# Performance Evaluation of IEEE 802.11 ah Networks With High-Throughput Bidirectional Traffic
## 4 Performance Evaluation and Discussion
### Theoretical Limits  
The duration of a single packet transmission \(t_{TX}\) at the 2 MHz channel with a short preamble is:  
\[t_{TX}=240~{}\upmu\text{s}+40~{}\upmu\text{s}\cdot N_{SYM}, \tag{6}\]  
with 240 \(\upmu\)s being the sum of preamble duration (160 \(\upmu\)s) and the SIGNAL field duration (80 \(\upmu\)s), 40 \(\upmu\)s the Orthogonal Frequency-Division Multiplexing (OFDM) symbol duration with normal guard interval and \(N_{SYM}\) the number of symbols for Binary Convolutional Code (BCC) encoding defined as:  
\[N_{SYM}=\left\lceil\frac{22 bits+8\cdot l}{N_{DBPS}}\right\rceil, \tag{7}\]  
where  
\[N_{DBPS}=DR\cdot 40~{}\upmu\text{s}. \tag{8}\]  
In Equations (7) and (8), 22 \(bits\) is the sum of bit-lengths of the _Service_ field and the tail bits per BCC encoder, \(l\) is the packet-size in bytes and \(DR\) is the data rate. The time needed to ensure successful transmission \(t_{TX}^{total}\) includes SIFS (160 \(\upmu\)s) and ACK (480 \(\upmu\)s) durations, and is expressed as:  
\[t_{TX}^{total}=t_{TX}+160~{}\upmu\text{s}+480~{}\upmu\text{s}. \tag{9}\]  
The RAW slot duration must be longer or equal to the transmission time of a segment (cf., Table 5) in order to allow a non-zero probability for successful transmission. The maximum number of transmissions in one beacon interval is:  
\[N_{TX_{mx}}^{b}=\left\lfloor\frac{N_{TIM}\cdot T_{TIM}}{t_{TX}^{total}} \right\rfloor. \tag{10}\]  
Assuming all packets have the same size on average and RAW(s) is (are) occupying the entire channel time. Figure 13: With two TIM groups and 10 RAW slots, up to 70% of all downlink packets can be immediately transmitted (AP reply) avoiding the need to wait until after the next DTIM beacon, thus halving the RTT. The packet-size \(l\) in the IP camera experiments equals the sum of the payload encapsulated in the TCP segment and 90 bytes of overhead (32 bytes for the TCP header, 20 bytes for the IPv4 header, eight bytes for LLC, 26 bytes for WLAN quality of service data and four bytes for the frame) if there is no IP fragmentation. 2680 and 3216 byte TCP segments need IP fragmentation and are broken into two smaller data segments: \(2272+440\) for 2680-byte segments and \(2272+976\) for 3216-byte segments. This fragmentation results in an overhead of 58 bytes per fragment (32 bytes of TCP header are included in fragments). The transmission duration for each fragment is then calculated using the packet size of the fragment (i.e., 2272 bytes of data +58 bytes of overhead). Note that \(N_{TX_{max}}^{b}\) successful transmissions cannot be guaranteed only with allowing enough time in RAW because stations employ random channel access. [PERSON] et al. (2017) proposed a model for calculating of transmission success probability. However, they assume each station has only one packet to transmit during its RAW slot (only uplink traffic, without TIM); thus, the model is not applicable for the case with TIM segmentation and DL data. The round trip time is largely influenced by TIM segmentation. In our experiments, stations exchange data with a server at the AP. Therefore, the RTT is at least 2\(T_{DTIM}\), unless an immediate reply is implemented. If stations would partake in bidirectional communication with each other, the minimal RTT would be 4\(T_{DTIM}\) since four hops are needed for a packet to complete the loop. Due to random channel access, these times will be often longer. Therefore, \(T_{DTIM}\) must be at least two or four times smaller than the smallest sampling interval in the sensor network in order to complete one transaction before the start of the next one, as in a reliable monitoring scenario. Taking into account the previous calculations, the maximum possible data rates achievable in reality are somewhat smaller than those specified by the standard.