# Physical Layer Latency Management Mechanisms: A Study for Millimeter-Wave Wi-Fi

^{*}

## Abstract

**:**

## 1. Introduction

#### 1.1. The Millimeter-Wave Spectrum for Time-Critical Applications

#### 1.2. Related Work on Latency Reduction

#### 1.3. Physical Layer Latency Probing

- PHY latency analysis: The dependency of time delays on PHY protocol data unit (PPDU) payload length, PPDU aggregation, the selected MCS, the employed demapping algorithm, and the number of LDPC decoding iterations is established
- Latency management mechanisms: Data transmission over an additive white Gaussian noise (AWGN) channel is carried out to study the trade-offs between the incurred latency and the resulting BER. The lowest achievable latency is determined in relation to PHY tuning parameters and using 10${}^{-5}$ as the BER constraint. Moreover, Pareto optimality in achieving minimal BER is addressed in light of different latency thresholds.
- Simulation framework: An open-source IEEE 802.11ad PHY latency and BER simulation framework has been designed during the course of the study. It closely complies with the WiGig standard, offers flexibility for future studies, and is shared in open access.

## 2. Latency Definition and the Ideal Case Study

#### 2.1. Physical Layer Latency

#### 2.2. Analytical Derivation of Latency in the Ideal Scenario

## 3. Latency-Inducing Receiver Digital Baseband

#### 3.1. Two Distinct Time Delays

#### 3.2. Performance Figure Derivation

#### 3.2.1. Noise and Channel Estimator

- Using the fast Golay correlation (FGC) algorithm [34] to calculate the cross-correlation between the received signal and the two known complementary Golay sequences $G{v}_{512}$ and $G{u}_{512}$. The process is repeated twice—once for each Golay sequence—and ultimately yields the channel input response (CIR).
- Converting the FGC results to the frequency domain via a fast Fourier transform (FFT) block, weighing them with $\frac{1}{2}$, and adding them together, forming the channel frequency response (CFR).
- Calculating the signal-to-noise ratio (SNR) using the CFR and the frequency-domain correlation results.
- Finally, obtaining the MMSE matrix using the CFR and SNR.

#### 3.2.2. Channel Equalizer

#### 3.2.3. Symbol Demapper

#### 3.2.4. LDPC Decoder

## 4. Simulation Environment

#### 4.1. Tracking Bit Errors

#### 4.2. Latency Probing

## 5. Results

#### 5.1. Steering the Physical Layer in an Ideal Scenario

#### 5.2. Including Physical Layer Latency and Channel Noise

#### 5.3. Tuning the RX DBB Components

## 6. Discussion

#### 6.1. Allowing More Iterations for Using up Additional Time

#### 6.2. Latency Versus Bit Error Rate

#### 6.3. Pareto Optimality

#### 6.4. Summary of Simulation Results

## 7. Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

## References

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**Figure 1.**Observed latency: from an MPDU entering the PHY at the TX to its hand-off between the RX’ PHY and MAC layer.

**Figure 3.**IEEE 802.11ad PHY receiver digital baseband. Above each component lies its input buffer with the corresponding base unit size noted on its left. Solid connections show data propagation paths, while dashed lines correspond to flag indicators. The processing operations contributing to latency beyond the finite symbol rate are written in bold. Those with additional control over the inflicted latency are colored in blue.

**Figure 5.**Task execution flow in the channel and noise estimation block. Vertical task stacking represents parallel execution.

**Figure 6.**Two-part error and latency simulation framework. Blocks with a dashed outline change depending on the study step, while the number of decoder iterations is passed on between the two parts.

