BACKGROUNP Purpose of the invention: General Statement of the problem Improve ability to localize transmission of diverse signals to a multiplicity of geographically distinct destinations Improve downlink and uplink channel reuse in a given area Improve reception of wireless broadcast signals from users by sampling an array of directional antennae to derive the local transmission field strength. The basic method uses a lumped location model as an approximation to computationally isolate dispersed multi-user transmission and reception. • Methods utilizing this approach rely on a combination of antennas and signal processing to transmit and receive user transmissions. Application Examples • Base station transceivers wherein the uplink bandwidth is comparable to the downlink bandwidth. Such applications include situations wherein there is a greater density of users than can readily be afforded. Such applications include but are not limited to: • CDMA multi-user base station transceivers in densely populated areas. • FDMA, TDMA and GSM multi-user base station transceivers in densely populated areas. • SDMA multi-user base station transceivers in densely populated areas. • Other spread spectrum base station transceivers where the downlink bandwidth is a multiplicative factor greater than the uplink bandwidth: National Information Infrastructure (Nil) neighborhood base station transceivers • Video and Movie On Demand wireless base station transceivers • Improved multi-carrier transceivers Prior Art Approaches Overview This section discusses location determination based upon several different kinds of antennas: • Single omni-directional antenna determination. • Lee style pair of receiving antennas to minimize cochannel interference. • Phased array background • Macro-diverse location determination Single omni-directional antenna determination. • Basic Mechanism • Advantages • Disadvantages Lee style wireless base station antenna sets • Basic Mechanism • Advantages • Disadvantages • Directional antenna discussion Phased array background • Basic Mechanism Advantages • Disadvantages D3 Domed Lens phased arrays • Basic Mechanism • Advantages • Disadvantages Circular Phased Arrays • Basic Mechanism • Advantages • Disadvantages Macro-diverse location determination Basic Mechanism Advantages Disadvantages D3 Spectrum Patent 1 Very Large Array and other long distance interferometers NASA deep space communication systems References 1 Viterbi, Andrew J., CDMA: principles of spread spectrum communication, (c) 1995, Addison Wesley Longman, Inc., ISBN 0-201-63374-4 2. Mouly, Michel and Marie-Bemadette Pautet, The GSM System for Mobile Communications (c) 1992, Mouly and Pautet, ISBN 2-9507190-0-7 3. Lee, William C. Y., Mobile Cellular Telecommunications: Analog and Digital Systems. 2"" ed., (c) 195, 1989 McGraw Hill, Inc., ISBN 0-07-038089-9 a. Chapter 5: "Cell-Site Antennas and Mobile Antennas" b. Chapter 6: "Co-channel Interference Reduction" 4. Mehrota, Asha, Cellular radio: analog and digital systems, (c) 1994 Artech House, Inc., ISBN 0-89006-731-7 5. Sreetharan, Mothothamby and Rajiv Kumar, Cellular digital packet data, (c) 1996 Artech House, Inc., ISBN 0-89006-709-0 6. Toh, C-K, Wireless ATM and ad-hoc networks: protocols and architectures, (c) 1997 Kluwer Academic Publishers, ISBN 0-7923-9822-X 7. Monzingo, Robert A., Introduction to adaptive arrays, (c) 1980 John Wiley and Sons, Inc., ISBN 0-471-05744-4 8. Simon, Marvin K., Jim K. Omura, Robert A. Schultz, Barry K. Levitt, Spread Spectrum Communications, vol. Ill, (c) 1985 Computer Science Press, Inc. ISBN 0-88175-015-8 (v. Ill), ISBN 0-88175-017-4 (Set) 9. Balanis, Constantine A. Antenna Theory: Analysis and Design, (c) 1982 Harper & Row, Publishers, Inc., ISBN 0-06-040458-2 10. Shannon, Claude E. and Warren Weaver, The Mathematical Theory of Communication, (c) 1949 Board of Trustees of the University of Illinois, mini Books edition, 1963, ISBN 0-252-72548-4 11. Gibson, Jerry D. (editor) The mobile communications handbook, (c) 1996 CRC Press, Inc., ISBN 0-8493-8573-3 a. Milstein, L. B. and M. K. Simon, "Spread Spectrum Communications" 12. Sklar, Bernard, Digital Communications: Fundamentals and Applications- (c) 1988 P. T. R. Prentice Hall, ISBN 0-13-211939-0 13. Wilson, Stephen G, Digital Modulation and Coding, (c) 1996 Prentice-Hail, Inc., ISBN 0-13-210071-1 14. Kesteloot, Andre, Charles L. Hutchinson and Joel P. Kleinman (editors). The ARRL Spread Spectrum Sourcebook, (c) 1991 American Radio Relay League, ISBN 0-87259-317-7 15. Papas, Charles Herach, Theory of electromagnetic wave propagation, (c) 1965, 1988 Charles Herach Papas, Dover edition, ISBN 0-486-65678-0 16. Doble, John, Introduction to radio propagation for fixed and mobile communications, (c) 1996 Artech House, Inc., ISBN 0-89006-529-2 17. Straw, R. Dean, Gerald L. Hall, Brian Beezley, The ARRL Antenna Book, (c) 1994 American Radio Relay League, ISBN 0-87259-473-4 18. Danzer, Paul, Joel P. Kleinman, R. Dean Straw (editors). The ARRL Hg.ndbook for Radio Amateurs. 