Several efforts are currently underway in investigating multiple-input multiple-output (MIMO) communication systems. MIMO technology promises high data rate wireless communications and/or the potentiality of exploiting transmit and receive diversity schemes. For WLAN (Wireless Local Area Networks) scenarios most investigations focus on OFDM (Orthogonal Frequency Division Multiplexing) transmission. In this paper we discuss spatial multiplexing in conjunction with optimal matched filtering and MMSE-Equalization for SC/FDE (Single Carrier Transmission with Frequency Domain Equalization), a single carrier technology closely related to OFDM due to its frequency domain signal processing characteristics. We show that the conventional MMSE-Equalizer equation is not suited in conjunction with optimal matched filtering and we derive a novel MMSE structure.