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It may be argued that, in a rather loose sense, transmit-diversity and receive-diversity antenna configurations are the dual of each other, as illustrated in Figure.

a. Taking a general viewpoint, justify the mathematical basis for this duality

b. However, we may cite the example of frequency-division diplexing (FDD) for which, in a strict sense, we find that the duality depicted in Figure is violated. How is it possible for the violation to arise in this example?

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