75* edition, (c) 1997 American Radio Relay League, ISBN 0-87259-178-6 19. Johnson, Richard C, Henry Jacik (ed.). Antenna Engineering Handbook 3^" ed.. (c) 1993, 1984, 1961 McGraw-Hill, Inc., ISBN 0-07-032381-X 20. Lo, Y. T., S. W. Lee (ed.), Antenna Handbook vol 11: Antenna Theory, (c) 1993 Van Nostrand Rheinhold, ISBN 0-442-01593-3 a. Lo, Y. T., "Array Theory", Chapter 11 b. Mailloux, R. J., "Periodic Arrays", Chapter 13 c. Lo, Y. T., "Aperiodic Arrays", Chapter 14 d. Rahmat-Samii, Y., "Reflector Antennas", Chapter 15 e. Lee, J. J., "Lens Antennas", Chapter 16 21. Lo, Y. T., S. W. Lee (ed.). Antenna Handbook vol IIL Applications, (c) 1993 Van Nostrand Rheinhold, ISBN 0-442-01594-1 a. Tang, Raymond, "Practical Aspects of Phased Array Design", Chapter 18 22. Courant, R. and D. Hilbert, Methods of Mathematical Physics vol. L Chapter 1: "The Algebra of Linear Transformations and Quadratic Forms", (c) 1937 Julius Springer, Berlin, 1" English edition, republished by John Wiley & Sons, 1989, ISBN 0-471-50447-5. 23. Kaiser, Gerald, A friendly guide to wavelets, (c) 1994 Birkhauser, Boston, ISBN 0-8176-3711-7 Patent References 24. Stangel, John J., et. al., USPTN 3,755,815, "Phased Array Fed Lens Antenna", filed Dec. 20, 1971, issued Aug. 28, 1973 25. Giannini, Richard J., USPTN 3,816,830, "Cylindrical Array Antenna", filed Nov. 27, 1970, issued June 11, 1974. 26. Stangel, John J., et. al. USPTN 4,451,831, "Circular array scanning network", filed June 29, 1981, issued May 29, 1984 SUMMARY OF THE INVENTION Definitions Convex shape • Normal • Cellular communications system Base Station uplink downlink users charmels Antenna • Directional • Omnidirectional • Antenna Attributes Anterma Array • Phased array • Dual cochannel interference canceling • Micro-diverse • Macro-diverse Goals of this family of mechanisms Improve ability to transmit to a large number of spatially distributed users by geometrically partitioning the transmission process. Improved downlink support for increased channel reuse. Improved ability to isolate uplink user transmissions by means of geometrically partitioning the space-time delay domain of transmission. This geometrical partitioning of the downlink and uplink transmission domain is made possible by the geometry of the claimed anterma arrays and claimed signal processing which is derived based upon the claimed antenna array geometry. Basic Mechanism A micro-diverse directional transmitting antenna array positioned proximately upon the boundary of a convex shape whereby the primary attenuation lobes of neighboring antennae overlap. Distinct transmissions by distinct directional antenna components can utilize the same channel resources if the transmitting directional antenna components are not adjacent. Further, a micro-diverse directional antenna array comprising both transmitting and receiving directional antenna components positioned proximately upon the boundary of a convex shape whereby • the primary attenuation lobes of nearest neighbor transmitting directional anterma components overlap and the primary attenuation lobes of nearest neighbor receiving directional antenna components overlap. This creates a situation in which the reception of signals by said array fi-om the user (uplink) space-time- delay domain of transmission can be effectively modeled as a banded linear transformation upon discretized space-time-delay domain of transmission yielding the antenna reception at discrete time steps. • Distinct transmissions by distinct directional antenna components can utilize channel resources if the transmitting directional anterma components are not adjacent. The discretized space-time-delay domains of uplink and downlink transmission have favored coordinate systems which will be seen to simplify calculation of said linear transformation. Said banded linear uplink and downlink transformations are approximations of the collective attenuation map of the uplink and downlink antenna array components, respectively. Said banded uplink linear transformations under very broad conditions are known to be invertible with numerically stable inverses, which are also banded. Said numerically stable inverse implies that the discretized space-time-delay domain of transmission can be derived by a said inverse of said banded linear transformation of the discretized space-time-delay domain of transmission applied to the discretely sampled received signals by said antenna array over time. Stated in a mathematically equivalent form: The discretized space-time-delay uplink domain