Joint relay selection and max‐min energy‐efficient power allocation in downlink multicell NOMA networks: A matching‐theoretic approach

Abstract

In this paper, the problem of joint relay selection and max‐min energy‐efficient power allocation (J‐RS‐MMEE‐PA) in downlink multicell nonorthogonal multiple access (NOMA) networks is studied. In particular, the goal is to perform relay selection for each cellular user within each cell, so as to achieve max‐min energy efficiency while satisfying quality‐of‐service (QoS) constraints. However, the formulated J‐RS‐MMEE‐PA problem happens to be nonconvex (ie, computationally intensive). In turn, a solution procedure for max‐min energy‐efficient power allocation is devised to determine the energy efficiency of each user per potential relay while meeting the target minimum rate per user. After that, the relay selection problem is modeled as a student‐project allocation with preferences over projects matching problem. A polynomial‐time complexity stable matching (SM) algorithm is proposed, which takes into account the maximum number of users that can select a relay as well as the number of users that can be associated with a base station. However, the proposed SM algorithm can only guarantee an SM size that is at least half the size of the maximum “optimal” cardinality SM. Thus, the improved SM (I‐SM) algorithm with polynomial‐time complexity is devised, so as to guarantee an SM size that is at least two‐thirds of that of the optimal matching. Lastly, simulation results are presented to compare the proposed matching algorithms to the J‐RS‐MMEE‐PA scheme, where it has been shown that the I‐SM algorithm is superior to its SM counterpart and yields comparable energy efficiency per cellular user to the J‐RS‐MMEE‐PA scheme while satisfying QoS constraints.

An Algorithm for Strong Stability in the Student-Project Allocation Problem with Ties

“…3 We note that we only remove this edge to form Gr, we do not delete the edge from G. 4 If si is bound to more than one projects offered by l k , for all the bound edges involving si and these projects that we remove from Gr, we only reduce l k 's quota in Gr by one. 5 An intuition as to why we add dummy students to Gr is as follows. Given a lecturer l k whose project is provisionally assigned to a student in Gr.…”

“…For each of these dummy vertex, say s di , and for each project p j ∈ P k ∩ P r that is adjacent to a student vertex in S r via a lower rank edge, we add the edge (s di , p j ) to E r . 5 Given a set X ⊆ S r of students, define N (X), the neighbourhood of X, to be the set of project vertices adjacent in G r to a student in X. If for all subsets X of S r , each student in X can be assigned to one project in N (X), without exceeding the revised quota of each project in N (X) (i.e., |X| ≤ {q * j : p j ∈ N (X)} for all X ⊆ S r ); then we say G r admits a perfect matching that saturates S r .…”

“…These include SPA with lecturer preferences over (i) students [15], (ii) projects [13,22,23], and (iii) (student, project) pairs [2]. Outwith assigning students to projects, applications of each of these three variants can be seen in multi-cell networks where the goal is to find a stable assignment of users to channels at base-stations [3,4,5].…”

Uplink grant‐free pattern division multiple access transmission scheme by exploiting poly complementary sequence

“…In uplink NOMA, multiple users transmit non‐orthogonal signals on the same resource block (RB) to the base station, and each UE transmits its signal independently with the maximum transmission power or controlled transmission power 29 . In Reference 30, the problem of joint relay selection and max‐min energy‐efficient power allocation in downlink multicell NOMA networks is studied. In order to meet the quality of service constraints and achieve maximum minimum energy efficiency, it performs relay selection for each cellular user in each cell.…”