Recent work has shown that adaptive CSMA algorithms can achieve throughput optimality. However, these adaptive CSMA algorithms assume a rather simplistic model for the wireless medium. Specifically, the interference is typically modelled by a conflict graph, and the channels are assumed to be static. In this work, we propose a distributed and adaptive CSMA algorithm under a more realistic signal-to-interference ratio (SIR) based interference model, with time-varying channels. We prove that our algorithm is throughput optimal under this generalized model. Further, we augment our proposed algorithm by using a parallel update technique. Numerical results show that our algorithm outperforms the conflict graph based algorithms, in terms of supportable throughput and the rate of convergence to steady-state.
- Instantaneous channel gains are assumed to be known at each time slot. - Channel statistics (such as average channel gains or distribution) are assumed to be known. A time-varying channel is considered between the transmitter of a link and its corresponding receiver in @cite_9 . However, the channel gains between the interfering links are assumed to be static. In @cite_12 , time varying channels are considered among all the links, and the interference is modelled by a conflict graph. However, the algorithm @cite_12 can support only a fraction of the achievable rate region. A SIR model is considered in @cite_6 to a propose conservative algorithm that is suboptimal. An adaptive Aloha based algorithm is proposed in @cite_14 under time-varying channels. However the algorithm can only maximize some utility functions and is not throughput optimal.
@cite_9 @cite_14 @cite_6 @cite_12
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Recent studies on MAC scheduling have shown that carrier sense multiple access (CSMA) algorithms can be throughput optimal for arbitrary wireless network topology. However, these results are highly sensitive to the underlying assumption on static' or fixed' system conditions. For example, if channel conditions are time-varying, it is unclear how each node can adjust its CSMA parameters, so-called backoff and channel holding times, using its local channel information for the desired high performance. In this paper, we study channel-aware' CSMA (A-CSMA) algorithms in time-varying channels, where they adjust their parameters as some function of the current channel capacity. First, we show that the achievable rate region of A-CSMA equals to the maximum rate region if and only if the function is exponential. Furthermore, given an exponential function in A-CSMA, we design updating rules for their parameters, which achieve throughput optimality for an arbitrary wireless network topology. They are the first CSMA algorithms in the literature which are proved to be throughput optimal under time-varying channels. Moreover, we also consider the case when back-off rates of A-CSMA are highly restricted compared to the speed of channel variations, and characterize the throughput performance of A-CSMA in terms of the underlying wireless network topology. Our results not only guide a high-performance design on MAC scheduling under highly time-varying scenarios, but also provide new insights on the performance of CSMA algorithms in relation to their backoff rates and underlying network topologies. We study the problem of distributed scheduling in multi-hop MIMO networks. We first develop a MIMO-pipe" model that provides the upper layers a set of rates and SINR requirements, which capture the rate-reliability tradeoff in MIMO communications. The main thrust of this study is then dedicated to developing CSMA-based MIMO-pipe scheduling under the SINR model. We choose the SINR model over the extensively studied matching or protocol-based interference models because it more naturally captures the impact of interference in wireless networks. The coupling among the links caused by the interference makes the problem of devising distributed scheduling algorithms particularly challenging. To that end, we explore CSMA-based MIMO-pipe scheduling, from two perspectives. First, we consider an idealized continuous time CSMA network. We propose a dual-band approach in which control messages are exchanged instantaneously over a channel separate from the data channel, and show that CSMA-based scheduling can achieve throughput optimality under the SINR model. Next, we consider a discrete time CSMA network. To tackle the challenge due to the coupling caused by interference, we propose a conservative" scheduling algorithm in which more stringent SINR constraints are imposed based on the MIMO-pipe model. We show that this suboptimal distributed scheduling can achieve an efficiency ratio bounded from below. Developing scheduling mechanisms that can simultaneously achieve throughput optimality and good delay performance often require solving the Maximum Independent Weighted Set (MWIS) problem. However, under most realistic network settings, the MWIS problem can be shown to be NP-hard. In non-fading environments, low-complexity scheduling algorithms have been provided that converge either to the MWIS solution in time or to a solution that achieves at least a provable fraction of the achievable throughput. However, in more practical systems the channel conditions can vary at faster time-scales than convergence occurs in these lower-complexity algorithms. Hence, these algorithms cannot take advantage of the opportunistic gain, and may no longer guarantee good performance. In this paper, we propose a low-complexity scheduling scheme that performs provably well under fading channels and is amenable to implement in a distributed manner. To the best of our knowledge, this is the first scheduling scheme under fading environments that requires only local information, has a low complexity that grows logarithmically with the network size, and achieves provable performance guarantees (which is arbitrarily close to that of the well-known centralized Greedy Maximal Scheduler). Through simulations we verify that both the throughput and the delay under our proposed distributed scheduling scheme are close to that of the optimal solution to MWIS. Further, we implement a preliminary version of our algorithm in a testbed by modifying the existing IEEE 802.11 DCF. The preliminary experiment results show that our implementation successfully accounts for wireless fading, and attains the opportunistic gains in practice, and hence substantially outperforms IEEE 802.11 DCF.