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We study quantized beamforming in wireless amplify-and-forwardrelay-interference networks with any number of transmitters, relays, andreceivers. We design the quantizer of the channel state information to minimizethe probability that at least one receiver incorrectly decodes its desiredsymbol(s). Correspondingly, we introduce a generalized diversity measure thatencapsulates the conventional one as the first-order diversity. Additionally,it incorporates the second-order diversity, which is concerned with thetransmitter power dependent logarithmic terms that appear in the error rateexpression. First, we show that, regardless of the quantizer and the amount offeedback that is used, the relay-interference network suffers a second-orderdiversity loss compared to interference-free networks. Then, two differentquantization schemes are studied: First, using a global quantizer, we show thata simple relay selection scheme can achieve maximal diversity. Then, using thelocalization method, we construct both fixed-length and variable-length local(distributed) quantizers (fLQs and vLQs). Our fLQs achieve maximal first-orderdiversity, whereas our vLQs achieve maximal diversity. Moreover, we show thatall the promised diversity and array gains can be obtained with arbitrarily lowfeedback rates when the transmitter powers are sufficiently large. Finally, weconfirm our analytical findings through simulations.

Distributed Beamforming in Wireless Multiuser Relay-Interference Networks with Quantized Feedback