of transmission can be approximately derived fi^om a collection Finite Impulse Response filters applied to the antenna array reception samples. The issue of side lobes for both uplink and downlink antenna components in said directional antenna arrays are rendered secondary and the issue of structuring the attenuation contour map to support acceptable linear transformations primary, thus leading to a new paradigm in antenna architecture. Basic Advantages The downlink transmissions achieve the ability to densely reuse the downlink channels for a given geographical area. Wireless muhimedia distribution in densely populated urban settings is significantly improved. This greatly reduces the cost of deployment and maintenance of the transceivers necessary for such applications. It also aids support of cellular telephone usage in extremely dense urban settings such as rush hour and the crowds near sporting, entertainment and other highly populous events. The entire discretized space-time-delay uplink transmission domain can be approximated by the filtered reception of said antenna arrays. This has the advantage of isolating the number of cellular users to be processed to a reasonable number for base station call processing in application situations experiencing extremes in user density. This has the advantage of providing a significant processing gain to the reception of start of communications messages from wireless communications system users. This has the advantage of providing a means of isolating much of the multi-path components of uplink transmission into manageable time-step related dispersion patterns, which can then be integrated to increase processing gain. Use of two or more of these antenna arrays in a macro-diverse configuration fiirther refines a said approximation of the discretized uplink space-time-delay user transmission domain. Said refinements increase the accuracy of said uplink models. Said increases in accuracy bring greater gain to the derived received signals of the user transmission domain. Versions of the invention which cover a symmetric convex shape's surface, such as a sphere's or octagon's, with symmetrically positioned and oriented directional antenna components will possess symmetric attenuation contour maps, which means that there will be no non-uniform side lobes. BRIEF DESCRIPTION OF THE DRAWINGS FIG. 1 depicts a 2-D circular a directional antenna array embodiments. FIG. 2 depicts a typical directional antenna components FIG. 3 depicts a basic 2-D picture of a space-time-delay user transmission domain relative to the antenna array coordinate system and collective attenuation contour map. FIG. 4 depicts a discrete user domain where 0=7r/four modeling four sampling time step radii. FIG. 5 depicts a discrete user domain where 0=7i/eight modeling four sampling time step radii. FIG. 6 depicts a stacked circular directional antenna array embodiment. FIG. 7 depicts a schematic apartment house coverage scheme showing a primary attenuation lobe contour map. FIG. 8 depicts a hemisphere covered on one side by a collection of directional antennae. FIG. 9 depicts a Sphere covered by a collection of directional antennae. FIG. 10 depicts a partial schematic figure showing some of the primary attenuation lobes of directional antenna arrays as in FIGs. 8 and 9. FIG. 11 depicts a hemisphere H proximately covered by a multiplicity of direction antennae of more than one aperture size. FIG. 12 depicts a hemisphere H proximately covered by a multiplicity of direction antennae of more than one aperture size. FIG. 13 depicts a hemisphere H proximately covered by a multiplicity of direction antennae of more than one aperture size. FIG. 14 depicts an ellipsoidal directional antenna array. FIG. 15 depicts a cylindrical directional antenna array. FIG. 16 depicts placement of a multiplicity of ball antenna arrays on a tall building. FIG. 17 depicts an improved antenna set for cellular base station. FIG. 18 depicts an application in a region possessing a major thoroughfare twisting through a mountainous region. FIG. 19 depicts an augmentation of location finding capability over strictly omnidirectional receiving antenna set capability. FIG. 20 depicts multiple spaced-apart collectors to facilitate hand-off and aggregation. FIG. 21 depicts an overview of problem of user reception in densely concentrated areas users. FIG. 22 depicts a hexagonal grid showing uplink and downlink primary attenuation lobe contour map from one or more of the claimed ball antenna arrays. FIG. 23 depicts ball arrays positioned outside a domed stadium. FIG. 24 depicts ball arrays suspended from the ceiling of a domed stadium. FIG. 25 depicts ball arrays stationarily positioned about an amphitheater. FIG. 26 depicts ball arrays suspended from flotation devices such as balloons and anchored to earth. FIG. 27 depicts ball arrays carried by an airborne device such as a blimp or Unmanned Airborne Vehicle. DETAILED DESCRIPTION Directional antenna circular array (FIG.. 1. 