**Figure 7.**Difference between the blocks in the bit error simulation process, dependent on the study step.

**Figure 9.**From left to right: latency’s dependency on the MCS and payload length (

**a**); Increase in latency per each additional kB of data, dependent on the MCS (

**b**). White curves represent latency isohypses.

**Figure 10.**Counterclockwise from top left: incurred BER during transmission (

**a**); average number of executed decoding iterations (

**b**); resulting MPDU latency (

**c**). Obtained using the decision threshold demapper and allowing up to 10 LDPC decoding iterations. The dashed line in (

**a**) represents the ${10}^{-5}$ BER limit, as defined by 5G NR.

**Figure 11.**MPDU latency for exact, approximative, and decision threshold demapping. The maximum number of decoding iterations is 10.

**Figure 12.**From left to right: incurred MPDU latency (

**a**) and BER (

**b**) when setting the largest allowed number of LDPC decoding iterations to 100. MCS colour codes are the same as in previous figures. The white region on the left subplot represents the expected latency region, governed by MCS and $\frac{{E}_{b}}{{N}_{0}}$.

**Figure 13.**Minimal achievable latency at different channel noise levels and maximum allowed number of LDPC decoding iterations. The colour represents the MCS at which minimal latency was achieved.

**Figure 14.**From the top down and left to right: incurred latency when increasing the number of allowed decoding iterations (

**a**); resulting BER for given MCS and $\frac{{E}_{b}}{{N}_{0}}$ combinations—the latter is represented by line width (

**b**); BER difference when comparing 1- to 10- (

**c**) and 10- to 100 decoding iterations (

**d**).

**Figure 15.**Trade-off between latency and BER at two distinct MCS and $\frac{{E}_{b}}{{N}_{0}}$ combinations. Marker size represents the average number of incurred iterations, ranging from 1 to 4.75. The grey curve represents a reference $\frac{1}{x}$ function fitted to the data points. Both Y-axes are rounded to two decimal points. The 0.13 µs MCS 2 latency difference from top to bottom is contained within the roundoff.

**Figure 16.**From left to right: Pareto optimal latency points with regard to the 10${}^{-5}$ BER constraint; Pareto optimal curves for achieving minimal BER at different maximal latency constraints. Colours represent the MCS at which the Pareto optimal points are achieved.

**Figure 17.**Selection of points with minimal latency that satisfy the ${10}^{-5}$ BER constraint. Colours represent the MCS at which the Pareto optimal points are achieved, the expected latency region is highlighted by the white polygon on the back plane, and iteration-independent optimal points are circled in grey.

**Figure 18.**Left to right: comparison of expected latency regions (

**a**); BER comparison for the two PHY simulation cases (

**b**), with the left and right parts of the distributions corresponding to study steps 2 and 3, respectively.

Industry | Application | Max. Latency (ms) | Latency Type | Ref. |
---|---|---|---|---|

XR | VR entertainment | 20 | RTT and E2E | [4,5] |

Professional AR/MR usage | 10 | RTT and E2E | [6,7] | |

V2X, UVs | Platooning | 25 | RTT | [6,8,9] |

and | Remote control | 10 | E2E | [6,7,8,9] |

drones | Cooperative driving/flight | 10 | RTT | [6,7,8,9] |

i4.0 | Remote control and monitoring | 50 | E2E | [10] |

Cooperative robots | 1 | RTT | [10] |

BPSK | QPSK | 16QAM | 64QAM | |
---|---|---|---|---|

$\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$2$}\right.$ | 2 | 6 | 10 | / |

$\raisebox{1ex}{$5$}\!\left/ \!\raisebox{-1ex}{$8$}\right.$ | 3 | 7 | 11 | 12.3 |

$\raisebox{1ex}{$3$}\!\left/ \!\raisebox{-1ex}{$4$}\right.$ | 4 | 8 | 12 | 12.4 |

$\raisebox{1ex}{$13$}\!\left/ \!\raisebox{-1ex}{$16$}\right.$ | 5 | 9 | 12.1 | 12.5 |

**Table 3.**Throughput performance metrics and demapping algorithms associated with the three different demapper instances. The throughput applies to five parallel demappers, as described in the corresponding references. All throughput values and the set of demapping equations in the last row correspond to 16QAM mapping.

