METHOD AND APPARATUS FOR REDUCING COMBINING LOSSES IN A

MULTI-BEAM ANTENNA ARRAY

FIELD OF THE INVENTION

The present invention relates to antenna elements and in particular to beamformed antenna elements .

BACKGROUND TO THE INVENTION

In beamformed or steerable antenna systems, such as may be used in base stations for cellular telephone networks, an antenna may be comprised of an array of identical antenna elements mutually spatially arranged in a grid of m by n elements in either a planar or surface conformal arrangement.

As transmission and user bandwidths and capacities increase in order to meet user demand, the number of signals that will be radiated will also increase.

One method of achieving such increase is by high- order sectorization. Many cellular networks apply a sectorization concept to improve spectrum efficiency of cellular systems, in which an omni-directional antenna, traditionally placed in the centre of a cell, has been replaced by a plurality of N directional antennas. Thus, for the same area, the number of cells, and consequently, the number of subscribers within the network, has been approximately increased by a factor of N.

The use of directional or sector antennas has thus further reduced the amount of interference in the

network and has resulted in more spectrally efficient networks. A sector is generally symmetrical and wedge- shaped, with N sectors generally extending outward from the traditional centre of a cell. Each sector may now be considered a distinct cell, with its antenna extending from an extremity thereof.

A conventional means of increasing network capacity, known as cell splitting, is to reduce the coverage of existing sites and to introduce a new site in the newly created coverage holes. However, cell splitting is very expensive for an operator, since new locations for the tower and equipment for the new site, such as high-rise buildings, have to be located and leased. In many dense urban environments, where increased network capacity is required, it is no longer possible to find suitable new site locations.

In a network employing sectorization, capacity may be increased without identifying any additional site location by replacing a sector antenna with a split-sector antenna that generates a plurality of beam coverage areas that in combination mimic the beam coverage area of the replaced antenna, but do so in a plurality of sub-sectors. Because resources can be re-used between sectors, the introduction of sub-sectors effectively increases the subscriber bandwidth of the network.

Typically, the cost of such increase is in installing more antennas, even if no additional sites are needed, as each additional coverage area is associated with a corresponding antenna.

One approach has been to combine multiple transmitters to a common antenna. Unfortunately, in so doing, significant combining losses may be incurred. It is generally accepted as a rule of thumb that the cost of combining transmitters is 3 dB of the transmitted power for each combination. Thus, to combine 4 transmitters to a common antenna imposes a 6 dB power loss. To combine 8 transmitters to a common antenna imposes a staggering 9 dB loss .

Thus, an alternative approach is to add additional antennas. However, with the advent of modern beamforming antenna arrays, the addition of another antenna is no longer a trivial task, as the array comprises a monolithic structure for which a suitable footprint must be obtained. Unfortunately the demand for transmission and user bandwidth tends to concentrate in highly urban areas where physical space is often at a premium. As a result, many site managers now rent available footprint space according to the number of antennas.

Some efficiency was obtained with the development of the dual polarized antenna, where the polarizations are orthogonally oriented at 90° to one another. The component antenna elements generally have one port per polarization and a transmitter can be connected to each port without any combination losses.

Even with the introduction of dual polarized antennas, capacity is still outstripping the number of antennas available, so further economy is desirable in order to avoid the combination power loss problem.

Another approach has been to reorganize the antenna array elements to form two antennas in place of one. For example, where one formerly had an 8 column by 12 row antenna array, one could simply allocate half of the columns to a first 4 column by 12 row antenna array and the remaining elements to a second 4 column by 12 row antenna array. Clearly, however, the trade-off of such a solution is reduced flexibility or sensitivity in the beam formed by such reduced complexity antenna arrays. The number of rows and or columns can be related to the number of sample bits and/or sampling rate in the audio realm. As is well known, the greater the number of sample bits and/or sampling rate the higher the fidelity of reproduction. Similarly, the greater the number of rows and/or columns (sample rate) and or phase amplitude accuracy (sample bits) the more precisely the beam can be generated.

