Detection Performance in m-ary Relay Trees with Link Failures and Unreliable Communications

Abstract: We study the detection performance in an m-ary relay tree with link failures and unreliable communications under the majority dominance rule. The leaves of the tree correspond to N identical and independent sensors generating binary messages, the root of the tree represents a fusion center that makes the overall detection decision, every other node of the tree is a relay node that combines m binary messages from its immediate child nodes to form a new binary messages by using the majority dominance rule. We first derive the evolution of the detection error probabilities. Then, we prove the monotonicity of the detection error probability at next level as the silence probability or the bit-error probability increases. Further, we derive the limit performance of the detection error probability as N goes to infinity. This limit performance also shows that the detection error probability cannot converge to 0 if the bit-error probability is not equal to 0.