Wireless SC-FDMA communications system

A wireless device SC-FDMA communications system, comprising:

• a wireless device comprising a transmitter to transmit an RF signal, and
• a base station comprising a receiver to receive the RF signal,
• wherein the wireless device comprises circuitry configured to
• generate a plurality of signal matrices based on received signals,
• determine feedforward coefficients for an adaptive frequency-domain decision feedback equalizer (AFD-DFE) based in part on the signal matrices,
• generate a plurality of decision matrices based on transformed feedforward coefficients,
• determine feedback coefficients for the AFD-DFE based in part on the plurality of decision matrices,
• generate a first matrix having the plurality of signal matrices and the decision matrices,
• generate a second matrix including the feedforward coefficients and a third matrix including the feedback coefficients of the AFD-DFE,
• determine an equalizer output as a function of the first matrix, the second matrix and the third matrix such that the function includes adding a first product comprising the plurality of signal matrices premultiplied by a variation of the second matrix and a second product comprising the plurality of decision matrices being premultiplied by a variation of the third matrix, wherein the equalizer output is determined for Spatially-Multiplexed (SM)SC-FDMA signals
• update the feedforward and feedback coefficients of the AFD-DFE based on the equalizer output,
• equalize the received signals using the equalizer output, and
• decode the equalized signals.