Those having ordinary skill in this art will readily appreciate that there may be instances, other than by replacing a sector antenna with a single antenna for servicing a plurality of sub-sectors, where it would be advantageous to combine several signals at a common antenna array without incurring the cost of significant combining losses .

SUMMARY OF THE INVENTION

Accordingly, it is desirable to provide a method and apparatus for processing a plurality of beamformed signals at a common antenna array with minimal combining losses .

It is further desirable to combine a plurality of signals at an antenna array without substantially adding to the number of antenna array elements or significantly reducing the sensitivity of the beam design.

The present invention accomplishes these aims by providing to a multiple beam antenna array, a plurality of signals that are allocated to the plurality of array elements in such a manner that combining losses are restricted to those elements that contribute minimally to the beamformed coverage area. In so doing, the combining losses are restricted to low power elements and are effectively attenuated.

Alternatively, the plurality of antenna elements may be effectively organized into a plurality of overlapping antenna arrays, each having more sensitivity than would be obtainable simply by dividing or allocating the antenna elements among the desired number of antennas.

Some configurations involve the use of a Butler matrix to feed different signals into a plurality of elements that contribute a significant amount of power to the beamformed coverage area. The Butler matrix effectively eliminates combining loss, but this option is available only if the dominant elements are effectively of equal amplitude and mutually orthogonal, or can be made effectively so.

According to a first broad aspect of an embodiment of the present invention, there is disclosed a beamforming network comprising a plurality of radio- frequency transmission components, the network having a

first plurality of connections, each with an associated antenna beam pattern and a second plurality of connectors, each with an associated antenna element, wherein each antenna beam pattern has a proportion of its radiated power concentrated in a subset of the plurality of antenna elements, wherein powers, corresponding to each of the plurality of patterns and associated with the antenna elements in the subset, are processed in a first manner, while powers, corresponding to each of the plurality of patterns and associated with the remaining antenna elements, are processed in a second manner, wherein a loss of total radiated power due to processing of the powers corresponding to the plurality of patterns, of the elements in the subset in the first manner and of the remaining elements corresponding to the plurality of patterns in the second manner is less than a loss of total radiated power due to processing of the powers of all of the elements corresponding to the plurality of patterns in the second manner.

According to a second broad aspect of an embodiment of the present invention, there is disclosed a method for combining a plurality of signals to generate a plurality of antenna beam patterns at a common antenna comprising a plurality of antenna elements, each pattern having a proportion of its radiated power concentrated in a subset of the plurality of elements, the method comprising the steps of processing powers corresponding to the plurality of patterns and associated with the elements in the subset, in a first manner; and processing powers corresponding to the plurality of patterns and associated with the remaining elements, in a second manner; wherein a

loss of total radiated power due to processing of the powers corresponding to the plurality of patterns, associated with the elements in the subset, in the first manner and due to processing of the powers corresponding to the plurality of patterns, associated with the remaining elements, in the second manner, is less than a loss of total radiated power due to processing of the powers corresponding to the plurality of patterns, of all of the elements, in the second manner.

BRIEF DESCRIPTION OF THE DRAWINGS

The embodiments of the present invention will now be described by reference to the following figures, in which identical reference numerals in different figures indicate identical elements and in which:

Figure 1 is an artwork layout for an exemplary prior art power divider/beamformer of weights shown in Table 3;

Figure 2 is an artwork layout for an exemplary 2x8 beamforming network layout in accordance with an exemplary embodiment of the present invention; and

Figure 3 is a plot of beam power as a function of angle for an exemplary beam;

Figure 4 is a plot of beam power as a function of angle for the exemplary beam of Figure 3, after processing according to the embodiment of Figure 2;

Figure 5 is an artwork layout for a beamformer in accordance with a second exemplary embodiment of the present invention; and

Figure 6 is a plot of beam power as a function of angle for an exemplary beam in accordance with the embodiment of Figure 5.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENT

In a beamformed antenna array, an array of antenna elements are varied in amplitude and phase in order to create a beam coverage area that is shaped to a desired contour. Such arrays could be one- or two-dimensional. In the latter situation, not infrequently, the beamforming is done on a row-wise or column-wise basis.

