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The quantize-map-and-forward (QMF) has been recently proved to achieve the capacity of arbitrary networks within a bounded gap and optimal diversity-multiplex tradeoff performance. This paper investigates and analyzes the QMF for the full-duplex (FD) relaying. Different from previous works, the relay has no access to any instantaneous channel state information (CSI), and only the statistical CSI of all channels is available. A closed-form expression for the outage probability is then derived. Due to the nonsmoothness of the resulting expression, an approximate one with the smooth outage performance is further given. However, the resulting one is non-convex in general, and four suboptimal solutions of the quantizer design are derived. For comparison, the FD relaying with hybrid QMF/decode-and-forward is also studied. Besides, when the direct transmission (DT) is not available in both schemes, outage probability analysis and optimal quantizer design are also investigated. Simulation results demonstrate the correctness and tightness of the derived closed-form expressions for outage probabilities and close-to-optimal performance of the suboptimal quantizer design with DT.INDEX TERMS Full-duplex, quantize-map-and-forward, hybrid quantize-map-and-forward/decode-andforward.

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