  In-band full-duplex (FD) operation is practically more suited for short-range
communications such as WiFi and small-cell networks, due to its current
practical limitations on the self-interference cancellation. In addition,
cell-free massive multiple-input multiple-output (CF-mMIMO) is a new and
scalable version of MIMO networks, which is designed to bring service antennas
closer to end user equipments (UEs). To achieve higher spectral and energy
efficiencies (SE-EE) of a wireless network, it is of practical interest to
incorporate FD capability into CF-mMIMO systems to utilize their combined
benefits. We formulate a novel and comprehensive optimization problem for the
maximization of SE and EE in which power control, access point-UE (AP-UE)
association and AP selection are jointly optimized under a realistic power
consumption model, resulting in a difficult class of mixed-integer nonconvex
programming. To tackle the binary nature of the formulated problem, we propose
an efficient approach by exploiting a strong coupling between binary and
continuous variables, leading to a more tractable problem. In this regard, two
low-complexity transmission designs based on zero-forcing (ZF) are proposed.
Combining tools from inner approximation framework and Dinkelbach method, we
develop simple iterative algorithms with polynomial computational complexity in
each iteration and strong theoretical performance guaranteed. Furthermore,
towards a robust design for FD CF-mMIMO, a novel heap-based pilot assignment
algorithm is proposed to mitigate effects of pilot contamination. Numerical
results show that our proposed designs with realistic parameters significantly
outperform the well-known approaches (i.e., small-cell and collocated mMIMO) in
terms of the SE and EE. Notably, the proposed ZF designs require much less
execution time than the simple maximum ratio transmission/combining.
