Patent Document

RELATED APPLICATIONS  
       [0001]     This is a Divisional of U.S. patent application Ser. No. 09/472,300, filed Dec. 27, 1999, which is a Divisional of U.S. application Ser. No. 08/862,859, filed May 23, 1997, now U.S. Pat. No. 6,008,760. 
     
    
     BACKGROUND OF THE INVENTION  
       [0002]     The present invention relates generally to free-space radio frequency (RF) communication systems and, more particularly, to isolation systems that separate the receive signal from interfering signals in a RF communications system. Interfering signals include signals received by the communications antenna causing co-channel interference and transmit signal leakage of the antenna&#39;s transmitter signal into the receiver. Many electronic systems, such as radar and wireless communication systems, operate over a wide range of microwave frequencies. For example, many radar and communication systems operate in what is known as a frequency-hopping or a frequency-agile manner over very wide microwave bandwidths. The bandwidth can vary up to an octave or more, and the frequencies can range from the S to Ku bands. The main objectives of an isolation system used in a full-duplex communication system is to provide low transmitter-loss and a high degree of isolation over a wide dynamic range of frequencies.  
         [0003]     Non-reciprocal devices, such as circulators, are commonly used to provide isolation between a transmitter and receiver in a microwave antenna system. However, the degree of isolation is severely limited by the operating frequency range, and a circulator&#39;s isolation and transmission deteriorate as the input ports become unmatched. Direct leakage between the transmitter and receiver is usually the primary cause of interference, particularly in systems that do not employ circulators. U.S. Pat. No. 5,373,301 discloses a means for canceling direct leakage in an antenna system that has simple resistive three-port junctions which use a signal derived from a dummy circuit receiving a large portion of the transmit signal. However, this design requires at least half of the signal power produced by the transmitter to be used to cancel the interference.  
         [0004]     Environmental effects, such as temperature changes and aging, cause an antenna&#39;s impedance to change, resulting in changes in the impedance-matching within the antenna circuit and unbalancing of any cancellation signal synthesized and applied to the receiver for canceling transmit interference. U.S. Pat. No. 4,970,519 shows a circuit that adjusts the amplitude and phase of a cancellation signal in order to optimize cancellation of transmit interference at a receiver. Signal phase-adjustment is performed by adjustment of delay lines in order to equalize the propagation paths of the cancellation signal and leakage signal. The signal level at the receiver is used as an error signal and fed back in a “control loop” for adjusting the amplitude and phase of the cancellation signal on the basis of minimizing the error signal. As a result, the receive signal corrupts the error signal and cannot be entirely removed by cancellation or correlation using the transmit signal. In addition, the cancellation must have frequency-dependent amplitude and phase characteristics that closely match those characteristics of the transmit signal in order to attain effective cancellation over a broad spectrum of transmit frequencies. Because interference occurs until the cancellation signal&#39;s parameters are optimized, continual adjustment of the cancellation signal will cause an interference signal whose magnitude depends on the response-rate of the signal-optimization process. Finally, intermodulation and distortion products are produced by the non-linear response of ferrite materials, which are commonly used as part of the antenna structure or circulator. Such interference is commonly removed by filtering, which has the undesirable consequence of limiting the effective bandwidth of operation of the antenna.  
         [0005]     Some techniques for reducing co-channel interference include frequency-separation, time-division, orthogonal polarization, and spatial separation. Further reduction of interference requires some type of cancellation. U.S. Pat. No. 5,432,522 shows a canceller that reduces cross-polarization interference in two orthogonally polarized channels. U.S. Pat. No. 5,515,378 applies adaptive phased-array technology to wireless communications in order to provide spatial multiplexing and demultiplexing of communications channels. This prior-art adaptive processing in an antenna array is essentially a cancellation process. Each element of the array has an associated electrical signal that is adjusted by a complex-valued weight, then summed to provide an antenna beam pattern having nulls (canceled responses) in a predetermined direction. Problems with this technique include the inability to resolve co-located or closely-spaced radio sources and increased side-lobe structures relative to main-beam magnitude that results when the width of the main beam is narrowed. If wide-band or multiple frequencies are transmitted, this causes distortion of the main beam and variance in the location of the nulls.  
       SUMMARY OF THE INVENTION  
       [0006]     The present invention addresses the lack of available frequency bandwidth allocation for wireless RF communications. Effects of these problems include limited data transmission capacity, co-channel interference, and limited access to wireless services resulting from increased demand for those services. Substantial improvements in frequency reuse are implemented through innovations in spatial multiplexing and isolation technologies disclosed herein. Applications of these new techniques are directed toward, but not limited to, stationary line-of-sight microwave communications systems. One embodiment of the present invention is a microwave antenna array that receives a plurality of signals having a common frequency channel that is transmitted from a remote location. This antenna array is able to resolve signals from even co-located sources and consequently provides a frequency reuse improvement of at least several orders of magnitude over the prior art.  
         [0007]     Accordingly, it is a first object of the invention to utilize a new type of spatial demultiplexing technique that makes use of spatial gain distribution characteristics of received signals to resolve closely-spaced and co-located sources. The spatial gain distribution of each receive signal has known characteristics that provide ratios of co-channel interference terms at the antenna elements. These ratios are used to weight a cancellation circuit, which separates the received signals. Shaping of the spatial gain distributions may be accomplished using a microwave lens at either or both the transmit antenna or the receive antenna. Adjustment of the spatial gain distribution may be accomplished by aperture synthesis, beam-steering or interferometric combining of a plurality of beam patterns. Another application of the demultiplexing technique includes separating polarized receive signals having known cross-polarization terms.  
         [0008]     Another object of the present invention is to provide an interferometric beam-shaping means whereby multiple antenna beam patterns are combined to provide cancellation in predetermined directions without reducing the magnitude of the main beam. A beam-shaping circuit provides frequency-dependent weights to the electrical signals that create the beam pattern. This is done to preserve the shape of the beam pattern for broad-frequency band transmission and reception, and is applied to each component beam pattern of the interferometric beam pattern.  
         [0009]     Therefore it is another object of the present invention to provide a frequency-dependent beam-shaping means to compensate for frequency-dependent distortions in the main beam and variance in the locations of the nulls.  
         [0010]     A wireless communications environment imposes a number of constraints and performance limitations on an adaptive cancellation system used to cancel transmitter interference at the receiver. Therefore, it is an object of the present invention to provide an adaptive canceller that utilizes an error signal free from receiver signals. Thus the adaptive canceller is made more suitable for optimizing the amplitude and phase of a cancellation signal.  
         [0011]     It is another object of the present invention to utilize a distributed impedance circuit as a dummy circuit in order to approximate the distributed impedance of an antenna for attaining broad-band cancellation of transmit signals in the receiver.  
         [0012]     Another object of the present invention is to model the distributed impedance of an antenna using finite elements in a dummy circuit for attaining broad-band cancellation of transmit signals in the receiver.  
         [0013]     It is another object of the present invention to cancel transmit leakage signals resulting from impedance-differences between the antenna and the compensating dummy circuit without canceling the receive signal.  
         [0014]     It is still another object of the present invention to cancel harmonic and intermodulation distortion signals resulting from the non-linear response of ferrite materials to the transmit signal, thereby providing the antenna system with broad-band capabilities.  
         [0015]     It is a final object of the present invention to provide a dummy circuit in a transmit signal cancellation network for canceling direct leakage from the transmitter that provides better than fifty percent transmit efficiency to the antenna.  
     
    
     BRIEF DESCRIPTION OF THE DRAWINGS  
       [0016]      FIG. 1  is an embodiment of an antenna array of the present invention.  
         [0017]      FIG. 2  is a graphic illustration of beam pattern components that comprise an interferometric beam pattern.  
         [0018]      FIG. 3  is a plot of antenna element excitation phasors on the complex plane.  
         [0019]      FIG. 4  illustrates components of a beam-shaping circuit described as part of the embodiment of the present invention.  
         [0020]      FIG. 5  is a graphic illustration of two beam patterns produced by signals having different frequencies when shaped by a beam-shaping circuit of the present invention.  
         [0021]      FIG. 6  is a graphic illustration of five individual beam patterns produced by an antenna array of the present invention that is excited by five excitation signals.  
         [0022]      FIG. 7  is a graphic illustration of interferometric beam-forming comprising the sums of five individual beam patterns.  
         [0023]      FIG. 8  is a graphic representation of spatial gain distribution of two receive signals across two antenna elements of the antenna array of the present invention.  
         [0024]      FIG. 9  is a diagram showing the components of a three-port isolator device described in the embodiment of the present invention.  
         [0025]      FIG. 10  is a plot of magnetic flux density of a ferrite material verses applied magnetic field strength.  
         [0026]      FIG. 11  illustrates an embodiment of a dc bias field adjustment circuit described as a component of the three-port isolator device.  
         [0027]      FIG. 12  shows three ferrite circulator three-port devices that are components of the three-port isolator device described in the embodiment of the present invention.  
         [0028]      FIG. 13  is an embodiment of a distributed impedance element described as a component of the three-port isolator device and used for approximating a distributed impedance.  
     
    
     DETAILED DESCRIPTION OF PREFERRED EMBODIMENTS  
       [0029]      FIG. 1  shows part of an antenna array  100  of the present invention comprising a first antenna  101  and a second antenna  102  coupled to an interferometric beam-narrowing processor  303 . The first antenna  101  is coupled to the processor  303  by a first three-port device  104 A, and the second antenna  102  is coupled to the processor  303  by a second three-port device  104 B. The processor  303  has a receiver output  313 . Although only two elements  101  and  102  are shown in this array  100 , the principles regarding the operation of this antenna array  100  may be extended to more than two antennas.  
         [0030]     A first distant radio-frequency source  91  is spatially separated from a second distant radio-frequency source  92 . In this case, both sources  91  and  92  radiate at a common wavelength λ; however, these sources may radiate at different wavelengths. Radiation from the first source  91  is shown as a plane wave  119  representing a common phase-front incident at the antennas  101  and  102  at a first incidence angle θ 1  relative to normal incidence  90 . A plane wave  129  represents a common phase-front of radiation from the second source  92  impinging on the antenna elements  101  and  102  at a second incidence angle θ 2  relative to normal incidence  90 .  
         [0031]     Radiation  119  received by antenna  101  induces a first electrical receive signal S 11 =S 1  Sin(ωt+φ 1 ) that is coupled to a first weight-and-sum processor  330 , where ω=2πc/λ, c is the speed of light constant, S 1  is the magnitude of the induced signal S 11 , t is time, and φ 1  is an arbitrary phase constant. A first electrical receive signal S 21 =S 1  Sin((ωt+φ 1 +D 1 ) at the second antenna  102 , which is induced by radiation  119 , is coupled to the first processor  330 . D 1  is delay in radians: D 1 =2π(d Sin θ 1 )/λ where d is the separation between the antennas  101  and  102 . The first processor  330  includes a first weighting element  331  which applies a complex weight W 1  to signal S 11 , delaying signal S 11  by an amount equal to the delay D 1 . The first processor  330  also includes a first combining circuit  333  to sum electrical signals from the antennas  101  and  102  and output the summed signals at a first output port  334 . In this case, the weighting element  331  provides unity gain in accordance with the assumptions of substantially identical antenna responses of both antennas  101  and  102  to radiation  119  and substantially uniform intensity of the radiation  119  (minimal spatial gain variance) at both of the antenna  101  and  102  locations. The first processor  330  may also include a second weighting element  332  coupled between the second antenna  102  and the combining circuit  333 . For the purpose of this discussion, the second weighting element  332  does not provide delay or gain adjustment. The signals S 11  and S 12  are combined in-phase to provide totally constructive interference.  
         [0032]     Radiation  129  received at the first antenna  101  induces a second electrical receive signal at the antenna  101 : S 12 =S 2  Sin(ωt+φ 2 ), where S 2  is the magnitude of the induced signal S 12  Radiation  129  received at the second antenna  102  induces a second receive signal at the antenna  102 : S 22 =S 2  Sin(ωt+φ 2 +D 2 ), where D 2  is delay in radians: D 2 =2π(d Sin θ 2 )/π. A receiver output signal S c1  of the first processor  330  at output port  334  is expressed as: 
 
 S   c1   =S   1  Sin(ω t+φ   1   +D   1 )+ S   2  Sin(ω t+φ   2   +D   1 )+ S   2  Sin(ω t+φ   2   +D   2 ) 
 
         [0033]     The output S c1  can also be written:  
         S   c1     =           S   1     ⁡     [       Sin   ⁡     (       π   2     -     b   1       )       +     Sin   ⁡     (       π   2     -     b   1     +     Δ   ⁢           ⁢     D   1         )         ]       ⁢           ⁢     Sin   ⁡     (       ω   ⁢           ⁢   t     +     ϕ   1     +     b   1       )         +         S   2     ⁡     [       Sin   ⁡     (       π   2     -     b   21       )       +     Sin   ⁡     (       π   2     -     b   21     +     Δ   ⁢           ⁢     D   21         )         ]       ⁢           ⁢     Sin   ⁡     (       ϖ   ⁢           ⁢   t     +     ϕ   2   ′     +     b   21       )               
 
 where b 1 =ΔD 1 /2, b 21 =ΔD 21 /2, φ 2 ′=φ 2 +D 1 , ΔD 21 =D 2 −D 1 , ΔD 21 =D 2 −D 1 =0. 
 
