  In this paper, we propose a distributed cluster formation (CF) and resource
allocation (RA) framework for non-ideal non-orthogonal multiple access (NOMA)
schemes in heterogeneous networks. The imperfection of the underlying NOMA
scheme is due to the receiver sensitivity and interference residue from
non-ideal successive interference cancellation (SIC), which is generally
characterized by a fractional error factor (FEF). Our analytical findings first
show that several factors have a significant impact on the achievable NOMA
gain. Then, we investigate fundamental limits on NOMA cluster size as a
function of FEF levels, cluster bandwidth, and quality of service (QoS) demands
of user equipments (UEs). Thereafter, a clustering algorithm is developed by
taking feasible cluster size and channel gain disparity of UEs into account.
Finally, we develop a distributed alpha-fair RA framework where alpha governs
the trade-off between maximum throughput and proportional fairness objectives.
Based on the derived closed-form optimal power levels, the proposed distributed
solution iteratively updates bandwidths, clusters, and UEs' transmission
powers. Numerical results demonstrate that proposed solutions deliver a higher
spectral and energy efficiency than traditionally adopted basic NOMA cluster
size of two. We also show that an imperfect NOMA cannot always provide better
performance than orthogonal multiple access under certain conditions. Finally,
our numerical investigations reveal that NOMA gain is maximized under
downlink/uplink decoupled (DUDe) UE association.
