This paper studies receiver antenna selection (AS) for multi-antenna systems operating over frequency selective channels, where the channel state information (CSI) is neither known at the transmitter nor at the receiver. We consider AS for noncoherent space-time-frequency (STF) coded orthogonal frequency division multiplexing (OFDM) systems that employ unitary signals. An OFDM receiver with a single RF chain is employed, and the selection is based on the received signal power, where the receive antenna with the largest received signal power averaged over all subcarriers is chosen. Theoretical analysis and simulations show that using AS, the maximum spatial and multipath diversity can still be obtained without CSI at the receiver, the same as the full-complexity multi-antenna OFDM systems. We simplify code design and decoding using subcarrier grouping, which enables us to apply existing full diversity codes for noncoherent STF-OFDM systems to each group, in order to obtain maximum spatial and multipath diversity when AS is used. We also present a low-complexity suboptimal decoder that achieves full diversity and can be easily implemented in practice.