A least-squares (LS) channel estimation technique is investigated to extend pseudo-random-postfix orthogonal-frequency-division multiplexing (PRP-OFDM) techniques onto mobile applications in rapidly time-variant frequency-selective fading environments. The proposed method exploits self-interference cancellation to effectively reduce a variety of interferences; and thus, it can overcome not only frequency-selectivity caused by multipath reception but also time-selectivity caused by mobility; in particular, OFDM communications are often expected to operate in the presence of both wide Doppler spread and long delay spread. As a result, the proposed technique can achieve lower channel estimation errors and lower bit error probabilities than the conventional techniques exploiting a time-averaging method. Since sufficiently long PRP sequences have never been found in the previous works regarding PRP-OFDM, an application of the proposed technique using chirp signals for mobile PRP-OFDM communication is investigated because the chirp signals exhibit good training properties.