Patent ID: 8193975

Claim:
A method of operating a transceiver including an antenna having a plurality of antenna feed elements, the method comprising: defining a plurality of antenna gain constraint values g k associated with K geographic constraint points within a geographic region; iteratively generating M antenna feed element weights w M in an antenna feed element weight vector wεC M×1 that result in antenna response values f K at the K geographic constraint points such that beam gain response values |f k | converge on the corresponding antenna gain constraint values g K ; forming an antenna beam from the antenna to the geographic region using the antenna feed element weights w M ; and communicating information over the antenna beam; wherein iteratively generating the antenna feed element weight vector w comprises: defining a cost function that relates the antenna beam gain constraint values g K to the antenna feed element weights w M ; specifying an initial vector w 1 of the antenna feed element weights w M ; evaluating the cost function using the initial vector w 1 of the antenna feed element weights w M ; generating a gradient of the cost function, and iteratively modifying the antenna feed element weight vector w and evaluating the cost function using the antenna feed element weight vector w while the value of the cost function is decreasing, wherein iteratively modifying the antenna feed element weight vector w comprises adjusting the antenna feed element weight vector w in the direction of the gradient of the cost function.