In this paper, we present the error performance of a multi-relay network scenario for the unmanned aerial vehicle (UAV)-base stations (BS). In the considered system, multiple ground relays assist the transmission, using distributed spatial modulation (DSM) technique, from the UAV-BS to the ground destination. UAV-BS to ground links are affected by both path loss and shadowed-Rician fading, while the ground to ground link is affected by both path loss and Rayleigh fading. In the proposed system, indices of the relays are also used to convey information, and only one relay whose index is matched to the determined relay index can be active in transmission depending on the success of cyclic redundancy checking (CRC). The bit error probability (BEP) for the considered system is derived and validated by Monte Carlo simulations. The effects of different shadowing severities are investigated. Moreover, the considered DSM system is compared against the conventional decode and forward (DF) system, and it is shown that DSM provides a better error probability, especially under lower shadowing severity.