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?