Patent Publication Number: US-7720449-B2

Title: Fault-tolerant amplifier matrix

Description:
FIELD OF THE INVENTION 
     This invention relates generally to amplification matrixes, and more particularly to a fault-tolerant amplifier matrix. 
     BACKGROUND OF THE INVENTION 
     Amplifier matrixes such as the well-known Butler matrix have been used in cellular base stations for quite some time. An illustration of a butler matrix used to evenly distribute power amongst three amplifiers  14  is provided in  FIG. 1 . Typically, a butler matrix has an input matrix portion  12 , an output matrix portion  16 , amplifiers  14  coupled therebetween, and antennas  18  coupled to the outputs of the output matrix. 
     Under normal conditions, the amplified outputs of the input portion  12  (i.e., outputs Y 1  through Y 3 ) have well-defined mathematical relationships such as, for example, 
     
       
         
           
             
               
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     The outputs of the output portion  16  (i.e., outputs Z 1  through Z 3 ) have the following mathematical relationships: 
     
       
         
           
             
               
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             = 
             
               
                 
                   
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     Applying the Y equations to the Z equations produces the following relationships: 
     
       
         
           
             
               
                 
                   
                     
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     These equations reflect a desired isolation characteristic at the outputs of the output portion  16 .  FIG. 2  shows by way of example reference  20 , which depicts the code domain power of a UMTS (Universal Mobile Telecommunications Service) signal at the output portion  16  with all amplifiers operating properly. Under normal operating conditions, for example, the EVM (Error Vector Magnitude) of the UMTS signal of output portion  16  is 5% and peak code domain error is −45.7 dB. 
     If, however, one of the amplifiers  14  experiences a fault which renders it inoperable, the operation of the Butler matrix can be impacted severely at all outputs of the output portion. This becomes evident in the case where the Y 1  amplifier is removed from operation. Under these circumstances, the Z equations result in the following relationships: 
     
       
         
           
             
               
                 Z 
                 -&gt; 
               
               ⁢ 
               1 
             
             = 
             
               
                 
                   2 
                   3 
                 
                 ⁢ 
                 
                   S 
                   -&gt; 
                 
                 ⁢ 
                 1 
                 ⁢ 
                 ∠120° 
               
               + 
               
                 
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                   3 
                 
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                   S 
                   -&gt; 
                 
                 ⁢ 
                 2 
                 ⁢ 
                 ∠30° 
               
               + 
               
                 
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                   3 
                 
                 ⁢ 
                 
                   S 
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                 ⁢ 
                 3 
                 ⁢ 
                 ∠ 
               
               - 
               
                 150 
                 ⁢ 
                 ° 
               
             
           
         
       
       
         
           
             
               
                 Z 
                 -&gt; 
               
               ⁢ 
               2 
             
             = 
             
               
                 
                   1 
                   3 
                 
                 ⁢ 
                 
                   S 
                   -&gt; 
                 
                 ⁢ 
                 1 
                 ⁢ 
                 ∠ 
               
               - 
               
                 90 
                 ⁢ 
                 ° 
               
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                   2 
                   3 
                 
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                 ⁢ 
                 2 
                 ⁢ 
                 ∠180° 
               
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                   3 
                 
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                 3 
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                 Z 
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             = 
             
               
                 
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                   3 
                 
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                   S 
                   -&gt; 
                 
                 ⁢ 
                 ∠ 
               
               - 
               
                 30 
                 ⁢ 
                 ° 
               
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                 ⁢ 
                 ∠60° 
               
               + 
               
                 
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                   3 
                 
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     As should be evident from these equations, sector-to-sector isolation degrades severely because of the residual terms between sectors. Consequently, a branch failure within a Butler matrix can cause major degradation in waveform quality at the outputs of the output portion  16 . This can cause considerable, if not complete, failure in radio communications to all sectors.  FIG. 2  shows by way of example reference  22 , which depicts the code domain power of the UMTS signal at the output portion  16  with amplifier Y 1  disabled. Under these conditions, the code domain noise has risen 20 dB compared to reference  20 , and the EVM and peak code domain error of the UMTS signal of output portion  16  have degraded to 65.5% and −26.5 dB, respectively. A need therefore arises for a fault-tolerant amplifier matrix. 
     SUMMARY OF THE INVENTION 
     Embodiments in accordance with the invention provide a fault-tolerant amplifier matrix. 
     In a first embodiment of the present invention, an amplifier matrix has a plurality of inter-coupled matrix clusters, and a controller. The controller is programmed to detect a fault in an amplification path of one of the matrix clusters, and update vector relationships in the matrix clusters to minimize inter-sector isolation at the outputs of the matrix clusters. 
     In a second embodiment of the present invention, a computer-readable storage medium in an amplifier matrix has a plurality of matrix clusters. The storage medium includes computer instructions for detecting a fault in an amplification path of one of the matrix clusters, and updating vector relationships in the matrix clusters to minimize inter-sector isolation at the outputs of the matrix clusters. 
     In a third embodiment of the present invention, a base station has a controller, a receiver, and a transmitter. The transmitter has an amplifier matrix having a plurality of inter-coupled matrix clusters, and a plurality of antennas coupled to the outputs of the amplifier matrix for radiating message signals to selective call radios (SCRs). The controller is programmed to detect a fault in an amplification path of one of the matrix clusters, update vector relationships in the matrix clusters to minimize inter-sector isolation at the outputs of the matrix clusters, and radiate signals from the transmitter to one or more SCRs. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         FIG. 1  is a block diagram of a prior art Butler matrix in a cellular system. 
         FIG. 2  depicts measurements of the prior art Butler matrix of  FIG. 1  before and after a fault in said system. 
         FIG. 3  is a block diagram of a base station in accordance with an embodiment of the present invention. 
         FIGS. 4 and 5  depict block diagrams of an amplifier matrix of the base station in accordance with an embodiment of the present invention. 
         FIG. 6  depicts a flowchart of a method operating in a transmitter of the base station in accordance with embodiments of the present invention. 
         FIG. 7  depicts a table comparing operating results of the transmitter before and after a fault is corrected in accordance with embodiments of the present invention. 
     
