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The combination of bit-interleaved coded modulation (BICM), orthogonal space-time block coding (OSTBC) and orthogonal frequency division multiplexing (OFDM) has been shown recently to be able to achieve maximum spatial-frequency diversity in frequency selective multi-path fading channels, provided that perfect channel state information (CSI) is available to the receiver. In view of the fact that perfect CSI can be obtained only if a sufficient amount of resource is allocated for training or pilot data, this paper investigates pilot-efficient noncoherent decoding methods for the BICM-OSTBC-OFDM system. In particular, we propose a noncoherent maximum-likelihood (ML) decoder that uses only one OSTBC-OFDM block. This block-wise decoder is suitable for relatively fast fading channels whose coherence time may be as short as one OSTBC-OFDM block. Our focus is mainly on noncoherent diversity analysis. We study a class of carefully designed transmission schemes, called perfect channel identifiability (PCI) achieving schemes, and show that they can exhibit good diversity performance. Specifically, we present a worst-case diversity analysis framework to show that PCI-achieving schemes can achieve the maximum noncoherent spatial-frequency diversity of BICM-OSTBC-OFDM. The developments are further extended to a distributed BICM-OSTBC-OFDM scenario in cooperative relay networks. Simulation results are presented to confirm our theoretical claims and show that the proposed noncoherent schemes can exhibit near-coherent performance.