2 and 31 Overview: Consider FIG. 1: Disclosed therein is a collection of reflector directional antennae wherein the component directional antenna architecture incorporates two or more of the directional antenna components disclosed in but not limited to FIG. 2. The 2-D attenuation contour map of the primary lobes of each of the directional antennae is shown superimposed in FIG. 3. FIG. 1: The preferred embodiment is an array of 16 directional reflector antenna components arranged optimally in a uniform pattern such that the reflecting surfaces associated with said directional antenna components form a connected surface when in operation. Note that any of the four basic directional antennas disclosed in FIG. 2 can be used as the component directional antenna to give distinct embodiments. Note also that the number of directional antenna components may vary. Certain preferred embodiments will utilize more than one type of directional antenna component, or may vary the parameters of said directional antenna components, such as aperture width. It is apparent to one skilled in the art, that the 2-D attenuation contour maps will differ depending not only on which type of directional antenna is used, but also on the carrier frequency(ies) employed, the length of the antenna elements, shape of the reflectors and the geometric parameters characterizing the relationship between the antenna element and reflector of each antenna component. While these are relevant and essential issues which must be addressed in developing working antenna systems, these issues tend to obscure the architectural issues which are central to this invention. They will not be mentioned hereafter because of this. The discussion of attenuation will instead focus on a general discussion so that the primary insights and their application to this invention will be less clouded in detail. The directional antenna components are denoted by 1-1 to 1-16. Each directional antenna component comprises a reflector, and one or more radiating components designated by 2. Note that only one directional antenna component n has had its radiating components designated, but that all directional antenna components have appropriate radiating components. There is a membrane 3 which encapsulates the antenna array so that the array presents a smooth surface to the external environment. The membrane is composed of one or more materials which are transparent to the operational frequencies of the antenna array. In certain preferred embodiments, portions of the membrane covering a given antenna component may be opaque to certain frequencies or polarizations used by adjacent antenna components. In some preferred embodiments, said radiating elements of said directional antenna components are not in line of sight with each other. The reflector components of said directional antenna components block line of sight. This situation has the advantage of limiting the inductive coupling of one radiating component of a directional antenna component upon the radiating component of an adjacent directional antenna component's radiating component. The discussions of covering membranes and line of sight issues for the radiating components of the directional antenna components apply to all discussed preferred embodiments hereafter and will not be repeatedly discussed in the interest of brevity. In certain preferred embodiments, alternating antenna components are employed for reception and for transmission. FIG. 2: This invention will focus its discussion but is not limit its claims to four basic directional antenna components, all of a reflector type. In any of the directional array antenna configurations, unless explicitly noted, similar application discussions could be developed based upon all the components listed in this figure and discussed hereafter. Type A directional antenna component: This preferred embodiment is a parabolic reflector antenna with radiating component approximately located along the major axis of the paraboloidal reflector. The radiating component will be assumed to be attached approximately along this axis to the reflector. Note that in some preferred embodiments, the radiating component may optimally be a helical configuration. The base location vector will be considered to be the point of intersection of the major axis and the reflector surface. The orientation direction vector will be defined to be the vector from the base location vector which ends at the extreme end of the radiating component. Type Al directional antenna component: This preferred embodiment