Optimal Joint Subcarrier and Power Allocation in NOMA is Strongly NP-Hard

International audienceNon-orthogonal multiple access (NOMA) is a promising radio access technology for 5G. It allows several users to transmit on the same frequency and time resource by performing power-domain multiplexing. At the receiver side, successive interference cancellation (SIC) is applied to mitigate interference among the multiplexed signals. In this way, NOMA can outperform orthogonal multiple access schemes used in conventional cellular networks in terms of spectral efficiency and allows more simultaneous users. This paper investigates the computational complexity of joint subcarrier and power allocation problems in multi-carrier NOMA systems. We prove that these problems are strongly NP-hard for a large class of objective functions, namely the weighted generalized means of the individual data rates. This class covers the popular weighted sum-rate, proportional fairness, harmonic mean and max-min fairness utilities. Our results show that the optimal power and subcarrier allocation cannot be computed in polynomial time in the general case, unless P = NP. Nevertheless, we present some tractable special cases and we show that they can be solved efficiently

Weighted Sum-Rate Maximization in Multi-Carrier NOMA with Cellular Power Constraint

International audienceNon-orthogonal multiple access (NOMA) has received significant attention for future wireless networks. NOMA outperforms orthogonal schemes, such as OFDMA, in terms of spectral efficiency and massive connectivity. The joint subcarrier and power allocation problem in NOMA is NP-hard to solve in general, due to complex impacts of signal superposition on each user's achievable data rates, as well as combinatorial constraints on the number of multiplexed users per sub-carrier to mitigate error propagation. In this family of problems, weighted sum-rate (WSR) is an important objective function as it can achieve different tradeoffs between sum-rate performance and user fairness. We propose a novel approach to solve the WSR maximization problem in multi-carrier NOMA with cellular power constraint. The problem is divided into two polynomial time solvable sub-problems. First, the multi-carrier power control (given a fixed subcarrier allocation) is non-convex. By taking advantage of its separability property, we design an optimal and low complexity algorithm (MCPC) based on projected gradient descent. Secondly, the single-carrier user selection is a non-convex mixed-integer problem that we solve using dynamic programming (SCUS). This work also aims to give an understanding on how each sub-problem's particular structure can facilitate the algorithm design. In that respect, the above MCPC and SCUS are basic building blocks that can be applied in a wide range of resource allocation problems. Furthermore, we propose an efficient heuristic to solve the general WSR maximization problem by combining MCPC and SCUS. Numerical results show that it achieves near-optimal sum-rate with user fairness, as well as significant performance improvement over OMA

Joint Subcarrier and Power Allocation in NOMA: Optimal and Approximate Algorithms

Non-orthogonal multiple access (NOMA) is a promising technology to increase the spectral efficiency and enable massive connectivity in 5G and future wireless networks. In contrast to orthogonal schemes, such as OFDMA, NOMA multiplexes several users on the same frequency and time resource. Joint subcarrier and power allocation problems (JSPA) in NOMA are NP-hard to solve in general. In this family of problems, we consider the weighted sum-rate (WSR) objective function as it can achieve various tradeoffs between sum-rate performance and user fairness. Because of JSPA's intractability, a common approach in the literature is to solve separately the power control and subcarrier allocation (also known as user selection) problems, therefore achieving sub-optimal result. In this work, we first improve the computational complexity of existing single-carrier power control and user selection schemes. These improved procedures are then used as basic building blocks to design new algorithms, namely OPT-JSPA, ε-JSPA and GRAD-JSPA. OPT-JSPA computes an optimal solution with lower complexity than current optimal schemes in the literature. It can be used as a benchmark for optimal WSR performance in simulations. However, its pseudo-polynomial time complexity remains impractical for real-world systems with low latency requirements. To further reduce the complexity, we propose a fully polynomial-time approximation scheme called ε-JSPA. Since, no approximation has been studied in the literature, ε-JSPA stands out by allowing to control a tight trade-off between performance guarantee and complexity. Finally, GRAD-JSPA is a heuristic based on gradient descent. Numerical results show that it achieves near-optimal WSR with much lower complexity than existing optimal methods

Maximizing Connection Density in NB-IoT Networks with NOMA

International audienceWe address the issue of maximizing the number of connected devices in a Narrowband Internet of Things (NB-IoT) network using non-orthogonal multiple access (NOMA). The scheduling assignment is done on a per-transmit time interval (TTI) basis and focuses on efficient device clustering. We formulate the problem as a combinatorial optimization problem and solve it under interference, rate and sub-carrier availability constraints. We first present the bottom-up power filling algorithm (BU), which solves the problem given that each device can only be allocated contiguous sub-carriers. Then, we propose the item clustering heuristic (IC) which tackles the more general problem of non-contiguous allocation. The novelty of our optimization framework is twofold. First, it allows any number of devices to be multiplexed per sub-carrier, which is based on the successive interference cancellation (SIC) capabilities of the network. Secondly, whereas most existing works only consider contiguous sub-carrier allocation, we also study the performance of allocating non-contiguous sub-carriers to each device. We show through extensive simulations that non-contiguous allocation through IC scheme can outperform BU and other existing contiguous allocation methods

