In this chapter, we discuss single and double-differential coding for a two-user cooperative communication system. The single-differential coding is important for the cooperative systems as the data at the destination/relaying node can be decoded without knowing the channel gains. The double-differential modulation is useful as it avoids the need of estimating the channel and carrier offsets for the decoding of the data. We explain single-differential coding for a cooperative system with one relay utilizing orthogonal transmissions with respect to the source. Next, we explain two single-differential relaying strategies: active user strategy (AUS) and passive users relaying strategy (PURS), which could be used by the base-station to transmit data of two users over downlink channels in the two-user cooperative communication network with decode-and-forward protocol. The AUS and PURS follow an improved time schedule in order to increase the data rate. A probability of error based approach is also discussed, which can be used to reduce the erroneous relaying of data by the regenerative relay. In addition, we also discuss how to implement double-differential (DD) modulation for decode-and-forward and amplify-and-forward based cooperative communication system with single source-destination pair and a single relay. The DD based systems work very well in the presence of random carrier offsets without any channel and carrier offset knowledge at the receivers, where the single differential cooperative scheme breaks down. It is further shown that optimized power distributions can be used to improve the performance of the DD system.
Performance analysis of the decode‐and‐forward relay‐based RF‐FSO communication system in the presence of pointing errors