         [0034]     The delay factor D 1  applied to signals induced at antenna  101  causes the antenna array  100  to have maximum signal reception in the direction θ 1 . In  FIG. 2 , the direction θ 1  represents the orientation direction of a first main beam  151  of the array&#39;s  100  receiver output signal S c1 . As the location of a source, such as the second source  92 , departs from the orientation direction θ 1 , the responsiveness of the array  100  to the source  92  diminishes. The responsiveness of the array  100  to the second source  92  is nulled when the delay difference ΔD 21  equals a half-cycle of the signal&#39;s  129  wavelength λ, resulting in totally destructive interference. In this case, however, it is assumed that the direction θ 2  of the second source  92  is inside the beam width of the first main beam  151 . The invention is able to provide a null in the direction θ 2 , thus decreasing the width of the main beam  151  without reducing the magnitude of the main beam&#39;s  151  peak.  
         [0035]     The receive signals S 11 , S 12 , S 21 , and S 22  are coupled to a second weight-and-sum processor  340 . Signals S 11  and S 12  are delayed by an amount D 3  and adjusted in gain by a first weighting element  341  before being summed together with signals S 21  and S 22  in a second combining circuit  343 . The second processor  340  may also include a second weighting element  342  coupled between the second antenna  102  and the combining circuit  343 . For the purpose of this discussion, the second weighting element  342  does not provide delay or gain adjustment. A receiver output signal S c2  at output port  344  is expressed as: 
 
 S   c2   =S   1  Sin(ω t+φ   1 ″)+ S   1  Sin(ω t+φ   1   ″+ΔD   13 )+ S   2  Sin(ω t+φ   2 ″)+ S   2  Sin(ω t+φ   2   +ΔD   23 ) 
        where φ 1 ″=φ 1 +D 3 , φ 2 ″=φ 2 +D 3 , ΔD 13 =D 1 −D 3 , ΔD 23 =D 2 −D 3 ·S c2  may also be expressed as:  
                   S   c2     =         S   1     ⁡     [       Sin   ⁡     (       π   2     -     b   13       )       +     Sin   ⁡     (       π   2     -     b   13     +     Δ   ⁢           ⁢     D   13         )         ]       ⁢           ⁢   Sin       )     ⁢   ω   ⁢           ⁢   t     +     ϕ   1   ″     +     b   13       )     +         S   2     ⁡     [       Sin   ⁡     (       π   2     -     b   23       )       +     Sin   ⁡     (       π   2     -     b   23     +     Δ   ⁢           ⁢     D   23         )         ]       ⁢           ⁢     Sin   ⁡     (       ω   ⁢           ⁢   t     +     ϕ   2   ″     +     b   23       )             
 
 where b 13 =ΔD 13 /2 and b 23 =ΔD 23 /2. 
       
 
         [0037]     A second main beam  152  representing the receiver output signal S c2  has an orientation direction  03  relative to the direction of normal incidence  90 . The output receive signals S c1  and S c2  are combined by a third weight-and-sum processor  350 , which outputs a composite receive signal S c3 . The signal S c3  is represented by an interferometric beam pattern  153  in  FIG. 2  that has a null in the direction θ 2 . Before being summed in a combining element  353 , the signal S c1  is delayed by D 4  and adjusted in magnitude by a scalar weight factor g in a weighting element  351 . The value of D 4  is an amount required to match the phases of the contributions of signals from the second source  92  to S c1  and S c2 : D 4 =φ 2 ″+b 23 −φ 2 ′−b 21 =(D 3 −D 1 )/2. The scalar weight factor g has the value:  
       g   =       [       Sin   ⁡     (       π   2     -     b   23       )       +     Sin   ⁡     (       π   2     -     b   23     +     Δ   ⁢           ⁢     D   23         )         ]       [       Sin   ⁡     (       π   2     -     b   21       )       +     Sin   ⁡     (       π   2     -     b   21     +     Δ   ⁢           ⁢     D   21         )         ]           
 
         [0038]     The magnitude-adjusted delay-adjusted signal S c1  is subtracted from signal S S c2  to cancel the responses of the main beams  151  and  152  to a source, such as source  92  in the direction θ 2 , to provide the composite receive signal:  
         S   c3     =       g   ⁢           ⁢       S   1     ⁡     [       Sin   ⁡     (       π   2     -     b   1       )       +     Sin   ⁡     (       π   2     -     b   1     +     Δ   ⁢           ⁢     D   1         )         ]       ⁢           ⁢     Sin   ⁡     (       ω   ⁢           ⁢   t     +     ϕ   1     +     b   1     +     D   4       )         -         S   1     ⁡     [       Sin   ⁡     (       π   2     -     b   13       )       +     Sin   ⁡     (       π   2     -     b   13     +     Δ   ⁢           ⁢     D   13         )         ]       ⁢           ⁢     Sin   ⁡     (       ω   ⁢           ⁢   t     +     ϕ   1   ″     +     b   13       )               
 
         [0039]     The delay D 3  may be selected so that ΔD 13 =π: D 3 =π(2d Sin θ 1 −λ)/λ. Then the second main beam  152  has a null in the direction θ 1  of the first source  91  but is non-null in the direction θ 2  of the second source  92 . In this case, the interferometric beam pattern  153  is narrower than the first main beam  151  but has the same peak magnitude as the first main beam  151 .  
         [0040]     Signal decorrelation occurs between the antennas  101  and  102  when radiation having non-zero bandwidth is incident upon the array  100  from some angle other than the broadside direction. The propagation time delay of the radiation incident at each pair of antennas, such as antennas  101  and  102 , produces a phase shift that is proportional to the signal frequency f. Therefore, complex weights W n (f 1 ) required to null a signal at one frequency f. 1  will be slightly different from weights W n (f 2 ) required to null a signal at another nearby frequency f.sub.2. If the interfering signal has a significant bandwidth and if the signal arrives from some angle other than broadside, the array  100  will require several closely spaced nulls to null all frequency components simultaneously.  
         [0041]     The antenna array  100  may have a plurality M of reception patterns corresponding to a plurality of signal frequencies f m . Each m of these reception patterns is given by the following equation:  
             R   a     ⁡     (   ϑ   )       m     =       ∑     n   =     -   N       N     ⁢         l   am       l   o       ⁢           ⁢     ⅇ     ⅈ   ⁢           ⁢   n   ⁢           ⁢   k   ⁢           ⁢   d   ⁢           ⁢   cos   ⁢           ⁢   ϑ               
 
 where 2N+1 is the number of array elements, I nm  is the electrical excitation current produced by the weighting of induced signals S nm  at each element n, k is the wavenumber of the excitation current, d is the interelement spacing, and θ is the azimuthal direction in the plane of the array  100 . Control of the radiation pattern R a (θ) m  is achieved by relative positioning of the elements n (number N and spacing d) and the relative electrical excitations I nm  of the individual array elements n. 
 
         [0042]      FIG. 3  illustrates a sum of phasors that represents the radiation pattern R a (θ) m  of a uniformly excited array: I nm /I 0 =1. At θ=π/2, all the phasors are real and add to a maximum, which is the peak of the main lobe of the radiation pattern R a (θ) m . As θ departs from π/2, the phasors fan out across the complex plane. A minimum occurs at θ 1 min  for  
         cos   ⁢           ⁢     ϑ     1   ⁢           ⁢   min         =     ±     λ     L   ′                      where λ is the signal wavelength and L is the length of the array  100 : L=(2N+1)d. This could be represented by a phasor diagram, such as the one shown in  FIG. 3 , where the phasors have fanned out so that they are equally spaced in the complex plane. Subsequent maxima occur at  
         cos   ⁢           ⁢     ϑ     n   ⁢           ⁢   min         =     ±       n   ⁢           ⁢   λ       L   ′             
 
 and correspond to sidelobes of the radiation pattern R a (θ) m . The sidelobes can be reduced in height relative to the main lobe by tapering the magnitudes of the excitation currents I nm  toward the ends of the array  100 . However, the phasors will fan out beyond one full sheet in the complex plane before the first minimum occurs, resulting in broadening of the main lobe. This and other methods of aperture synthesis, such as Dolph-Chebyshev and Taylor synthesis, are oriented toward reducing sidelobe levels. However, these techniques are used in the present invention for adjusting the main lobe and the position of the minima. 
         
         [0044]      FIG. 4  shows the components of the weighting element  331 , which define it as a beam-shaping circuit. The other weighting elements  332 ,  341 , and  342  may similarly be designed as beam-shaping circuit  331 . A distributed-frequency signal S 11  comprising two frequency components S 11 (f 1 ) and S 11 (f 2 ) is input to the weighting element  331  where it is coupled through a parallel arrangement of a first and a second filter  135  and  136 , respectively, which separate the signal components S 11 (f 1 ) and S 11 (f 2 ). The first filter  135  allows through-put of the first signal component S 11 (f 1 ), and the second filter  136  allows through-put of the second signal component S 11 (f 2 ). The first signal component S 11 (f 1 ) is weighted by a first weighting element  137 , and the second signal component S 11 (f 2 ) is weighted by a second weighting element  138 . Thus each of the signal components is adjusted in magnitude in accordance with its frequency (f 1 ) or (f 2 ) by the beam-shaping circuit  331 . The weighted components I 11  and I 12  are then combined after acquiring the frequency-dependent weights. Likewise, signal S 12  is separated into its components by frequency, separately weighted, and then combined.  
         [0045]     In this case, signals I n1  uniformly excite the array  100  (I n1 =I 0  for all n), whereas the signals I n2  are tapered in magnitude toward the ends of the antenna array  100 .  FIG. 5  shows a first and second reception radiation pattern  171  and  172  produced by the array  100  when it is excited by the weighted components I n1  and I n2 . Because the first minima  
         θ     1   ⁢           ⁢   min       =       cos     -   1       (     ±     λ   L       )         
 
 depends on the wavelength λ it will not occur at the same position θ 1 min  for different signal wavelength values λ 1  and λ 2  (λ=c/f, λ 1 &gt;λ 2 ) if the excitations I n1  and I n2  are similar. The beam-shaping circuit  331  broadens the main beam of the second radiation pattern  172  to match the broader main beam of the first radiation pattern  171  resulting from the larger signal wavelength λ 1  of the corresponding excitation signals I n1 . Each of the radiation patterns  171  and  172  has a first minima which is located at θ 1 min . Thus, the antenna array  100  will neither transmit nor receive from the azimuthal direction θ 1 min . 
 
