The results in [8], [10], [11], however, have considered only the real passband or, equivalently, the complex baseband transmission of a proper-complex **data** sequence. Hence, these results are not directly applicable to, e.g., the real passband transmission of a BPSK **data** sequence, which is an impropercomplex **data** sequence in complex baseband. Recall that complex-valued random variables, vectors, and processes are called proper if their complementary covariance, complementary covariance matrix, and complementary auto-covariance function (a.k.a. pseudo-covariance, pseudo-covariance matrix, and pseudocovariance function) vanish, respectively [12]. Otherwise, they are called improper [13]. Although the complex envelopes of the majority of digitally modulated signals are proper, there still remain other digitally modulated signals whose complex envelopes have non-vanishing complementary auto-covariance functions [13]. For example, the complex envelopes of PAM, vestigial sideband PAM, unbalanced QAM, offset quaternary phase-shift keying (OQPSK), and Gaussian minimum shift keying are improper.