It has been observed that for some beamformed coverage patterns designed for use in higher order split- sectorization as discussed previously, that is, for the two (in this case) beam patterns, a significant proportion of the power is drawn primarily from a small number of the elements available to it. In many instances, the relative phase delay between such dominant (in terms of power draw) elements is 90° or relatively close to 90° so as to be considered roughly orthogonal signals, or the beamforming weights may be adjusted so that this is effectively the case.

For example, consider an exemplary beamforming 2x8 network, that is, one supporting 2 different antenna beams, each carrying the signal content presented to it at

corresponding beam ports denoted respectively Bl and B2. The beams are each generated by a plurality, 8 in this exemplary embodiment, of element ports, denoted El through E8 respectively.

In practice, the amplitude of each signal to be radiated by the beamforming antenna may be adjusted by splitting the available power among a plurality of (sets of) columns or rows of elements. For convenience, this is typically done on a pair-wise basis. Thus, there may be multiple layers of power-splitting (usually \og ₂ n layers, where n is the number of rows or columns available) and the amplitude of each row or column will be in proportion to the amount of power ultimately provided to it. This is generally achieved by the relative widths of the conductor traces. The determination of the track widths is well known to practitioners of the art. As it is dependent upon a number of factors, including but not limited to the implementation methods used, such as tri-plate, microstrip, suspended substrate and waveguide, the dielectric properties of the materials used, and substrate thickness, the calculations will not be described here. Figure 1 shows an exemplary artwork layout of a 1x8 beam-forming network showing a number of examples of such splitters 110 - 116.

The phase delay associated with each row or column may be adjusted by progressively introducing judiciously chosen delay elements along the power supply lines corresponding to each row or column so that the phase delay of each row or column will be in proportion to the total delay imparted to it. This is generally achieved by

the relative lengths of the conductor. The determination of the track lengths is well known to practitioners of the art. As it is dependent upon a number of factors, including but not limited to the implementation methods used, such as tri-plate, microstrip, suspended substrate and waveguide, the dielectric properties of the materials used, and substrate thickness, the calculations will not be described here. Figure 1 shows a number of examples of such lines 120-127 with varying lengths. The undulating nature of such lines permits minor adjustments to the delay values and tends to minimize the board real estate taken- up.

Both the power-splitting and the introduction of delay are thus effectively lossless, in contrast to the significant losses that accumulate when signals are combined into a column or row. Combination of signals typically occurs at the element points and is conventionally accomplished using combiners 281-283 and 286-288 such as those shown in Figure 2, discussed below, at element ports E1-E3 221-223 and E6-E8 226-228 respectively.

Those having ordinary skill in this art will readily recognize that the order by which the power- splitting takes place remains at the discretion of the antenna designer, although, for consistency purposes, in the beamformer layout, typically adjacent columns have been grouped together both for convenience and to avoid having to crossover tracks between beamformer outputs and their relevant groups of elements.

For example, consider Table 1 below, which represents the elemental powers from the dual beam eight element beamforming network described above, for a first signal. Table 1 shows that for the exemplary eight element antenna array design, fully 80% of the radiated power is concentrated in two beam elements, in this case E4 and E5, while miniscule amounts of power are allocated to elements E2 and E7 and only slightly greater amounts of power are allocated to elements El and E8.

Table 1

Table 1 also shows that approx 72° of phase difference exists between the 4 central elements which control approximately 90% of the radiated power. Accordingly, the exemplary beams are close to having a 90° phase difference between elements E4 and E5, the two

highest power elements. It is well known to antenna array designers that phase errors of ±10° are acceptable in many cases. The phases of elements E4 and E5 may thus be adjusted to be -45° and +45° respectively for Beam A and +45° and -45° for Beam B, so as to introduce a 90° phase difference.

As such, elements E4 and E5 are close to being orthogonal and radiate the majority of the available power.

