GB1605336A - Improvements in or relating to solar beam forcing systems - Google Patents

Description

(54) IMPROVEMENTS IN OR RELATING TO SONAR BEAMFORMING SYSTEMS 1 THE SECRETARY OF STATE FOR DEFENCE.

London, do hereby declare the invention. for which I pray that a patent may be granted to me, and the method by which it is to be performed. to be particularly described in and by the following statement: This invention relates to sonar beamforming systems, and more particularly to apparatus for reducing the effects of phase ambiguities experienced in the use of sonar transducer arrays.

Conventional sonar transducer arrays are commonly two dimensional, but analyses of the operation of such arrays are often based on a one dimensional array for ease of calculation. The techniques obtained from considerations of one dimensional linear arrays are applicable to two and three dimensional arrays. If a one dimensional. linear array is divided centrally into two linear sub-arrays with contiguous base lines.

then the phase difference between the two array or beamformer outputs is directly related to the direction of propagation of the sonar wave with respect to the array. In principle therefore, a measurement of phase difference between the outputs of the half arrays would provide the direction of a target relative to the array.

Unfortunately, in the case of sonar, such a measurement presents great difficulties because sonar transducer array or beamformer outputs typically exhibit a signal to noise ratio which is much less than unity. This low signal to noise ratio adds considerably to the every-present problem of distinguishing between weak signals within side lobes of the array. The consequent ambiguity in phase measurements and corresponding uncertainty as to target bearing is a major area of concern in conventional sonar beamforming systems.

It is an object of the present invention to provide a sonar beamforming device adapted to reduce target bearing uncertainties experienced with conventional systems.

According to the present invention. a sonar beamforming system comprises an array of sonar transducers consisting of two sub-arrays, the transducers in each sub-array being weighted such that the transducer sensitivity varies across each sub-array in accordance with a respective weighting function effective to increase the beamwidth and to reduce the side lobe amplitude of said array, variable delay means adapted to introduce relative delays between transducer output signals thereby enabling the beam of each sub-array to be steered and means to combine the outputs of the transducers in each sub-array, the said combining means being adapted to provide both a measure of the phase difference between the sub-array output signals or the amplitude of at least one of the sub-array output signals.

The sub-arrays may conveniently, although not necessarily, each be half of the array. It is also convenient. although by no means essential, if the same weighting function is applied to each sub-array. The weighting function or functions are preferably effective to reduce the side lobe amplitude by between 4 and 16 db and to increase the beamwidth by 10 to 40%.

Convenient weighting functions include cos2 on a pedestal. Dolph-Tchebychev and binomial functions.

It has been found, surprisingly. that one effect of applying a weighting function across a transducer array in accordance with the present invention is to produce an ambiguity-free region in the phase anglelbroadside angle relation characteristic of the array. Conventional electronic techniques, such as for example phase comparator circuits, can be employed to inhibit signals corresponding to phases outside the said ambiguity-free region. It is accordingly a major and unprecedented advantage of the present invention that the weighted array beamformer system can be rendered totally ambiguity-free by the additional use of means to discriminate between signals phase angles and to inhibit signals having phase angles outside given limits.

In order that the invention might be more fullv understood. an embodiment thereof will now be described with reference to the drawings accompanying the provisional specification. in which: Figures 1. 2 and 3 illustrate sonar array beamsteering using delays.

Figure 4 illustrates a weighting function for an N-element linear transducer array.

Figure 5 is a graph of sensitivity against broadside angle for a uniformly weighted array.

Figure 6 is a graph of phase angle against broadside angle for the array of Figure 5.

Figures 7 and 8 correspond respectively to Figures 5 and 6 with a non-uniform weighting function applied to the array.

Figures 9 and 10 correspond respectively to Figures 7 and 8, with a second non-uniform weighting function applied to the array.

