A least-squares (LS) channel estimation (CE) technique is investigated to apply pseudo-random-postfix orthogonal-frequency-division multiplexing (PRP-OFDM) communications onto mobile applications, which often operate on a rapidly time-varying frequency-selective fading channel. Since conventional techniques exploiting a moving averager cannot function on a rapidly time-varying channel, the proposed technique takes advantage of several self-interference cancellation (SIC) methods to effectively and timely reduce inter-path interference, inter-symbol interference (ISI) and inter-block interference (IBI). The proposed technique can therefore overcome frequency selectivity caused by multipath fading and time selectivity caused by mobility; in particular, OFDM communication is often anticipated to operate in environments where both wide Doppler spread and long delay spread exist. Meanwhile, lower mean-square estimation errors, lower error probabilities and lower error floors can also be achieved using the proposed technique. Since conventional techniques based on minimum-mean-square-error (MMSE) CE usually highly require a priori channel information or many training preambles, a generic estimator assisted from LS CE is exploited as it can be performed serially, block by block, to reduce computational complexity. Extensive computer simulations in conjunction with strict statistical analysis are carried out to verify the improvements provided by the proposed technique.