    
    
     DETAILED DESCRIPTION 
     While the specification concludes with claims defining the features of embodiments of the invention that are regarded as novel, it is believed that the embodiments of the invention will be better understood from a consideration of the following description in conjunction with the figures, in which like reference numerals are carried forward. 
       FIG. 3  is a block diagram of a base station  100  in accordance with an embodiment of the present invention. The base station  100  comprises a conventional receiver  102  for intercepting signals from one or more selective call radios (SCRs)  101 , a transmitter  104  for radiating message signals directed to the SCRs  101 , and a conventional controller  106 . The controller  106  can utilize one or more computing devices such as microprocessors, and/or DSPs (Digital Signal Processors) each with associated storage media for controlling operations of the receiver  102  and the transmitter  104 . 
     The transmitter  104  comprises an amplifier matrix  112  coupled to a plurality of antennas  114  for radiating message signals to selective call radios (SCRs). Signals delivered to the amplifier matrix  112  can be baseband signals generated by the controller  106  having an embedded message intended for processing by a user of the SCR  101 . 
     The foregoing components of the base station  100  can be powered by a conventional power supply  108 . 
       FIGS. 4 and 5  depict block diagrams of the amplifier matrix  112  in accordance with an embodiment of the present invention. The amplifier matrix  112  comprises a plurality of inter-coupled matrix clusters  201  (only two are shown for illustration). Each matrix cluster  201  comprises a digital matrix  202 , an analog matrix  204 , and up-converted amplifiers  206  coupled therebetween. The outputs of the analog matrix  204  are coupled to the antennas  114 , and can be individually decoupled to a conventional load  208 . The up-converted amplifiers  206  can comprise a conventional up-converter  220  and a corresponding conventional amplifier  222  as shown in  FIG. 5 . Utilizing conventional technology, the up-converter  220  transforms the operating frequency of the baseband signals supplied by the digital matrix  202  to a carrier signal operating at a carrier frequency such as, for example, 880 MHz (a typical cellular carrier band). The amplifiers  222  supply to the analog matrix  204  amplified up-converted signals for further processing. 
       FIG. 6  depicts a flowchart of a method  300  operating in the transmitter  104  of the base station  100  in accordance with embodiments of the present invention. Method  300  begins with step  302  where the controller  106  utilizes conventional methods to monitor faults in the amplification paths of the matrix clusters  201  shown in  FIG. 4 . If a no fault is detected in step  304 , the controller  106  proceeds to step  306  where it radiates signals to the SCRs  101  in accordance with normal operations. If, on the other hand, a fault is detected (such as an inoperable amplifier  206 ), the controller  106  asserts an alarm in step  308 . The alarm can, for example, notify personnel of an infrastructure carrier managing the base station  100  of the fault. The notification can be an email, an over-the-air message, or other form of notification suitable for the carrier&#39;s business operations. 
     In step  309 , the controller  106  is programmed to select an input of the digital matrix  202  having the lowest power and a corresponding output of the analog matrix  204 . In steps  309 ,  310  and  312 , the controller  106  takes a first mitigation step which is to decouple the antenna from the output of the analog matrix  204  selected in step  309  of the affected matrix cluster  201 A and apply a load to the decoupled output. These steps are shown in cluster  201 A of  FIG. 4  on output Z 3 . The controller  106  can be further programmed in step  314  to nullify the input (S 3 ) of the digital matrix  202  selected in step  309  corresponding to the decoupled output Z 3 . From these steps, the controller  106  in step  316  updates vector relationships in the matrix clusters  201 A and  201 B to minimize inter-sector isolation at the outputs of the matrix clusters. 
     Steps  310  through  316  can be explained mathematically from the illustrations of  FIG. 4 . For the affected cluster  201 A, the following relationships apply: 
     
       
         
           
             
               
                 Y 
                 -&gt; 
               
               
                 2 
                 ⁢ 
                 A 
               
             
             = 
             
               
                 
                   
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                         S 
                         1 
                       
                       ⁢ 
                       A 
                     
                   
                   · 
                   
                     
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                     1 
                   
                 
                 ⁢ 
                 ∠90° 
               
               + 
               
                 
                   
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                         S 
                         2 
                       
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                     2 
                   
                 
                 ⁢ 
                 ∠ 
               
               - 
               
                 120 
                 ⁢ 
                 ° 
               
               + 
               
                 0 
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                     S 
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                   3 
                 
               
             
           
         
       
       
         
           
             
               
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                     1 
                   
                 
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                 ∠180° 
               
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                         2 
                       
                       ⁢ 
                       A 
                     
                   
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                 ∠ 
               
               - 
               
                 150 
                 ⁢ 
                 ° 
               
               + 
               
                 0 
                 · 
                 
                   
                     S 
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                   3 
                 
               
             
           
         
       
       
         
           
             
               S 
               
                 1 
                 ⁢ 
                 A_AvailablePower 
               
             
             = 
             
               
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                 ( 
                 
                   
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                   2 
                 
                 ) 
               
             
           
         
       
       
         
           
             
               S 
               
                 1 
                 ⁢ 
                 _APower 
               
             
             = 
             
               MIN 
               ⁡ 
               
                 ( 
                 
                   
                     S 
                     
                       1 
                       ⁢ 
                       A_OriginalPower 
                     
                   
                   , 
                   
                     S 
                     
                       1 
                       ⁢ 
                       A_AvailablePower 
                     
                   
                 
                 ) 
               
             
           
         
       
       
         
           
             
               S 
               
                 2 
                 ⁢ 
                 A_Power 
               
             
             = 
             
               MIN 
               ⁡ 
               
                 ( 
                 
                   
                     S 
                     
                       2 
                       ⁢ 
                       A_OriginalPower 
                     
                   
                   , 
                   
                     S 
                     
                       2 
                       ⁢ 
                       A_AvailablePower 
                     
                   
                 
                 ) 
               
             
           
         
       
       
         
           
             
               Y 
               
                 
                   S 
                   1 
                 
                 ⁢ 
                 A 
               
             
             = 
             
               
                 
                   S 
                   
                     1 
                     ⁢ 
                     A_Power 
                   
                 
                 
                   S 
                   
                     1 
                     ⁢ 
                     A_OriginalPower 
                   
                 
               
