A Switched Pattern Radar Antenna Array

Absfract-A procedure to design a switched pattern antenna array is developed and demonstrated on a 16and eightelement array. The variable spacing of elements allows us to reduce the number of switchable elements to a minimum and to ac-3 of the effective pattern. Based on this design we have built and tested an eightelement prototype array. Measurements demonstrate the feasibility of the pattern switching concept for improved sidelobe performance.


I. INTRODUCTION
THEORETICAL STUDY of the possible &lobe A s u m r e s s b in radar array antennas with the use of a dual pattern switching technique and the associated signal processing has shown significant reduction in sidelobe level of the effective pattern [l].The technique of manipulation of sidelobe signal spectrum via pattern switching enables filtering of sidelobe signals using a suitable processing technique, and thus allows near-elimination of the effects of sidelobe power on spectral moment estimates in a Doppler radar.An important advantage of this technique is the realization of a low sidelobe pattern without sacrifice of beam width.Further, because the individual patterns of a switched pattern antenna can have high sidelobes, realization of such patterns is much easier than an unswitched low sidelobe pattern.The unswitched low sidelobe pattern requires large current gradients across the aperture, which is very difficult to maintain due to mutual coupling.Though theoretically a Chebyshev (mini- mum beamwidth solution) pattern can be designed with any sidelobe level, practical limitations on the excitation tolerances and current gradients limit the lowest achievable sidelobe level to approximately -40 dB.
Pattern switching allows realization of an effective low sidelobe pattern using easily realizable higher sidelobe patterns with narrower beamwidth.Thus, besides being easily realizable, we obtain narrower beamwidth as well (narrower than an equivalent Chebyshev pattern with low sidelobes).This paper discusses the practical aspects of the realization of a prototype dual switched pattern linear array, and demonstrates the feasibility of the principle of pattern switching.Such aspects as the excitation tolerances, complexity of the scheme, and cost considerations are addressed with the practicality of a planar array realization in mind.

II. SWITCHED PAITERN RADAR CONCEPT
The basic idea underlying the concept of pattern switching is to enable alteration of the sidelobe signal spectrum without affecting the main lobe signal spectrum.In a coherent radar the signal spectrum can be altered by altering the phase of the received signal in a predetermined fashion.However, to alter the phase of only the sidelobe signal without affecting the main lobe signal, the phase change must be introduced through manipulation of antenna pattern function.If we design two patterns with identical main lobes and sidelobes of opposite phases (180" phase difference), switcbg between the two patterns in a predetermined sequence would alter only the sidelobe signal spectrum.These criteria can be written as and gl(U) = -gZ(U); us< u< 1, u in the sidelobe region Here, it is emphasized that gl(u) and g2(u) are two-way voltage gain patterns of a radar antenna which are not line& functions of excitation currents, and precisely because of this reason, it is possible to satisfy the criteria (1).Thus, the technique of pattern switching, as delineated in this paper, is applicable only to two-way patterns in coherent pulsed Doppler radars, and not to one-way antenna patterns.For simplicity we examine here a linear array; analogous results apply to a rectangular array for which the theory is given in []I.
If F(x) is a real current distribution, Fourier transform of

