  In this paper, we consider a multi-user wireless system with one full duplex
(FD) base station (BS) serving a set of half duplex (HD) mobile users.To cope
with the in-band self-interference (SI) and co-channel interference, we
formulate a quality-of-service (QoS) based linear transceiver design problem.
The problem jointly optimizes the downlink (DL) and uplink (UL) beamforming
vectors of the BS and the transmission powers of UL users so as to provide both
the DL and UL users with guaranteed signal-to-interference-plus-noise ratio
performance, using a minimum UL and DL transmission sum power.The considered
system model not only takes into account noise caused by non-ideal RF circuits,
analog/digital SI cancellation but also constrains the maximum signal power at
the input of the analog-to-digital converter (ADC) for avoiding signal
distortion due to finite ADC precision. The formulated design problem is not
convex and challenging to solve in general. We first show that for a special
case where the SI channel estimation errors are independent and identically
distributed, the QoS-based linear transceiver design problem is globally
solvable by a polynomial-time bisection algorithm.For the general case, we
propose a suboptimal algorithm based on alternating optimization (AO). The AO
algorithm is guaranteed to converge to a Karush-Kuhn-Tucker solution.To reduce
the complexity of the AO algorithm, we further develop a fixed-point method by
extending the classical uplink-downlink duality in HD systems to the FD
system.Simulation results are presented to demonstrate the performance of the
proposed algorithms and the comparison with HD systems.
