# Physical Layer Latency Management Mechanisms: A Study for Millimeter-Wave Wi-Fi
## 2 Latency Definition and the Ideal Case Study
### Analytical Derivation of Latency in the Ideal Scenario  
The only contribution to latency in an ideal scenario is caused by the finite signal bandwidth and the propagation speed of electromagnetic waves. All data processing in the PHY is assumed to be instantaneous. The data propagation speed through the channel comes close to 3 \(\times\)\(10^{8}\) ms\({}^{-1}\) when traveling through air. The resulting time delays are less than 100 ns at practical mmWave indoor communication distances of up to 30 m. Consequently, electromagnetic wave propagation delays are discarded early on. The remaining delay is attributed to the finite symbol rate of the communication standard. With the IEEE 802.11 ad channels occupying 2.16 GHz of the spectrum and providing 1.76 GHz of usable bandwidth, the symbol rate is limited to 1.76 Gsps. As a result, individual symbols take up roughly 0.57 ns of airtime. The otherwise small delay is magnified by long symbol sequences, prepended to the packet payload. The 4416-symbol long preamble, header, and initial guard interval (GI) cause a 2.5 us delay to the first data payload symbol. This delay further increases for each succeeding symbol by the sum of individual symbol delays before it, which also include a GI, prepended to every block of 448 data symbols. The worst case symbol delay dictates the total packet delay. Depicted in Figure 2, the waiting time for a single PPDU is associated with the reception of all of its data bits and the corresponding overhead. The preamble is skipped in aggregated PHY protocol data units (A-PPDUs). Figure 1: Observed latency: from an MPDU entering the PHY at the TX to its hand-off between the RX’ PHY and MAC layer. Reducing the MPDU delay is directly achieved by shortening the MPDU itself. Secondly, switching the modulation and coding scheme (MCS) will provoke different amounts of coding overhead and determine the number of bits carried per symbol. The ideal scenario analysis initially studies the combined MPDU length and MCS effects on MPDU latency. Equations (1) and (2) describe the incurred latency:  
\[Latency_{PPDU}=\frac{(L_{P}+L_{H}+L_{D}+64)}{1.76\,\mathrm{Gsps}} \tag{1}\]  
\[L_{D}=\lceil\lceil\frac{l}{672\cdot R_{c}}\rceil\frac{672}{448\cdot R_{m}} \rceil\cdot 512 \tag{2}\]  
where \(L_{P}\), \(L_{H}\), and \(L_{D}\) represent the length of the preamble, header, and data in symbols. Together with the final GI, and divided by the symbol rate, they yield the packet's latency. The length of \(L_{D}\) is calculated on the basis of the payload data length (\(l\)), code rate (\(R_{c}\)), and modulation rate (\(R_{m}\)). \(L_{P}\) and \(L_{H}\) take up 3328 and 1024 symbols, accordingly. The evaluated MCSs are listed in Table 2.  
Following the first part of the ideal case study, the payload length has been set to the highest value supported by the IEEE 802.11 ad PHY, 262.143 kB. This applies to all subsequent study steps. Long PPDU payloads are studied with the goal of analyzing high-throughput low-overhead transmission in more detail. Moreover, emphasis is put on XR use cases, where the data-hungry interactive streaming applications require multi-Gbps data rates. This is also the worst-case latency, as longer packets inherently feature longer transmission delays. Therefore, time-critical applications that require shorter payload transmission are expected to achieve lower latency. Given a \(10^{-5}\) BER, every 262 kB packet on average includes 21 bit errors. Real-time streaming applications in general allow for a certain extent of erroneous data as long as their throughput and latency requirements are met. Consequently, the \(10^{-5}\) BER threshold is kept as a reference throughout the manuscript. In PPDU aggregation, multiple PPDUs and their headers are appended to a single preamble. This decreases the relative overhead, while latency is described by Equation (3):  
\[Latency_{A-PPDU}=\frac{(L_{P}+N\cdot(L_{H}+L_{D}))}{1.76\,\mathrm{Gsps}}, \tag{3}\]  
where \(N\) stands for the total number of aggregated packets preceding the observed A-PPDUs.