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An AWSN composed of bird-sized Unmanned Aerial Vehicles (UAVs) equipped with sensors and wireless radio, enables low cost high granularity three-dimensional sensing of the physical world. The sensed data is relayed in real-time over a multi-hop wireless communication network to ground stations. The following characteristics of an AWSN make effective multi-hop communication challenging - (i) frequent link disconnections due to the inherent dynamism (ii) significant inter-node interference (iii) three dimensional motion of the UAVs. In this paper, we investigate the use of a hybrid antenna to accomplish efficient neighbor discovery and reliable communication in AWSNs. We propose the design of a hybrid Omni Bidirectional ESPAR (O-BESPAR) antenna, which combines the complimentary features of an isotropic omni radio (360 degree coverage) and directional ESPAR antennas (beamforming and reduced interference). Control and data messages are transmitted separately over the omni and directional modules of the antenna, respectively. Moreover, a communication protocol is presented to perform fast neighbor discovery and beam steering. We present results from extensive simulations then consider three different real-world AWSN application scenarios and empirical aerial link characterization and show that the proposed antenna design and protocol reduces the packet loss rate, as compared to a single omni or ESPAR antenna.