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Decision-directed adaptive receivers suffer performance degradation on time varying and intersymbol interference-impaired links because of two major problems: the use of predicted channel estimates due to the unavoidable decision delay of any detector, and the unreliability of hard decisions used for channel estimation and tracking. It is shown here that combining a recursive nonlinear symbol estimator with a channel estimator with a low prediction order may alleviate this performance degradation. In particular, it is here proposed to employ the nonlinear minimum mean-square error (NL-MMSE) filtered and fixed-lag smoothed estimates of the transmitted symbols in place of the usual hard decisions for channel estimation and tracking. It is also shown that these NL-MMSE estimates can be recursively computed on the basis of a linear transformation of the vector of the a posteriori probabilities (APPs) of the states of the channel. This approach allows the prediction order of the channel estimates to be limited and, at the same time, limits the performance degradation due to erroneous hard decisions. Another result presented here is that the use of NL-MMSE estimates in place of hard decisions is not based on mere intuition only, but is a straightforward consequence of the statement of the problem of MMSE channel estimation when the overly optimistic assumption of correct decisions is dropped. On the basis of this novel approach, a new family of soft-output adaptive receivers is presented for time-division multiple-access-based radio communications. The proposed family of adaptive receivers is based on an APP-computer and exploits the APPs for both channel estimation and detection. The versatility of the APPs ensures that the architecture of the proposed receiver is flexible, so that several estimators and detectors can be embedded in it.