR filter; * non-adaptivebeamformer + adaptive temporal filter
always superior to conventional beamforming + adaptive temporal clutterfiltering.
6. For circular arrays (in contrast to linear or rectangular arrays) the performance ofthe space-time FIR filter can be improved by increasing the temporal filter lengthL. This has to do with the fact that for circular arrays it is difficult to generateequal subarrays.9 Increasing the number of temporal degrees of freedom has tobe paid for in terms of computational complexity.
9It is basically possible. One way of designing equal subarrays was indicated in Figure 6.18.
F
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Figure 8.36: Effect of tapering (<pL = 45°, CNR = 20 dB, linear array, FL): x optimumprocessing; o space-time adaptive FIR filter; * non-adaptive beamformer + adaptivetemporal filter
Figure 8.37: Space-time processing, no tapering (circular array, FL): o < L̂ = 0°; *<pL = 20°; x ipL = 40°; + <pL = 60°
F
IF[d
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F
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Figure 8.38: BF + adaptive temporal filter, no tapering (circular array, FL): o <p L = 0°;*<PL = 20°; x ifL = 40°; + <pL = 60°
Figure 8.39: Space-time processing, 40 dB Taylor weighting (circular array, FL): o(̂ L = 0°; * (pL = 20°; x ipL = 40°; + y?L = 60°
F
IF[d
B]
F
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Figure 8.40: BF + adaptive temporal filter, 40 dB Taylor weighting (circular array, FL):o (̂ L = 0°; * v?L = 20°; x <pL = 40°; + ipL = 60°
Figure 8.41: BF + adaptive temporal filter, 40 dB Taylor weighting (CNR=40 dB;circular array, FL): o yL = 0°; * <pL = 20°; x <pL = 40°; + v?L = 60°
F
CDLL
F
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Figure 8.42: Effect of temporal filter length (L = 2, FL, <p = 45°). Upper curve:space-time FIR filter; lower curve: BF + adaptive temporal filter
Figure 8.43: Effect of temporal filter length (L = 6, FL, y = 45°). Upper curve:space-time FIR filter; lower curve: BF + adaptive temporal filter
F
F
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Figure 8.44: The crow's nest antenna: o optimum space-time processing; *beamformer + optimum temporal filter
Figure 8.45: Impact of PRF (forward looking, ip = 45°; upper curves: space-time FIRfilter, lower curves: BF + adaptive temporal filter): a. PRF = / N y ; b. PRF = /Ny/2; c.PRF = / N y /4 ;d .PRF = / N y / 8
F
a. b.
c. d.