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In this paper, a full-duplex (FD) amplify-andforward (AF) relay is designed to compensate for the duplexing loss of the half-duplex (HD) AF relay. In particular, when there is no direct link between a source and a destination, joint analog domain self-interference suppression and digital domain residual self-interference cancellation is considered with an FD-AF relay having single receive antenna but multiple transmit antennas. Unlike previous approaches, a nonconvex quadratically constrained quadratic programming problem is formulated to find the optimal solution. The end-to-end spectral efficiency or, equivalently, the end-to-end signal-to-interference-plus-noise ratio from the source to the destination is chosen as the objective function to be maximized subject to the average transmit power constraint at the relay. In addition, an average power constraint is imposed on the output of the relay's receive antenna to avoid the nonlinear distortion in the low noise amplifier and the excessive quantization noise in the analog-to-digital converter. Through the systematic reduction and the partitioning of the constraint set, the optimal solution is derived in a closed algorithmic expression and shows how it allocates the transmission power not only in the direction of maximal performance improvement but also in the orthogonal direction in order to balance the system performance and the amount of self interference. It is shown that the optimal FD-AF relay significantly outperforms the optimal HD-AF relay even with the hardware limitations in the RF chain of the relay's receiver being well taken into account.Index Terms-Full-duplex relay, amplify-and-forward relay, self-interference cancellation, nonconvex quadratically constrained quadratic programming.

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Random access schemes for packet networks featuring distributed control require algorithms and protocols for resolving packet collisions that occur as the uncoordinated terminals contend for the channel. A widely used collision resolution protocol is the exponential backoff (EB). New analytical results for the stability of the (binary) EB are given. Previous studies on the stability of the (binary) EB have produced contradictory results instead of a consensus: some proved instability, others showed stability under certain conditions. In these studies, simplified and/or modified models of the backoff algorithm were used. In this paper, care is taken to use a model that reflects the actual behavior of backoff algorithms. We show that EB is stable under a throughput definition of stability; the throughput of the network converges to a non-zero constant as the offered load N goes to infinity. We also obtain the analytical expressions for the saturation throughput for a given number of nodes, N. The analysis considers the general case of EB with backoff factor r, where BEB is the special case with r = 2. We show that r = 1/(1 − e−1) is the optimum backoff factor that maximizes the throughput. The accuracy of the analysis is checked against simulation results.