             
           
         
       
       
         
           
             
               Y 
               
                 
                   S 
                   2 
                 
                 ⁢ 
                 A 
               
             
             = 
             
               
                 
                   S 
                   
                     2 
                     ⁢ 
                     A_Power 
                   
                 
                 
                   S 
                   
                     2 
                     ⁢ 
                     A_OriginalPower 
                   
                 
               
             
           
         
       
     
     In the above equations, CLA represents matrix cluster  201 A. The term “CLA Total Available Power” refers to the maximum summed power capability of the enabled amplification paths. This term is divided by two because half of the power will be dissipated in a load, while the other half is available to be radiated at the antennae. For the unaffected matrix cluster  201 B, the following relationships apply: 
     
       
         
           
             
               
                 Y 
                 -&gt; 
               
               
                 1 
                 ⁢ 
                 B 
               
             
             = 
             
               
                 
                   
                     Y 
                     
                       
                         S 
                         1 
                       
                       ⁢ 
                       B 
                     
                   
                   · 
                   
                     
                       S 
                       -&gt; 
                     
                     1 
                   
                 
                 ⁢ 
                 ∠ 
               
               - 
               
                 90 
                 ⁢ 
                 ° 
               
               + 
               
                 
                   
                     Y 
                     
                       
                         S 
                         2 
                       
                       ⁢ 
                       B 
                     
                   
                   · 
                   
                     
                       S 
                       -&gt; 
                     
                     2 
                   
                 
                 ⁢ 
                 ∠0° 
               
               + 
               
                 
                   
                     Y 
                     
                       
                         S 
                         3 
                       
                       ⁢ 
                       B 
                     
                   
                   · 
                   
                     
                       S 
                       -&gt; 
                     
                     3 
                   
                 
                 ⁢ 
                 ∠ 
               
               - 
               
                 180 
                 ⁢ 
                 ° 
               
             
           
         
       
       
         
           
             
               
                 Y 
                 -&gt; 
               
               
                 2 
                 ⁢ 
                 B 
               
             
             = 
             
               
                 
                   
                     Y 
                     
                       
                         S 
                         1 
                       
                       ⁢ 
                       B 
                     
                   
                   · 
                   
                     
                       S 
                       -&gt; 
                     
                     1 
                   
                 
                 ⁢ 
                 ∠60° 
               
               + 
               
                 
                   
                     Y 
                     
                       
                         S 
                         2 
                       
                       ⁢ 
                       B 
                     
                   
                   · 
                   
                     
                       S 
                       -&gt; 
                     
                     2 
                   
                 
                 ⁢ 
                 ∠ 
               
               - 
               
                 90 
                 ⁢ 
                 ° 
               
               + 
               
                 
                   
                     Y 
                     
                       
                         S 
                         3 
                       
                       ⁢ 
                       B 
                     
                   
                   · 
                   
                     
                       S 
                       -&gt; 
                     
                     3 
                   
                 
                 ⁢ 
                 ∠ 
               
               - 
               
                 150 
                 ⁢ 
                 ° 
               
             
           
         
       
       
         
           
             
               
                 Y 
                 -&gt; 
               
               
                 3 
                 ⁢ 
                 B 
               
             
             = 
             
               
                 
                   
                     Y 
                     
                       
                         S 
                         1 
                       
                       ⁢ 
                       B 
                     
                   
                   · 
                   
                     
                       S 
                       -&gt; 
                     
                     1 
                   
                 
                 ⁢ 
                 ∠ 
               
               - 
               
                 150 
                 ⁢ 
                 ° 
               
               + 
               
                 
                   
                     Y 
                     
                       
                         S 
                         2 
                       
                       ⁢ 
                       B 
                     
                   
                   · 
                   
                     
                       S 
                       -&gt; 
                     
                     2 
                   
                 
                 ⁢ 
                 ∠ 
               
               - 
               
                 180 
                 ⁢ 
                 ° 
               
               + 
               
                 
                   
                     Y 
                     
                       
                         S 
                         3 
                       
                       ⁢ 
                       B 
                     
                   
                   · 
                   
                     
                       S 
                       -&gt; 
                     
                     3 
                   
                 
                 ⁢ 
                 ∠ 
               
               - 
               
                 120 
                 ⁢ 
                 ° 
               
             
           
         
       
       
         
           
             
               S 
               
                 1 
                 ⁢ 
                 B_DesiredPower 
               
             
             = 
             
               
                 ( 
                 
                   Total_Original 
                   ⁢ 
                   _S1 
                   ⁢ 
                   _Frame 
                   ⁢ 
                   _Power 
                 
                 ) 
               
               - 
               
                 S 
                 
                   1 
                   ⁢ 
                   A_Power 
                 
               
             
           
         
       
       
         
           
             
               S 
               
                 2 
                 ⁢ 
                 B_DesiredPower 
               
             
             = 
             
               
                 ( 
                 
                   Total_Original 
                   ⁢ 
                   _S2 
                   ⁢ 
                   _Frame 
                   ⁢ 
                   _Power 
                 
                 ) 
               
               - 
               
                 S 
                 
                   2 
                   ⁢ 
                   A_Power 
                 
               
             
           
         
       
       
         
           
             
               S 
               
                 3 
                 ⁢ 
                 B_DesiredPower 
               
             
             = 
             
               
                 ( 
                 
                   Total_Original 
                   ⁢ 
                   _S3 
                   ⁢ 
                   _Frame 
                   ⁢ 
                   _Power 
                 
                 ) 
               
               - 
               
                 S 
                 
                   3 
                   ⁢ 
                   A_Power 
                 
               
             
           
         
       
       
         
           
             
               S 
               
                 1 
                 ⁢ 
                 B_AvailablePower 
               
             
             = 
             
               
                 ( 
                 
                   
                     S 
                     
                       1 
                       ⁢ 
                       B_DesiredPower 
                     
                   
                   
                     
                       S 
                       
                         1 
                         ⁢ 
                         B_DesiredPower 
                       
                     
                     + 
                     
                       S 
                       
                         2 
                         ⁢ 
                         B_DesiredPower 
                       
                     
                     + 
                     
                       S 
                       
                         3 
                         ⁢ 
                         B_DesiredPower 
                       
                     
                   
