In this paper, we developed a novel Bayesian game theoretic framework to study the coexistence problem between two FD-capable wireless links, where nodes have heterogeneous SIC capabilities. Although the throughput of a single link enhances significantly when operating in the FD mode, the additional caused interference (compared to the HD case) may limit its coexistence with a neighboring link. Our analysis revealed that the SIC capability of each link (which is the type of each player) has a double-threshold structure, i.e., the range of the SIC values can be divided into three regions. When the SIC capability is very good, operating in the FD mode strictly dominates the HD mode, whereas when the SIC capability is very poor, operating in the HD mode strictly dominates the FD mode. When the SIC capability is in the middle region, we derived the conditions on the probability distribution of the types of the other link under which HD (FD) strictly dominates FD (HD).
Accounting for Link Outages We now relax the technical conditions ((6) and (7) for P1 and the two similar conditions for P2), and assume that any of the forward/reverse links may experience outage. In this case, the relation between χ∗ i and χ∗∗ i is not fixed (i.e., χ∗ i could be larger or smaller than χ∗∗ i ). The reason is that in the case of outage, if P2 operates in the FD mode, then U(FF) 1 may decrease faster with χ1 compared to U(FH) 1 , and hence the condition U(FF) 1 = U(HF) 1 may be satisfied before the condition U(FH) 1 = U(HH) 1 . Therefore, χ∗∗ 1 < χ∗ 1 (recall the definition of χ∗ 1 and χ∗∗ 1 in Section III-A). The same situation arises in the case of P2 when outage is likely to happen.