Butler matrices are a well-known mechanism for forming multiple orthogonal antenna beams by "lossless" power combination, where the antenna patterns are mutually orthogonal .

For near orthogonal patterns, such as disclosed in Table 1 for elements E4 and E5, the weights for the dominant central elements can be made orthogonal and thus losslessly power combined using a Butler matrix. The remaining weights, which fine tune the antenna patterns, are then combined using conventional means, which imposes a 3dB loss for two-way combining.

The 2 x 2 Butler matrix used to combine the central two elements may be implemented using a standard 90° hybrid coupler, the design of which is well-known in this art.

Thus a revised weighted set, after adjusting the dominant elements to make them orthogonal and without fine tuning the remaining elements to compensate for such adjustment, is shown in Table 2. This is the set of weights actually applied by the beamformer network.

Table 2

The advantage of using a 2x2 Butler matrix in the beamformer, such as to inject a different signal corresponding to each of the two beam signals into each of the two input ports of the Butler matrix, is that the signals injected into one port will form part of the first of the two beams, and the signals injected into the second port will form part of the second of the two beams at the output element ports without any significant combining loss at these element ports.

The implementation of a 2x2 Butler matrix to reduce combining losses in a 2x8 beamformer network is shown in diagrammatic form in Figure 2.

The two beam signals are input at sector ports Bl 212 and B2 211 respectively.

For descriptive purposes, only the transmit paths are described herein. Those having ordinary skill in this art will appreciate that the transmitted and received beams will, by reciprocity, be identical for each of the two ports. The beam signals are each fed into a sampling coupler 241 and 242, which couples off a fraction of the available power according to the weights set out in Table 2, that is, 20% of the power input at second port B2 211 is coupled off to drive the beamformer network leading to element ports E1-E3 221-223 and E6-E8 226-228 at coupler 241, with the remaining portion being fed into an input port 251 of 2x2 Butler matrix 250. Similarly, 20% of the power input at sector port Bl 212 is coupled off to drive the beamformer network to element ports E1-E3 221-223 and E6-E8 226-228 at coupler 242, with the remaining portion being fed into an input port 252 of 2x2 Butler Matrix 250. Directional couplers 241, 242 are shown in Figure 2 as being terminated by suitable load resisters 243, 244 respectively.

The signals input to Butler matrix 250 are losslessly combined and output at output ports 253, 254 for connection to element ports E4 and E5 224, 225, while the power coupled off by coupler 241 is connected to T-splitter

261, where it is split into appropriate powers, as determined from the weights set out in Table 2, to be fed to T-splitters 262, 263 respectively.

One output of T-splitter 262 is connected to one input of each of couplers 281 and 282 at element ports El 221 and E2 222 respectively through T-splitter 264 while

the other output is connected to one input of coupler 283 at element port E3 223.

One output of T-splitter 263 is connected to one input of each of couplers 287 and 288 at element ports E7 227 and E8 228 respectively through T-splitter 265, while the other output is connected to one input of coupler 286 at element port E6 226. These powers provide the signals that comprise Beam A.

Similarly, the power coupled off by coupler 242 is connected to T-splitter 271, where it is split into appropriate powers to be fed to T-splitters 272, 273. One output of T-splitter 272 is connected to a second input each of coupler 281 and 282 at element ports El 221 and E2

222 respectively through T-splitter 274, while the other output is connected to a second input of coupler 283 at element port E3 223.

One output of T-splitter 273 is connected to a second input of each of couplers 287 and 288 at element ports E7 227 and E8 228 respectively through T-splitter 275, while the other output is connected to a second input of coupler 286 at element port E6 226. These powers provide the signals that comprise Beam B.

The outputs of couplers 281-283 and 286-288 are connected to element ports E1-E3 221-223, E6-E8 226-228 and terminations 291-293, 296-298 respectively.

The relative phases of each of the ports E1-E8 221-228 are set by careful selection of the line lengths of the interconnecting circuitry, in manners well known to practitioners of the art of beamforming. Similarly the

determination of the coupler and power splitter division ratios is not described here as it is well known and understood by practitioners of the art, often being optimised to suit the physical beamformer parameters by computer-aided methods, as in many cases, more than one solution may be valid.

