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

Millimeter-wave (mmWave) cellular systems are power limited and susceptible to blockages. One promising approach to increasing mmWave connectivity and range is to use relays. Device-to-device (D2D) communications open the door to the vast opportunities of D2D relaying for mmWave cellular systems. In this paper, we study how to select a good relay for a given source-destination pair in a two-hop mmWave cellular system, where the mmWave links are subject to random Bernoulli blockages. In such a system, probing more relays could potentially lead to the discovery of a better relay but at the cost of more overhead. We find that the throughput-optimal relay probing strategy is a pure threshold policy: The system can stop relay probing once the achievable spectral efficiency of the currently probed two-hop link exceeds an optimized threshold. We further characterize the optimal spectral efficiency threshold via a fixed-point equation.