Multi-Power Irregular Repetition Slotted ALOHA in Heterogeneous IoT networks

International audienceIrregular Repetition Slotted Aloha (IRSA) is one candidate member of a family of random access protocols to provide solutions for massive parallel connections in the Internet of Things (IoT) networks. The key features of this protocol are repeating the transmitted packets several times and using Successive Interference Cancellation (SIC) at the decoder to resolve the collisions, which dramatically increases the performance of Slotted ALOHA. Motivated by multiple previous studies of IRSA performance in different settings, we focus on the scenario of an IoT network where the packets of different nodes are received with different powers at the base station, either per design due to different transmission power, or induced by the fact that the nodes are at different distances from the base station. In such a scenario, the capture effect emerges at the receiver, which in turn enhances the protocol performance. We analyze the protocol behavior using a new density evolution which is based on dividing nodes into classes with different powers. By computing the probability to decode a packet in the presence of the interference, we explore the achievable throughput and its associated gain and show the excellent performance of Multi-Power IRSA

Unsupervised Graph-based Learning Method for Sub-band Allocation in 6G Subnetworks

In this paper, we present an unsupervised approach for frequency sub-band allocation in wireless networks using graph-based learning. We consider a dense deployment of subnetworks in the factory environment with a limited number of sub-bands which must be optimally allocated to coordinate inter-subnetwork interference. We model the subnetwork deployment as a conflict graph and propose an unsupervised learning approach inspired by the graph colouring heuristic and the Potts model to optimize the sub-band allocation using graph neural networks. The numerical evaluation shows that the proposed method achieves close performance to the centralized greedy colouring sub-band allocation heuristic with lower computational time complexity. In addition, it incurs reduced signalling overhead compared to iterative optimization heuristics that require all the mutual interfering channel information. We further demonstrate that the method is robust to different network settings

CARA: Connectivity-Aware Relay Algorithm for Multi-Robot Expeditions

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Analysis of Downlink Connectivity in NB-IoT Networks Employing NOMA with Imperfect SIC

International audienceWe study the problem of maximizing the number of served devices in a non-orthogonal multiple access (NOMA) based Narrowband Internet of Things (NB-IoT) network for supporting massive connectivity in the downlink. We analyze this problem under practical system limitations of imperfect successive interference cancellation (SIC) at the receiver along with data rate, power and bandwidth constraints. We propose a strategy for joint device and power allocation through an iterative solution for a system of linear equations on each sub-carrier that maximizes the number of connected devices. We evaluate the performance of the proposed solution over a wide range of service scenarios through extensive computer simulations and demonstrate the sensitivity of connectivity in power domain NOMA based NB-IoT systems to the residual interference resulting from imperfect SIC

Subcarrier and Power Allocation for the Downlink of Multicarrier NOMA Systems

International audienceThis paper investigates the joint subcarrier and power allocation problem for the downlink of a multi-carrier non-orthogonal multiple access (MC-NOMA) system. A novel three-step resource allocation framework is designed to deal with the sum rate maximization problem. In Step 1, we relax the problem by assuming each of the users can use all subcarriers simultaneously. With this assumption, we prove the convexity of the resultant power control problem and solve it via convex programming tools to get a power vector for each user; In Step 2, we allocate subcarriers to users by a heuristic greedy manner with the obtained power vectors in Step 1; In Step 3, the proposed power control schemes used in Step 1 are applied once more to further improve the system performance with the obtained sub-carrier assignment of Step 2. To solve the maximization problem with fixed subcarrier assignments in both Step 1 and Step 3, a centralized power allocation method based on projected gradient descent algorithm and two distributed power control strategies based respectively on pseudo-gradient algorithm and iterative waterfilling algorithm are investigated. Numerical results show that our proposed three-step resource allocation algorithm could achieve comparable sum rate performance to the existing near-optimal solution with much lower computational complexity and outperforms power controlled OMA scheme. Besides, a tradeoff between user fairness and sum rate performance can be achieved via applying different user power constraint strategies in the proposed algorithm

Constant Delivery Delay Protocol Sequences for the Collision Channel Without Feedback

International audienceWe consider a collision channel model without feedback based on a time-slotted communication channel shared by K users. In this model, packets transmitted in the same time slot collide with each other and are unrecoverable. Each user accesses the channel according to an internal periodical pattern called protocol sequence. Due to the lack of feedback, users cannot synchronize their protocol sequences, leading to unavoidable collisions and varying throughput. Protocol sequences that provide constant throughput regardless of delay offsets between users are called shift-invariant (SI), they have been studied and characterized in previous work. We propose a new class of SI sequences: Constant Individual Delivery Delay (CIDD) sequences which ensure that the delay between two successfully delivered packets is constant for each user. We present a characterization of CIDD sequences. We also prove that CIDD sequences can achieve the lower bound of SI sequences period but not the optimal throughput