Adaptive Repetitions Strategies in IEEE 802.11bd

A new backward compatible WiFi amendment is under development by the IEEE bd Task Group towards the so-called IEEE 802.11bd, which includes the possibility to transmit up to three repetitions of the same packet. This feature increases time diversity and enables the use of maximum ratio combining (MRC) at the receiver to improve the probability of correct decoding. In this work, we first investigate the packet repetition feature and analyze how it looses its efficacy increasing the traffic as an higher number of transmissions may augment the channel load and collision probability. Then, we propose two strategies for adaptively selecting the number of transmissions leveraging on an adapted version of the channel busy ratio (CBR), which is measured at the transmitter and is an indicator of the channel load. The proposed strategies are validated through network-level simulations that account for both the acquisition and decoding processes. Results show that the proposed strategies ensure that devices use optimal settings under variable traffic conditions.


I. INTRODUCTION
Vehicle-to-everything (V2X) communications will play a key role to address the so-called vision zero for traffic safety, where there will be no more deaths on the road. In current implementations, V2X is used by vehicles to inform the neighbors about their own status and movements; in the future, the exchanged packets will include information about the sensed environment and coordinating manoeuvres. After decades of researches and experiments [1], [2], the IEEE 802.11p-based V2X is reaching the mass market. 1 Given the increased interest on V2X and the necessity to improve its efficiency and reliability, a new IEEE WiFi Task Group called "bd" was established, which is expected to publish the new amendment by the end of 2022. The so-called IEEE 802.11bd is designed with the following objectives: i) improved performance, with higher spectral efficiency (meaning higher data-rate), increased reliability, and extended range; and ii) smooth transition between IEEE 802.11p and IEEE We would like to thank the China Scholarship Council that is supporting Wu Zhuofei during his visiting scholarship at the University of Bologna. 1 At the beginning of 2021, the first cars started being sold in Europe with on-board units (OBUs) implementing ITS-G5, based on IEEE 802.11p, as standard equipment and over 6000 km of roads were already covered by commercially distributed road side units (RSUs) with the same technology (source: C-Roads at C2C-CC Forum, November 2020). 802.11bd, with attention to coexistence, backward compatibility, interoperability, and fairness, allowing to switch when needed between the legacy mode (i.e., IEEE 802.11p) and the Next Generation V2X (NGV) mode (i.e., IEEE 802.11bd).
The main features introduced by the IEEE 802.11bd are [3], [4]: new modulation and coding schemes (MCSs) based on low-density parity-check (LDPC) or dual carrier modulation (DCM); a known pilot sequence located periodically in the data part of the signal, which is called midamble and allows to improve the channel estimation when large packets are transmitted; the possibility to use channel bonding; the possibility to use mmWave bands; and, finally, to blindly retransmit the same packet up to three times more as a burst.
Retransmissions are in general a commonly used method to increase the packet reception ratio (PRR), especially in the unicast communications where acknowledgments messages can be sent back from the receiver. Differently, when transmissions are performed in broadcast like in most V2X scenarios, the presence of multiple receiving stations makes it difficult to determine if and when to perform retransmissions. Nonetheless, the 3GPP in its long term evolution (LTE)-V2X and 5G new radio (NR)-V2X sidelink added the possibility to perform the so-called blind retransmissions, which correspond to the transmission of the same content more than once based on a decision made a priori by the transmitter, independently on what happens at the receiver [5], [6].
IEEE 802.11bd introduces the possibility of blind retransmissions, hereafter called repetitions, which may be more effective than simply lowering the MCS, especially in case of sporadic and strong interference or in case of high velocity conditions and deep fade. Specifically, up to three repetitions can follow the first transmission of the packet, which all carry exactly the same data (therefore, at most four copies of the same content can be overall sent). For legacy IEEE 802.11p receivers, the probability of correct decoding of the packet is inherently improved by the increased time diversity. Additionally, IEEE 802.11bd receivers can detect the repetitions and use maximum ratio combining (MRC) on the received signals to further increase the reliability of the communication.
This feature appears relevant to increase reliability and range, but comes at the cost of an increased channel load. Therefore, the choice to use it or not is subject to a trade- Fig. 1. An example of transmission with two repetitions. At the packet generation, the channel is sensed busy. Once the busy condition ends, the transmission starts after sensing the medium idle for a time interval (AIFS) followed by the random backoff. Two repetitions follow the first transmission, separated by a time gap (SIFS, which is shorter than the AIFS). Each transmission starts with a preamble indicating the presence of the packet. off which has not yet been deepened in the literature. Indeed, most of the existing studies explore the physical layer aspects of packet repetitions, i.e., looking at probability of correct reception of a generic link without interference, see e.g. [4] and related works, whereas only [7] provides early results on the impact of packet repetitions at a network level.
In this work, we analyse the impact of the repetitions on the performance from a network point of view, considering different channel models, varying the vehicles' densities, and including the effects of preamble detection (i.e., considering that the received signals can only be combined when their preambles are detected). Then, we propose two adaptive strategies, called deterministic and probabilistic, to opportunistically set the number of repetitions in order to maximise the network performance. The proposed approach is distributed, as it leverages on an adapted version of the channel busy ratio (CBR), which is a metric already measured at each single node. Results, obtained by the use of an open source simulator, show that the proposed approach is effective and enables fair access to the channel.