         [0046]     The distributed-frequency characteristics of the signal S.sub.1 may imply a number m greater than two of the discreet signal frequencies. The signal S.sub.1 then may be separated into m signals, each of the m signals being filtered by a filter (not shown) for providing a total of m signal components separated by frequency f.sub.m. Each of the signal components may be adjusted by a weighting element (not shown), the weighting elements providing a frequency-dependent weight to each of the signal components.  
         [0047]     The distributed frequency characteristics of the signal S 1  may imply a broad continuous frequency band. In this case, the signal S 1  may be divided into a plurality of discreet frequencies f m  in a similar manner as explained above. Alternatively, the signal S 1  may have a continuous frequency-dependent weight applied to it in which the value of the weight applied to the signal S 1  obtains its frequency-dependent characteristics from the frequency-dependent characteristics of impedance elements (not shown) used to divide or provide gain to the signal S 1 .  
         [0048]     Weighting elements, such as the weighting elements  137  or  138 , may provide complex weights to signals S 1  and S 2 . The complex weights may contain progressive phase factors that steer the antenna pattern  171  or  172  in order to position a minima in a predetermined spatial region. In this case, a predetermined spatial region is the azimuthal location of a signal source at which we attempt to orient the direction of the minima of the beam patterns  171  and  172  generated by the array  100 . However, another predetermined spatial region may require reception of non-minima portions of the beam patterns  171  and  172 . A predetermined spatial region may include multiple directions in which the beam patterns  171  and  172  must have minima or a predetermined ratio of magnitudes with respect to each other.  
         [0049]     In the same way that a plurality of weights can be applied to receive signals induced at each antenna  101  and  102  to create multiple overlapping reception beam patterns  151  and  152 , a plurality of weights W m  may be applied to a transmit signal X Tn  at each n of the antennas  101  and  102  to generate multiple transmit beam patterns that overlap at some predetermined location.  FIG. 1  shows an interferometric transmitter  356  of the present invention comprising a transmitter  350  coupled to an interferometric transmit signal adapter  365 , which is coupled to the antennas  101  and  102 . The adapter  365  includes a first and second weighting processor  360  and  370  for each antenna  101  and  102 , respectively.  
         [0050]     A transmit signal X T  generated by the transmitter  350  is coupled into the first processor  360  and split into a first and a second split transmit signal, X T1  and X T2 . A first weighting element  361  applies a first predetermined weight W 11  to the first signal X T1 . A second weighting element  362  applies a second predetermined weight W 12  to the second signal X T2 . The first and second weighting elements  361  and  362  are coupled to a combining circuit  363  for combining the weighted signals W 11 ·X T1  and W 12 ·X T2  into a first combined signal X TC1 . The first combined signal X TC1  is amplified by a first amplifier  364  to produce a first excitation signal X E1 , which is radiated at the first antenna  101 . The first amplifier  364  may be eliminated, particularly if the three-port device  104 A includes amplification means.  
         [0051]     The transmit signal X T  is also coupled into the second processor  360 , which splits the signal X T  into a third and a fourth split transmit signal, X T3  and X T4 . A third weighting element  371  applies a third predetermined weight W 21  to the third signal X T3 , and a fourth weighting element  372  applies a fourth predetermined weight W 22  to the fourth signal X T4 . The third and fourth weighting elements  371  and  372  are coupled to a combining circuit  373  for combining the weighted signals W 3 ·X T3  and W 4 ·X T4  into a second combined signal S TC2 . The second combined signal S TC2  is amplified by a second amplifier  374  to produce a second excitation signal S E2 , which is radiated at the second antenna  102 . The second amplifier  374  may be eliminated, particularly if the three-port device  104 B includes amplification means. In this case, the weight factors W 11  and W 21  are phased so that the excitation of the array produces a first transmit antenna pattern shown as pattern  151  in  FIG. 2  that has a main beam orientation in the direction θ 1  and also produces a second transmit antenna pattern represented by pattern  152  having a main beam orientation in the direction θ 3 . The beams  151  and  152  combine destructively to provide a null in the direction θ 2 .  
         [0052]     The patterns  151  and  152  may induce complementary signals in a receiver (not shown) located in direction θ 2 . Alternatively, the patterns  151  and  152  may be seperable from each other at the receiver (not shown), the separability being provided by the signals S E1  and S E2 , which have different frequencies, time-domains, polarizations, or the like. When processed and combined, the patterns  151  and  152  provide a null in the direction θ 2 .  
         [0053]     The transmit signal X T  has a carrier frequency f whose value changes as the signal X T  is generated. The transmitter  350  includes a frequency-control processor  358  that changes the carrier frequency f of the transmit signal X T  and provides control to the weighting elements  361 ,  362 ,  371 , and  372  for changing the values of the weights W 11 , W 12 , W 21 , and W 22  with respect to frequency f. The values of the weights W 11 , W 12 , W 21 , and W 22  are adjusted to provide the appropriate aperture synthesis to maintain a null in the direction θ 2  for all values of signal frequency f generated by the transmitter  350 .  
         [0054]     The beam width of a uniformly excited array is based on the array length L in the Fourier transform equation:  
                     f   ⁡     (   x   )       =     {       1   ⁢     (       1   ⁢   x1     ≤   d     )       ,                 0   ⁢     (       1   ⁢   x1     &gt;   d     )       }                       F   ⁡     (   k   )       =         1       2   ⁢           ⁢   π         ⁢           ⁢       ∫     -   d       +   d       ⁢       ⅇ     ⅈ   ⁢           ⁢   k   ⁢           ⁢   x       ⁢           ⁢     ⅆ   x           =         2   π     ⁢       Sin   ⁡     (     d   ⁢           ⁢   k     )       k                     
 
         [0055]     The Fourier transform of a linear aperture function produces a sinc function that illustrates the beam pattern amplitude produced by an antenna array. The number of array elements and their spacing determine how many main beams occur in the visible antenna pattern.  
         [0056]      FIG. 6  shows a beam pattern generated by an antenna array that is excited according to a method of the present invention. There is a plurality N of antenna elements (not shown) in the array. A transmit signal X is split into N transmit signals X n (t), where n=1 to N. Thus, the distribution of transmit signals to the antenna array is X=[X 1 (t), X 2 (t), . . . , X N (t)]. The vector X is multiplied by a complex weight vector W=[W 1 , W 2 , . . . , W N ] T  to produce an array output S=W T X. The array output S is ordinarily a sum of one particular (m=1) weighted distribution of split transmit signals X n (t), providing a single beam pattern. In the present invention, each of the N elements W n  of the weight vector W is a vector having a number M of elements w nm  equal to a number (M=5 in this case) of individual output signals s m (t) in the output signal S. The individual output signals s m (t) sum together to provide an interferometric composite beam pattern  80  shown in  FIG. 7 . In the case where cancellation signals are multiplexed onto a plurality n C  of channels, the transmit signal vector&#39;s X elements, X n  may be represented as a vector having a plurality of components equal to n C .  
         [0057]     The array produces a first array output signal s 1 (t) with an antenna beam amplitude pattern  70  that has a peak oriented in a direction θ 1  and a beam width defined by a pair of first minima symmetrically positioned at a distance θ 1 min  on either side of the orientation direction θ 1 . A second and a third array output signal s 2 (t) and s 3 (t) are produced by the antenna array  100  and have beam amplitudes indicated by beam patterns  71  and  72 , respectively. The second and third beam patterns  71  and  72  have the same beam width as the first pattern  70 . The second pattern  71  is oriented in a direction θ 2 =θ 1 +θ 1 min  and the third pattern  72  is oriented in a direction θ 3 =θ 1 −θ 1 min . A fourth and a fifth output signal s 4 (t) and s 5 (t) are produced by the array having beam amplitudes illustrated by a fourth and a fifth pattern,  73  and  74 , respectively. The fourth pattern has its peak oriented in a direction θ 4 &gt;θ 1 +θ 1  neon and the fifth pattern has its peak oriented in a direction θ 5 &lt;θ 1 −θ 1 min .  
         [0058]     The fourth and fifth beam patterns  73  and  74  each have beam widths that are smaller than the beam width of the first pattern  70 . The second and third patterns  71  and  72  are illustrated as having negative amplitude peaks because these patterns  71  and  72  represent cancellation signals for canceling signals shown in  FIG. 6  with positive amplitude peaks, such as patterns  70 ,  73 , and  74 . The cancellation signals  71  and  72  induce receive signals in a remote antenna (not shown) that cancel the array&#39;s transmission at that location. The cancellation signals may also provide a spatially diverse gain to the incident radiation at the antenna array  100  in order to null the array&#39;s reception of signals from specific spatial locations. The methods of inducing cancellation signals in electromagnetic receivers and producing cancellation fields at remote locations is discussed in PCT patent application PCT/US/08247, which is hereby incorporated by reference.  
         [0059]      FIG. 7  illustrates the beam pattern  80  that results from the sum of the beam patterns  70 ,  71 ,  72 ,  73 , and  74  in  FIG. 17 . The beam pattern&#39;s  80  peak has a beam width equal to θ 1 min  and an amplitude that is approximately equal to the amplitude of the first pattern  70  in  FIG. 6 . To cancel signals in the first channel, the cancellation signals  71  and  72  may be multiplexed into a separate channel separated by frequency, time, polarization, or the like before being processed at the remote antenna (not shown).  
         [0060]      FIG. 1  shows a spatial demultiplexer  403  of the present invention which makes use of known spatial gain variations of a plurality of receive signals s n (t) across the antenna array. The antenna array has a plurality M of antenna elements  101  and  102 , in this case M=2. An electrical receive signal r m (t) is induced at each antenna element by incoming signals s n (t), and is expressed by:  
           r   m     ⁡     (   t   )       =         ∑     n   =   1     N     ⁢       a   n     ⁢       s   n     ⁡     (   t   )       ⁢           ⁢     ⅇ     ⅈ   ⁢           ⁢     π   (         x   m     ⁢           ⁢   sin   ⁢           ⁢     ϑ   n       +     y   m     cos   ⁢           ⁢     ϑ   n           )             +       n   m     ⁡     (   t   )               
 where a n  is the antenna gain, x m  and y m  are Cartesian coordinates of the m th  antenna element location normalized by signal wavelength λ, θ n  is the angle of incidence of the signals s n (t), and n m (t) is a noise component corresponding to the m th  antenna element. In this case, the two antenna elements  101  and  102  receive two incoming signals s 1 (t) and s 2 (t) from sources  91  and  92 , which induce two receive signals: 
        r.sub.1 (t)=a.sub.1 s.sub.1 (t)e.sup.i.pi.(x.sbsp.1 .sup.sin .theta..sbsp.1.sup.+y.sbsp.1 .sup.cos .theta..sbsp.1.sup.)+a.sub.2 s.sub.2 (t)e.sup.i.pi.(x.sbsp.1 .sup.sin .theta..sbsp.2.sup.+y.sbsp.1 .sup.cos .theta..sbsp.2.sup.)  
           r   1     ⁡     (   t   )       =         a   1     ⁢       s   1     ⁡     (   t   )       ⁢     ⅇ     ⅈπ   ⁡     (       x1   ⁢           ⁢   sin   ⁢           ⁢     θ   1       +       y   1     ⁢   cos   ⁢           ⁢     θ   1         )           +       a   2     ⁢       S   2     ⁡     (   t   )       ⁢     ⅇ     ⅈπ   ⁡     (       x1   ⁢           ⁢   sin   ⁢           ⁢     θ   2       +       y   1     ⁢   cos   ⁢           ⁢     θ   2         )                 
           r   2     ⁡     (   t   )       =         a   1     ⁢       s   1     ⁡     (   t   )       ⁢     ⅇ     ⅈπ   ⁡     (       x2   ⁢           ⁢   sin   ⁢           ⁢     θ   1       +       y   2     ⁢   cos   ⁢           ⁢     θ   1         )           +       a   2     ⁢       S   2     ⁡     (   t   )       ⁢     ⅇ     ⅈπ   ⁡     (       x2   ⁢           ⁢   sin   ⁢           ⁢     θ   2       +       y   2     ⁢   cos   ⁢           ⁢     θ   2         )                 
         
