An Energy-Based Comparison of Long-Hop and Short-Hop Routing in MIMO Networks

This paper considers the problem of selecting either routes that consist of long hops or routes that consist of short hops in a network of multiple-antenna nodes, where each transmitting node employs spatial multiplexing. This distance-dependent route-selection problem is approached from the viewpoint of energy efficiency, where a route is selected with the objective of minimizing the transmission energy consumed while satisfying a target outage criterion at the final destination. Deterministic line networks and 2-D random networks are considered. It is shown that short-hop routing requires less energy than long-hop routing when (1) the number of hops traversed between the source and destination grows large, (2) the target success probability approaches one, or (3) the number of transmit and/or receive antennas grows large. It is also shown that if both routing strategies are subject to the same delay constraint, long-hop routing requires less energy than short-hop routing as the target success probability approaches one. In addition, a numerical analysis indicates that, given loose outage constraints, only a small number of transmit antennas are needed for short-hop routing to have its maximum advantage over long-hop routing, while given stringent outage constraints, the advantage of short-hop over long-hop routing always increases with additional transmit antennas.