This paper deals with the development of a spherical array to acoustically find the direc- tion of broadband, low frequency, airborne sound sources in presence of ground reflec- tions. The array consists of four virtual directional microphones arranged at the vertex of a regular tetrahedron. Each virtual directional microphone is obtained by synthesizing the signals of a pair of omnidirectional microphones, thus the total number of micro- phones in the physical array is eight. The directional microphones, are used to reduce the influence of the ground reflections, and allow the use of simpler time difference of arrival techniques. The performance of the array is analyzed through computer simu- lations showing that the error in the estimation of the source direction depends on the ground impedance and on the vertical angle of the source (not on the horizontal angle). The experimental tests show that the combination of directional microphones and a simple TDOA technique provides good direction estimates in the presence of ground reflection.