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Millimeter-wave (mmWave) cellular systems are power-limited and susceptibleto blockages. As a result, mmWave connectivity will be likely to beintermittent. One promising approach to increasing mmWave connectivity andrange is to use relays. Device-to-device (D2D) communications open the door tothe vast opportunities of D2D and device-to-network relaying for mmWavecellular systems. In this correspondence, we study how to select a good relayfor a given source-destination pair in a two-hop mmWave cellular system, wherethe mmWave links are subject to random Bernoulli blockages. In such a system,probing more relays could potentially lead to the discovery of a better relaybut at the cost of more overhead. We find that the throughput-optimal relayprobing strategy is a pure threshold policy: the system can stop relay probingonce the achievable spectral efficiency of the currently probed two-hop linkexceeds some threshold. In general, the spectral efficiency threshold can beobtained by solving a fixed point equation. For the special case with on/offmmWave links, we derive a closed-form solution for the threshold. Numericalresults demonstrate that the threshold-based relay probing strategy can yieldremarkable throughput gains.

Optimal Relay Probing in Millimeter Wave Cellular Systems with Device-to-Device Relaying