is a parabolic sheet reflector antenna with radiating component approximately located along the focal line of the parabolic sheet reflector. The radiating component can be considered to be a rigid wire attached to the reflector sheet in any of several ways including but not limited to being attached at the ends or being attached to the back of the sheet. Dipole versions of Al are preferred embodiments in some applications wherein the radiating component comprises two rigid wires instead of one. Dipole wiring is well understood in the art, with typical attachment of antenna feed being in the midpoint of the radiating component. The base location vector will be considered to be the point of intersection of the major axis and the reflector surface. The orientation direction vector will be defined to be the vector from the base location vector which ends at the extreme end of the radiating component. Type A2 directional antenna component: This preferred embodiment is a parabolic sheet reflector antenna with radiating component approximately located along the major axis of the parabolic sheet reflector. The radiating component can be considered to be a pair of parallel rigid wires attached to the reflector sheet in any of several ways including but not limited to being attached at the ends or being attached to the back of the sheet. In certain preferred embodiments either the other radiating component wires located closer or further away from the reflector sheet will reside at the focal line of the reflector sheet. Certain preferred embodiments will incorporate a distance between the two radiating component wires which is related to the carrier wavelength. Certain preferred embodiments will incorporate radiating component wires of differing length. Dipole versions of A2 are preferred embodiments in some applications wherein the radiating component comprises two rigid coplanar wires are used instead of one wire in one or both of the wire components of the radiating components. Dipole wiring is well understood in the art, with typical attachment of antenna feed being in the midpoint of the radiating component. The base location vector will be considered to be the midpoint of the reflector surface. The orientation direction vector will be defined to be the vector from the base location vector which ends at one end of the furthest wire radiating component. The choice of which end is arbitrary, but should be consistent within instances of this class of components in a specific embodiment such that antenna polarization can be derived in a consistent fashion. Type A4 directional antenna component: This preferred embodiment is a quadra-pole parabolic sheet reflector antenna with radiating component approximately located along the focal lines of the four parabolic sheet reflectors. Each said radiating component can be considered to be a rigid wire attached to said corresponding reflector sheet in any of several ways including but not limited to being attached at the ends or being attached to the back of the sheet. Preferred embodiments include use of two or more rigid wires in each of the four radiating components in a fashion as disclosed in the discussion of A2 directional antenna component above. The base location vector will be considered to be the point of intersection of the midpoint lines of the four reflector surfaces. The orientation direction vector will be defined to be the vector fi^om the base location vector which ends at an end furthest removed from the base location vector of the furthest wire radiating component. Which one of said radiating components is arbitrary, but should be consistent within instances of this class of components in a specific embodiment such that anterma polarization can be derived in a consistent fashion. FIG. 3: A schematic view of the contour map of a typical attenuation function of such a circular directional antenna array. The coordinate frame used hereafter is constructed as follows: A polar coordinate system is used. Radial distance is in units of the propagation distance within the medium traversed in the sampling time step. Angular measure is taken relative to some axis. This axis can be arbitrarily chosen in theory. However, the practical choice will be to make optimal use of the uniformity of the antenna array. Best choices are to design the array to have a multiple of 4 directional antenna components. The angular measures would then be done fi"om an axis chosen so that the contour map of the primary attenuation lobes is as symmetrical as possible to simplify calculations. Discrete models of the uplink user transmission domain (FIGs. 4 and 5): FIGs. 4 and 5 shows two discrete models of the user domain in said coordinate system. In FIG. 4, 6=7t/4=27T/8. Four layers of sampling are shown, corresponding to 5 time steps removed from current time, due to the time to propagate. InFIG. 