Kalman Filter Estimation of the Number of Competing Terminals in an IEEE 802.11 network Giuseppe Bianchi, Ilenia Tinnirello Universita’ di Palermo, Dipartimento di Ingegneria Elettrica Viale delle Scienze, 90128, Palermo, Italy bianchi@elet.polimi.it, ilenia.tinnirello@tti.unipa.it Abstract— Throughput performance of the IEEE 802.11 Dis- tributed Coordination Function (DCF) is very sensitive to the number n of competing stations. The contribute of this paper is threefold. First, we show that n can be expressed as function of the collision probability encountered on the channel; hence, it can be estimated based on run-time measurements. Second, we show that the estimation of n, based on exponential smoothing of the measured collision probability (specifically, an ARMA filter), results to be a biased estimation, with poor performance in terms of accuracy/tracking trade-offs. Third, we propose a methodology to estimate n, based on an extended Kalman filter coupled with a change detection mechanism. This approach shows both high accuracy as well as prompt reactivity to changes in the network occupancy status. Numerical results show that, although devised in the assumption of saturated terminals, our proposed approach results effective also in non saturated conditions, and specifically in tracking the average number of competing terminals. I. I NTRODUCTION IEEE 802.11 [1] employs DCF (Distributed Coordination Function) as primary mechanism to access the medium. DCF is a random access scheme, based on the Carrier Sense Multiple Access with Collision Avoidance (CSMA/CA) pro- tocol and binary exponential backoff. Several performance evaluation studies of the IEEE 802.11 DCF [2], [3], [4], [5] show that performance is very sensitive to the number of stations competing on the channel, especially when the Basic Access mode is employed. Specifically, performance strongly depends on the number n of ”competing” stations, i.e. the number of terminals that are simultaneously trying to send a packet on the shared medium. This information cannot be retrieved from the protocol operation. On one side, DCF does not rely on a privileged station to control the access to the channel. But even considering the existence of an Access Point (AP), as in Infrastructured 802.11 Networks, the information available at the AP is limited to the number of ”associated” stations, a number which may be very different from the number of competing stations, i.e. stations that are actually in the process of transmitting packets. The ability to acquire knowledge of n leads to several implications. It has been shown [6], [7] that, in order to maximize the system performance, the backoff window should be made depend upon n. While, in the standard IEEE 802.11 protocol [1], the backoff parameters were hard-wired in the PHY layer, the idea of adaptively setting the backoff window has been recently taken into consideration in the activities of the 802.11e working group. Indeed, the knowledge of n has several possible practical implications also in currently deployed 802.11 networks. The 802.11 standard is designed to allow both Basic Access and RTS/CTS access modes to coexist. The standard suggests that the RTS/CTS access mode should be chosen when the packet payload exceed a given RTS threshold. However, it has been shown [4] that the RTS threshold which maximizes the system throughput is not a constant value, but significantly depends on the number n of competing stations. Specifically, as the number of stations in the network increases, the Basic Access becomes ineffective and it results convenient to switch to the RTS/CTS mode even in the presence of short packets. Clearly, this operation requires each station to be capable of estimating n. A second application scenario of emerging importance occurs when Infrastructured 802.11 networks are arranged in a cellular-like pattern, to provide wireless access in confined high-populated terrestrial areas, called ”hot spots”, such as convention centers, malls, university campus, residential ar- eas, etc. It appears that, in the very last months, 802.11 is becoming a complementary (or even an alternative) access infrastructure to 3G systems, thus offering new perspectives and market shares for emerging wireless Internet providers. In this cellular-like 802.11 scenario, the estimated knowledge of traffic load and number of terminals sharing an 802.11 cell might effectively drive load-balancing and handover al- gorithms to achieve better network resource utilization. In this paper, we propose an efficient tecnique to estimate the number of competing stations in an 802.11 network. Our technique is based on an Extended Kalman filter approach, coupled with a change detection mechanism to capture varia- tions in the number of competing terminals in the network. The estimation methodology builds on the existence of a mathematical relationship between the number of competing stations and the packet collision probability encountered on the shared medium. Such a relation is a straightforward, although originally unforeseen, extension of the analysis carried out in [4]. It is obtained in the assumption of terminals in saturation conditions (i.e. always having a packet waiting for transmis- sion), and in the assumption of ideal channel conditions, i.e. no packet corruption and no hidden terminals and capture [8], [9]. Since this relationship is independent of the access mode adopted, it is suited for application to any DCF access mode scenario, including hybrid Basic-RTS/CTS operation. 0-7803-7753-2/03/$17.00 (C) 2003 IEEE IEEE INFOCOM 2003