Tech Report - University of Virginia

31) Overlapped Contention: In the first approach, the contentionwindows of all nodes share the same lower bound of“0” as CSMA/CA does, but have different initial upper boundsthat are determined by the channel conditions in terms ofachievable bit rates. Therefore, the contention windows of allnodes overlap in ranges as plotted on the left plot in Figure 1.The initial upper bound CW is inversely proportional to theratio of current achievable bit rate over the basic bit rate andcomputed as in Formula 1 below whenever a node is ready tocontend on the channel for a new transmission.CW = ⌈α × R bR i× CW base ⌉ (1)where R i refers to the current achievable bit rate of a particularnode i, R b denotes the basic rate in a bit rate set and CW baseis a constant base value, e.g. 15 in IEEE 802.11n. Note that R bR i6.5Mbps600Mbps ismay be very small, for example, in IEEE 802.11n,almost 0.01. Therefore, a coefficient, α, is introduced to makesure that the computed window for the highest bit rate is noless than a certain small value to maintain a random access.From this formula, intuitively, a high bit rate, namely goodchannel conditions, leads to a small CW and thereby a largerprobability to win the channel contention with the uniformselection of a backoff value from the contention window. Then,the computed CW can be used by the Binary ExponentialBackoff procedure in the CSMA/CA to fulfill the opportunisticaccess.Fig. 1: Illustration of Contention WindowNote that, in the Overlapped Contention, a node with lowbit rate still has the probability to beat another node with ahigh bit rate: the lower rate node still has chance to select asmaller backoff value because their contention windows havethe same lower bound of ”0”.2) Segmented Contention: To strictly grant a higher priorityof accessing channel to the users with better channel conditions,another algorithm separates the contention windowsfor nodes at different bit rates as illustrated on the right ofFigure 1. In this approach, the initial contention window is stillcomputed as in Formula 1. However, unlike the OverlappedContention that maintains the same lower bound of “0”for all contention windows, this algorithm differentiates thelower bounds of the contention window for different channelconditions. A higher bit rate results in an upper bound of thecontention window smaller than the lower bound of a node ata lower bit rate. For example, on the right of Figure 1, W i maxand W i+1 max respectively denote the computed initial upperbounds of the contention window of bit rate R i and R i+1according to Formula 1. Then, the lower bound of the contentionwindow CW i of bit rate R i is assigned the value that islarger by one than W i+1 max , the upper bound of CW i+1 , i.e.the window is [W i+1 max + 1, W i max ]. This segments thecontention of nodes with different channel conditions in that anode at bit rate R i can never get a backoff value smaller than anode at bit rate R i+1 . This approach can be considered semiprobabilisticin that (1) the access of the nodes at the same bitrate is random since they have the same initial window size torandomly generate a backoff value, but (2) the access of nodesat different rates is deterministically prioritized because thelower rate nodes can never get a smaller backoff value than thehigher rate nodes. This approach provides a tight opportunismby grouping nodes with similar channel conditions into thesame random access team at the cost of randomness acrossteams. Note that this approach leads to a significant problem:starvation of nodes with poor conditions. This problem willbe addressed in Section IV-C.B. Normal Distribution Based Backoff SelectionIn the Overlapped Contention, although nodes with differentchannel conditions obtain different initial contention windows,each node still uses a uniform distribution to select thebackoff value from its contention window. The third proposedopportunistic access approach consists of using a normal ratherthan a uniform distribution, in selecting the backoff value oncethe contention window is determined as in the OverlappedContention. With the expectation of the normal distribution setto a proper value within the contention window and a properstandard deviation, a node with higher bit rate has significantlygreater probability to obtain a smaller backoff value than alower bit rate node. Systematically, the expectation of thenormal distribution of a node at rate R is computed as below:E = ⌈ CW 2 ⌉ (2)where CW is computed as in Formula 1.Let us examine anexample where a networkhas two nodesA at rate R andB at rate R 2 . Then,the expectations ofthe normal distributionat A and Bare respectively setas N 4 and N 2to selecttheir backoff valuesas shown in Figure 2.As a result, in thelong run, A will selecta smaller backoff value than B because most likelyFig. 2: Normal Distribution Backoffthe