                 
                 ) 
               
               ⁢ 
               
                 ( 
                 
                   CLB_Total 
                   ⁢ 
                   _Available 
                   ⁢ 
                   _Power 
                 
                 ) 
               
             
           
         
       
       
         
           
             
               S 
               
                 2 
                 ⁢ 
                 B_AvailablePower 
               
             
             = 
             
               
                 ( 
                 
                   
                     S 
                     
                       2 
                       ⁢ 
                       B_DesiredPower 
                     
                   
                   
                     
                       S 
                       
                         1 
                         ⁢ 
                         B_DesiredPower 
                       
                     
                     + 
                     
                       S 
                       
                         2 
                         ⁢ 
                         B_DesiredPower 
                       
                     
                     + 
                     
                       S 
                       
                         3 
                         ⁢ 
                         B_DesiredPower 
                       
                     
                   
                 
                 ) 
               
               ⁢ 
               
                 ( 
                 
                   CLB_Total 
                   ⁢ 
                   _Available 
                   ⁢ 
                   _Power 
                 
                 ) 
               
             
           
         
       
       
         
           
             
               S 
               
                 3 
                 ⁢ 
                 B_AvailablePower 
               
             
             = 
             
               
                 ( 
                 
                   
                     S 
                     
                       3 
                       ⁢ 
                       B_DesiredPower 
                     
                   
                   
                     
                       S 
                       
                         1 
                         ⁢ 
                         B_DesiredPower 
                       
                     
                     + 
                     
                       S 
                       
                         2 
                         ⁢ 
                         B_DesiredPower 
                       
                     
                     + 
                     
                       S 
                       
                         3 
                         ⁢ 
                         B_DesiredPower 
                       
                     
                   
                 
                 ) 
               
               ⁢ 
               
                 ( 
                 
                   CLB_Total 
                   ⁢ 
                   _Available 
                   ⁢ 
                   _Power 
                 
                 ) 
               
             
           
         
       
       
         
           
             
               S 
               
                 1 
                 ⁢ 
                 B_Power 
               
             
             = 
             
               MIN 
               ⁡ 
               
                 ( 
                 
                   
                     S 
                     
                       1 
                       ⁢ 
                       B_DesiredPower 
                     
                   
                   , 
                   
                     S 
                     
                       1 
                       ⁢ 
                       B_DesiredPower 
                     
                   
                 
                 ) 
               
             
           
         
       
       
         
           
             
               S 
               
                 2 
                 ⁢ 
                 B_Power 
               
             
             = 
             
               MIN 
               ⁡ 
               
                 ( 
                 
                   
                     S 
                     
                       2 
                       ⁢ 
                       B_DesiredPower 
                     
                   
                   , 
                   
                     S 
                     
                       2 
                       ⁢ 
                       B_DesiredPower 
                     
                   
                 
                 ) 
               
             
           
         
       
       
         
           
             
               S 
               
                 3 
                 ⁢ 
                 B_Power 
               
             
             = 
             
               MIN 
               ⁡ 
               
                 ( 
                 
                   
                     S 
                     
                       2 
                       ⁢ 
                       B_DesiredPower 
                     
                   
                   , 
                   
                     S 
                     
                       2 
                       ⁢ 
                       B_DesiredPower 
                     
                   
                 
                 ) 
               
             
           
         
       
       
         
           
             
               Y 
               
                 
                   S 
                   1 
                 
                 ⁢ 
                 B 
               
             
             = 
             
               
                 
                   S 
                   
                     1 
                     ⁢ 
                     B_Power 
                   
                 
                 
                   3 
                   ⁢ 
                   
                     S 
                     
                       1 
                       ⁢ 
                       B_OriginalPower 
                     
                   
                 
               
             
           
         
       
       
         
           
             
               Y 
               
                 
                   S 
                   2 
                 
                 ⁢ 
                 B 
               
             
             = 
             
               
                 
                   S 
                   
                     2 
                     ⁢ 
                     B_Power 
                   
                 
                 
                   3 
                   ⁢ 
                   
                     S 
                     
                       2 
                       ⁢ 
                       B_OriginalPower 
                     
                   
                 
               
             
           
         
       
       
         
           
             
               Y 
               
                 
                   S 
                   3 
                 
                 ⁢ 
                 B 
               
             
             = 
             
               
                 
                   S 
                   
                     3 
                     ⁢ 
                     B_Power 
                   
                 
                 
                   3 
                   ⁢ 
                   
                     s 
                     
                       3 
                       ⁢ 
                       B_OriginalPower 
                     
                   
                 
               
             
           
         
       
     
     Similar to the prior equations, CLB represents matrix cluster  201 B. 
       FIG. 7  depicts a table comparing operating results of the transmitter  104  before and after the fault is corrected in accordance method  300  described earlier. In this table, sectors S 1  through S 3  are assumed to output 40, 30, and 10 Watts, respectively, and each amplification path has a maximum power capability of 20 W. Applying the above equations to the affected matrix cluster  201 A with these assumptions leads to the following results: 
     
       
         
           
             
               S 
               
                 1 
                 ⁢ 
                 A_AvailablePower 
               
             
             = 
             
               
                 
                   ( 
                   
                     
                       S 
                       
                         1 
                         ⁢ 
                         A_OriginalPower 
                       
                     
                     
                       
                         S 
                         
                           1 
                           ⁢ 
                           A_OriginalPower 
                         
                       
                       + 
                       
                         S 
                         
                           2 
                           ⁢ 
                           A_OriginalPower 
                         
                       
                     
                   
                   ) 
                 
                 ⁢ 
                 
                   ( 
                   
                     
                       CLA_Total 
                       ⁢ 
                       _Available 
                       ⁢ 
                       _Power 
                     
                     2 
                   
                   ) 
                 
               
               = 
               
                 
                   
                     ( 
                     
                       20 
                       35 
                     
                     ) 
                   
                   ⁢ 
                   
                     ( 
                     
                       40 
                       2 
                     
                     ) 
                   
                 
                 = 
                 
                   11.4 
                   ⁢ 
                   
                       
                   