Because outlying elements El 221 through E3 223, E6 226 through E8 228 have been combined in conventional fashion, following the above-described rule, they would suffer approximately 3 dB of loss upon being so combined. However, because these six ports only account for approximately 20% of the power in the signal, the total power loss from combining is only 50% of 20% of the total power, or about 10% of the total power. Those having ordinary skill in this art will readily recognize that this is equivalent to a 0.5 dB loss and thus a considerable improvement over the conventional means of combining two signals at each element of one antenna, which results in a 3 dB loss.

The 2x2 Butler Matrix 250 may be implemented in this case as a branch arm coupler as is well-known in this art.

As indicated, the only trade-off for achieving such an improvement beam combining losses is that the elements (in this case central elements E4 224 and E5 225) should be sufficiently close to orthogonal that one may combine them using a 2x2 Butler matrix 250, which is a very cost-effective trade-off.

This may be seen with regard to Figure 3 and 4 which respectively show simulated plots of beam power as a function of angle for the beamformers of Table 1 (using conventional combining only) and Table 2 (using the inventive embodiment of Figure 2) .

In Figure 3, the power of the generated beam A 300 is shown. The dominant portion 310 of the beam 300 is relatively flat about the desired angle which appears to be around -25°, and there are minimal side lobes 320. The power curve of the generated Beam B (not shown) would be a mirror image of Figure 3.

In Figure 4, the power of the modified beam 400 is shown. Again, the dominant portion 410 of the beam 400 is relatively flat about the desired angle, namely -25°, and relatively unchanged from that portion 310 of the original beam 300, while the side lobes 420 are considerably increased. However, at a level below - 18dB relative to the peak of beam 400, the side lobes 420 are still acceptable. Moreover, the side lobes 420 and beam shape can be further refined by adjustment of the weights of elements E1-E3 221-223 and E6-E8 226-228 if desired.

In effect, by combining power in this manner, one is able to effectively save an antenna by generating two independent antennas from one antenna without the conventional 3dB performance penalty, at the cost of some adjustments to the beamforming weights and some consequent minimal degradation in interference immunity, in order to permit the dominant elements to be as orthogonal or as nearly so as possible to permit combining them using a Butler Matrix. This saving could be realized by reducing

the cost in terms of antenna elements of implementation, such as by introduction of sub-sectors or by increasing the accuracy of the beam pattern designs (in the exemplary situation for the sub-sector patterns) by applying a greater number of antenna elements to each beam pattern design.

In order to deal with this trade-off, one may adjust the beamforming weights, because the dominant elements will be orthogonal (or have a 90° relative phase shift) as a result of the processing through the 2x2 Butler matrix 250 in the example of Figure 2, rather than the desired 72° phase shift. This can be accommodated by altering the power and phase relationships of the non- dominant elements in a manner well known to those having ordinary skill in the relevant art.

Those having ordinary skill in this art will readily recognize that if one is prepared to compromise slightly on the accuracy of the beam design, one could dispense with the Butler matrix 250 entirely. That is to say, for beam designs in which the power was again concentrated in a small number of elements, but those predominant beams did not share a near orthogonal relationship, by slightly reducing the number of columns, one could again achieve savings in terms of overall signal degradation due to combining losses.

Consider for example, the situation where the two beam patterns had for example, weights as set out below in

Tables 3 and 4. The beam power as a function of angle for the element weights of Table 3 are shown in Figure 6. A plot of the beam power as a function of angle for the

element weights of Table 3 would be a mirror image of Figure 6. (The numbers shown are approximations used for illustrative purposes.)

