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In this paper, noncoherent equalization is combined with multiple receive antennas. The resulting noncoherent space-time equalization (NSTE) schemes are analyzed and compared with the corresponding coherent receivers. In particular, noncoherent linear equalization (NLE), noncoherent decision-feedback equalization (NDFE), and noncoherent sequence estimation (NSE) are considered. For NLE and NDFE novel approximations for the signal-to-distortion ratio (SDR) are derived and verified by simulations. It is shown that NSTE can suppress interfering users and exploit diversity as efficiently as coherent STE. However, NSTE is more robust against channel phase variations than the combination of coherent STE and synchronization. Robust noncoherent recursive least squares (NC-RLS) algorithms, which compare favorably with the conventional RLS algorithm with additional carrier synchronization loop, are proposed for fast filter adaptation.