# A Self-Scrutinized Backoff Mechanism for IEEE 802.11 ax in 5G Unlicensed Networks
## 3 A Self-Scrutinized Backoff Mechanism for HEW
### Channel Observation-Based Scaled Backoff (COSB)  
In the proposed COSB protocol, after the communication medium has been idle for a distributed inter-frame space (DIFS), all the WEs competing for a channel proceed to the backoff procedure by selecting a random backoff value \(B\) as shown in Figure 3. The time immediately following an idle DIFS is slotted into observation time slots (\(\alpha\)). The duration of \(\alpha\) is either a constant slot time \(\sigma\) during an idle period or a variable busy (successful or collided transmission) period. While the channel is sensed to be idle during \(\sigma\), \(B\) decrements by one. A data frame is transmitted after \(B\) reaches zero. In addition, if the medium is sensed to be busy, the WE freezes \(B\) and continues sensing the channel. If the channel is again sensed to be idle for DIFS, \(B\) is resumed. Each individual WE can proficiently measure channel observation-based conditional collision probability \(p_{obs}\), which is defined as the probability that a data frame transmitted by a tagged WE fails. We discretize the time in \(B_{obs}\) observation time slots, where the value of \(B_{obs}\) is the total number of \(\alpha\) observation slots between two consecutive backoff stages as shown in Figure 3. A tagged WE updates \(p_{obs}\) from \(B_{obs}\) of backoff stage \(b_{i}\) at the \(i^{\text{th}}\) transmission as,  
\[p_{obs}=\frac{1}{B_{obs}}\times\sum_{k=0}^{B_{obs}-1}S_{k}, \tag{1}\]  
where for an observation time slot \(k\), \(S_{k}=0\) if \(\alpha\) is empty (idle) or the tagged WE transmits successfully, while \(S_{k}=1\) if \(\alpha\) is busy or the tagged WE experiences collision as shown in Figure 3. In the figure, WE 1 randomly selects its backoff value \(B=9\) for its \(b_{i}\) backoff stage. Since WE 1 observes nine idle slot times, two busy periods, and one collision (\(B_{obs}=9+2+1=12\)), \(p_{obs}\) is updated as \(\frac{2+1}{B_{obs}}=\frac{3}{12}=0.25\) in the next backoff stage \(b_{i+1}\). According to the channel observation-based conditional collision probability \(p_{obs}\), the adaptively scaled contention window value is \(W_{b_{i+1}}\) at backoff stage \(b_{i+1}\) of the transmission time \(i+1\), where \(b_{i+1}\in(0,m)\) for the maximum \(m\) number of backoff stages, and \(i\) is the discretized time for the data frame transmissions of a tagged WE. More specifically, when a transmitted data frame has collided, the current contention window \(W_{b_{i}}\) of backoff stage \(b_{i}\) at the \(i^{\text{th}}\) transmission time slot is scaled-up according to the observed \(p_{obs}\) at the \(i^{\text{th}}\) transmission, and when a data frame is transmitted successfully, the current contention window \(W_{b_{i}}\) is scaled-down according to the observed \(p_{obs}\) at the \(i^{\text{th}}\) transmission. Unlike the BEB (where backoff stage is incremented for each retransmission and resets to zero for new transmission as shown in Figure 4a), the backoff stage \(b_{i}\) in COSB at the \(i^{\text{th}}\) transmission has the following property of increment or decrement:  
\[b_{i+1}= \begin{cases}min[b_{i}+1,\ m],collision\ at\ \ i^{\text{th}}\ transmit\\ max[b_{i}-1,\ 0],\ success\ at\ \ i^{\text{th}}\ transmit\end{cases} . \tag{2}\]  
Figure 4b shows that the backoff stage does not reset after a successful transmission. Since the current backoff stage represents the number of collisions or successful transmissions of a tagged WE, it helps to scale the size of W efficiently. The incremented or decremented backoff stage \(b_{i}\) results