On the Complexity of Scheduling in Wireless Networks

We consider the problem of throughput-optimal scheduling in wireless networks subject to interference constraints. We model the interference using a family of K-hop interference models, under which no two links within a K-hop distance can successfully transmit at the same time. For a given K, we can obtain a throughput-optimal scheduling policy by solving the well-known maximum weighted matching problem. We show that for K > 1, the resulting problems are NP-Hard that cannot be approximated within a factor that grows polynomially with the number of nodes. Interestingly, for geometric unit-disk graphs that can be used to describe a wide range of wireless networks, the problems admit polynomial time approximation schemes within a factor arbitrarily close to 1. In these network settings, we also show that a simple greedy algorithm can provide a 49-approximation, and the maximal matching scheduling policy, which can be easily implemented in a distributed fashion, achieves a guaranteed fraction of the capacity region for "all K." The geometric constraints are crucial to obtain these throughput guarantees. These results are encouraging as they suggest that one can develop low-complexity distributed algorithms to achieve near-optimal throughput for a wide range of wireless networksopen1

On distributed scheduling in wireless networks exploiting broadcast and network coding

In this paper, we consider cross-layer optimization in wireless networks with wireless broadcast advantage, focusing on the problem of distributed scheduling of broadcast links. The wireless broadcast advantage is most useful in multicast scenarios. As such, we include network coding in our design to exploit the throughput gain brought in by network coding for multicasting. We derive a subgradient algorithm for joint rate control, network coding and scheduling, which however requires centralized link scheduling. Under the primary interference model, link scheduling problem is equivalent to a maximum weighted hypergraph matching problem that is NP-complete. To solve the scheduling problem distributedly, locally greedy and randomized approximation algorithms are proposed and shown to have bounded worst-case performance. With random network coding, we obtain a fully distributed cross-layer design. Numerical results show promising throughput gain using the proposed algorithms, and surprisingly, in some cases even with less complexity than cross-layer design without broadcast advantage

Achieving Optimal Throughput and Near-Optimal Asymptotic Delay Performance in Multi-Channel Wireless Networks with Low Complexity: A Practical Greedy Scheduling Policy

In this paper, we focus on the scheduling problem in multi-channel wireless networks, e.g., the downlink of a single cell in fourth generation (4G) OFDM-based cellular networks. Our goal is to design practical scheduling policies that can achieve provably good performance in terms of both throughput and delay, at a low complexity. While a class of $O(n^{2.5} \log n)$-complexity hybrid scheduling policies are recently developed to guarantee both rate-function delay optimality (in the many-channel many-user asymptotic regime) and throughput optimality (in the general non-asymptotic setting), their practical complexity is typically high. To address this issue, we develop a simple greedy policy called Delay-based Server-Side-Greedy (D-SSG) with a \lower complexity $2n^2+2n$, and rigorously prove that D-SSG not only achieves throughput optimality, but also guarantees near-optimal asymptotic delay performance. Specifically, we show that the rate-function attained by D-SSG for any delay-violation threshold $b$, is no smaller than the maximum achievable rate-function by any scheduling policy for threshold $b-1$. Thus, we are able to achieve a reduction in complexity (from $O(n^{2.5} \log n)$ of the hybrid policies to $2n^2 + 2n$) with a minimal drop in the delay performance. More importantly, in practice, D-SSG generally has a substantially lower complexity than the hybrid policies that typically have a large constant factor hidden in the $O(\cdot)$ notation. Finally, we conduct numerical simulations to validate our theoretical results in various scenarios. The simulation results show that D-SSG not only guarantees a near-optimal rate-function, but also empirically is virtually indistinguishable from delay-optimal policies.Comment: Accepted for publication by the IEEE/ACM Transactions on Networking, February 2014. A preliminary version of this work was presented at IEEE INFOCOM 2013, Turin, Italy, April 201

Resource allocation and feedback in wireless multiuser networks

This thesis focuses on the design of algorithms for resource allocation and feedback in wireless multiuser and heterogeneous networks. In particular, three key design challenges expected to have a major impact on future wireless networks are considered: cross-layer scheduling; structured quantization codebook design for MU-MIMO networks with limited feedback; and resource allocation to provide physical layer security. The first design challenge is cross-layer scheduling, where policies are proposed for two network architectures: user scheduling in single-cell multiuser networks aided by a relay; and base station (BS) scheduling in CoMP. These scheduling policies are then analyzed to guarantee satisfaction of three performance metrics: SEP; packet delay; and packet loss probability (PLP) due to buffer overflow. The concept of the τ-achievable PLP region is also introduced to explicitly describe the tradeoff in PLP between different users. The second design challenge is structured quantization codebook design in wireless networks with limited feedback, for both MU-MIMO and CoMP. In the MU-MIMO network, two codebook constructions are proposed, which are based on structured transformations of a base codebook. In the CoMP network, a low-complexity construction is proposed to solve the problem of variable codebook dimensions due to changes in the number of coordinated BSs. The proposed construction is shown to have comparable performance with the standard approach based on a random search, while only requiring linear instead of exponential complexity. The final design challenge is resource allocation for physical layer security in MU-MIMO. To guarantee physical layer security, the achievable secrecy sum-rate is explicitly derived for the regularized channel inversion (RCI) precoder. To improve performance, power allocation and precoder design are jointly optimized using a new algorithm based on convex optimization techniques