         [0062]     If the sources  91  and  92  are very close together in angular position: θ 1 ≈θ 2 ≅θ, then the equations for the receive signals are simplified: 
        r.sub.1 (t)=e.sup.i.pi.(x.sbsp.1 .sup.sin .theta.+y.sbsp.1 .sup.cos .theta.) [a.sub.1 s.sub.1 (t)+a.sub.2 s.sub.2 (t)] 
           r   1     ⁡     (   t   )       ⁢       ⅇ     ⅈπ   ⁡     (         x   1     ⁢   sin   ⁢           ⁢   θ     +       y   1     ⁢   cos   ⁢           ⁢   θ       )         ⁡     [         a   1     ⁢       s   1     ⁡     (   t   )         +       a   2     ⁢       s   2     ⁡     (   t   )           ]           
           r   2     ⁡     (   t   )       ⁢       ⅇ     ⅈπ   ⁡     (         x   2     ⁢   sin   ⁢           ⁢   θ     +       y   2     ⁢   cos   ⁢           ⁢   θ       )         ⁡     [         a   1     ⁢       s   1     ⁡     (   t   )         +       a   2     ⁢       s   2     ⁡     (   t   )           ]           
       
 
         [0064]     The exponent represents a steering vector of the array excitation and merely acts as a scaling factor for the expressions in the brackets, which are identical for the two receive signals r 1 (t) and r 2 (t). These two equations are algebraically identical, and therefore reduce to a single equation with two unknown quantities s 1 (t) and s 2 (t). This means that the two signals s 1 (t) and s 2 (t), cannot be resolved. In order to explicitly solve for the unknowns s 1 (t) and s 2 (t) it is necessary to develop at least two algebraically unique equations in s 1 (t) and s 2 (t). This is accomplished by providing the incoming signals with spatial gain variations: s n (t)≅s n (x,y,t).  
         [0065]     The magnitude of each incoming signal at each antenna  101  and  102  varies in accordance with the spatial gain characteristics of the signal: s mn ≅s n (t)b mn , where b mn  is a known weight factor expressing the magnitude of the signal s n (t) at the m th  antenna element. The received signals are expressed by the following equations: 
 
 r   1 ( t )= C   1   [a   1   s   1 ( t ) b   11   +a   2   s   2 ( t ) b   12 ]
 
 r   2 ( t )= C   2   [a   1   s   1 ( t ) b   21   +a   2   s   2 ( t )b 22 ]
 
         [0066]     The constants C 1  and C 2  represent the steering vector and are comprised of known quantities. These constants can be absorbed into the values of b mn  or the measured receive signals r 1 (t) and r 2 (t). Thus, the above equations allow a method of solving for the signals s 1 (t) and s 2 (t) explicitly. The signals s 1 (t) and s 2 (t) can be separated by weighting and summing the receive signals r 1 (t) and r 2 (t) in the following manner:  
             r   1     ⁡     (   t   )       -         b   11       b   21       ⁢       r   2     ⁡     (   t   )           =       a   2     ⁢         s   2     ⁡     (   t   )       ⁡     [       b   12     -         b   22     ⁢     b   11         b   21         ]             
             r   1     ⁡     (   t   )       -         b   12       b   22       ⁢       r   2     ⁡     (   t   )           =       a   1     ⁢         s   1     ⁡     (   t   )       ⁡     [       b   11     -         b   12     ⁢     b   21         b   22         ]             
 
         [0067]     These equations identify the boundary condition b 11 b 22 ≠b 12 b 21 , which represents the spatial gain profile of the signals s 1 (t) and s 2 (t) necessary for allowing resolution of the two sources.  
         [0068]     Each of the spatially separated antenna elements  101  and  102  receive a plurality of signals s 1 (t) and s 2 (t) with known spatial gain characteristics b nm  at the receiving elements  101  and  102 . Furthermore, the proportionality of the spatial gain characteristics  
         b   nm       b       n   ′     ⁢   m           
        (n≠n′) at each antenna element  101  and  102  is unique, as required by the boundary conditions described above. The first receive signal r 1 (t) is induced at antenna  102 . The second receive signal r 2 (t) from antenna element  101  is delayed by a delay element  400 , providing a delay equal to the difference in transit time for electromagnetic radiation to propagate from the desired source(s) to each of the antenna elements  101  and  102 . This is done to maximize reception of incident radiation from the desired source(s). The delayed signal r 2 (t) is split into a first and a second component r 21 (t) and r 22 (t). The first component r 21 (t) has a weight b 11 /b 21  applied to it by a first weighting element  401 , and the second component r 22 (t) has a weight b 12 /b 22  applied to it by a second weighting element  402 . It is apparent that the delay element  400  could have been incorporated into the weighting elements  401  and  402 . The first receive signal r 1 (t) from antenna element  101  is split into a first and a second component r 11 (t) and r 12 (t). The first component r 11 (t) is coupled through a weighting element  421  and then into a first combining circuit  411 . In this case, the signals s 1 (t) and s 2 (t) do not have significant distributed-frequency characteristics so the weighting element  421  provides neither magnitude-adjustment nor delay to the first component r 11 (t). Likewise, the second component r 12 (t) is coupled through a weighting element  422  into a second combining circuit  412 . The weighting element  422  also provides neither magnitude-adjustment nor delay to signal r 12 (t). The weighted first component r 21 (t) is subtracted from the first signal&#39;s first component r 11 (t) in the first combining circuit  411 . The weighted second component r 22 (t) is subtracted from the first signal&#39;s second component r 12 (t) in the second combining circuit  412 . Outputs of the combining circuits  411  and  412  are proportional to the transmitted signals S 1 (t) and s 2 (t), respectively. These outputs are coupled to a receiver  430 , which may provide further signal processing such as equalization.        
 
