Non-orthogonal multipe access based multiple-input multiple-output system (MIMO-NOMA) has been widely used in improving user's achievable rate of millimeter wave (mmWave) communication. To meet different requirements of each user in multi-user beams, this paper proposes a power allocation algorithm to satisfy the quality of service (QoS) of head user while maximizing the minimum rate of edge users from the perspective of max-min fairness. Suppose that the user who is closest to the base station (BS) is the head user and the other users are the edge users in each beam in this paper. Then, an optimization problem model of max-min fairness criterion is developed under the constraints of users' minimum rate requirements and the total transmitting power of the BS. The bisection method and Karush-Kuhn-Tucher (KKT) conditions are used to solve this complex non-convex problem, and simulation results show that both the minimum achievable rates of edge users and the average rate of all users are greatly improved significantly compared with the traditional MIMO-NOMA, which only consider max-min fairness of users.

In this letter, unlike the previous work in [2], the optimal power allocation in a non-orthogonal, amplify-and-forward (AF) relay-assisted transmission is investigated in the uplink. Here, the inter-user-interference among the signals from MTs and relays exists due to non-zero interference suppression factor (ISF), i.e., finite spreading factor. In this letter, we show that the optimal solution to achieve a 'max-min fairness' among mobile terminals can be alternatively obtained by solving its inverse problem. The impact of various ISFs as well as the Jain's fairness is investigated in comparison with the equal power allocation.

The Generalized Max-Min Fairness policy (GMM) allocates in a fair way the available bandwidth among elastic calls by taking into account their minimum and maximum rate requirements. The GMM has been described in a five-step procedure, which has the advantage of an easy presentation, but does not come into details, as far as its computer implementation is concerned, and fails to describe the policy in a clear mathematical way. We propose a new algorithm for the GMM policy, in a clear mathematical way, based on Linear Programming (LP). The new algorithm is directly convertible into software. Numerical examples clarify our algorithm.

We consider a rate control algorithm for elastic services to allocate bandwidth in a network subject to throughput and fairness constraints. Our algorithm achieves a max-min fair bandwidth allocation among contending elastic connections, and has desirable properties in that it can operate in a decentralized and asynchronous manner accounting in part for heterogeneity in round trip delays. The algorithm is simple and scalable in that, 1) the network links make local measurements of capacity and calculate local 'explicit rates' which are fed back to sources without requiring knowledge of the number of on-going connections, while 2) sources adjust their transmission rates so as not to exceed the received explicit rate indication. The algorithm is designed to track a "dynamic" network environment. We discuss its stability, convergence, and feasibility issues related to fair allocation and rate-based flow control. We also consider the role of sessions with priorities to differentiate among users with elastic services. Through rigorous analysis and simulations, we have shown that it has indeed desirable characteristics for networks with elastic services as well as other service types, which are expected to be common in future network environment.

The available bit rate (ABR) is an ATM service category that provides an economical support of connections having vague requirements. An ABR session may specify its peak cell rate (PCR) and minimum cell rate (MCR), and available bandwidth is allocated to competing sessions based on the max-min policy. In this paper, we investigate the ABR traffic control from a different point of view: Based on the decentralized bandwidth allocation model studied in [9], we prove that the max-min rate vector is the equilibrium of a certain system of noncooperative optimizations. This interpretation suggests a new framework for ABR traffic control that allows the max-min optimality to be achieved and maintained by end-systems, and not by network switches. Moreover, in the discussion, we consider the constrained version of max-min fairness and develop an efficient algorithm with theoretical justification to determine the optimal rate vector.