Figures 1. 2 and 3 schematically illustrate the general principles of sonar beamforming. All three figures show linear arrangements of omnidirectional transducers I indicated by crosses and associated delay units 2 indicated by circles. Figure 1 shows a straight linear array 3.

whereas Figures 2 and 3 show respectively convex and concave parabolic arrays 4 and 5. In all three Figures, the respective delay units are arranged to produce time delays varying across each array such that each array is "steered" to "look" in a North East direction. In other words, appropriate relative delays are applied across each array such that the electrical outputs of the transducers of each array are in-phase with respect to plane acoustic waves 6 approaching from the North East: alternatively, in-phase electrical activation of the transducers of each array via the delay units produces a respective plane acoustic wave travelling North-East. The effect of delay units 2 is therefore to convert the arrays into apparent linear arrays indicated by base lines 7 each along the North West-South East direction. In addition, the aperture of each array is reduced by cosine of the angle between the respective baseline 7 and a respective line (not shown) through the outermost transducers of the corresponding array.

Directional variation in sonar array sensitivity in this and related way is known as beamsteering.

Figure 4 is a schematic representation of a straight linear array of transducers across the full aperture of which a weighting function has been applied. The transducers of the linear array are indicated by crosses 10, and the array comprises N equi-spaced transducers disposed symmetrically about a centre line 11. the transducers being numbered sequentially from -'/2N to +'/2N. The weighting function is of the "cos2 on a pedestal" type, the expression for the weighting factor Wn to be applied to the nih transducer of the array being

The weighted transducer array is illustrated schematically by the lower part of Figure 4, in which crosses 12 indicate the transducers disposed on the cos2 curve of equation 1. the cos2 curve being raised above the horizontal axis 13 by the height P of the pedestal 14.

Figures 5 to 10 inclusive comprise three sets of sensitivity and phase diagrams for the same transducer array but with differing weighting functions. The weighting function of equation was employed to produce each of Figures 5 to 10, but the value of the factor P in the equation was altered.

For Figures 5 and 6: P 1, .', W= 1 (2) For Figures 7 and 8: P=0.7.

For Figures 9 Y 10:

Figures 5 to 10 inclusive were calculated using a computer model comprising a linear array of 40 sonar transducers (N = 40 in equations (3) and (41). The transducers were equidistant from one another with a spacing of 1/3 of an acoustic wavelength. For the purposes of the calculations, the array of transducers was divided into two sub- or half-arrays of 20 transducers each. The output of each sub-array consisted of the sum of the outputs of the individual transducers in the respective sub-array.

The two sub-array outputs were then summed to produce the graphs of sensitivity versus angle relative to broadside shown in Figures 5. 7 and 9.

In addition, the phase difference between the two sub-array outputs was calculated to produce the graphs of phase difference against angle relative to broadside shown in Figures 6, 8 and 10. The angle relative to broadside is defined as the angle between the baseline (see Figures 1, 2 and 3) of the array and a plane wave incident on the array.

Figures 5 and 6 correspond to a uniformly weighted array. since from equation (2) the weighting factor Wn does not vary between transducers. In Figures 7 and 8. equation (3) shows that a small amount of non-uniformity in the weighting has been introduced by setting P = 0.7. and in Figures 9 and 10, P = 0.3 gives a correspondingly greater degree of non-uniform weighting.

Figure 5 consists of a central lobe 20 or main sensitivity maximum flanked by side lobes or subsidia maxima diminishing in magnitude with divergence of the angle relative to broadside from zero. The beamwidth of a sonar array is defined as the width of the central lobe between its 3 db points. and is measured in terms of the number of degrees of angle relative to broadside between these points. For this particular case of an equi-spaced transducer array of straight linear form. the transducer spacing being not more than half a wavelength, it can be shown that the sensitivity of Figure 5 is of the form: Sensitivity = 20 log (Sin X) x Where X is a linear function of the angle relative to broadside. The beamwidth of the array is approximately inversely proportional to the effective aperture in wavelengths, and the number of side lobes is approximately directly proportional to that aperture.

