Wireless Sensor Networks (WSNs) incorporate smart antennas for information propagation to offer connected coverage with reduced interference. This paper presents an omni directional antenna assisted scheme for WSNs to reduce network redundancy besides offering connected coverage. The directivity of an omni directional antenna outfitted on a sink node is exploited to reduce network redundancy and at the same time the connectivity of sensor nodes with the sink node is retained. The relationship between lobe count, beam width, rotation angle and directivity of an omni directional antenna in context of sensor networks is also discussed. Simulation results show a significant reduction in overall network redundancy if the rotation angle of the omni directional antenna fitted on the sink node is minimized from 360° to 30°.