                   ⁢ 
                   W 
                 
               
             
           
         
       
       
         
           
             
               S 
               
                 2 
                 ⁢ 
                 A_AvailablePower 
               
             
             = 
             
               
                 
                   ( 
                   
                     
                       S 
                       
                         2 
                         ⁢ 
                         A_OriginalPower 
                       
                     
                     
                       
                         S 
                         
                           1 
                           ⁢ 
                           A_OriginalPower 
                         
                       
                       + 
                       
                         S 
                         
                           2 
                           ⁢ 
                           A_OriginalPower 
                         
                       
                     
                   
                   ) 
                 
                 ⁢ 
                 
                     
                 
                 ⁢ 
                 
                   ( 
                   
                     
                       CLA_Total 
                       ⁢ 
                       _Available 
                       ⁢ 
                       _Power 
                     
                     2 
                   
                   ) 
                 
               
               = 
               
                 
                   
                     ( 
                     
                       15 
                       35 
                     
                     ) 
                   
                   ⁢ 
                   
                     ( 
                     
                       40 
                       2 
                     
                     ) 
                   
                 
                 = 
                 
                   8.6 
                   ⁢ 
                   
                       
                   
                   ⁢ 
                   W 
                 
               
             
           
         
       
       
         
           
             
               S 
               
                 1 
                 ⁢ 
                 A_Power 
               
             
             = 
             
               
                 MIN 
                 ⁡ 
                 
                   ( 
                   
                     
                       S 
                       
                         1 
                         ⁢ 
                         A_OriginalPower 
                       
                     
                     , 
                     
                       S 
                       
                         1 
                         ⁢ 
                         A_AvailablePower 
                       
                     
                   
                   ) 
                 
               
               = 
               
                 11.4 
                 ⁢ 
                 
                     
                 
                 ⁢ 
                 
                   W 
                 
               
             
           
         
       
       
         
           
             
               S 
               
                 2 
                 ⁢ 
                 A_Power 
               
             
             = 
             
               
                 MIN 
                 ⁡ 
                 
                   ( 
                   
                     
                       S 
                       
                         2 
                         ⁢ 
                         A_OriginalPower 
                       
                     
                     , 
                     
                       S 
                       
                         2 
                         ⁢ 
                         A_AvailablePower 
                       
                     
                   
                   ) 
                 
               
               = 
               
                 8.6 
                 ⁢ 
                 
                     
                 
                 ⁢ 
                 
                   W 
                 
               
             
           
         
       
       
         
           
             
               Y 
               
                 
                   S 
                   1 
                 
                 ⁢ 
                 A 
               
             
             = 
             
               
                 
                   
                     S 
                     
                       1 
                       ⁢ 
                       A_Power 
                     
                   
                   
                     S 
                     
                       1 
                       ⁢ 
                       A_OriginalPower 
                     
                   
                 
               
               = 
               0.756 
             
           
         
       
       
         
           
             
               Y 
               
                 
                   S 
                   2 
                 
                 ⁢ 
                 A 
               
             
             = 
             
               
                 
                   
                     S 
                     
                       2 
                       ⁢ 
                       A_Power 
                     
                   
                   
                     S 
                     
                       2 
                       ⁢ 
                       A_OriginalPower 
                     
                   
                 
               
               = 
               0.756 
             
           
         
       
       
         
           
             
               
                 Y 
                 -&gt; 
               
               
                 2 
                 ⁢ 
                 A 
               
             
             = 
             
               
                 
                   0.756 
                   · 
                   
                     
                       S 
                       -&gt; 
                     
                     1 
                   
                 
                 ⁢ 
                 ∠90° 
               
               + 
               
                 
                   0.756 
                   · 
                   
                     
                       S 
                       -&gt; 
                     
                     2 
                   
                 
                 ⁢ 
                 ∠ 
               
               - 
               
                 120 
                 ⁢ 
                 ° 
               
               + 
               
                 0 
                 · 
                 
                   
                     S 
                     -&gt; 
                   
                   3 
                 
               
             
           
         
       
       
         
           
             
               
                 Y 
                 -&gt; 
               
               
                 3 
                 ⁢ 
                 A 
               
             
             = 
             
               
                 
                   0.756 
                   · 
                   
                     
                       S 
                       -&gt; 
                     
                     1 
                   
                 
                 ⁢ 
                 ∠180° 
               
               + 
               
                 
                   0.756 
                   · 
                   
                     
                       S 
                       -&gt; 
                     
                     2 
                   
                 
                 ⁢ 
                 ∠ 
               
               - 
               
                 150 
                 ⁢ 
                 ° 
               
               + 
               
                 0 
                 · 
                 
                   
                     S 
                     -&gt; 
                   
                   3 
                 
               
             
           
         
       
       
         
           
             
               
                 Z 
                 -&gt; 
               
               
                 1 
                 ⁢ 
                 A 
               
             
             = 
             
               
                 
                   
                     0.436 
                     · 
                     
                       
                         S 
                         -&gt; 
                       
                       1 
                     
                   
                   ⁢ 
                   ∠150° 
                 
                 + 
                 
                   
                     0.436 
                     · 
                     
                       
                         S 
                         -&gt; 
                       
                       2 
                     
                   
                   ⁢ 
                   ∠ 
                 
                 - 
                 
                   60 
                   ⁢ 
                   ° 
                 
                 + 
                 
                   
                     0.436 
                     · 
                     
                       
                         S 
                         -&gt; 
                       
                       1 
                     
                   
                   ⁢ 
                   ∠90° 
                 
                 + 
                 
                   
                     0.436 
                     · 
                     
                       
                         S 
                         -&gt; 
                       
                       2 
                     
                   
                   ⁢ 
                   ∠120° 
                 
               
               = 
               
                 
                   0.756 
                   · 
                   
                     
                       S 
                       -&gt; 
                     
                     1 
                   
                 
                 ⁢ 
                 ∠120° 
               
             
           
         
       
       
         
           
             
               
                 Z 
                 -&gt; 
               
               
                 2 
                 ⁢ 
                 A 
               
             
             = 
             
               
                 
                   
                     0.436 
                     · 
                     
                       
                         S 
                         -&gt; 
                       
