User-cooperation-based multihop wireless communication networks (MH-WCNs) as the key communication technological component of mobile social networks (MSNs) can be exploited to enhance data rates and extend coverage. As one of the most promising and efficient user cooperation techniques, network coding can increase the potential cooperation performance gains among selfishly driven users in MSNs. To take full advantages of network coding in MH-WCNs, a network coding transmission strategy and its corresponding channel estimation technique are studied in this paper. Particularly, a four-hop network coding transmission is presented first, followed by an extension strategy for the arbitrary    $2N$  -hop scenario    $(N\geq 2)$  . The linear minimum mean square error (LMMSE) and maximum-likelihood (ML) channel estimation methods are designed to improve the transmission quality in MH-WCNs. Closed-form expressions in terms of the mean square error (MSE) for the LMMSE channel estimation method are derived, which allows the design of the optimal training sequence. Unlike the LMMSE method, it is difficult to obtain closed-form MSE expressions for the nonlinear ML channel estimation method. In order to accomplish optimal training sequence design for the ML method, the Cramer–Rao lower bound is employed. Numerical results are provided to corroborate the proposed analysis, and the results demonstrate that the analysis is accurate and the proposed methods are effective.
['Mugen Peng', 'Qiang Hu', 'Xinqian Xie', 'Zhongyuan Zhao', 'H. Vincent Poor']
Network Coded Multihop Wireless Communication Networks: Channel Estimation and Training Design