5, 6=7T/8=27r/16. Five layers of sampling are shown, corresponding to six time steps removed from current time, due to the time to propagate. Let us generalize the situation discussed in these two figures; Assume that the user transmission domain is discretely partitioned into K^LyNu areas where • Ky is the radial distance units in signal propagation of time step duration in the communication medium before the signal is too weak to be received. • Nu is the number of directional antenna components in the claimed 2-D array embodiment Lu is an integer where 8=27T;/LUNU. Let U[t,j,k] be the state of the discretized uplink user transmission domain at time step t, radiusjcAT polar coordinate k6. • where • t is a discrete value, assumed to be integer • k ranges from 1 to LyNu. j ranges from 0 to K^-1. • c is the propagation rate in the communicating medium, which is assumed constant in this discussion. • AT is the sampling time step. Note that this analysis assumes that only a scalar such as signal strength is being described at U[t,j,k]. In some preferred embodiments, more sophisticated assumptions are optimal. However, the basic discussion outlined here will remain applicable, though the mathematics will become more complicated. Let Ru[i,t] be a vector of received uplink sampled states for antenna component i, • where i ranges fi^om 1 to Ny at discrete time step t. In certain preferred embodiments, Ru[i,t] can be the sampled state of a collection of filters, including but not limited to bandpass, sub-band and discrete wavelet based fihers. In certain preferred embodiments, Ru[i,t] can be the sampled states of a multiplicity of specific radiating elements within the radiating component(s) of each said directional antenna component. These sampled states may be fiirther modified by phase alignment and signal combining techniques which are known in the art. It can be seen that each sampled state of said directional antenna components is modeled as a linear fiinction of the user transmission domain state generated in the past. This is due to the finite propagation speed of the communicating medium. Consider the attenuation contour map 3. Each directional antenna component receives a time-displaced contribution fi^om each user transmission domain component. This can be approximated by a linear combination of the time-displaced contributions of said discrete user transmission domain components. Let Au[i,j,k] be the linear contribution factor for antenna component i, from time-displaced user component jcAT at polar coordinate k0. Thus the contribution to Ru[i,t] by U[t-j,j,k] is scaled by Au[i,j,k]. Note that each Au[i,j,k] component is a vector of the same size as Ru[i,t]. Thus the matrix A can be seen as a 4-D matrix of real numbers, which may reasonably be embodied as floating point numbers and in many cases approximated fiirther as fixed point numbers. Given the above discussion, we can assume the following linear equation system approximately describes the relationship between the discretized user transmission domain and the reception state vector of the claimed antenna arrays: Ku i„iV„ RA},t\=Yu E At{i,j,k]u[t-j,j,kj=\ k=Ku L,K = llMu,k]u[t-j,j,k] The question at hand becomes how to extract information about U from knowledge of Au and Ru. Linear Algebra teaches us readily that the system of linear equations above can only be solved if there are as many terms Ru as there are terms Uu. This condition will be met if there are K^L^ linearly independent samples and/or quantities taken or derived from each sampling time step at each directional antenna component. The following considerations will be relevant in a broad class of preferred embodiments: • There could be K^Ly such filter banks for each of the N^ said directional antenna components. Thus Ru[i,t] would be a vector with KyLu components RUj[i,t]. • The above equation system is an FIR(Finite Impulse Response) filter system. FIR's form banded linear transformations, in that multipliers Au[i,j,k] occur at offset locations in each subsequent time step's linear transformation between the user transmission states and the reception state matrix(fihered sub band samples by antenna component) of the antenna array. • Given certain conditions well documented in the mathematical disciplines regarding such systems, inverse linear transformations, also FIR's, exist and are numerically stable. • Such an inverse transformation would have the form N,. N, K,L, u[tjA=^^ llBu[aXcJ,k]RuXb,c+ t] c=\ b=\ a=A Linear Discrete Model of the downlink transmission and reception: Let us now consider the downlink transmission model. Assume that the downlink reception domain is discretely partitioned into K