Research On Throughput-optimal Random Access Algorithms With Imperfect Carrier Sensing In VLC

Free-space visible light communication (VLC) has several advantages of low power, highbandwidth and unregulated spectrum. Rapid increase of mobile devices has pushed the radiofrequency (RF)-based wireless technologies to their limits. As the spectrum resources of RFare not enough to respond to the ever-increasing wireless spectrem demand, we focus on VLC.Recently, the theoretical researches of VLC have attracted much attention. The researchresults mostly concentrate on the techniques of physical layer and the works on the theoriesand algorithms of upper logic link layer are rarely. The well-known IEEE802.15.7standardprovides framework of PHY and MAC layer for short-range optical wireless communicationsusing visible light. The standard recommends “scheduling and collision avoidance randomaccess”, but does not involve a specific random access algotithm. Carrier sense multipleaccess (CSMA)-type algorithms are an important class of scheduling algorithms due to theirsimplicity of implementation and the characteristics of throughput-optimal. This paperinvestigates the optical CSMA algorithm abstracted from IEEE802.15.7.The high dynamic random feature of VLC channels and the asymmetric interference leadto the decrease of carrier sensing efficiency, which brings imperfect carrier sensing capabilityand brings great challenges to implement global stability for distributed CSMA network. Weuse logic conflict graph to abstract the complex mutual restriction raltionships between opticalnodes of unregular light fields. The optical CSMA network is regarded as conflictmulti-queuing system and a markov chain is used to model the dynamics of service. Thecarrier sensing failures are analyzed as probability statistics problems and the random accessequals to sampling from the independent sets by using a Markov chain. We study randomaccess algorithms for throughput-optimal and low delay with imperfect carrier sensing.(1) This paper proposes new CSMA type random access algorithms abstracted from thestructure of the IEEE802.15.7standard. Considering discrete backoff time, non-zero carriersense delay and data packet collision, this paper presents the preemptive CSMA which isproven to be throughput-optimal. In order to introduce the carrier-sensing result and confinethe data packets loss only to the carrier sensing failures, we modify the above preemptiveCSMA and propose the advanced preemptive CSMA. The advanced preemptive CSMA achieves throughput optimality with the assumption that carrier sensing is ideal.(2) There are two types of imperfect carrier sensing: false positive and false negativecarrier sensing. We model carrier sensing failures by Bernoulli trials. We analyze thedynamics of the advanced preemptive CSMA under false positive carrier sensing. Throughobtaining the resulting transition probability and unique stationary distribution, we can provethat the advanced preemptive CSMA is throughput-optimal under the false positive carriersensing. Considering false negative carrier sensing, the resulting markov chain is notreversible and the derivation of the stationary distribution is challenging. Instead, wecharacterize the stationary distribution of false negative carrier sensing by viewing themarkov chain as a perturbed version of the markov chain for the ideal carrier sensing case.Research results state that the algorithm can achieve an arbitrary fraction of the capacityregion if certain access probabilities are set appropriately.(3) The access probilities of probe packets affect the mixing time of the advancedpreemptive CSMA markov chain, which, in turn, have a significant impact on the delayperformance of the algorithm. Based on the second largest eigenvalue modeulus and theconductance of the transition matrix, we relate the mixing time of markov chain to thefunction of access probabilities of probe packets. Then we derive the optimal accessprobabilities for throughput-optimal and low delay under perfect and imperfect carriersensing.This paper investigates random access algorithms from a new point of view and ourresearch results maybe are useful for future visible light communication.