                       1 
                     
                   
                   ⁢ 
                   ∠0° 
                 
                 + 
                 
                   
                     0.436 
                     · 
                     
                       
                         S 
                         -&gt; 
                       
                       2 
                     
                   
                   ⁢ 
                   ∠150° 
                 
                 + 
                 
                   
                     0.436 
                     · 
                     
                       
                         S 
                         -&gt; 
                       
                       1 
                     
                   
                   ⁢ 
                   ∠180° 
                 
                 + 
                 
                   
                     0.436 
                     · 
                     
                       
                         S 
                         -&gt; 
                       
                       2 
                     
                   
                   ⁢ 
                   ∠ 
                 
                 - 
                 
                   150 
                   ⁢ 
                   ° 
                 
               
               = 
               
                 
                   0.756 
                   · 
                   
                     
                       S 
                       -&gt; 
                     
                     2 
                   
                 
                 ⁢ 
                 ∠180° 
               
             
           
         
       
     
     Applying the above equations to the unaffected matrix cluster  201 B with these assumptions leads to the following results: 
     
       
         
           
             
               S 
               
                 1 
                 ⁢ 
                 B_DesiredPower 
               
             
             = 
             
               
                 
                   ( 
                   
                     Total_Original 
                     ⁢ 
                     _S1 
                     ⁢ 
                     _Frame 
                     ⁢ 
                     _Power 
                   
                   ) 
                 
                 - 
                 
                   S 
                   
                     1 
                     ⁢ 
                     A_Power 
                   
                 
               
               = 
               
                 
                   40 
                   - 
                   11.4 
                 
                 = 
                 
                   28.6 
                   ⁢ 
                   
                       
                   
                   ⁢ 
                   
                     W 
                   
                 
               
             
           
         
       
       
         
           
             
               S 
               
                 2 
                 ⁢ 
                 B_DesiredPower 
               
             
             = 
             
               
                 
                   ( 
                   
                     Total_Original 
                     ⁢ 
                     _S2 
                     ⁢ 
                     _Frame 
                     ⁢ 
                     _Power 
                   
                   ) 
                 
                 - 
                 
                   S 
                   
                     2 
                     ⁢ 
                     A_Power 
                   
                 
               
               = 
               
                 
                   30 
                   - 
                   8.6 
                 
                 = 
                 
                   21.4 
                   ⁢ 
                   
                       
                   
                   ⁢ 
                   
                     W 
                   
                 
               
             
           
         
       
       
         
           
             
               S 
               
                 3 
                 ⁢ 
                 B_DesiredPower 
               
             
             = 
             
               
                 
                   ( 
                   
                     Total_Original 
                     ⁢ 
                     _S3 
                     ⁢ 
                     _Frame 
                     ⁢ 
                     _Power 
                   
                   ) 
                 
                 - 
                 
                   S 
                   
                     3 
                     ⁢ 
                     A_Power 
                   
                 
               
               = 
               
                 
                   10 
                   - 
                   0 
                 
                 = 
                 
                   10 
                   ⁢ 
                   
                       
                   
                   ⁢ 
                   
                     W 
                   
                 
               
             
           
         
       
       
         
           
             
               S 
               
                 1 
                 ⁢ 
                 B_AvailablePower 
               
             
             = 
             
               
                 
                   ( 
                   
                     
                       S 
                       
                         1 
                         ⁢ 
                         B_DesiredPower 
                       
                     
                     
                       
                         S 
                         
                           1 
                           ⁢ 
                           B_DesiredPower 
                         
                       
                       + 
                       
                         S 
                         
                           2 
                           ⁢ 
                           B_DesiredPower 
                         
                       
                       + 
                       
                         S 
                         
                           3 
                           ⁢ 
                           B_DesiredPower 
                         
                       
                     
                   
                   ) 
                 
                 ⁢ 
                 
                   ( 
                   
                     CLB_Total 
                     ⁢ 
                     _Available 
                     ⁢ 
                     _Power 
                   
                   ) 
                 
               
               = 
               
                 
                   
                     ( 
                     
                       28.6 
                       60 
                     
                     ) 
                   
                   ⁢ 
                   
                     ( 
                     60 
                     ) 
                   
                 
                 = 
                 
                   28.6 
                   ⁢ 
                   
                       
                   
                   ⁢ 
                   
                     W 
                   
                 
               
             
           
         
       
       
         
           
             
               S 
               
                 2 
                 ⁢ 
                 B_AvailablePower 
               
             
             = 
             
               
                 
                   ( 
                   
                     
                       S 
                       
                         2 
                         ⁢ 
                         B_DesiredPower 
                       
                     
                     
                       
                         S 
                         
                           1 
                           ⁢ 
                           B_DesiredPower 
                         
                       
                       + 
                       
                         S 
                         
                           2 
                           ⁢ 
                           B_DesiredPower 
                         
                       
                       + 
                       
                         S 
                         
                           3 
                           ⁢ 
                           B_DesiredPower 
                         
                       
                     
                   
                   ) 
                 
                 ⁢ 
                 
                   ( 
                   
                     CLB_Total 
                     ⁢ 
                     _Available 
                     ⁢ 
                     _Power 
                   
                   ) 
                 
               
               = 
               
                 
                   
                     ( 
                     
                       21.4 
                       60 
                     
                     ) 
                   
                   ⁢ 
                   
                     ( 
                     60 
                     ) 
                   
                 
                 = 
                 
                   21.4 
                   ⁢ 
                   
                       
                   
                   ⁢ 
                   
                     W 
                   
                 
               
             
           
         
       
       
         
           
             
               S 
               
                 3 
                 ⁢ 
                 B_AvailablePower 
               
             
             = 
             
               
                 
                   ( 
                   
                     
                       S 
                       
                         3 
                         ⁢ 
                         B_DesiredPower 
                       
                     
                     
                       
                         S 
                         
                           1 
                           ⁢ 
                           B_DesiredPower 
                         
                       
                       + 
                       
                         S 
                         
                           2 
                           ⁢ 
                           B_DesiredPower 
                         
                       
                       + 
                       
                         S 
                         
                           3 
                           ⁢ 
                           B_DesiredPower 
                         
                       
                     