F(x) describes the far-field radiation pattern f(u):
Assuming F(x) to be equal to zero everywhere except in the range -a / 2 < x < a/2, and decomposing F(x) into symmetric part F,(x), and antisymmetric part Fa(x) about x = 0, we can write It is shown in The antisymmetric pattern has a natural zero at the main beam peak, and it has been our experience that when the criterion (4b) is approximately satisfied, the magnitude of the first lobe (of the antisymmetric pattern) is nearly 20 dB below the main lobe peak of the symmetric pattern.Hence, criterion (4a) can be neglected in the formulation of an objective function for the design of excitation currents.
III. LINEAR ARRAY DESIGN PROCEDURE For a linear array of Welements, the criteria (4a) and (4b) can be represented as If criterion (4b) could be satisfied exactly, the effective pattern would have no sidelobes.But, because it can be satisfied only approximately, geff will have sidelobes equal to the vector sum of the sidelobes of gl and g2.A root mean square (rms) pattern (g-) is defined as an equivalent unswitched two-way voltage pattern given by gL(e)=[lgl(ev+ 1g~(e)121/2= 1g~(e)12= 1g~(e)12, (7) where the rightmost equalities hold only in the absence of errors.The sidelobes of the effective pattern ultimately limit the performance of the switched antenna system.
A general method of pattern design using a numerical minimization algorithm is explained in [l].Only a brief description of the approach, specific for the linear array design considered here, is given in the following paragraphs.
The sidelobes of effective pattern depend mainly on the degree of match between symmetric and antisymmetric patterns in the sidelobe region (5b), and are independent of the sidelobe level of individual patterns gl(u) and g2(u).Thus, for a uniformly spaced array, the best design would be a symmetric pattern of a uniform distribution (a, = 1 , n = 1,2 -* * N) which has maximum main lobe gain and narrow beamwidth; and an antisymmetric pattern which hatches the sidelobes of the symmetric pattern exactly.However, because symmetric and antisymmetric pattern polynomials are of finite order with their constituent basis functions being orthogonal to each other, the degree of match that can be obtained between symmetric and antisymmetric patterns is limited when constrained to give maximum main lobe gain.The orthogonality of constituent basis functions of symmetric and antisymmetric patterns can be disturbed to some extent by nonuniform spacings, which gives us additional control in designing the patterns.To give the reader a physical explanation of why and how the spacing can alter the even and odd pattern functions, we offer the following heuristic argument.Consider a uniformly spaced array with unit amplitude illumination and spacing between elements d .The symmetric antenna pattern of such an array is the familiar sin (27rNA-'u)/sin (7rdX-Iu).Now add two more elements, one at each end, but spaced at d / 2 from the last element of the uniform array.Let the two new elements be out of phase from each other; one of them must be in phase with other elements of the array.The antisymmetric pattern sin (27rNdA-'u) is entirely due to the two added elements.Its first null at u = 0 coincides with the peak of the symmetric pattern and the rest of its nulls are colocated with the nulls of the symmetric pattern.The magnitudes of the two patterns in the sidelobe region are comparable so that this simple arrangement with two switchable elements could in principle achieve some reduction in sidelobes.With a proper taper, spacing control and more freedom for the choice of antisymmetric excitation, a better performance is expected.Thus, the best match of symmetric and antisymmetric patterns in the sidelobe region can be obtained by minimizing the objective function with respect to a,, b, , and $, .
Initial values for the spacings d, are chosen based on the computation of a few trial patterns and heuristic reasoning.An objective function cjja is formulated, in terms of the variables a,, which maximizes the main lobe directivity while constraining the maximum allowable sidelobe level [l].The initial values for a, can be taken to be unity corresponding to uniform distribution.Sidelobe constraint level is chosen to be approximately in the range -25 to -30 dB, which is easily realizable in a practical array.The objective function 4, is minimized to obtain a starting symmetric pattern coefficient a,.
Next, another objective function, &, is formulated, which is an integral of the magnitude of the difference between symmetric and antisymmetric patterns, over the entire sidelobe region (ue < u < 1).This integral is represented as a summation by sampling the patterns at regular sufficiently close intervals.The &, thus formed, is a function of a,, b, as well as $, in which a, and $, are as determined previously.
The &, is minimized with respect to b, to obtain a matching