From Figures 5 and 6, as the angle relative to broadside varies from -800 to +80 , the sensitivity passes through the various lobes of the beam and the relative phase angle passes from +180 to-180 every time the sensitivity passes through a lobe. This means that a particular value of relative phase angle and signal amplitude may either correspond to a comparatively weak target in the main lobe 20 or correspond to progressively stronger targets in progressively smaller side lobes. The present invention is directed to reducing the scope for target ambiguity of this nature.

Referring now to Figures 7 and 8, these Figures show the effect of applying a nonuniform weighting function to the transducer sub-arrays. Each sub-array was weighted with half of the weighting function of equation (3) applied across the whole array, ie the value of n in equation (3) goes from -i/2N to 1 for one subarray and from 1 to +t/2N for the other. Different weighting functions could be used for the two sub-arrays if this were to be required, but the weighting described was chosen for convenience.

The effect of the non-uniformity of the weighting function in equation (3) is to broaden the central lobe 30 somewhat and to reduce the height of the side lobes compared to Figure 5.

Moreover, in Figure 8. the non-uniformity of the weighting function introduces a non-ambiguous region 31 into the relative phase/broadside angle relationship: in addition. the non-ambiguous region 3 ] consists of a relative phase-angle interval between +90 and -90 , which corresponds to a broadside angle interval between +4 and -4 Outside these two intervals. ambiguities still exist for the reasons discussed with reference to Figures 5 and 6, although the sensitivity of the sonar array is reduced compared to that shown in Figures 5 and 6 at the angles relative to broadside which correspond to the ambiguities.

The weighting function of equation (4) was applied to the transducer arrangement used lo calculate the data points for Figures 5 to 8. The results are shown in Figures 9 and 10. which illustrate the effect of the increased degree of non-uniformity of the weighting functions of equation (4).

The sensitivity versus broadside angle relationship shown in Figure 9 demonstrates that the side lobe amplitude is more than 26 db, or a factor of 20, below the amplitude of the main lobe 40 since the side lobes do not appear above the -30 db level.

Figure I 10 shows an ambiguity-free region 41 in the graph of relative phase against angle relative to broadside. the region 41 occurring at relative phase angles between at least +13(( and -13() The region 41 corresponds to angles relative to broadside between +6 and -6" The ambiguity-free region of Figure 8 between +9() and -90" Those broadside angle ambiguities in Figure 10 slill remaining at phase angles beyond the -13() to +13 interval are largely unimportant, since Figure 9 shows that the array has become largely desensitised at the corresponding angles relative to broadside.

Accordingly. targets on bearings appropriate to give such ambiguities are not detected. or are detected so weakly as to be of negligible significance.

It is also possible to design the sonar electronic system to ignore signals at phase angles outside the ambiguity-free region. For example, a conventional phase comparator circuit may be employed to generate an electronic signal proportional to the magnitude of, and corresponding in polarity to. the phase difference of the incoming signals to the beamformer system. By using a further comparator arrangement, the incoming signals outside given voltage limits, thus desensitising the beamformer system to signals having phases outside corresponding phase limits. With reference once more to Figure 9, the sensitivity/broadside angle relation of the beamformer system then becomes a single main lobe with no side lobes whatsoever.

Accordingly, such a system is completely ambiguity-free. Those skilled in the field of sonar will appreciate that ambiguity-free sonar is a considerable technical advance in the art. It is accordingly a major and unprecedented advantage of the present invention that ambiguity-free sonar operation can be obtained simply by the additional use of means to discriminate between signal phases and to inhibit signals having phase angles outside given limits.

Comparison of Figures 7 to 10 with Figures 5 and 6 shows that. if a non-uniform weighting function is applied to an array of transducers divided into sub-arrays in accordance with the present invention. the effect is to produce an unambiguous region of the graph of relative phase against angle relative to broadside. It will be apparent to those skilled in the art of sonar that this is a verv desirable result. since the determination of unambiguous target bearings is a major objective of sonar. The unambiguous region can approach the full * 1 800 phase difference regime when an appropriate (see equation (41) weighting function is chosen. In addition. the side lobes of the array are reduced in amplitude by very useful proportions. and, although the beamwidth is Increased, the increase is within tolerable limits. Funhermore, the number of sonar beams required from an array to give an adequate arc of cover is also acceptable.

