## 3 The Modified BA Protocol (MBA)
Also, if the participated tag in the collision detection does not increase its _ASC_ counter by one according to Equation (1), it will repeat its transmission in the next cycle, since _ASC_ is equal to _pc_ for the participated tag and is twice _pc_ for some other unrecognized tags. Thus, after the tag's success response (conduct success cycle), the remaining unrecognized tags increase their _pc_ by one. Consequently, \(ASC\) is still greater than pc by one. Therefore, the unrecognized tags consume one idle cycle to make \(ASC\) equal to \(pc\) for some tags. As a result, BA consumes one more cycle compared to MBA for both cases in the period of the staying tags. To handle the capture-effect treatment, and the separation between collision and interference responses for the period of the staying tags, MBA protocol replaces steps 3, 4, and 5 of BA protocol with the following three steps, and its operation is shown in Figure 2.  
**Step 1:** After the transmission of the reader signal (starting frame or feedback signal), its counters \(T\), \(pcr\), and \(nc\), and the new flag (\(hr\)) is adjusted as follows according to the detected received signal:  
If the received signal is a non-blocking signal:  
\(pcr\ =\ pcr\ +\ 1\), state = \(s\), \(rq\) (new parameter) = \(1D\) & \(\{(nc\ =\ nc\ +\ 1,\ a\ =\ 0)\) if \(pcr\ >\ pcol\}\)  
If the received signal is a blocking signal:  
If \(pcr\ <\ pcol\) yields state = \(i\) (interference cycle)  
If \(pcr\ \geq\ pcol\) yields state = \(c\), \(T\ =\ T\ +\ 1\), \(a\ =\ 0\)  
If no signal detected (after a certain time delay):  
state = \(d\), \(T\ =\ T\ 1\), \(pcol\ =\ pcol\ 1\) & \(\{hr\ =\ hr\ 1\) if \(a\ =\ 1\}\)  
Figure 2: Modified BA operation: tags and reader. **Step 2:** Each tag, which received the starting command \(Sc\), adjusts its counters \(ASC\) and \(pc\) and the hidden new flag (\(h\)) if \(ASC\geq pc\) (not recognized/identified tag) according to the reader feedback signal (state), as follows:  
If state = \(s\)  
If \(Ac\ >\ pc\) yields \(pc\ =\ pc\ +\ 1\)  
If \(Ac\ =\ pc\ \&\ rq\ =\ ID\) yields \(pc\ =\ pc\ +\ 1,h\ =\ 0\)  
If \(Ac\ =\ pc\ \&\ rq\ \
eq\ ID\) yields \(pc\ =\ pc\ +\ 1,h\ =\ 1\)  
If state = \(c\)  
If \(Ac\ =\ pc\) yields \(Ac\ =\ Ac\ +\ random\ integer\ (0,\ 1)\)  
If \(Ac\ >\ pc\) yields \(Ac\ =\ Ac\ +\ 1\)  
If state = \(d\)  
\(Ac\ =\ Ac-1\)  
If state = \(i\)  
do nothing  
If state = \(e\)  
If \(Ac\ =\ pc\ \&\ rq\ =\ ID\) yields \(pc\ =\ pc\ +\ 1,h\ =\ 0\)  
If \(Ac\ =\ pc\ \&\ rq\ \
eq\ ID\) yields \(pc\ =\ pc\ +\ 1,h\ =\ 1\)  
Then, if \(h\ =\ 1\) yields (\(pc\ =\ pcr,\ Ac\ =\ pcr\))  
Then, each tag transmits its response to the reader only if \(Ac\ =\ pc\) or waits until the condition is met. **Step 3:** The reader checks if \(T\ <\ pcr\) in order to terminate the ongoing frame  
If the condition is true  
If \(hr\ =\ -1\), the frame is terminating as follows:  
State=terminating command (\(tc\)),  
\(T=0\) if \(T=-1\), \(pcold\ =\ pcr\),  
\(est=z*est\ +\ (1\ \ z)\ *nc\) and \(Tx=T\ +\ ceil(0.88*est)\)  
If \(hr\ =\ 0\), \(T\ =\ pcr\), \(a\ =\ 1\), state = \(e\) (new parameter), and the reader transmits its feedback signal (\(e,\ pcr,\ and\ rq\)) to the tags and repeat steps 1 and 2 until \(T\ <\ pcr\) condition met. If the condition is false  
The reader transmits its feedback signal (state) to the tags and repeats steps 1 and 2 until \(T\ <\ pcr\) condition met. Analytical Analysis of MBA Protocol  
The identification delay of tag anti-collision protocols is defined as the number of slots from multiple cycles as discussed in BT and GBT analysis, or the number of cycles from multiple rounds as discussed in MBA analysis and the rest of paper for all protocols; the reader needs to identify all the tags in its interrogation zone. The identification delay of GBT protocol (the multiple cycles protocol without blocking and interference distinguish) was analyzed under the hypothesis that the capture effect probability is \(\alpha\)[4]. GBT consists of multiple BT cycles.