N. PRACTICAL CONSIDERATIONS
In theory, patterns with any low sidelobe level can be obtained, though at the expense of wider beamwidth.However, the large current gradients across the aperture required for realization of such low sidelobe patterns set a lower limit to the realizable sidelobe level in practice.In general, current gradients required for less than -40 dB sidelobe level patterns are extremely difficult to maintain because of the mutual coupling and large Q factor.But -25 to -30 dB sidelobe patterns are easily realizable and do not require large current gradients.
It is stated earlier that with pattern switching the sidelobe level of effective pattern is dependent only on the degree of match between symmetric and antisymmetric components of the pattern in the sidelobe region, and is independent of the actual magnitude of the sidelobe.The high sidelobe (-25 to -30 dB), low Q patterns required for switched pattern radar are easily realizable, but the precision to which each element excitation current can be adjusted becomes important.While small changes in excitation currents would not change the sidelobe level of individual patterns appreciably, the match between symmetric and antisymmetric patterns may be altered resulting in an appreciable increase in the sidelobes of effective pattern.Thus, it is desirable to have some mechanism of fine tuning the phase and the relative amplitude of each .of the element excitation.It is also desirable to minimize the number of active devices whose stability can affect the pattern when used in the individual element feed path.
To switch between the patterns it is required to change the sign of antisymmetric excitation only.If an antisymmetric pattern can be generated using only a small number of elements, the complexity and cost of realization would be greatly reduced.However, this constraint is likely to produce a pattern with slightly reduced gain and larger beam width because of the limited degree of freedom available to change the antisymmetric pattern.Our theoretical analysis has shown that by proper selection of spacings an effective pattern with -50 dB sidelobe level is possible, in a 16-element array, with only two switchable elements.(See Table I and Fig. 1.)The individual patterns in this case have -30 dB sidelobe level, and the effective pattern has a beam width corresponding to the pattern with a -30 dB sidelobe level.Here the optimization procedure was slightly modified.Minimization of the q5b is with respect t o $, and a, only; the value of b, being zero for all elements except one, which is given as an input parameter.
Though the coefficients a,, and the spacings $, are computed to six-digit accuracy, the normalized coefficients are rounded off to second decimal digit before computing the pattern in Fig. 1.The increase in sidelobe level of effective pattern due to truncation is marginal.This shows that 1 percent accuracy in excitation currents is sufficient to give a -50 dB effective sidelobe level.
It may be noted that the procedure delineated earlier gives the array factor, which assumes isotropic radiators and no mutual coupling between the elements.Using pattern multipli-   I.
cation theorem, one can obtain the actual pattern as the product of the element pattern and the array factor, provided all the elements have identical radiation patterns.However, in an array environment, the element pattern and excitation currents are altered to some extent by mutual coupling.For an accurate design we need to include the effect of the mutual coupling and the position dependent element pattern in the design procedure which, though not impossible, would enormously increase the complexity of formulation and computer time.To circumvent this problem a procedure was evolved for adjusting the excitation currents which partly takes into account the mutual coupling effect.However, the procedure does not compensate for the variations in individual element patterns, induced by the mutual coupling and the relative position of the element in the array.The procedure is explained later in this paper.

PROTOTYPE ARRAY
Because of cost considerations, we decided to build only an eightelement prototype array to demonstrate the principle of pattern switching.Theoretical study shows that larger numbers of elements give better sidelobe cancellation because of more control available in designing the pattern.Again, due to cost considerations, the antisymmetric pattern was generated using only two elements symmetrically spaced about the array center, and symmetric coefficients and spacings are adjusted to match the patterns in the sidelobe region.The resulting Fig. 2. RMS and effective array patterns for eight-element dual-pattern switched array.Excitation coefficients and spacings are in Table II.
excitation coefficients are given in Table 11, and the corresponding effective and rms patterns are plotted in Fig. 2 .
In an operational antenna, excitation is controlled by power division using a properly designed power divider.For experimental simplicity, the excitation was controlled using adjustable attenuators in each element.A commercially available eight-way power divider was used to split the input power from the source, which also acts as a power combiner in the receive mode.A line-stretcher in each element was used to adjust the phase accurately.The two switchable elements have electronically controllable p-i-n diode attenuators which are switched between two preset attenuations.The rest of the elements had mechanically adjustable attenuators which were precisely set to give predetermined excitation currents in each element.The radiating elements were cylindrical cavity backed crossed dipoles which were readily available from an S-band array antenna.At our operating frequency of 3.2 GHz the elements had a reflection coefficient of 0.01.The coupling between the two crossed dipoles was less than -20 dB.Only the horizontal dipole was excited, and the vertical dipole was terminated.
Fig. 3(a) shows a schematic of switched pattern prototype array.The elements are mounted on a plexiglass sheet at precise spacings (Fig. 3(b)).An aluminum foil glued to the plexiglass sheet surface provides the ground plane for the array.