                   
                   ) 
                 
                 ⁢ 
                 
                   ( 
                   
                     CLB_Total 
                     ⁢ 
                     _Available 
                     ⁢ 
                     _Power 
                   
                   ) 
                 
               
               = 
               
                 
                   
                     ( 
                     
                       10 
                       60 
                     
                     ) 
                   
                   ⁢ 
                   
                     ( 
                     60 
                     ) 
                   
                 
                 = 
                 
                   10 
                   ⁢ 
                   
                       
                   
                   ⁢ 
                   
                     W 
                   
                 
               
             
           
         
       
       
         
           
             
               S 
               
                 1 
                 ⁢ 
                 B_Power 
               
             
             = 
             
               
                 MIN 
                 ⁡ 
                 
                   ( 
                   
                     
                       S 
                       
                         1 
                         ⁢ 
                         B_DesiredPower 
                       
                     
                     , 
                     
                       S 
                       
                         1 
                         ⁢ 
                         B_AvailablePower 
                       
                     
                   
                   ) 
                 
               
               = 
               
                 28.6 
                 ⁢ 
                 
                     
                 
                 ⁢ 
                 
                   W 
                 
               
             
           
         
       
       
         
           
             
               S 
               
                 2 
                 ⁢ 
                 B_Power 
               
             
             = 
             
               
                 MIN 
                 ⁡ 
                 
                   ( 
                   
                     
                       S 
                       
                         2 
                         ⁢ 
                         B_DesiredPower 
                       
                     
                     , 
                     
                       S 
                       
                         2 
                         ⁢ 
                         B_AvailablePower 
                       
                     
                   
                   ) 
                 
               
               = 
               
                 21.4 
                 ⁢ 
                 
                     
                 
                 ⁢ 
                 
                   W 
                 
               
             
           
         
       
       
         
           
             
               S 
               
                 3 
                 ⁢ 
                 B_Power 
               
             
             = 
             
               
                 MIN 
                 ⁡ 
                 
                   ( 
                   
                     
                       S 
                       
                         2 
                         ⁢ 
                         B_DesiredPower 
                       
                     
                     , 
                     
                       S 
                       
                         2 
                         ⁢ 
                         B_AvailablePower 
                       
                     
                   
                   ) 
                 
               
               = 
               
                 10 
                 ⁢ 
                 
                     
                 
                 ⁢ 
                 
                   W 
                 
               
             
           
         
       
       
         
           
             
               Y 
               
                 
                   S 
                   1 
                 
                 ⁢ 
                 B 
               
             
             = 
             
               
                 
                   
                     S 
                     
                       1 
                       ⁢ 
                       B_Power 
                     
                   
                   
                     3 
                     ⁢ 
                     
                       S 
                       
                         1 
                         ⁢ 
                         B_OriginalPower 
                       
                     
                   
                 
               
               = 
               
                 
                   
                     28.6 
                     60 
                   
                 
                 = 
                 0.69 
               
             
           
         
       
       
         
           
             
               Y 
               
                 
                   S 
                   2 
                 
                 ⁢ 
                 B 
               
             
             = 
             
               
                 
                   
                     S 
                     
                       2 
                       ⁢ 
                       B_Power 
                     
                   
                   
                     3 
                     ⁢ 
                     
                       S 
                       
                         2 
                         ⁢ 
                         B_OriginalPower 
                       
                     
                   
                 
               
               = 
               
                 
                   
                     21.4 
                     45 
                   
                 
                 = 
                 0.69 
               
             
           
         
       
       
         
           
             
               Y 
               
                 
                   S 
                   3 
                 
                 ⁢ 
                 B 
               
             
             = 
             
               
                 
                   
                     S 
                     
                       3 
                       ⁢ 
                       B_Power 
                     
                   
                   
                     3 
                     ⁢ 
                     
                       S 
                       
                         3 
                         ⁢ 
                         B_OriginalPower 
                       
                     
                   
                 
               
               = 
               
                 
                   
                     10 
                     15 
                   
                 
                 = 
                 
                   
                     2 
                     3 
                   
                 
               
             
           
         
       
       
         
           
             
               
                 Y 
                 -&gt; 
               
               
                 1 
                 ⁢ 
                 B 
               
             
             = 
             
               
                 
                   0.69 
                   · 
                   
                     
                       S 
                       -&gt; 
                     
                     1 
                   
                 
                 ⁢ 
                 ∠ 
               
               - 
               
                 90 
                 ⁢ 
                 ° 
               
               + 
               
                 
                   0.69 
                   · 
                   
                     
                       S 
                       -&gt; 
                     
                     2 
                   
                 
                 ⁢ 
                 ∠0° 
               
               + 
               
                 
                   
                     
                       2 
                       3 
                     
                   
                   · 
                   
                     
                       S 
                       -&gt; 
                     
                     3 
                   
                 
                 ⁢ 
                 ∠ 
               
               - 
               
                 180 
                 ⁢ 
                 ° 
               
             
           
         
       
       
         
           
             
               
                 Y 
                 -&gt; 
               
               
                 2 
                 ⁢ 
                 B 
               
             
             = 
             
               
                 
                   0.69 
                   · 
                   
                     
                       S 
                       -&gt; 
                     
                     1 
                   
                 
                 ⁢ 
                 ∠60° 
               
               + 
               
                 
                   0.69 
                   · 
                   
                     
                       S 
                       -&gt; 
                     
                     2 
                   
                 
                 ⁢ 
                 ∠ 
               
               - 
               
                 90 
                 ⁢ 
                 ° 
               
               + 
               
                 
                   
                     
                       2 
                       3 
                     
                   
                   · 
                   
                     
                       S 
                       -&gt; 
                     
                     3 
                   
                 
                 ⁢ 
                 ∠ 
               
               - 
               
                 150 
                 ⁢ 
                 ° 
               
             
           
         
       
       
         
           
             
               
                 Y 
                 -&gt; 
               
               
                 3 
                 ⁢ 
                 B 
               
             
             = 
             
               
                 
                   0.69 
                   · 
                   
                     
                       S 
                       -&gt; 
                     