         [0070]     If the signals s 1 (t) and s 2 (t) received by the antennas  101  and  102  have distributed-frequency characteristics that cause the receive signals r 1 (t) and r 2 (t) to have variable magnitudes with respect to frequency, the weighting elements  401 ,  402 ,  421 , and  422  are preferably beam-shaping circuits as described in reference to  FIG. 4 .  
         [0071]      FIG. 8  illustrates intensity profiles (spatial gain distributions) of the incident radiation  119  and  129  from the remote sources  91  and  92  in the vicinity of antennas  101  and  102 . A training sequence may be transmitted by the sources  91  and  92  in which the signals  119  and  129  are known, thus allowing for calibration of the weights of the spatial demultiplexer  403 . The first antenna  101  receives the first signal  119  having a first magnitude  91  and the second signal  129  having a first magnitude  81 . The second antenna  102  receives the first signal  119  at a second magnitude  92  and the second signal  129  at a second magnitude  82 . The spatial demultiplexer  403  may direct beam-shaping processes of the remote sources  91  and  92  to adjust the spatial gain distributions of the signals  119  and  129  at the array  100  in order to optimize reception. Reception-quality may be measured as a signal-to-noise or a signal-to-noise-plus-interference relationship. Communication between the array  100  and the remote sources  91  and  92  for optimizing reception may be accomplished by providing a feedback signal from the receiver  430  to the sources  91  and  92  that indicates the degree of reception quality. Shaping of the spatial gain distributions by the sources  91  and  92  may be accomplished by aperture synthesis, beam-steering, interferometric combining of multiple beam patterns, microwave lensing, or the like.  
         [0072]     Spatial multiplexing of communications signals and demultiplexing of those signals utilizing known spatial gain distribution ratios of the received signals s 1 (t) and s 2 (t) has been shown with respect to RF communications signals. However, this method of canceling interference may also be applied to electromagnetic signals in other frequency domains, such as optical frequencies. Optical transmitters may include collimated sources, such as lasers.  
         [0073]     In the case where the sources  91  and  92  have any angular separation, a microwave lens (not shown) may be utilized to provide gain differentials between the receive signals s 1 (t) and s 2 (t) which the lens then directs to a plurality of receivers (not shown). A microwave lens (not shown) receives incident radiation and focuses it onto receivers (not shown) located in the focal plane of the lens (not shown). The position of each receiver (not shown) receives an amount of the focused radiation depending on the receiver position and the directions of arrival θ 1  and θ 2  of the incident radiation. The angular separation between the sources  91  and  92  allows the lens (not shown) to adjust the spatial gain distribution of the signals s 1 (t) and s 2 (t) received by the receivers (not shown). The weight factors b mn  corresponding to the receive signals s 1 (t) and s 2 (t) at the receivers (not shown) comprise the spatial gain distributions of the transmit signals transmitted by the sources  91  and  92  and a multiplicative lensing factor resulting for adjusting the spatial gain distribution that is ultimately “seen” by the receivers (not shown), which results from the focusing effect by the lens (not shown) on the incident radiation. The weight factors b mn  may be determined by test sequences of known transmissions from the sources  91  and  92  or from calculations that utilize known spatial gain distributions transmitted by the sources  91  and  92 , known angular θ 1  and θ 2  of the sources  91  and  92 , and a known gain profile applied by the lens (not shown) to the receivers (not shown) relative to the directions of arrival θ 1  and θ 2  of incident radiation.  
         [0074]     The spatial demultiplexer  403  has been described with respect to its use for separating signals s 1 (t) and s 2 (t) that have different known spatial gain distributions (described by weight factors b mn ) across the antenna elements  101  and  102 . However, the spatial demultiplexer  403  may be used as a polarization demultiplexer to separate a plurality of received polarization signals p n (t) (n=1, . . . , N), each having a known linear polarization φ n . Each antenna of the array  100 , such as antennas  101  and  102 , may include a linear polarizer (not shown) oriented in a predetermined direction φ for attenuating the received signals p n (t). The attenuation may be represented by an attenuation factor that has a value α n =cos 2 (φ−φ n ) and that multiplies the intensity of each corresponding n received signal p n (t). The receive signals p n (t) have linear polarization orientations φ n  that are known. Consequently the signals s 1 (t) and s 2 (t) received at each antenna  101  and  102  have predetermined degrees of cross-polarization interference that are used to derive the weight factors b mn . In the case where only two receive signals are collected, it is preferable that the polarizations φ 1  and φ 2  of the signals s 1 (t) and s 2 (t) be orthogonal with presumably no cross-polarization interference. However, the present invention relates to a system in which the polarizations φ n  of the receive signals s n (t) have known but interfering polarizations. The advantage of this method is that it provides for polarization demultiplexing of more than two linearly polarized signals s n (t).  
         [0075]     An embodiment of an isolator three-port device  104  is shown in  FIG. 9 . This three-port device  104  represents one embodiment of the three-port devices  104 A and  104 B shown in  FIG. 1 . The transmitter  356  generates electrical signals represented by voltage V SG , which are passed to the inputs of amplifiers  105 ,  104  and  103 . The amplifiers  105 ,  104 , and  103  provide gain to the input signal V SG  represented by gains g 1 , g 2 , and g 3 , respectively. The output impedance of each amplifier  105 ,  104  and  103  is represented by impedance elements  111 ,  112  and  113 , respectively. The amplified signal from the output of the first amplifier  105  is represented by a first transmit current i 11T  that passes through an impedance element  121  to a three-port device  131 . The three-port device  131  splits the transmit current i 11T  into a first reference signal i 13T  and an output transmit signal i 12T . The first reference signal i 13T  exits the three-port device  131  and passes through a first reference branch which comprises an impedance element  161  and a variable-impedance element  171 . The variable impedance element  171  is coupled to an impedance controller  181 . The output transmit signal i 12T  flows through a transmit branch that is comprised of an impedance element  141  and the antenna  101 . The input impedance of the antenna  101  is represented as an antenna impedance element  151 .  
         [0076]     A second transmit current i 21T  from the second amplifier  104  passes through an impedance element  122  into a three-port device  132 . The three-port device  132  splits the second transmit current i 21T  into a second reference signal i 23T  and a first dummy transmit signal i 22T . The second reference signal i 23T  exits the three-port device  132  and flows through a second reference branch that is comprised of an impedance element  162  and a variable-impedance element  172 . The variable impedance element  172  is coupled to an impedance controller  182 . The first dummy transmit signal i 22T  flows through a first dummy antenna branch that includes an impedance element  142 , a variable distributed impedance element  147  and an output-impedance element  152 . The output-impedance element  152  represents the output impedance of an amplifier  160 .  
         [0077]     A third transmit current i 31T  from the third amplifier  103  passes through an impedance element  123  to a three-port device  133 . The three-port device  133  splits the third transmit current i 31T  into a third reference signal i 33T  and a second dummy transmit signal i 32T . The third reference signal i 33T  flows from the three-port device  133  through an impedance element  163  and then through a variable impedance element  173 . The variable impedance element  171  is coupled to an impedance controller  183 . The second dummy transmit signal i 32T  exits the three-port device  133  and flows through a second dummy antenna circuit that includes an impedance element  143  and a variable distributed impedance element  153 .  
         [0078]     A first sensing network is comprised of a sensing element  241  coupled to impedance element  141 , a second sensing element  261  coupled to impedance element  161 , and a combining circuit  291 . The electrical signals generated by the sensing elements  241  and  261  are input to the combining circuit  291  at input ports  291 A and  291 B, respectively. The output port  291 C of the combining circuit  291  is coupled to the input of amplifier  160 .  
         [0079]     A second sensing network is comprised of a third sensing element  221  coupled to the impedance element  121 , a fourth sensing element  222  coupled to the impedance element  122 , and a combining circuit  292 . The electrical signal generated at the sensing elements  221  and  222  are input to the input ports  292 A and  292 B of the combining circuit  292 . The output port  292 C of the combining circuit  292  is coupled to the variable impedance element  147  and also coupled to the variable impedance element  153 . An output of the sensing element  221  is coupled to the impedance controller  181 , and an output of the sensing element  222  is coupled to the impedance controller  182 .  
         [0080]     A third sensing network is comprised of a fifth sensing element  223  coupled to the impedance element  123 , a combining circuit  294  connected to the sensing element  223  through a first input port  294 A, and a second input port  294 B of the combining circuit  294  coupled to the sensing element  221 . An output signal from the sensing element  223  is coupled to the impedance-controller  183 .  
         [0081]     A fourth sensing network is comprised of a sixth sensing element  263  coupled to the impedance element  163 , an input port  293 A of a combining circuit  293  coupled to the output of the sensing element  263 , and an input port  293 B coupled to the output of the sensing element  261 . The output ports  293 C and  294 C of the combining circuits  293  and  294 , respectively, are coupled to a combining circuit  295  through input ports  295 B and  295 A, respectively. The output port  295 C of combining circuit  295  provides a receiver output signal from the antenna  101 .  
         [0082]     Circuit impedances are represented as lumped-circuit impedance elements, such as impedance elements  111 ,  112 ,  113 ,  121 ,  122 ,  123 ,  141 ,  142 ,  143 ,  147 ,  151 ,  152 ,  153 ,  161 ,  162 ,  163 ,  171 ,  172 , and  173 . Each of these lumped circuit elements is meant to convey an impedance comprised of inductance, capacitance resistance, and/or conductance. The antenna element  151  is modeled as a transmission line in that it has its inductance, resistance, capacitance, and conductance distributed along the line. Likewise, the variable distributed impedance elements  147  and  153  include distributed circuits or a combination of lumped circuit elements that approximate a distributed impedance. The three-port devices  131 ,  132 , and  133  may be T-junctions, resistive dividers, non-reciprocal devices, such as circulators, or any such power divider. The sensing elements  221 ,  222 ,  223 ,  241 ,  261 , and  263  sense electrical signal levels, either current or voltage, within the circuit at the locations represented by impedance elements  121 ,  122 ,  123 ,  141 ,  161 ,  163 , respectively.  
         [0083]     The values of the first, second and third transmit currents i T11 , i T12  and i T13  are as follows:  
         i   T11     =       (       V   A     /     Z   1       )       (       (       1   /     Z   1       +     1   /     Z   in1         )     ⁢     Z   in1       )           
         i   T12     =       i   T11     ⁢           ⁢       (       R   3     +     Z   3       )       (       R   3     +     Z   3     +     R   2     +     Z   2       )             
         i   T13     =       i   T11     ⁢           ⁢       (       R   2     +     Z   2       )       (       R   3     +     Z   3     +     R   2     +     Z   2       )             
        where Z 1 , R 1 , Z 3 , R 3 , and R 2  are the values of impedance elements  111 ,  121 ,  161 ,  171 , and  141 , respectively, Z 2  is the value of the impedance elements  151 , Z in1  has the value of R 1 +(R 2 +Z 2 )∥(R 3 +Z 3 ), and V A  is the signal voltage applied by the amplifier  105  output, where V A =g 1 V SG . The voltage of the transmit signal at the output of the amplifier  105  is:  
         V   T11     =       (       V   A     /     Z   1       )       (       1   /     Z   1       +     1   /     Z   in1         )           
       
 
         [0085]     Sensing elements  241  and  261  output electrical signals that are proportional to electrical signals flowing through impedance elements  141  and  161 , respectively. In this case, we require the first sum of impedances elements  161  and  171 , which comprise the first reference branch, to be proportional to the second sum of impedance elements  141  and  151 , which comprise the transmit branch. The values of impedance elements having either capacitive or inductive components will be frequency-dependent. Thus the proportionality between the first and second sums is preferably a real-valued constant. If we require Z 2  to be a real multiple of Z 3  (Z 2 =a Z 3 , where “a” is a real multiplier), the equations for transmit currents in the transmit branch and the first reference branch are as follows:  
         i   T12     =         i   T11     ⁢     a     (     a   +   1     )       ⁢           ⁢   and   ⁢           ⁢     i   T13       =       i   T11     ⁢     1     (     a   +   1     )               
 
         [0086]     It is preferable that the reference branch impedance be larger than the impedance of the transmit branch so that more transmitter power is routed through the transmit branch than the reference branch. Transmit efficiency is measured as the proportion of transmit power that is radiated by the antenna  101  relative to the transmit power at the output of the amplifier  105 . It is particularly desirable to have a high (greater than 50 percent) transmit efficiency for far-field communications and remote sensing applications. Additionally, designing the reference branch for high power levels (power levels approaching the transmit power in the transmit branch) adds expense and bulk to the circuit design as more precautions are needed for heat-dissipation and inductive coupling. It is important to balance the benefits of reducing power-handling in the reference branch with the problems of manipulating low-power signals. Signal-to-Noise levels for low-power signals are more adversely affected by additive environmental noise, such as electromagnetic interference (EMI), and additive amplifier noise. Thus, the value of “a” will depend on a compromise between different sets of boundary conditions.  
         [0087]     A voltage V R  is generated by the antenna  101  in response to received electromagnetic radiation. An electrical receive current i R12  flows through impedance element  141  as a result of this voltage V R . The current i R12  is split by the three-port device  131  into a pair of complementary receive signals i R11  and i R13 . Current i R11  flows through impedance elements  121  and  111 , and current i R13  flows through impedance elements  161  and  171 . The receive currents are given by the following relationships:  
         i   R12     =       (       V   R     /     Z   2       )       (       (       1   /     Z   2       +     1   /     Z   in2         )     ⁢     Z   in2       )           
         i   R13     =       i   R12     ⁢           ⁢       (       R   1     /     Z   1       )       (       R   1     +     Z   1     +     R   3     +     Z   3       )             
         i   R11     =       i   R12     ⁢           ⁢       (       R   3     /     Z   3       )       (       R   3     +     Z   3     +     R   1     +     Z   1       )             
     where     
         Z   in2     =       R   2     +         (       R   1     /     Z   1       )     ⁢     (       R   3     +     Z   3       )         (       R   1     +     R   3     +     Z   1     +     Z   3       )             
 
         [0088]     The sensing element  261  is responsive to the electrical signals i R12  and i T12  flowing through the impedance element  161  and generates an electrical response signal i S2 . Likewise, the sensing element  241  is responsive to electrical signals i R13  and i T13  flowing through impedance element  141  and generates an electrical response signal i S1 . The responses i S1 , and i S2  of the sensing elements  241  and  261  are adjusted in amplitude and phase relative to each other and combined in the combining circuit  291  such that the contributions of the transmit signals i T12  and i T13  cancel. The combining circuit  291  produces an electrical signal i 291  that is substantially proportional to the receive signal i R12  at output  291 C. This electrical signal i 291  is input to the amplifier  160 , which injects a gain-adjusted version i R22  of the signal i 291  into the first dummy antenna branch. The amplitude of the injected receive signal i R22  is adjusted such that it is proportional to signal i R12  by the same amount as the proportionality between the transmit signals i T22  and i T12 . Furthermore, phase-adjustment in the combining circuit  291  provides a relative phase between the signals i R22  and i T22  that is substantially identical to the relative phase between the signals i R12  and i T12 . The injected receive signal i R22  flows through the impedance element  142  into the three-port device  132 , which splits the injected signal i R22  into complementary injected receive signals i R21  and i R23 . The signal i R21  flows through impedance element  122 , and signal i R23  flows through impedance element  162 .  
         [0089]     The signals i R21  and i T21  flowing through impedance element  122  are sensed by sensing element  222 , which produces a proportional response signal i S4 . Likewise, the signals i R21  and i T21  flowing through impedance element  121  are sensed by sensing element  221 , which also generates a response signal i S3 . The signals i S3  and i S4  from both sensing elements  221  and  222  are combined in the combining circuit  292 , and an error signal i S  is produced at the output  292 C that represents any mismatch in the proportionality of the signals i S3  and i S4 . Such a mismatch in proportionality is likely to occur when the impedance of the antenna  101  changes due to environmental conditions, such as aging, temperature variations, and movement relative to nearby electrically grounded conductive objects. The output  292 C is connected to variable distributed impedance elements  147  and  153 , whose impedances change by an amount dictated by the error signal i S . The change in impedance of the variable impedance element  147  affects the error signal is. A logical circuit controller (not shown) within the variable impedance element  147  is responsive to the error signal i S  and adjusts the impedance in order to minimize the magnitude of the error signal i S .  
         [0090]     The error signal i S  provides an accurate controlling reference for adjusting the impedances of impedance elements  147  and  153  because the split signal i R21  from the injected signal i R22  enables cancellation of the split signal i R11  from the receive signal i R12  in the combining circuit  292 . This reduces the effect of the receive signal i R12  on the error signal i RS . The error signal i S  may be used to control the effective impedance of the antenna  101 , thus compensating for impedance changes by adjusting the impedance of a series impedance element such as impedance element  141 .  
         [0091]     A dc bias field adjustment circuit, as shown in  FIG. 11 , adjusts a dc magnetic field applied to the antenna element  101  for a coil-type antenna and a dc magnetic field applied to the impedance element  171 . An impedance element  141 A connected in series with a capacitor  141 B comprise the impedance element  141 . A variable dc-level current source  155  is connected between the capacitor  141 B and the antenna element  101 . In this case, the antenna element  101  includes a conductive wire  101 A coiled around a ferrite core  101 B. An impedance element  161 A and a capacitor  161 B comprise impedance element  161 . A variable dc-level current source  175  is connected between the capacitor  161 B and the impedance element  171 . The impedance element  171  includes a conductive wire  171 A wrapped around a ferrite core  171 B.  
         [0092]     For certain applications at relatively low signal frequencies (&lt;100 MHz), the antenna structure  101  is often smaller than the radiated wavelength and may take the form of a coil of wire surrounding a ferrite core. This is common for the operation of an antenna as an electromagnet. An electrical signal flowing through the coil serves to reinforce the radiated electromagnetic radiation by virtue of multiple additions of the radiation pattern of single loops of current. Additionally, harmonic distortion terms are introduced to this electrical signal due to the non-linear response of ferrites that may be used as part of the antenna structure  101  or may be in close proximity to the antenna  101 . Ferrite materials may also be used in three-port devices  131 ,  132 , and  133  to provide a non-reciprocal effect for isolation, such as for a circulator. Once again, harmonic and intermodulation products will be introduced into the electrical signals in the circuit.  
         [0093]     The magnetic permeability of the ferrite material changes as the slope of the resulting magnetic flux density B versus the magnetic field H applied to the material. A B vs. H curve  86 , along with the resulting distortion caused by the variation in magnetic permeability is shown in  FIG. 10 . Along the X-axis is a representation of two identical amplitude-modulated magnetic fields  81  and  82  as would be applied to the material, one field  81  having a relatively low bias field H DC1  and the other field  82  having a high, near-saturation bias field H DC2 . A distorted magnetic flux density  91  and  92  resulting from each applied external magnetic field  81  and  82  is illustrated along the Y-axis. By adjusting the bias field H DC1  or H DC2  of either of the identical amplitude-modulated magnetic fields  81  and  82 , it is possible to substantially reproduce the distortion pattern of the other magnetic flux profile  92  and  91  or create a complementary non-symmetric distortion pattern  92 , as shown in  FIG. 10 , that will cancel if combined out-of-phase with the first pattern  91 .  
         [0094]     The non-linear behavior of B vs. H results from the restoring force of the magnetic dipoles in the ferrite material, which causes a damping effect on the alignment of the dipoles due to an external magnetic field. The total force on the dipoles is approximated by: 
 
