For exhaustive search, note that the cardinal number of A is
|A| = (K − 1)!!. Therefore, the complexity of exhaustive
search for user pairing is at least O((K −1)!!N), and the proof
is finally completed.
Note that a greedy algorithm can also be straightforwardly
obtained, since the closed-form expressions of the cost function
P
PH−NOMA
i,σ(i)
can be acquired by (23) and (24). However,
this greedy algorithm cannot obtain satisfactory performance
since the weak users can lead to a significant performance
loss, which can be observed in the simulation results. In [13],
the author developed a simplified greedy algorithm by replacing
the cost function with the correlation between the two
channels in one group, also termed the correlation based user
pairing algorithm in this paper for simplicity. It is suggested
that one user pairs with another user with maximum correlation.
Although the complexity is reduced, the performance is
unsatisfactory.