VI. SENSITIVITY OF EFFECTIVE PATERN TO EXC~ATION ERRORS
Because the degree of match between the sidelobes of the two patterns, and not the sidelobe level, determines the sidelobes of the effective pattern, the accuracy with which excitation currents can be adjusted becomes particularly important for effective utilization of pattern switching technique.To evaluate the effect of random errors in excitation as well as spacings adjustment on the effective pattern, a computer simulation was carried out using a random number generating routine.
In practice, excitation errors are mainly due to stability and accuracy of the phase and amplitude measuring equipment, if mutual coupling effect is accounted for in the measurement set up.Though spacings can be accurately adjusted in fabrication, actual electrical phase center of each element may be affected by mutual coupling.
The results of the simulation presented in this section provides an idea of the order of accuracy required for a given We have analyzed the eight-element array pattern (Fig. 2), obtained with array coefficients listed in Table II.Random uniformly distributed perturbations were introduced with maximum perturbation limits of k 1 percent, k 1. Bo, and t-1 mm in amplitude, phase and spacings, respectively, about the designed values.Fig. 4 shows the upper and lower limits of the perturbed effective pattern.From these results and the designed effective pattern (Fig. 2) we can see that perturbations should be less than the above limits in orderto get 10 dB of sidelobe suppression (Le., geR/g,, 2 : 0.1).
In practice, mutual coupling can give rise to excitation errors of this order or more, depending on the spacings and excitation coefficients, and especially in switched pattern case, due to the presence of antisymmetric coefficients.One way to account for the mutual coupling is to make near-field measurements and adjust the excitation to match the theoretically computed near field.Due to lack of facilities for nearfield measurement, we had to resort to a less accurate method of adjustment in which individual element excitation is independently adjusted with the rest of the elements terminated by a matched impedance.Added to this, residual standing wave ratio (SWR) in each of the commercial components used further increases the error.

VII. PATERN MEASURE ME^
In order to demonstrate sidelobe whitening via pattern switching, the patterns have to be switched in a pseudorandom sequence and the received signal has to be processed for its spectra.This requires complete hardware of a radar; transmit-However, to demonstrate the feasibility it is sufficient to measure the antenna phase and amplitude patterns and show that two-way patterns with identical main lobes and sidelobes of opposite phase are realizable.The rest of the analysis As mentioned earlier in Section IV, the element excitation coefficients have to be adjusted to within 1 percent of the design values for good sidelobe suppression.Because the design procedure did not take into account mutual coupling, a procedure, which partly takes into account the mutual coupling, was used for adjusting the element excitation.
Fig. 5 gives a schematic of the measurement set up, which provides the phase and the amplitude at a far-field point with respect to some arbitrary reference signal.In our measurement the actual setup was slightly more complicated than the one illustrated.Namely, because the available vector phase meter operated in the frequency range below 1000 MHz, two signal generators and mixers had to be used to bring the frequency of the signals in the range of the meter.Before actual pattern measurements, each element excitation amplitude is adjusted using the variable attenuator, and the phase is adjusted to within 10" to 15" by trimming the cable length.Finer adjustment of the phase is made using line stretchers.The element excitation coefficients are adjusted as seen at a fixed far-field point on the main beam axis.The elements are excited one at a time, the rest of the elements being terminated.When , ter, receiver, PN sequence generator, signal processor, etc.
, follows directly from theory. the array excitation phases are uniform across the aperture, the measured phase at the far-field point would have progressively increasing phase shift as the measured element is farther away from the array center.By measuring the exact distance to the far-field point we can calculate these phase shifts and adjust the phase shifters accordingly.We had some difficulty in adjusting the phase of switched elements because the phase characteristics of p-i-n attenuator was not independent of attenuation.An error of k 3 O in phase with respect to the design value was incurred when switching from one pattern to the other.
The patterns were measured in an anechoic chamber.Phase and amplitudes of both patterns were recorded at regular angular intervals.One of the measured pairs of amplitude patterns is shown in Fig. 6 , where we have also superposed a designed rms pattern.The designed pattern is the one from Fig. 2 multiplied by the theoretical value of the element pattern cos 8. Evident in Fig. 6 is that the two measured patterns, gl and g2, have well-matched main lobes with a difference smaller than 1 dl3 near the nulls.Sidelobes are less well-matched (difference smaller than 2 dB), and they also differ more from the theoretical pattern.Furthermore, the asymmetry of the sidelobes suggests that the illumination across the aperture is not exactly in phase, in spite of the careful phase adjustment of each individual element.
For our purpose the phase difference between the two patterns is an important parameter, so we chose to plot it in Fig. 7, together with a theoretical value.Whereas the general shapes of the two curves agree and excellent performance in the main lobe region is achieved, there are significant differences in sidelobe regions where the required phase difference and the element pattern is cos 0) is also shown.
-  is f 90".This and the amplitude mismatch of sidelobes degrade the sidelobe performance of the effective pattern [ 11.
We have plotted in Fig. 8 the theoretical and measured effective patterns.Throughout most of the sidelobe region, the measured pattern is inferior to the theoretical by about 10 dB; in the far right sidelobes the difference is closer to 20 dB.Both the mismatch of the magnitudes between gl and g2, and the deviation of their phase difference from 180" are the cause of this degraded performance.That the phase deviation is the main culprit can be easily verified by computing g,, and g, R for some typical values of the measured patterns.Let us take a 2 dB difference in magnitudes between sidelobes of gl and g2.Then wherever the phase difference is 180" we would get a 6.5 dB of sidelobe improvement, which is still significant.But if the phase difference between gl and g2 is only 90", the improvement is only 1.5 dB.Note that in fig.7 the phase difference between the rightmost sidelobes offl and f2 is from 20" to 45 ", and it produces a 40" to 90" phase difference between the corresponding sidelobes of gl and g2.thus we attribute the degraded performance of the effective pattern in Fig. 8 to the nonideal phase characteristic of the measured patterns.
Even though the measured patterns deviate from the theoretical design, the principle of sidelobe reduction is quite evident in Fig. 9, where the effective and rms patterns are drawn.Rather than having a 10 dB improvement we see that the sidelobe peaks of the effective pattern are at least 2 dB below the peaks of the rms pattern.There are several reasons for less than optimum performance of the prototype array.Mutual coupling could shift laterally the phase centers of the array elements; we had no provision to measure or compensate for this effect.The switchable elements had a phase bias error of k 3" that could not be removed.Although random errors in the magnitudes of excitation currents where less than 1 dB and in phases were less than 1 "; they were a factor.Finally, the measurements of amplitude and phase of single elements were made with the rest of the radiators disconnected and with matching terminations on the power dividers and the elements.It was not possible to make controlled individual adjustments when all the elements were radiating.

