the rf spectrum of today is increasingly dense with the rapid introduction of commercial , civil and military emissions , which has placed extreme demands on military situation awareness and early - warning equipment and missions . the modern weapon and delivery systems have evolved to be silent and stealthy , and weapons are able to cruise at supersonic / hypersonic speeds . many of these threats employ low - probability - of - intercept ( lpi ) technology to further evade detection . similarly , reconnaissance and surveillance activities are hampered , lacking bandwidth , high sensitivity systems with direction finding ; to address complex scan - on - scan issues . detecting and analyzing signals of special interest is increasingly difficult . addressing these operation issues require system architectures which can instantaneously look in all hemispheric directions while monitoring the full frequency coverage ( typically several ghz ), have antenna gain for sensitivity , and precision signal direction - finding measurement accuracy . for those skilled in this technology sector , will readily recognize this as somewhat contradictory requirements and extremely challenging to accomplish . antenna gain / high sensitivity implies narrow antenna beam - width , or otherwise high processing gain . certainly it &# 39 ; s possible to configure a host of narrow - beam antennas dispersed spherically and provide requisite volumetric gain , but the number of antennas and receivers become extremely large in number . this invention can address all of these operational issues , by providing instantaneous hemispheric coverage for broad frequency bandwidths , using a multi - beam lens where signal energy is focused ( to provide high gain ) on a frequency - independent focal array feed - structure ; where the feed elements are split and combined in a novel manner that significantly minimizes the number of required rf channels and subsequent receivers , as compared with the number of elements used . channel and row summing forms narrow fan - beams covering the entire field - of - view in one axis , with an acceptable overall antenna gain penalty . further , row / column summing retains traceability back to the original focal point elements ; and by exploiting the differential - amplitude information for adjacent row / column , precision direction finding is achieved . with this implementation , the required number of rf channels and subsequently required receivers are typically reduced by a factor of 3 , as compared with the total number of elements . the ( hmfe ) lens has been extensively studied internationally and used for specialized microwave and millimeter applications for communications , commercial broadcast and satellite tracking . other recent areas of interest ( as indicated in open literature ) include collision avoidance and other millimeter wave applications . as an example , satellite tracking is accomplished by providing a reflective surface on the flat side of the hmfe lens , where the semi - spherical portion of the lens is oriented vertically , exposed to the satellite rf emission . an electro mechanical arm supports a receiving element , which is first scanned over a portion of the lens for acquiring the satellite signal and accurately positioned to maintain tracking of the satellite signal ( mostly geo - stationary ). other applications typically use patch antenna elements as a feed structure , for signal detection . in these applications , the actual signal direction is inconsequential with no necessity to measure the direction . these applications using the multi patch - element feed are narrow - band and primarily limited to communication . for this invention , a multifold solution is disclosed to address deficiencies of current art direction - finding systems . first , a relatively simple antenna and feed assembly , using the hmfe lens is disclosed . the lens shown in fig1 is composed of a non - homogenous medium with a dielectric gradient index , whose relative permittivity varies radial ( center to outer radial edge ) given by : where n ( r ) is the index of refraction of the spherical rf lens at a radial distance r from its center . a smooth variation of index of refraction from the radius is very difficult to achieve , but a step - wise shell construction has proven to be very successful by several vendors . rosedal associates , located in santa calif . produces a product line of lens antennas with a variety of sized and characteristics . another vendor offering a product line of lens antenna is lun &# 39 ; tech located in france . the operation of the lens 1 is best understood by tracing the rf ray path as the lens receives rf energy from an incoming plane wave 2 and migrates through the core of the lens . the index of refraction is graded in such a way as to cause the impinging ray to bend and focus 4 at a finite location on the semi - spherical side of the lens . the lens with either the rectilinear or angular conformal array feed structure is shown in fig2 