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We investigate the performances of two wireless multiuser space-time block coding (STBC) communication systems. In the first system, the notion of group signature (GS) proposed by Tran and Sesay (see IEEE Vehicular Technology Conference (VTC2002-Spring), Alabama, USA, May 2002) is applied and in the second system, all users communicate on the same channel and no GS is used. In both systems, a 4-state convolutional code is concatenated with the space-time block code proposed by Alamouti (see IEEE J. Select. Areas Commun., vol.16, no.8, p.1451-58, 1998). In the second system, the bandwidth allocated to the use of GS in the first system is allocated for the use of a stronger convolutional code such that both systems utilize the same bandwidth. Computer simulation results show that the first system, with the use of GSs, significantly outperforms the second system in the region of low signal-to-noise ratios, at the same hardware and computational complexities.