Vm. CONCLUSION
We have refiied a previously developed design procedure of a dual switched antenna array.The current modification allows the spacing between array elements to vary, and this additional degree of freedom is responsible for an improved effective antenna pattern.Furthermore, only a small number of elements need to be switched.For a 16-element array the number of switchable elements is two, and most of the effective pattern sidelobes are 20 dB below the rms sidelobes of the unswitched pattern.
An eight-element prototype antenna array was built and tested.The array consisted of cavity-backed dipoles, fed through attenuators and line stretchers for adjustments of amplitudes and equilization of phase.Two p-i-n diode attenuators were used to control the amplitudes of switchable elements.

[ 2 ]
that the two patterns, f l ( u ) and are obtained by the excitation currents F,(x) + Fa(x) and F'(x) -Because the two-way voltage patterns gl(u) and g2(u) are squares of one-way patternsfi(u) andfi(u), the two criteria in FAX).U.S. Government work not protected by U.S. copyright (1) can be expressed in terms of excitation currents as Fa(x) sin (ux) dx= 0; O < u < us, are the real symmetric excitation currents and b, are the real antisymmetric currents or coefficients, $, = 27rd,/h, X is the wavelength and d, is the element spacing measured from the array center to the nth element.In [l] we have defined the effective pattern as geff(e) = [gl(e) +g2(e)l/2.(6) antisymmetric pattern.Now, keeping a, and b, constant as obtained by the above procedure, the same objective function & is minimized with respect to $, .Then keeping $, and b, constant, & is minimized with respect to a,, and so on, cyclically taking a,, b, , and $, as variables of optimization.Two or three cycles of PROPAGATION, VOL.AP-35, NO. 10, OCTOBER 1987minimization are generally found to be sufficient to obtain a convergent solution.

Fig. 1 .
Fig. 1.RMS and effective array patterns for a 16-element dual-pattern switched array.Excitation coefficients and spacings are in TableI.

Fig. 3 .
Fig. 3. (a) Schematic of the switched pattern eight-element linear array prototype.(b) Back view of the eight-element linear array with driving circuits.

Fig. 4 .
Fig. 4. Variations of the effective array pattern due to changes in amplitude, phase, and spacings.ARRAY ANTENNA

Fig. 8 .
Fig. 8. Measured and designed effective antenna patterns.The elements of the theoretical pattern are assumed to be ideal dipoles.