incorporating an feed array 2 a and 2 b of frequency - independent elements 3 , approximately uniformly displaced to form an array of elements located at the lens focal plane . for surface platform applications , the lens and array feed structure may be constructed to provide near hemispheric coverage , or may utilize fewer elements and provide quadrant coverage . plane - waves arriving at the lens are focus 1 a and 1 b to illuminate one or more elements on the focal plane feed structure . the feed element spacing is matched to the lens focal - point spot - size for the systems highest operating frequency , such that when the lens focal - point spot is exactly centered on a single elements , the power level at the closest neighboring element is approximately 6 to 10 db down from the focal - point spot power . of course numerous other spacing to power relationships can be chosen based on application objectives . the choice of 6 to 10 db is partially for illustration purposes , but also based on previous experience , which favors using this value to accommodate widening spot - size for lower frequencies , constraining antenna - gain loss , and when the focal - point spot is centered exactly between two elements , the received power level of both elements are on - the - order of 3 db down from the spot power level . this geometry will assure that a useful differential amplitude condition between adjacent feed elements , while providing acceptable antenna gain and support fine direction - finding measurement , which will be further developed and described later . mutual coupling between feed elements can be a limiting factor particularly if chosen spacing is less than λ / 2 . also , constructing the feed array using planar antenna elements such as the spirals , sinuous exhibit broad bi - directional beams ( toward the lens and reverse direction ) needing a layer of rf absorber material applied to the reverse side of the feed - structure . also , it should be pointed out that the feed element should be extremely broad beam ( approximately 60 degrees of greater for maximum efficiency ) as compared with the lens focus - point beam . narrower beam width feed elements impose focal - beam side - lobe amplitude taper , which lowers the lens side - lobe level at the expense of some lens efficiency . to further define the feed element spacing , we must define the lens focal - point spot - width , which will influence the selected feed - element spacing . diffraction theory defines the minimum focal - point spot - radius ( r a ) for the lens aperture of diameter d is equal to : where d is the diameter of the lens ; f is the focal length of the lens ( from the center of the of the sphere to the focal point ), and r a is the first null location ; and λ is the free space wavelength for the design frequency ( highest frequency of operation ). therefore , the width ( first null to null ) of the focal - point spot - width is simply r a times 2 and the spot - width expressed in degrees is : 180 ( 2 r a /( πd / 2 )). an example antenna is comprised of a 112 mm ( 4 . 4 ″) diameter lens , with the design frequency of 18 . 0 ghz , provides 25 . 6 db gain , with a half - power (− 3 db ) beam - width ( hpbw − 3 ) of 10 . 7 degrees . fig3 shows the calculated focal - point spot beam - pattern 1 ( or the airy pattern , fig3 shows the pattern for a 3 . 5 ″ diameter lens ); where the focal - point spot is shown exactly centered on a single element ( centered at 0 degrees ) with the adjacent element to be located at approximately the − 10 db point 2 on the focal - point beam pattern . solving the focal - point radial spot - width ( null to null ) in inches is given by : where f is focal length of 4 . 4 / 2 and λ is 39 . 37 ( 299 . 792 / 18000 ) for 18 ghz design frequency and d of 4 . 4 , gives radius r a equal to 0 . 4 inches . also , expressed in degrees is 180 ( 2 r a /( πd / 2 )) which gives ( θ 2 r a )= 20 . 84 degrees . again , this represents null to null , and the airy pattern is known to approximate the bessel function , where the − 3 db and the − 10 db point to the first null is approximately a ratio 0 . 42 and 0 . 7 respectively . therefore , the − 10 db point , would equate to a spot beam - width of approximately 14 . 5 degrees . the number of required equally spaced elements to cover a half - spherical area , configured in rows and columns , can be estimated by : which equals approximately 30 for this example design . this formula works reasonably well for large population of elements , where the number of elements overlaying the spherical edge is a small percentage of the total . for illustration the flattened view of the semi - spherical feed structure is shown in fig4 a which contains 37 elements as opposed to the calculated 30 . the feed elements shown in fig4 a is organized for creating columns 4 and rows 3 . this is further described with fig4 b where each element is power divided 1 creating two paths for each element . the first path is 2 is summed to create rows and the second path is summed 3 to create columns . for this example , split and summing provides 7 rows , 7 columns for a beam broadening loss ( fan - beam ) of approximately 8 . 