 F ( x )=− kx+mx   2 λ
 
         [0095]     This is a linear oscillator equation with an additional nonlinear term proportional to the square of the displacement x. The differential equation of motion is: 
 
 x″+ω   0   2   x−λx   2 =0 
 
         [0096]     This equation is solved by using the method of perturbations in which the general solution is written as a power series in λ. Eliminating higher order terms yields the solution:  
         x   ⁡     (   t   )       =       Acos   ⁢           ⁢     ω   0     ⁢   t     -       λ   ⁢           ⁢       A   2     ⁡     (       cos   ⁢           ⁢   2   ⁢     ω   0     ⁢   t     -   3     )           6   ⁢     ω   0   2               
        which illustrates a second harmonic and a dc bias in addition to the harmonic oscillator solution. Higher powers of λ introduce higher harmonics, and solutions yield intermodulation as well as higher harmonic terms if impressed signals are added to the equation of motion. Harmonic and intermodulation distortions are introduced into the signal current used to apply the magnetic field to the ferrite. Thus, appropriate adjustment of the bias magnetic field impinging on the ferrite may be used to adjust the degree of harmonic and intermodulation distortion in one part of the circuit in order to cancel distortion generated by the non-linear response of a ferrite in another part of the circuit.        
 
         [0098]     The capacitors  141 B and  161 B provide a dc block so that dc bias currents produced by the dc-level current sources  155  and  175  remain in their associated circuit elements  101  and  171 , respectively. The relative magnitude and direction of the bias currents generated by the dc-level current sources  155  and  175  are adjusted to provide the appropriate orientation and magnitude of the magnetic bias field such that the proportion of the harmonic distortion amplitude imparted to the electrical signal in the wire  171 A compared to the amplitude of the non-distorted signal in the wire  171 A is substantially equal to the proportion of the amplitude of the harmonic distortion imparted to the antenna element wire  101 A compared to the amplitude of the non-distorted signal in the antenna element wire  101 A. In this way, the signals sensed by the sensing elements  241  and  261  may be combined in the combining element  291  such that the contributions of harmonic distortion substantially cancel. Other types of de bias field adjustment circuits may be utilized. For example, an electromagnet (not shown) that is electrically separated from the impedance element  221  may be used to adjust magnetic bias fields, or such adjustment may be performed using permanent magnets (not shown) and position-adjustment devices (not shown). A dc bias field adjustment circuit such as the one shown in  FIG. 10 , may be used for adjusting dc magnetic fields. These fields can be applied to other elements that include ferrite materials such as elements  147 ,  153 ,  162 , and  173 .  
         [0099]     The three-port devices  131 ,  132  and  133  shown in  FIG. 9  may each comprise one or more ferrite circulators in order to improve isolation between their transmit and receive ports. A magnetic bias field is applied across a ferrite material to achieve the nonlinear response that effects the Faraday rotation of electromagnetic waves guided through the material. However, this nonlinearity causes harmonic and intermodulation distortion of the electromagnetic waves.  
         [0100]      FIG. 12  shows the ferrite circulator three-port devices  131 ,  132 , and  133 . An electromagnet  191  with a conductive wire  197  coiled around a core  194  is connected to an adjustable dc electric current generator  201 . The electromagnet  191  imparts a dc bias magnetic field to the ferrite circulator  131 . An electromagnet  192  with a conductive wire  198  coiled around a core  195  is connected to an adjustable dc electric current generator  202 . The electromagnet  192  imparts a dc bias magnetic field to the ferrite circulator  132 . Likewise, an electromagnet  193  with a conductive wire  199  coiled around a core  196  is connected to an adjustable dc electric current generator  203 . The electromagnet  193  imparts a dc bias magnetic field to the ferrite circulator  133 . The distortion products imparted to the output signals i S3  and i S4  of sensing elements  221  and  222  may be canceled in the combining circuit  292  by adjusting the dc level of the magnetic field impinging upon either or both ferrite circulators  131  and  132 . The sensing element  223  is responsive to the transmit current i.sub.31T flowing through the impedance element  123  and generates an electrical response signal i S5 . The responses i S5  and i S3  of the sensing elements  223  and  221  are adjusted in amplitude and phase and are combined in the combining circuit  294  for producing an output signal i 294  that is substantially free of the transmit components i 31T  and i 11T . The distortion products resulting from distortion of the transmit signals i 31T  and i 11T  in the response signals i S3  and i S5 , respectively, may be canceled in the combining circuit  294  by the appropriate adjustment of the magnetic bias field of either or both of the ferrite circulators  131  and  133 .  
         [0101]     The sensing element  263  is responsive to the transmit current i 33T  flowing through the impedance element  163  for producing an electrical response signal i S6 . The responses i S6  and i S2  of the sensing elements  263  and  261  are adjusted in amplitude and phase and are combined in the combining circuit  293  for producing an output signal i 293  that is substantially free of the transmit components i 33T  and i 13T . Adjustment of the magnetic bias field of either or both of the ferrite circulators  131  and  133 , as described above, may also be used to substantially cancel distortion terms in the output signal i 293  of the combining circuit  293 . Finally, residual harmonic and intermodulation distortion persisting in the output signals i 293  and i 294  of the combining circuits  293  and  294  may be canceled in the combining circuit  295  most effectively if the harmonic distortion components in the signal outputs i 293  and i 294  are made to add together destructively, whereas the undistorted signals add constructively.  
         [0102]     A circuit illustrating the components of one version of the variable distributed impedance element  147  is shown in  FIG. 13 . In this case, the element  147  includes an input terminal  147 A, an output terminal  147 B, and a control terminal  147 C. A first adjustable inductor L 1 , a second adjustable inductor L 2 , and a third adjustable inductor L 3 , are connected in series between the input and output terminals  147 A and  147 B, respectively. A first adjustable capacitor C 1  is connected to the junction of the first and second inductors, L 1  and L 2 , and to electrical ground. A second adjustable capacitor C 2  is connected to the junction between the second and third inductors, L 2  and L 3 , and to electrical ground. The impedance of each of the inductors L 1 , L 2 , and L 3  is controlled by an inductance control circuit  148  that processes the error signal i S  received from the control terminal  147 C. Either or both the amplitude and phase of the error signal i S  provides information for how much the values of the inductors L 1 , L 2 , and L 3  need to be adjusted. Likewise, a capacitance control circuit  149  receives the error signal i S  for adjusting the values of the capacitors C 1  and C 2 .  
         [0103]     The error signal i S  represents the impedance-change of the antenna  101  relative to the impedance of the distributed impedance element  147 . The error signal i S  magnitude increases as the impedance change of the antenna  101  causes the proportion of the transmit signals  121 T to i 11T  to change. The error signal i S  may be derived from a reference signal V Ref  of a known amplitude and phase that is embedded in the transmitter  356  voltage V SG . A comparison of either or both the amplitude and phase of the error signal i S  to the reference signal V Ref  provides information about the degree of inductive and capacitive changes in the impedance-change of the antenna  101 . Therefore, appropriate impedance-changes may be performed in the distributed impedance element  147  to minimize the error signal i S . A predetermined algorithm may be used to dither the values of the inductors L 1 , L 2 , and L 3  and the capacitors, C 1  and C 2 , and to utilize feedback-response in order to minimize the error signal i S . The reference signal V Ref , and hence the error signal i S  are preferably outside the bandwidth of the transmit and receive signals. Transmit and receive signal components within the error signal i S  may be removed by filters (not shown) in the combining circuit  292  or in the inductance or capacitance control circuits  148  and  149 .  
         [0104]     The circuit shown in  FIG. 13  is a three-stage approximation of a distributed impedance that has distributed inductance L d  and capacitance C d . In order to best approximate the distributed impedance, the values of L 1 , L 2 , and L 3  are substantially equal to L d /3, and the values of C 1  and C 2 , are substantially equal to C d /2. For an n-stage approximation of a distributed impedance, where n is a positive integer greater than two, the values of each of the lumped inductors L 1  to L n  and lumped capacitors C 1  to C n-1  would be L d /n and C d /(n−1), respectively. Distributed resistance and conductance could also be approximated using lumped circuit elements in the method just described. A better approximation of distributed impedance is obtained by utilizing a larger number n of stages. To support this conclusion, one may examine the simplest approximation of a distributed impedance using an inductor L and capacitor C (not shown) whose values are L d  and C d , respectively. This circuit is suitable for single-frequency signals. For multiple-frequency or broadband signals, the values of the inductor L and capacitor C must be changed as signal frequency is changed in order to compensate for an apparent change in the distributed impedance components L d  and C d . The actual values of the distributed impedance components L d  and C d  do not change. Rather, the approximation of distributed impedance using only a single lumped inductor L and capacitor C breaks down for signals having broad band or multiple frequencies. Higher n-stage approximations of distributed impedance result in less variation in the apparent values of distributed inductance L d  and capacitance C d . The value of the impedance Z dia3  of the three-stage circuit shown in  FIG. 13  and the impedances Z dia4  and Z dia5  of four-stage and five-stage distributed impedance approximation circuits are as follows:  
         Z     dia   ⁢           ⁢   3       =         (     ⅈ   ⁢           ⁢     L   d     ⁢     ω   /   3       )     ⁢     (       -   18     +       C   d     ⁢     L   d     ⁢     ω   2         )     ⁢     (       -   6     +       C   d     ⁢     L   d     ⁢     ω   2         )         (     36   -     18   ⁢     C   d     ⁢     L   d     ⁢     ω   2       +       C   d   2     ⁢       L   ⁢             d   2     ⁢     ω   4         )           
         Z     dia   ⁢           ⁢   4       =         (     ⅈ   ⁢           ⁢     L   d     ⁢     ω   /   4       )     ⁢     (       -   24     +       C   d     ⁢     L   d     ⁢     ω   2         )     ⁢     (     288   -     48   ⁢     C   d     ⁢     L   d     ⁢     ω   2       +       C   d   2     ⁢     L   d   2     ⁢     ω   4         )         (       -   1728     +     864   ⁢     C   d     ⁢     L   d     ⁢     ω   2       +     60   ⁢     C   d   2     ⁢     L   d   2     ⁢     ω   4       +       C   d   3     ⁢     L   d   3     ⁢     ω   6         )           
         Z     dia   ⁢           ⁢   5       =               (     ⅈ   ⁢           ⁢     L   d     ⁢     ω   /   5       )     ⁢     (     2000   -     100   ⁢     C   d     ⁢     L   d     ⁢     ω   2       +         C   ⁢             d   2     ⁢     L   d   2     ⁢     ω   4         )                 (     400   -     60   ⁢     C   d     ⁢     L   d     ⁢     ω   2       +       C   d   2     ⁢     L   d   2     ⁢     ω   4         )                   (       -   20     +       C   d     ⁢     L   d     ⁢     ω   2         )               (       -   1728     +     3600   ⁢     C   d     ⁢     L   d     ⁢     ω   2       -     120   ⁢     C   d   2     ⁢     L   d   2     ⁢     ω   4       +       C   d   3     ⁢     L   d   3     ⁢     ω   6         )                 
 
