A joint sensing/communication problem is considered for sensor networks. Herein, the channel(s) between a source and destination are the parameters to be sensed and communicated over the network. Lower bounds on the end-to-end distortion are developed for a multihop, linear network. Inter-node communication is assumed to be done via an amplify-and-forward approach and the results are compared to those previously presented for an encode-and-forward approach. It is shown that amplify-and-forward has the potential to significantly outperform encode-and-forward. Furthermore, with respect to an asymptotic measure which evaluates the rate of decay of the mean-squared error with respect to the SNR, amplify-and-forward can achieve the maximal possible decay rate.
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