5 db , reducing the lens gain to approximately 16 db . through split / summing the 37 discrete elements are reduced to 15 channels . fig5 shows the row / column segmentations , where the intersection of any row and column identifies the elements illuminated by the lens . with the antenna subsystem described , the second solution is further disclosed . as shown in fig6 , the row / column outputs 2 are passed from the antenna subsystem and interfaced over coax , waveguide or rf over fiber or other interface media to the multi - channel activity detection receiver ( mcadr ) subsystem , potentially located in an enclosed space or below - deck in the case of a naval vessel or other platforms , for final processing . the mcadr has a matching number of parallel channels for simultaneously processing all column / rows for signal activity . upon amplitude threshold crossing of any column / row pair , the mcadr and the parameter encoder ( pe ) derives the signal features and amplitudes for the primary column / row and their adjacent . the mcadr activity receiver will typically be a broadband digital or analog channelizer , an instantaneous frequency measurement ( ifm ), wideband logarithmic amplifier / detector or other suitable high - probability - of - intercept receiver . the signal processor 5 receives the measurement data to include amplitude for each active row / column and their highest amplitude adjacent elements . the signal processor 6 utilizes the df decode table to convert the maximum amplitude pair of column / row to course directional estimate . using the amplitude data as shown in fig7 the highest adjacent pair in both row and column are subtracted to create differential - amplitude measurement , having a magnitude versus frequency slope , 2 appropriately scaled by frequency ( correct for lens - focal point changes with operating frequency , etc .). both ( row and column ) differential amplitude measurements , and identified highest row and column are used by the signal processor to calculate the precision bearing for both azimuth and elevation . again , the highest identified row and column provide the first - order bearing measurement and the corresponding differential amplitude measurements are then applied for fine correction . the described first - order bearing and fine correction process , using the identified highest row / column and differential amplitude data , can be potentially processed through a variety of means other than that described by direct table lookup ; i . e . algorithmic conversion and use of kinematic tracker algorithms , etc . to further improve tracking accuracy for signals traversing the volume . it is pointed out that the row / column fan - beams have considerable gain which maintain high signal - to - noise ( snr ) for improved directional estimation accuracy . numerous other variations can be adapted for this invention , such as further summing of either column or rows will provide an all sum , an equivalent of an omni with little to no gain , but high probability of intercept detection with a single channel . when omni activity detection is acceptable , the all sum and a single broadband activity receiver can rapidly measure frequency to initiate a fast - call operation utilizing narrow - band fast tuning rf receivers , for subsequent processing of column / row channels . this is often referred to as a fast - call mono - pulse receiver architecture , which typically utilizes a delay line to delay the channel / row rf allowing time for the fast - call receiver to tune to the same detected pulse for column / row processing . another option is to use tune step - and - dwell of row / column narrow band receivers , time - sharing a limited number of receivers , and avoid the need for rf delay and wideband activity receivers . further , each row and column 1 to n could have an incremental increase in rf delays , where the incremental value exceeds the required time - time of the multi - channel fast - call receivers . such an implementation would allow am n - position switch to cycle through the incremental rf delay and process all rows / columns with a single narrow band fast - call receiver . the notional design described in this disclosure was modeled as an 7 × 7 row / column receiver system , utilizing the 4 . 4 inch hmfe lens , with the sinuous semi - spherical feed structure . fig8 shows the summary performance covering 8 to 18 ghz with directional accuracies ranging from 1 . 7 to 0 . 44 degrees rms . though not specifically stated elsewhere , the sinuous antenna elements used in the lens feed , can be dual polarization elements to support signal polarization measurement . this can be accomplished through switching between orthogonal polarizations or simultaneous processing of both polarizations without switching . other elements that can be utilized include the horn or the vivaldi .