 where ω is the signal frequency. Using arbitrary values for inductance L d , capacitance C d , and frequency ω(L d =1, C d =100, ω=1), the difference in the impedance between a two-stage and a three-stage distributed impedance approximation circuit is approximately 0.0545, and the difference in impedance between a four-stage and five-stage circuit is approximately 0.000091. To reproduce distributed impedance exactly using n-stage circuits, n must be infinite. However, the accuracy of the approximation increases asymptotically as n increases. 
 
         [0105]     The circuit shown in  FIG. 13  may also be used in place of the distributed impedance that has distributed inductance L d  and capacitance C d . In order to best approximate the distributed impedance, the values of L 1 , L 2 , and L 3  are substantially equal to L d /3, and the values of C 1  and C 2 , are substantially equal to C d /2. For an n-stage approximation of a distributed impedance, where n is a positive integer greater than two, the values of each of the lumped inductors L 1  to L n  and lumped capacitors C 1  to C n-1  would be L d /n and C d /(n−1), respectively. Distributed resistance and conductance could also be approximated using lumped circuit elements in the method just described. A better approximation of distributed impedance is obtained by utilizing a larger number n of stages. To support this conclusion, one may examine the simplest approximation of a distributed impedance using an inductor L and capacitor C (not shown) whose values are L d  and C d , respectively. This circuit is suitable for single-frequency signals. For multiple-frequency or broadband signals, the values of the inductor L and capacitor C must be changed as signal frequency is changed in order to compensate for an apparent change in the distributed impedance components L d  and C d . The actual values of the distributed impedance components L d  and C d  do not change. Rather, the approximation of distributed impedance using only a single lumped inductor L and capacitor C breaks down for signals having broad band or multiple frequencies. Higher n-stage approximations of distributed impedance result in less variation in the apparent values of distributed inductance L d  and capacitance C d . The value of the impedance Z dia3  of the three-stage circuit shown in  FIG. 13  and the impedances Z dia4  and Z dia5  of four-stage and five-stage distributed impedance approximation circuits are as follows:  
         Z     dia   ⁢           ⁢   3       =         (     ⅈ   ⁢           ⁢     L   d     ⁢     ω   /   3       )     -   18   +       C   c     ⁢     L   d     ⁢     ω   2           (     36   -     18   ⁢     C   d     ⁢     L   d     ⁢     ω   2       +     C   ⁢           ⁢     2   d     ⁢   L   ⁢           ⁢     2   d     ⁢     ω   4                 
         Z     dia   ⁢           ⁢   4       =         (     ⅈ   ⁢           ⁢     L   d     ⁢     ω   /   4       )     ⁢     (       -   24     +       C   d     ⁢     L   d     ⁢     ω   2         )     ⁢     (     288   -     48   ⁢     C   c     ⁢     L   d     ⁢     ω   2       +     C   ⁢           ⁢     2   d     ⁢   L   ⁢           ⁢     2   d     ⁢     ω   4         )             -   1728     +     864   ⁢     C   d     ⁢     L   d     ⁢     ω   2       +     60   ⁢   C   ⁢           ⁢     2   d     ⁢   L   ⁢           ⁢     2   d     ⁢     ω   4       +     C   ⁢           ⁢     3   d     ⁢   L   ⁢           ⁢     3   d     ⁢     ω   6         )           
         Z     dia   ⁢           ⁢   5       =               (     ⅈ   ⁢           ⁢     L   d     ⁢     ω   /   5       )     ⁢     (     2000   -     100   ⁢     C   d     ⁢     L   d     ⁢     ω   2       +     C   ⁢           ⁢     2   d     ⁢   L   ⁢           ⁢     2   d     ⁢     ω   4         )                 (     400   -     60   ⁢     C   d     ⁢     L   d     ⁢     ω   2       +     C   ⁢           ⁢     2   d     ⁢   L   ⁢           ⁢     2   d     ⁢     ω   4         )                   (       -   20     +       C   d     ⁢     L   d     ⁢     ω   2         )               (       -   1728     +     3600   ⁢     C   d     ⁢     L   d     ⁢     ω   2       -     120   ⁢   C   ⁢           ⁢     2   d     ⁢   L   ⁢           ⁢     2   d     ⁢     ω   4       +     C   ⁢           ⁢     3   d     ⁢   L   ⁢           ⁢     3   d     ⁢     ω   6         )                 
 
 where ω is the signal frequency. Using arbitrary values for inductance L d , capacitance C d , and frequency ω(L d =1, C d =100, ω=1), the difference in the impedance between a two-stage and a three-stage distributed impedance approximation circuit is approximately 0.0545, and the difference in impedance between a four-stage and five-stage circuit is approximately 0.000091. To reproduce distributed impedance exactly using n-stage circuits, n must be infinite. However, the accuracy of the approximation increases asymptotically as n increases. 
 
         [0106]     The circuit shown in  FIG. 13  may also be used in place of the distributed impedance element  153 . It will be appreciated that the most accurate means to approximate a distributed impedance is to utilize another distributed impedance whose components are variable.  
         [0107]     The compensation for changes in an antenna&#39;s distributed impedance may be extended to different types of antennas and different frequencies of operation. In the derivation of the radiation field of a center-fed dipole, Elliot shows that the transmission line feeding the antenna can be said to be delivering power to a radiative resistance placed across its terminus. The current distribution on the dipole is used to solve for the input impedance of the dipole antenna. This impedance is a function of the length of the dipole and the wavelength of the antenna signal.  
         [0108]     The development of the field equations due to a center-fed dipole can be extended to the case of a monopole above a ground plane. Current elements above the ground plane will induce a current distribution in the plane that can be approximated by image current elements located a distance d below the plane in accordance with the location d of each of the actual current elements above the plane. The positions of the current elements relative to the ground plane figure into the radiation field equations for the antenna and, consequently, the radiative resistance of the antenna. Thus, as the relative location of nearby highly conductive electrically grounded objects changes, such as in a mobile cellular communications environment, the impedance of the antenna element will also change.  
         [0109]     A set of transmission line equations are typically used to characterize wave propagation along a transmission line structure, such as an antenna, in terms of voltage and current instead of in terms of fields. The transmission line equations define inductance L d , capacitance C d , and conductance Y d  (reciprocal of resistance) per unit length. The unit-length representation of these values implies distributed circuit quantities rather than lumped circuit elements. The general solutions to the transmission line equations lead to a representation of the characteristic impedance of the transmission line structure:  
         Z   0     =       (       ⅈω   ⁢           ⁢     L   d           Y   d     +     ⅈω   ⁢           ⁢     C   d           )           
 
 In the solution for a coaxial transmission line with the additional assumption of Y d =0, Rao shows that the characteristic impedance of the line is:  
         Z   0     =           L   d       C   d         =       1     2   ⁢   π       ⁢         μ   ɛ     ⁢     ln   ⁡     (     b   /   a     )                   
 
 where a is the radius of the inner signal conductor and b is the radius of the outer ground conductor. This solution indicates that the characteristic impedance of the line, thus the characteristic impedance of an antenna, is affected by the relative position and geometry of the ground conductor to the signal conductor. The equation for the characteristic impedance also indicates that the ratio of permeability to permittivity could be changed in order to compensate for the change in Z 0  that would result from variations in the relative positions between the signal conductor and the ground conductor. To best approximate variations in the antenna impedance where Y d =0 is not a valid assumption, it is preferable to utilize a variable distributed impedance element that has distributed conductance (preferably variable distributed conductance), inductance that is variable, and a value of capacitance that is variable. 
 
         [0110]     As the antenna impedance Z 2  changes (Z 2 →Z 2 +δZ), the voltage of the transmit signal at the output of the amplifier  105  changes to:  
         V   T11   ′     =         V   T11     +     δ   ⁢           ⁢     V   T11         =               V   A     (         (       R   2     +     Z   2     +     δ   ⁢           ⁢   Z       )     ⁢     (       R   3     +     Z   3       )       +                     R   1     ⁡     (       R   2     +     Z   2     +     δ   ⁢           ⁢   Z     +     R   3     +     Z   3       )       )                 (       R   2     +     Z   2     +     δ   ⁢           ⁢   Z       )     ⁢     (       R   3     +     Z   3       )       +             
 
 The values of the transmit currents i T11 , i T12  and i T13 , being related to V T11 , change accordingly: 
 
 i′   T11   =i   T11   +di   T11  
 
 i′   T12   =i   T12   +di   T12  
 
 i′   T13   =i   T13   +di   T13  
 
         [0111]     The values of the receiver currents are i′ R11 , i′ R12 , and i′R 13 :  
         i   R12   ′     =       V   R12   ′       Z   in2           
         i   R11   ′     =       i   R12   ′     ⁢           ⁢       (       R   3     +     Z   3       )       (       R   3     +     Z   3     +     R   1     +     Z   1       )             
         i   R13   ′     =       i   R12   ′     ⁢           ⁢       (       R   1     +     Z   1       )       (       R   3     +     Z   3     +     R   1     +     Z   1       )             
         where   ⁢           ⁢     V   R12   ′       =       (       V   R12     /     (       Z   2     +   dZ     )       )       (       1   /     (       Z   2     +   dZ     )       +     1   /     Z   in2         )           
 
 A three-branch circuit shown in  FIG. 9  is comprised of the transmit branch, the first reference branch, the three-port device  131  (which in this case is a simple linear junction such as a resistive divider and thus defines the circuit as a simple three-branch circuit) and a transmit signal output branch that includes impedance element  121 . Applicant has determined that in each branch of the simple three-branch circuit, the ratio of the change in the transmit current δi T11 , δi T12 , and δi T13 , to the receive current i′ R11 , i′R 12 , and i′R 13  is substantially equal:  
           di   T11       i   R11   ′       =         di   T12       i   R12   ′       =       di   T13       i   R13   ′             
 
 Furthermore, applicant has determined experimentally that this relation holds for the case of non-linear three-port networks. Thus, any attempt to compensate for the change in transmit current in one branch by canceling it with the change in transmit current in one of the other branches results in cancellation of the receive signal. However, if the impedance of one of the branches besides the transmit branch is made to change in response to a change in the impedance of the antenna element  101  and that change is a known relation to the change δZ in the antenna impedance  151 , then the change in the transmit current in one branch of a three-branch circuit may be used to cancel the change in transmit current in one of the other branches without canceling all of the receive signal. 
 