Table 3-Beam A

Table 4-Beam B

Again, in both Table 3 and Table 4, the majority of the power, in this case 90% of the power, is confined to two elements. In this example the four outer elements are

fed directly by their appropriate beamforming networks with no loss associated, because there is no combining. The central four elements, however are fed with power from both beamforming networks. In this case, knowledge of the relative weights from each beamforming network permits optimisation of the power combining ratios both within the individual beamforming networks and at the point of combining at the element, to significantly reduce power losses compared with conventional power combining methods that lead to a 3 dB loss. For the weights shown in Table 3 and Table 4, the use of 7.83 dB couplers for elements E3 and E6, together with 5.0 db couplers for elements E4 and E5, reduces the overall combining loss from 3 dB to 0.75 dB (~50% to ~16% of available power) . The coupler values are calculated to minimise the lost power. To calculate the coupling ratio r, the following equations may be used:

"inA ⁼ "outA ' ( ^■ * ~~ ^r ) I ' 'r

P, _nTo , _a , = P _outA «y - r) + P _oulB I T

For optimum coupler efficiency, P _mTotal must be minimised by adjusting the value of r. This can be achieved by mathematical analysis, graphing of the equation or computer aided techniques such as using the solver function in a spreadsheet program.

The coupler value is normally expressed in decibel terms such that:

Coupler value=10*loglO (r) .

Once this principle is understood the skilled practitioner of the art will be able to determine optimal coupling ratios in accordance with the present invention for any required power distribution.

Figure 5 is an illustration of the beamformer for a split-sector array 500 using the weights of Tables 3 and 4. The elements are numbered El 521 through E8 528, with elements E3 523, E4 524, E5 525 and E6 526, being the centermost elements containing a major (95%) proportion of the radiated power between the two beams, being combined, while elements El 521, E2 522, E7 527, and E8 528, bearing less than 5% of the radiated power, are left not combined. The signals for the two beams, Beams A and Beams B (not shown) , enter through the beamports Bl 511 and B2 512 respectively, and are divided out as shown using the weights described in Tables 3 and 4, to excite elements El- E8 521-528.

The second exemplary beam-forming network shown in Figure 5 has two ports, one for Beam A (input port Bl 511) and one for Beam B (input port B2 512) . For descriptive purposes only, the transmit paths will be described herein. Those having ordinary skill in this art will appreciate that the transmit and receive beams will, by reciprocity, be identical for each of the two ports.

Input port Bl 511 is connected to the input port of T-splitter 531 where it is split into appropriate powers determined from the weights set out in Table 3. One output of T-splitter 531 is connected to the input port of T- splitter 532 where it is split into the appropriate powers determined from the weights in Table 3.

One of the output ports of T-splitter 532 is connected to the input port of T-splitter 534, where it is split into appropriate powers determined from the weights set out in Table 3 and the other output to coupler 553. The output ports of T-splitter 534 are connected to elements El 521 and E2 522 respectively.

The second output port of T-splitter 531 is connected to the input port of T-splitter 533, where it is split into appropriate powers determined from the weights set out in Table 3.

One of the output ports of T-splitter 533 is connected to the input port of T-splitter 535, where it is split into appropriate powers determined from the weights set out in Table 3 and the other output to coupler 554.

Input port B2 512 is connected to the input port of T-splitter 541 where it is split into appropriate powers determined from the weights set out in Table 4. One output of T-splitter 541 is connected to the input port of T- splitter 543 where it is split into appropriate powers determined from the weights set out in Table 4.

One of the output ports of T-splitter 543 is connected to the input port of T-splitter 545, where it is split into appropriate powers determined from the weights set out in Table 4, and the other output to coupler 556. The output ports of T-splitter 545 are connected to elements E7 527 and E8 528 respectively.

The second output port of T-splitter 541 is connected to the input port of T-splitter 542, where it is

split into appropriate powers determined from the weights in Table 4.

One of the output ports of T-splitter 542 is connected to the input port of T-splitter 544 where it is split into appropriate powers determined from the weights in Table 4, and the other output to coupler 555.

One of the output ports of T-splitter 544 is connected to an input port of coupler 553. The second of the output ports of T-splitter 544 is connected to an input port of coupler 554.

The coupler 553 is used to combine the signals for both Beam A and Beam B prior to connecting the combined signals to antenna element E3 523. In this case, a directional coupler is used, whose value is determined from the weights in Tables 2, 3 and 4. The unused port of coupler 553 is connected to an appropriate terminating resister 563.

