## 4 Reader Collision  
In order to avoid reader collisions effectively, pulse protocol can be applied in a more promising manner. By modifying the waiting state of the reader after the reading operation is completed, the proposed pulse protocol differs from the conventional one. If more than one reader initiates the same random backoff time, the probability of collision increases. As a result, in the proposed method, the waiting time is modified in such a way that the probability of a collision between readers is reduced and the probability of reading the tags increases. A standard pulse protocol reader transmission is shown in Figure 7a [19], and a modified pulse protocol reader transmission is shown in Figure 7b. Figure 7a illustrates how the reader reads the tag during the time slot as follows: During the period of while communicating with tags, the reader \(R_{1}\) sends beacon signals to the readers \(R_{2}\) and \(R_{3}\) over the control channel. We are unable to read any tags during this time \(T_{read}\). For a period of time \(T_{read}\) after transmission ends, all readers enter a waiting state for a period of \(T_{min}\). They will resume their backoff time at the end of the time slot. The backoff time in \(R_{2}\) is two time slots. A new random backoff time is chosen by \(R_{1}\), which is also two time slots. At the end of the backoff time slots of and, both attempt to read the tag simultaneously, resulting in reader collisions. As shown in the figure, within the given time frame, due to uniform waiting time \(T_{min}\) for all readers irrespective of whether they have communicated with a tag or not and random selection of backoff time, \(R_{2}\) is not getting a chance to communicate with a tag. Corresponding, algorithm is formulated in terms of modifying waiting time. As illustrated in Figure 7b, in the proposed algorithm, instead of having uniform waiting time, the waiting time is expanded after the reading slot of each reader. After \(T_{read}\) operation of reader \(R_{1}\)\({}^{\prime}\), wait time for \(R_{1}\)\({}^{\prime}\) is \(T_{max}\) instead of \(T_{min}\) (\(T_{max}>T_{min}\)) whereas for the remaining readers \(R_{2}\)\({}^{\prime}\) and \(R_{3}\)\({}^{\prime}\), the wait time remains \(T_{min}\). Therefore, while \(R_{1}\)\({}^{\prime}\) is still in waiting state, \(R_{2}\)\({}^{\prime}\) and \(R_{3}\)\({}^{\prime}\) start the residual backoff time. As depicted in the figure, the backoff time of \(R_{2}\)\({}^{\prime}\) ends prior to \(R_{3}\)\({}^{\prime}\) and \(R_{2}\)\({}^{\prime}\) starts to communicate with tag. The cycle repeats and \(R_{3}\)\({}^{\prime}\) gets the chance to read tag. Hence, this process minimizes the reader. Figure 6: Graphical representation of placing two reader antennas. Collision probability as well as gives all the readers opportunity to communicate with the tags. The following algorithm describes the graphical representation of the operation. \(T_{max}\) is the maximum waiting time after successful reading and it is considered as \(T_{max}\) = 3 \(T_{min}\). The following assumptions are taken to develop the algorithm:  
* Consistently all the readers can establish the communication with tag. But, at a specified time, no more than one reader can communicate. * All the readers receive the beacon which implies that there is no hidden reader. * One slot size is equivalent to one time unit with the value of beacon interval (\(T_{bi}\)). The maximum length of the contention window considered as CW. Reader selects random value from the contention window [0, CW]. Contend backoff time is decreased to zero count and then reader starts communication [20]. In the proposed protocol, the probability distribution of the contention window is considered as monotonically decreasing triangular function. It implies that lesser the backoff time, more is the probability of the reader transmission to tag. The distribution function of the contention window can be expressed mathematically as [30].