On analysis of wireless uplink using analog network coding with non-coherent modulations

Analog network coding (ANC) has been widely used in wireless uplink to improve throughput and provide spatial diversity. However, the receiver has to estimate the channel coefficients of all users to perform coherent detection, thus the signaling overhead is sometimes formidable and may even outweigh the performance gain. To reduce the channel estimation overhead, we study non-coherent modulations in this work with emphasis on receiver design and performance analysis. Depending on channel state information, we first develop the coherent, partial coherent and non-coherent receivers based on maximum likelihood (ML) principle. As the ML non-coherent receiver has a non-tractable integral form, we further propose two suboptimum receivers depending on the relative quality of source-relay channel and relay-destination channel.We also study the pairwise error probability, and show that full diversity is still achievable at high signal-to-noise ratios using non-coherent modulations; however, the error rate decreases much slower than that of coherent systems due to the incapability to efficiently suppress multi-user interferences. Extensive simulations are also given to verify our analytical results.