                     1 
                   
                 
                 ⁢ 
                 ∠ 
               
               - 
               
                 150 
                 ⁢ 
                 ° 
               
               + 
               
                 
                   0.69 
                   · 
                   
                     
                       S 
                       -&gt; 
                     
                     2 
                   
                 
                 ⁢ 
                 ∠ 
               
               - 
               
                 180 
                 ⁢ 
                 ° 
               
               + 
               
                 
                   
                     
                       2 
                       3 
                     
                   
                   · 
                   
                     
                       S 
                       -&gt; 
                     
                     3 
                   
                 
                 ⁢ 
                 ∠ 
               
               - 
               
                 120 
                 ⁢ 
                 ° 
               
             
           
         
       
       
         
           
             
               
                 Z 
                 -&gt; 
               
               
                 1 
                 ⁢ 
                 B 
               
             
             = 
             
               
                 1.2 
                 · 
                 
                   
                     S 
                     -&gt; 
                   
                   1 
                 
               
               ⁢ 
               ∠120° 
             
           
         
       
       
         
           
             
               
                 Z 
                 -&gt; 
               
               
                 2 
                 ⁢ 
                 B 
               
             
             = 
             
               
                 1.2 
                 · 
                 
                   
                     S 
                     -&gt; 
                   
                   2 
                 
               
               ⁢ 
               ∠180° 
             
           
         
       
       
         
           
             
               
                 Z 
                 -&gt; 
               
               
                 3 
                 ⁢ 
                 B 
               
             
             = 
             
               
                 
                   2 
                   · 
                 
               
               ⁢ 
               
                 
                   S 
                   -&gt; 
                 
                 3 
               
               ⁢ 
               ∠60° 
             
           
         
       
     
       FIG. 7  shows the results of these calculations, assuming ideal combining of clusters A and B, and the results if no modification takes place in accordance with method  300 . If the matrix clusters  201 A and  201 B remain unmodified (i.e., method  300  is not applied), cluster  201 A will generate at 8.9 Watts at Z 1  for sector  1  (S 1 ), 6.7 Watts at Z 2  for S 2 , and 2.2 Watts at Z 3  for S 3 . Each of Z 1  through Z 3  for non-corresponding sectors will receive a total noise term ranging between 2.3 Watts and 3.9 Watts as indicated in  FIG. 7 . Matrix cluster  201 B, on the other hand, will generate 20 Watts at Z 1  for S 1 , 15 Watts at Z 2  for S 2 , and 5 Watts at Z 3  for S 3 . All other non-corresponding sectors will receive 0 Watts as expected. The resulting desired sector power at Z 1  is 28.9 Watts with an isolation of −11 dBc, the resulting desired sector power at Z 2  is 21.7 Watts with an isolation of −8.9 dBc, and the resulting desired sector power at Z 3  is 7.2 Watts with an isolation of −2.7 dBc. Generally, an isolation less than −15 dBc is considered unacceptable. Present systems are requiring isolation as high as −25 dBc. Clearly, the unmodified matrix cluster  201 A falls short of this goal. 
     Compare, on the other hand, the performance of the clusters  201 A and  201 B modified in accordance with method  300 . Cluster  201 A will generate 11.4 Watts at Z 1  for S 1 , 8.6 Watts for Z 2  for S 2 , and 0 Watts at Z 3  for S 3 . Each of Z 1  through Z 3  for non-corresponding sectors will generate 0 Watts of noise. Matrix cluster  201 B will generate 28.6 Watts at Z 1  for S 1 , 21.4 Watts at Z 2  for S 2 , and 10 Watts at Z 3  for S 3 . All other non-corresponding sectors will generate 0 Watts also. The resulting desired sector power at Z 1  is 40 Watts, at Z 2  it is 30 Watts, and at Z 3  it is 10 Watts with ideally infinite dBc isolation across all sectors. Obviously, the results presented in the modified clusters  201 A and  201 B is far superior to prior art systems with no fault-tolerance capability. 
     It should be evident to an artisan with skill in the art that portions of embodiments of the present invention can be embedded in a computer program product, which comprises features enabling the implementation stated above. A computer program in the present context means any expression, in any language, code or notation, of a set of instructions intended to cause a system having an information processing capability to perform a particular function either directly or after either or both of the following: a) conversion to another language, code or notation; b) reproduction in a different material form. 
     It should also be evident that the present invention can be realized in hardware, software, or combinations thereof. Additionally, the present invention can be embedded in a computer program, which comprises all the features enabling the implementation of the methods described herein, and which enables said devices to carry out these methods. A computer program in the present context means any expression, in any language, code or notation, of a set of instructions intended to cause a system having an information processing capability to perform a particular function either directly or after either or both of the following: a) conversion to another language, code or notation; b) reproduction in a different material form. Additionally, a computer program can be implemented in hardware as a state machine without conventional machine code as is typically used by CISC (Complex Instruction Set Computers) and RISC (Reduced Instruction Set Computers) processors. 
     The present invention may also be used in many arrangements. For example, the digital and analog matrixes  202  and  204  can utilize other dimensions such as, for example, 3 by 3, 4 by 4, 6 by 6, or 8 by 8 matrixes, just to mention a few. Method  300  in  FIG. 6  can be simplified by integrating steps  314  and  316  in a single step. Portions of the embodiments described above can also be reconfigured to work with other matrix implementations. For instance, instead of using a digital matrix  202  operating at baseband, a programmable analog input matrix could be used. The up-converters  220  in this configuration could be placed prior to the analog input matrix, and the vector relationships could be controlled via a combination of gain and phase adjusters such that similar results as described above can be attained. Thus, although the description is made for particular arrangements and methods, the intent and concept of the invention is suitable and applicable to other arrangements and applications not described herein. The embodiments of method  300  therefore can in numerous ways be modified with additions thereto without departing from the spirit and scope of the invention. 
     Accordingly, the described embodiments ought to be construed to be merely illustrative of some of the more prominent features and applications of the invention. It should also be understood that the claims are intended to cover the structures described herein as performing the recited function and not only structural equivalents. Therefore, equivalent structures that read on the description are to be construed to be inclusive of the scope of the invention as defined in the following claims. Thus, reference should be made to the following claims, rather than to the foregoing specification, as indicating the scope of the invention.