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In the reported metrics of the existing literature, the realistic wireless channel situation is generally ignored in selecting the appropriate next-hop relay node during packet forwarding in wireless sensor networks (WSNs). In this paper, we propose a new energy-efficient local metric, which is called the efficient advancement metric (EAM), for sensor networks. EAM considers both the maximum forwarding distance and the packet's successful transmission probability by taking into account the wireless channel condition. This will enable the forwarding node to choose the most energy-efficient relay node in the geographic-informed routing protocol. Theoretically, we show the existence of the unique optimal relay node to maximize EAM over a typical Nakagami-m channel of a code-division multiple-access (CDMA)-based WSN. Furthermore, based on the proposed metric EAM, we present a cross-layer packet-forwarding protocol channel-aware geographic-informed forwarding (CAGIF) by optimally selecting the relay nodes. CAGIF only requires that nodes have the knowledge of their own location information and the location information of the source and destination nodes. Numerical examples are presented to show the characteristics of EAM and the optimal distance. Compared with the previous geographic packet-forwarding schemes in WSNs, CAGIF consumes much lower energy and generates a significantly decreased signal overhead.