In multiuser relay systems, if the relay does not have sufficient degrees of freedom to eliminate multiuser interference, the spectral efficiency gain of two-way relay (TWR) transmission may vanish. Signal alignment (SA) signaling is possible to recover this gain but may suffer from a signal power loss. To improve the spectral efficiency of multicarrier code-division multiple-access (MC-CDMA) TWR systems, we develop an equivalent SA (ESA) signaling procedure. Simply by aligning the received symbols after despreading instead of aligning the received signals as in SA signaling, ESA signaling has more feasible solutions than SA signaling, and its performance and complexity depend on the spreading sequences. This allows us to improve the system performance by optimizing ESA signaling and to reduce its complexity by designing the spreading sequences. Specifically, we develop optimal ESA signaling to maximize the signal-to-noise-ratio (SNR) under the interference-free constraint. Then, we design the spreading sequence to obtain a low-complexity ESA-based frequency-domain equalizer (FDE), i.e., ESA-based one-tap FDE, and to provide the maximal diversity gain for the one-tap FDE. Both theoretical analysis and simulation results demonstrate that ESA signaling is more spectral efficient than SA signaling for MC-CDMA TWR systems.

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