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The differential encoding/decoding setup introduced by Kiran et al,Oggier-Hassibi and Jing-Jafarkhani for wireless relay networks that usecodebooks consisting of unitary matrices is extended to allow codebooksconsisting of scaled unitary matrices. For such codebooks to be usable in theJing-Hassibi protocol for cooperative diversity, the conditions involving therelay matrices and the codebook that need to be satisfied are identified. Usingthe algebraic framework of extended Clifford algebras, a new class ofDistributed Differential Space-Time Codes satisfying these conditions for powerof two number of relays and also achieving full cooperative diversity with alow complexity sub-optimal receiver is proposed. Simulation results indicatethat the proposed codes outperform both the cyclic codes as well as thecirculant codes. Furthermore, these codes can also be applied as DifferentialSpace-Time codes for non-coherent communication in classical point to pointmultiple antenna systems.

Algebraic Distributed Differential Space-Time Codes with Low Decoding Complexity