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In this paper, a non-regenerative differential distributed space-frequency coding is developed for broadband cooperative communication networks with arbitrary number of relays. Based on an elaborated symbol-to-subcarrier allocation method, the differential encoding across subcarriers is performed at the source. In the proposed scheme, a simple circular shift of the received signal is implemented at each relay, and a low-complexity linear prediction-based adaptive decision-feedback differential detection (DF-DD) is employed at the destination. This detection algorithm even can start without a priori knowledge of the channel statistics. Theoretical analysis and simulation results confirm that the proposed scheme exploits both spatial and frequency diversity.