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Using cooperative transmission, two or more single- antenna users can share their antennas to achieve spatial diversity in a slow fading channel. One relaying protocol that achieves diversity, amplify-and-forward (AF), is striking in its simplicity, but prior analysis has been concerned with an idealized version of AF. In practice, the signal received by the relay must be quantized and stored in finite memory before retransmission. This paper examines a quantize-and-forward (QF) relaying approach that is amenable to implementation on resource-constrained relays. We describe QF relaying with M-ary phase shift keying (PSK) and derive the maximum likelihood-based soft-decision metric for this scheme. When each M-PSK channel symbol is quantized with q bits at the relay, simulation results show that quantizing with q = 1 + log2 M bits (i.e., only one extra bit per symbol) provides comparable performance in Rayleigh fading to the idealized (unquantized) AF protocol as well as to an adaptive decode- and-forward protocol at frame error rates of practical interest. Furthermore, this performance is achieved without requiring channel decoding or channel state information at the relay (i.e., using only non-coherent detection at the relay). The proposed QF scheme allows the use of resource-limited relays (with low processing power and low memory) to achieve cooperative diversity.