         [0112]     The reference signal V Ref  embedded in signal V SG  appears as a reference transmit component i RT11  embedded in the transmit signal i T11  generated by the first amplifier  105 . Therefore, the other transmit currents i T21  and i T31  will each include a reference transmit component i RT21  and i RT31 , respectively. Thus, the signal i S3  has a component reference transmit signal i RS3  that is proportional to the transmit component i RT11 . In addition, the signal i S2  has a component reference transmit signal i RS2  that is proportional to a transmit component i RT13  that flows through impedance element  161 . The electrical signal i PU1  is input to the impedance controller  181 , which may include one or more signal filters (not shown). The signal filter(s) removes components that are not used for providing a measure of the change in antenna impedance. The impedance controller  181  adjusts the impedance of impedance element  171  by a predetermined amount dR that is proportional to the change in the amplitude and or phase of the reference transmit signal i RS   3 , thus reflecting a change in at least one of the real and imaginary parts of the antennaOs  101  impedance. The ideal change iδ RS3  in the reference transmit signal i RS3  due to an impedance change δ 6 Z in the antenna impedance  151  is shown as follows:  
         i   ARS3     =     -     (       (     δ   ⁢           ⁢         ZV   A     ⁡     (       R   3     +     Z   3       )       2       )     /     (       (         R   1     ⁢     R   2       +       R   1     ⁢     R   3       +       R   2     ⁢     R   3       +       R   2     ⁢     Z   1       +       R   3     ⁢     Z   1       +       R   1     ⁢     Z   2       +       R   3     ⁢     Z   2       +       Z   1     ⁢     Z   2       +       R   1     ⁢     Z   3       +       R   2     ⁢     Z   3       +       Z   1     ⁢     Z   3       +       Z   2     ⁢     Z   3         )     ⁢     (       δ   ⁢           ⁢     ZR   1       +       R   1     ⁢     R   2       +     δ   ⁢           ⁢     ZR   3       +       R   1     ⁢     R   3       +       R   2     ⁢     R   3       +     δ   ⁢           ⁢     ZZ   1       +   R2Z1   +   R3Z1   +   R1Z2   +   R3Z2   +   Z1Z2   +     δ   ⁢           ⁢   ZZ3     +   R1Z3   +   R2Z3   +   Z1Z3   +   Z2Z3     )       )       )           
 
 For small impedance changes δZ, the signal-change iδ RS3  is substantially proportional to δZ. Signal change iδ RS3  establishes boundary conditions on how large δR can be. This is affected by changes δR in the impedance of impedance element  171 . The actual signal-change iδ RS3  is shown in the following equation:  
         i   ARS3     =     -     (       (       V   A     ⁡     (       2   ⁢   δ   ⁢           ⁢   R   ⁢           ⁢   δ   ⁢           ⁢     ZR   2       +     2   ⁢   δ   ⁢           ⁢     RR   2   2       +     2   ⁢   δ   ⁢           ⁢   R   ⁢           ⁢   δ   ⁢           ⁢     ZR   3       +     δ   ⁢           ⁢     ZR   3   2       +     2   ⁢   δ   ⁢           ⁢   R   ⁢           ⁢   δ   ⁢           ⁢     ZZ   2       +     4   ⁢   δ   ⁢           ⁢     RR   2     ⁢     Z   2       +     2   ⁢   δ   ⁢           ⁢     RZ   2   2       +     2   ⁢   δ   ⁢           ⁢   R   ⁢           ⁢   δ   ⁢           ⁢     ZZ   3       +     2   ⁢   δ   ⁢           ⁢     ZR   3     ⁢     Z   3       +     δ   ⁢           ⁢     ZZ   3   2         )       )     /     (       (         R   1     ⁢     R   2       +       R   1     ⁢     R   3       +       R   2     ⁢     R   3       +       R   2     ⁢     Z   1       +       R   3     ⁢     Z   1       +       R   1     ⁢     Z   2       +       R   3     ⁢     Z   2       +       Z   1     ⁢     Z   2       +       R   1     ⁢     Z   3       +       R   2     ⁢     Z   3       +       Z   1     ⁢     Z   3       +       Z   2     ⁢     Z   3         )     ⁢     (       2   ⁢   δ   ⁢           ⁢   R   ⁢           ⁢   δ   ⁢           ⁢   Z     +     2   ⁢   δ   ⁢           ⁢     RR   1       +     δ   ⁢           ⁢     ZR   1       +     2   ⁢   δ   ⁢           ⁢     RR   2       +       R   1     ⁢     R   2       +     δ   ⁢           ⁢     ZR   3       +       R   1     ⁢     R   3       +       R   2     ⁢     R   3       +     2   ⁢   δ   ⁢           ⁢     RZ   1       +     δ   ⁢           ⁢     ZZ   1       +       R   2     ⁢     Z   1       +       R   3     ⁢     Z   1       +     2   ⁢   δ   ⁢           ⁢     RZ   2       +       R   1     ⁢     Z   2       +       R   3     ⁢     Z   2       +       Z   1     ⁢     Z   2       +     δ   ⁢           ⁢     ZZ   3       +       R   1     ⁢     Z   3       +       R   2     ⁢     Z   3       +       Z   1     ⁢     Z   3       +       Z   2     ⁢     Z   3         )       )       )           
 
 It is important that the impedance-change δR of element  171  has a smaller effect on the signal i S3  than the impedance-change δZ of the antenna  101 . This is to avoid a positive feedback condition where the change in impedance of the impedance element  171  causes the controller  181  to create an even larger impedance change in the impedance element  171 . In this case, the impedance change δR is set proportional to impedance change δZ by a scaling factor b whose value is determined by this boundary condition. 
 
         [0113]     The electrical signal i S5  includes a reference transmit signal i RS5  that is used to measure the impedance-change of the impedance element  153  and is interpreted by the impedance controller  183  for adjusting the variable impedance element  173  by a predetermined amount. The ratio of the impedance-change of element  173  to the impedance-change of the element  153  is proportional to the ratio of the impedance-change of element  171  to change in impedance of the antenna  101 . The output signal i 294  of the combining circuit  294  includes a receive component i R3  and a transmit component i T3  that is proportional to iδ RS3 .  
         [0114]     The output signal i 293  of the combining circuit  293  includes a receive component i R2  and a transmit component i T2  proportional to a change in the reference transmit component signal i RT13  at element  161 , iδ RS2 , given by the following equation:  
         i   ARS3     =     (     (       g   Ref   V     ⁢   δ   ⁢           ⁢       Z   ⁡     (         -   2     ⁢   b   ⁢           ⁢   δ   ⁢           ⁢     ZR   2       -     2   ⁢     bR   1     ⁢     R   2       -     2   ⁢     bR   2   2       -       R   1     ⁢     R   3       -     2   ⁢     bR   2     ⁢     Z   1       +       R   3     ⁢     Z   1       -             2   ⁢   b   ⁢           ⁢   δ   ⁢           ⁢     ZZ   2       -     2   ⁢     bR   1     ⁢     Z   2       -     4   ⁢     bR   2     ⁢     Z   2       -     2   ⁢     bZ   1     ⁢     Z   2       -     2   ⁢     bZ   2   2       +       R   1     ⁢     R   3       +       Z   1     ⁢     Z   3         )       )       /     (       (         R   1     ⁢     R   2       +       R   1     ⁢     R   3       +       R   2     ⁢     R   3       +       R   2     ⁢     Z   1       +       R   3     ⁢     Z   1       +       R   1     ⁢     Z   2       +       R   3     ⁢     Z   2       +       Z   1     ⁢     Z   2       +       R   1     ⁢     Z   3       +       R   2     ⁢     Z   3       +       Z   1     ⁢     Z   3       +       Z   2     ⁢     Z   3         )     ⁢     (       2   ⁢   b   ⁢           ⁢   δ   ⁢           ⁢     Z   2       +     δ   ⁢           ⁢     ZR   1       +     2   ⁢   b   ⁢           ⁢   δ   ⁢           ⁢     R   1       +     2   ⁢   b   ⁢           ⁢   δ   ⁢           ⁢     ZR   2       +     R   1     +     R   2     +     δ   ⁢           ⁢     ZR   3       +       R   1     ⁢     R   3       +       R   2     ⁢     R   3       +     δ   ⁢           ⁢     ZZ   1       +     2   ⁢   b   ⁢           ⁢   δ   ⁢           ⁢     ZZ   1       +       R   2     ⁢     Z   1       +       R   3     ⁢     Z   1       +     2   ⁢   b   ⁢           ⁢   δ   ⁢           ⁢     ZZ   2       +       R   1     ⁢     Z   2       +       R   3     ⁢     Z   2       +       Z   1     ⁢     Z   2       +     δ   ⁢           ⁢     ZZ   3       +       R   1     ⁢     R   3       +       R   2     ⁢     Z   3       +       Z   1     ⁢     Z   3       +       Z   2     ⁢     Z   3         )       )         )           
 
 The output signals i 293  and i 294  include non-zero transmit components i T3  and i T 2, particularly when the antenna impedance  151  is not proportional to the impedance of element  153 . This can occur due to a time-lag in the compensation of the impedance of element  153  to impedance-changes of the antenna impedance  151 . The output signals i 293  and i 294  are combined in the combining circuit  295  such that the transmit components iδ RS3  and iδ RS2  cancel. In this case, a constant gain G having the value:  
       G   =         2   ⁢       b   ⁡     (       R   2     +     Z   2       )       2       +       (       R   3     +     Z   3       )     ⁢   2             -   2     ⁢     b   ⁡     (       R   2     +     Z   2       )       ⁢     (       R   2     +     R   1     +     Z   2     +     Z   1       )       +       (       R   1     +     Z   1       )     ⁢     (       R   3     +     Z   3       )               
 
 applied to the output signal i 294  will result in substantial cancellation of the transmit components iδ S3  and iδ S2  from the output of the combining circuit  295  while preserving some of the receive signal components i R3  and i R2 . 
 
         [0115]     In the preferred experimental circuit ( FIG. 9 ), the cancellation of many varieties of direct transmit-signal interference has been demonstrated in order to provide a basic understanding of the types of direct transmit-signal interference that exist and the methods needed to cancel this interference. With respect to this understanding, many aspects of this invention may vary, such as in accordance with signal-frequency of operation. For example, the concepts explained with respect to the three-port isolator design shown in  FIG. 9  also apply to an electromagnetic pickup/driver assembly that could be used to both sense the motion of a ferromagnetic object and impart a force upon that object simultaneously. In this regard, it should be understood that such variations will fall within the scope of the present invention, its essence lying more fundamentally with the design realizations and discoveries achieved than merely the particular designs developed.  
         [0116]     The foregoing discussion and the claims which follow describe the preferred embodiments of the present invention. Particularly with respect to the claims, it should be understood that changes may be made without departing from its essence. In this regard, it is intended that such changes would still fall within the scope of the present invention. It simply is not practical to describe and claim all possible revisions to the present invention which may be accomplished. To the extent such revisions utilize the essence of the present invention, each naturally fall within the breadth of protection encompassed by this patent. This is particularly true for the present invention since its basic concepts and understandings are fundamental in nature and can be broadly applied.

Technology Category: 5