This paper studies the diversity-encoded differential amplitude and phase shift keying (DAPSK) for orthogonal frequency-division multiplexing (OFDM) systems with uniformly interleaved subcarrier grouping and multiple receive antennas over independent but not identically distributed (i.n.i.d.) frequency-selective Rayleigh fading channels. An asymptotic maximum-likelihood (AML) receiver is developed for differentially detecting the received diversity-encoded DAPSK OFDM signal. The bit error probability (BEP) upper bound for the AML receiver is analytically formulated by using the residue theorem. Particularly, an approximate BEP upper bound of the AML receiver is derived for large received signal-to-noise power ratios (SNRs). By virtue of this approximate bound, a design criterion is developed to determine the diversity encoding coefficients for the proposed DAPSK OFDM system. Performance results show that the AML receiver for diversity-encoded DAPSK OFDM can provide better error performance than conventional noncoherent OFDM systems under the same data throughput.