In cognitive radio systems, it is very challenging to estimate the channel gains from the cognitive transmitter to the primary receiver and even those between primary transceivers. Recent studies show that both kinds of the channel gains can be obtained if the cognitive user acts as a full-duplex relay in symmetric time-division duplex (TDD) primary systems. However, in practice, most systems are asymmetric, which have different data rates in the forward and backward transmission. In this paper, we will develop two proactive estimation algorithms to obtain the channel gains in asymmetric TDD primary systems, where different types of primary receivers are considered. Our results indicate that the proposed estimators work very well in asymmetric TDD systems, whose estimation errors are below 5%.