The coupler 554 is used to combine the signals for both Beam A and Beam B prior to connecting the combined signals to antenna element E4 524. In this case, a directional coupler is used, whose value is determined from the weights set out in Tables 3 and 4. The unused portion of coupler 554 is connected to an appropriate terminating resister 564.

One of the output ports of T-splitter 535 is connected to an input port of coupler 555. The second of the output ports of T-splitter 535 is connected to an input port of coupler 556.

The coupler 555 is used to combine the signals for both Beam A and Beam B prior to connecting the combined signals to antenna element E5 525. In this case a directional coupler is used, whose value is determined from the weights in Tables 3 and 4. The unused port of coupler 555 is connected to an appropriate terminating resister 565.

The coupler 556 is used to combine the signals for both Beam A and Beam B prior to connecting the combined signals to antenna element E6 526. In this case, a directional coupler is used, whose value is determined from the weights set out in Tables 3 and 4. The unused port of coupler 556 is connected to an appropriate terminating resister 566.

The relative phases of each of the port elements

E1-E8 521-528 are set by careful selection of the line lengths of the interconnecting circuitry in manners well known to practitioners of the art of beamforming. Similarly, the determination of the coupler and power splitter division ratios is not described here as it is well known and understood by practitioners of the art, often being optimised to suit the physical beamformer parameters by computer-aided methods, as in many cases, more than one solution may be valid.

In Figure 6, the power of the generated Beam

A 600 from the weights detailed in Table 3 is shown. The dominant portion 610 of Beam 600 is relatively flat about the desired angle which appears to be around -25°, and there are minimal side lobes 620. The power curve of the generated Beam B (not shown) from the weights detailed in

Table 4 would be a mirror image of Figure 6. The side lobes 620 and beam shape can be further refined by adjustment of the weights of elements E1-E6 521-526 in the case of Beam A and E3-E8 523-528 in the case of Beam B if desired.

Other embodiments consistent with the present invention will become apparent from consideration of the specification and the practice of the invention disclosed therein.

The present invention can be implemented in digital electronic circuitry, or in computer hardware, firmware, software, or in a combination thereof. Apparatus of the invention can be implemented in a computer program product tangibly embodied in a machine-readable storage device for execution by a programmable processor; and actions can be performed by a programmable processor executing a program of instructions to perform functions of the invention by operating on input data and generating output. The invention can be implemented advantageously in one or more computer programs that are executable on a programmable system including at least one input device, and at least one output device. Each computer program can be implemented in a high-level procedural or object oriented programming language, or in assembly or machine language if desired; and in any case, the language can be a compiled or interpreted language.

Suitable processors include, by way of example, both general and specific microprocessors. Generally, a processor will receive instructions and data from a read- only memory and/or a random access memory. Generally, a

computer will include one or more mass storage devices for storing data files; such devices include magnetic disks, such as internal hard disks and removable disks; magneto- optical disks; and optical disks. Storage devices suitable for tangibly embodying computer program instructions and data include all forms of non-volatile memory, including by way of example semiconductor memory devices, such as EPROM, EEPROM, and flash memory devices; magnetic disks such as internal hard disks and removable disks; magneto-optical disks; CD-ROM disks; and buffer circuits such as latches and/or flip flops. Any of the foregoing can be supplemented by, or incorporated in ASICs (application- specific integrated circuits), FPGAs (field-programmable gate arrays) or DSPs (digital signal processors) .

The system may comprise a processor, a random access memory, a hard drive controller, and an input/output controller coupled by a processor bus.

It will be apparent to those skilled in this art that various modifications and variations may be made to the embodiments disclosed herein, consistent with the present invention, without departing from the spirit and scope of the present invention.

Other embodiments consistent with the present invention will become apparent from consideration of the specification and the practice of the invention disclosed therein.

Accordingly, the specification and the embodiments are to be considered exemplary only, with a

true scope and spirit of the invention being disclosed by the following claims.