In addition to the "cos on a pedestal" weighting function employed to derive the graphs shown in Figures 5 to l(), the Dolph Tchebychev and binomial functions may he used.

More generally, the benefits of the present invention will be obtained to at least some extent if the weighting function is effective to widen the beamwidth (width of central lobe between 3 db points ) by 1 1(04 to 40S and to reduce side lobe amplitude by 4to16db. Figures 7 and 8 were used to illustrate the effects of a comparatively small degree of non-uniformity in the weighting function, and in this case side lobe amplitude is reduced by about 5 db with an ambiguity-free region of the corresponding phase diagram between +90 and -90" It has been found to be comparatively straightforward to find a weighting function giving an acceptable degree of freedom from ambiguities, together with only minor penalties in terms of increased beamwidth and number of beams required to give an adequate arc of cover. The use of weighting functions in the foregoing description has been considered from the mathematical standpoint only. Weighting functions may be applied to a real array by, for example, introducing varying degrees of amplification or attenuation into the signal processing channel of each transducer.

Alternatively, the geometrical spacing between transducer may be varied.

The foregoing description has related. as have been said. to a computer model of a linear array.

The results obtained have been confirmed experimentally after detailed investigation using two different two dimensional sonar arrays. a large cylindrical array and a large planar array.

after allowance for the directivity of the sensitivity patterns of individual transducers.

Cost and space limitations dictated that only one value of weighting factor could be employed for each transducer in these large arrays. This necessitated the weighting function being applied across the full apertures of the arrays. ie across left and right half-arrays combined; the resulting non-optimum asymetric weighting of the left and right beam had to be tolerated. Even so, these systems both demonstrated the ambiguity-free region of the phase characteristic illustrated in Figures 8 and 10. in spite of the constraints involved. The constraints mentioned are not necessarily always present. their existence depends on the array concerned. Accordingly. the weighting function or functions should be optimised for any particular array. Where space and cost considerations permit flexibility, there may be advantages in optimising separately the weighting functions applied to the full array and the half arrays. This may result in the half arrays having different weighting functions, in contrast to the single weighting function applied across the full aperture which was used to derive Figures 5 to 10.

The foregoing description demonstrates the usefulness of the technique and associated apparatus for applying weighting junctions to sonar sub-arrays in accordance with the invention. Sonar arrays were considered which employed comparatively simple output signal processing. The importance of the invention is enhanced considerably in systems employing more sophisticated signal processing. It is accordingly to be understood that the scope of the present invention is by no means restricted either by the signal processing electronics employed or by the geometry of the array.

WHAT I CLAIM IS: 1. A sonar beamforming system comprising an array of sonar transducers consisting of two sub-arrays. the transducers in each sub-array being weighted such that the transducer sensitivity varies across each sub-array in accordance with a respective weighting function effective to increase the beamwidth and to reduce the side lobe amplitude of said array, variable delay means adapted to introduce relative delays between transducer output signals thereby enabling the beam of each sub-array to be steered. and means to combine the outputs of the transducers in each sub-array. the said combining means being adapted to provide both a measure of the phase difference between the sub-array output signals and a "aloe of either the amplitude of the sum of the sub-array output signals or the amplitude of at least one of the sub-array output signals.

2. A sonar beamforming system according to claim 1 wherein the respective weighting functions are effective to reduce the side lobe amplitude by between 4 and 16 db and to increase the beamwidth by IOcii to 40%.

3. A sonar beamforming system according to claim ] or 2 wherein each sub-array is half of the said array.

4. A sonar beamforming system according to any one preceding claim wherein the transducers of each sub-array are equi-spaced on a linear base. the base lines thus formed being contiguous.

5. A sonar beamforming system according to any one preceding claim therein the same weighting function is applied to each sub-array.

6. A sonar beamforming system according to any one preceding claim wherein there is provided means to inhibit signals corresponding to phase differences outside predetermined limits.