Name | Throughput ($\frac{\mathit{MLLR}}{\mathit{s}}$) | Demapping Algorithm | Ref. |
---|---|---|---|

Exact | 800 | $LLR\left[k\right]=ln{\displaystyle \frac{{\sum}_{i=0}^{{2}^{M}-1}\phantom{\rule{0.277778em}{0ex}}exp(-\frac{1}{2{\sigma}^{2}}\phantom{\rule{0.166667em}{0ex}}\xb7\phantom{\rule{0.166667em}{0ex}}\parallel r-{c}_{i,1}{\parallel}^{2})}{{\sum}_{i=0}^{{2}^{M}-1}\phantom{\rule{0.277778em}{0ex}}exp(-\frac{1}{2{\sigma}^{2}}\phantom{\rule{0.166667em}{0ex}}\xb7\phantom{\rule{0.166667em}{0ex}}\parallel r-{c}_{i,0}{\parallel}^{2})}}$ | [36] |

Approximative | 3030 | $LLR\left[k\right]=\frac{1}{2{\sigma}^{2}}\phantom{\rule{0.166667em}{0ex}}\xb7\phantom{\rule{0.166667em}{0ex}}[min(\parallel r-{c}_{i,0}{\parallel}^{2})-min(\parallel r-{c}_{i,1}{\parallel}^{2}\left)\right]$ | [37] |

Decision threshold | 6640 | $LLR\left[0\right]=\frac{1}{2{\sigma}^{2}}\phantom{\rule{0.166667em}{0ex}}\xb7\phantom{\rule{0.166667em}{0ex}}Re\left(r\right)$ $LLR\left[1\right]=\frac{1}{2{\sigma}^{2}}\phantom{\rule{0.166667em}{0ex}}\xb7\phantom{\rule{0.166667em}{0ex}}(2-|Re\left(r\right)\left|\right)$ $LLR\left[2\right]=\frac{1}{2{\sigma}^{2}}\phantom{\rule{0.166667em}{0ex}}\xb7\phantom{\rule{0.166667em}{0ex}}Im\left(r\right)$ $LLR\left[3\right]=\frac{1}{2{\sigma}^{2}}\phantom{\rule{0.166667em}{0ex}}\xb7\phantom{\rule{0.166667em}{0ex}}(2-|Im\left(r\right)\left|\right)$ | [38] |

**Table 4.**Total MPDU latency without aggregation (0) and when appending a single A-PPDU (1), per MCS index. All values are in milliseconds.

A-PPDU | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 12.1 | 12.3 | 12.4 | 12.5 |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|

0 | 2.73 | 2.18 | 1.82 | 1.68 | 1.36 | 1.09 | 0.91 | 0.84 | 0.68 | 0.55 | 0.46 | 0.42 | 0.37 | 0.31 | 0.28 |

1 | 5.45 | 4.36 | 3.63 | 3.36 | 2.73 | 2.18 | 1.82 | 1.68 | 1.37 | 1.09 | 0.91 | 0.84 | 0.73 | 0.61 | 0.56 |

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**MDPI and ACS Style**

Marinšek, A.; Delabie, D.; De Strycker, L.; Van der Perre, L.
Physical Layer Latency Management Mechanisms: A Study for Millimeter-Wave Wi-Fi. *Electronics* **2021**, *10*, 1599.
https://doi.org/10.3390/electronics10131599

**AMA Style**

Marinšek A, Delabie D, De Strycker L, Van der Perre L.
Physical Layer Latency Management Mechanisms: A Study for Millimeter-Wave Wi-Fi. *Electronics*. 2021; 10(13):1599.
https://doi.org/10.3390/electronics10131599

**Chicago/Turabian Style**

Marinšek, Alexander, Daan Delabie, Lieven De Strycker, and Liesbet Van der Perre.
2021. "Physical Layer Latency Management Mechanisms: A Study for Millimeter-Wave Wi-Fi" *Electronics* 10, no. 13: 1599.
https://doi.org/10.3390/electronics10131599