7. A sonar beamforming system according to ny one preceding claim wherein the weighting function IS of the "cosy on a pedestal" type.

8. A sonar beamformlng system substantially' as herein described with reference to the figures I to 4. 7 and 8 or figures 1 to 4. 9 and 10 of the drawings accompanying the provisional specificatio

**WARNING** end of DESC field may overlap start of CLMS **.

Claims (8)

**WARNING** start of CLMS field may overlap end of DESC **. region of the corresponding phase diagram between +90 and -90" It has been found to be comparatively straightforward to find a weighting function giving an acceptable degree of freedom from ambiguities, together with only minor penalties in terms of increased beamwidth and number of beams required to give an adequate arc of cover. The use of weighting functions in the foregoing description has been considered from the mathematical standpoint only. Weighting functions may be applied to a real array by, for example, introducing varying degrees of amplification or attenuation into the signal processing channel of each transducer. Alternatively, the geometrical spacing between transducer may be varied. The foregoing description has related. as have been said. to a computer model of a linear array. The results obtained have been confirmed experimentally after detailed investigation using two different two dimensional sonar arrays. a large cylindrical array and a large planar array. after allowance for the directivity of the sensitivity patterns of individual transducers. Cost and space limitations dictated that only one value of weighting factor could be employed for each transducer in these large arrays. This necessitated the weighting function being applied across the full apertures of the arrays. ie across left and right half-arrays combined; the resulting non-optimum asymetric weighting of the left and right beam had to be tolerated. Even so, these systems both demonstrated the ambiguity-free region of the phase characteristic illustrated in Figures 8 and 10. in spite of the constraints involved. The constraints mentioned are not necessarily always present. their existence depends on the array concerned. Accordingly. the weighting function or functions should be optimised for any particular array. Where space and cost considerations permit flexibility, there may be advantages in optimising separately the weighting functions applied to the full array and the half arrays. This may result in the half arrays having different weighting functions, in contrast to the single weighting function applied across the full aperture which was used to derive Figures 5 to 10. The foregoing description demonstrates the usefulness of the technique and associated apparatus for applying weighting junctions to sonar sub-arrays in accordance with the invention. Sonar arrays were considered which employed comparatively simple output signal processing. The importance of the invention is enhanced considerably in systems employing more sophisticated signal processing. It is accordingly to be understood that the scope of the present invention is by no means restricted either by the signal processing electronics employed or by the geometry of the array. WHAT I CLAIM IS:

1. A sonar beamforming system comprising an array of sonar transducers consisting of two sub-arrays. the transducers in each sub-array being weighted such that the transducer sensitivity varies across each sub-array in accordance with a respective weighting function effective to increase the beamwidth and to reduce the side lobe amplitude of said array, variable delay means adapted to introduce relative delays between transducer output signals thereby enabling the beam of each sub-array to be steered. and means to combine the outputs of the transducers in each sub-array. the said combining means being adapted to provide both a measure of the phase difference between the sub-array output signals and a "aloe of either the amplitude of the sum of the sub-array output signals or the amplitude of at least one of the sub-array output signals.

2. A sonar beamforming system according to claim 1 wherein the respective weighting functions are effective to reduce the side lobe amplitude by between 4 and 16 db and to increase the beamwidth by IOcii to 40%.

3. A sonar beamforming system according to claim ] or 2 wherein each sub-array is half of the said array.

4. A sonar beamforming system according to any one preceding claim wherein the transducers of each sub-array are equi-spaced on a linear base. the base lines thus formed being contiguous.

5. A sonar beamforming system according to any one preceding claim therein the same weighting function is applied to each sub-array.

6. A sonar beamforming system according to any one preceding claim wherein there is provided means to inhibit signals corresponding to phase differences outside predetermined limits.

7. A sonar beamforming system according to ny one preceding claim wherein the weighting function IS of the "cosy on a pedestal" type.

8. A sonar beamformlng system substantially' as herein described with reference to the figures I to 4. 7 and 8 or figures 1 to 4. 9 and 10 of the drawings accompanying the provisional specificatio