II. REPETITIONS IN IEEE 802.11BD
As a feature of IEEE 802.11bd, up to three repetitions can be optionally performed after the first transmission of the packet. More specifically, as exemplified in Fig. 1, a station accesses the channel through the carrier sense multiple access with collision avoidance (CSMA/CA) mechanism which requires that the medium is idle for at least an arbitration interframe space (AIFS); the repetitions that may follow the first transmission are then separated by a time gap lasting a short inter-frame space (SIFS), which is shorter than the AIFS, thus ensuring that the use of the channel is not released.
In 802.11bd, each packet consists of preamble and data field. The receiver can decode the data field only if it firstly detects the preamble. At the receiver side, once the packet is correctly decoded, the subsequent repetitions are ignored. Otherwise, the receiver can store the signals of the undecoded packets for which the preambles are detected. Such stored signals can be combined through MRC to improve the probability of correct reception of the packet. Note that if the preamble is not detected, the receiver is not aware of the presence of the signal and cannot perform the storage and MRC.
The signal-to-interference-plus-noise ratio (SINR) corresponding to the j th transmission can be modeled as where P rj is the received power; P n is the average noise power; I j is the set of nodes that are interfering with the reception under examination; and P Iji is the average power from the i th interferer. Then, the average SINR of the signals combined by the MRC receiver can be modeled as where M is total number of transmissions, including the first transmission and the repetitions; α j = 1 if the preamble is detected, otherwise α j = 0.

III. REPETITION STRATEGIES
In this Section, we first introduce a general approach for the setting of the number of repetitions based on the channel load and then specify two strategies (called deterministic and probabilistic) that can be distributively applied by the stations.
Net channel busy ratio. The decision on the number of repetitions N rep to be transmitted needs to be made autonomously by each station, based on its knowledge about the channel load. To this aim, the station already collects what is called CBR [8], which is a metric used for congestion control and is defined as the average time for which the signal received from the other stations has a power above a given threshold θ CBR , and it is updated every T CBR . However, the CBR depends on the number of repetitions, and therefore we here define the net CBR, also updated every T CBR , calculated as where T CBR is the duration of the observation and T net is the sum of the intervals during T CBR where the first detected copy of a packet is received and the power of the received signal is above the threshold θ CBR . The use of the net CBR in place of the total CBR is necessary to avoid a loop triggering, in which the decision on the number of repetitions relies on a metric which in turn depends on the decision itself. Note also that the identification of the first copy of a packet is easily performed by the receiving station, since the repetitions that follow are spaced by a short SIFS gap. Approach of the strategies. We propose two strategies where each station autonomously sets the number of repetitions so that a target performance metric ψ Nrep (γ) is optimized. The target performance metric ψ Nrep (γ) (which can represent, e.g., the maximum distance for a given PRR) is a function of the net CBR, and also depends on the number of repetitions N rep . In both the proposed strategies, the average number of repetitions N rep (γ) is first evaluated as a non-increasing function of the net CBR, with the net CBR domain divided into intervals. Then, the number of repetitions N rep is determined based on N rep (γ). Following this approach, we first define the net CBR intervals and then specify the function N rep (γ) for the two strategies and the value of N rep deriving from it.
Net CBR intervals. For a fixed number of repetitions N rep , it is expected that the performance ψ Nrep (γ) decreases with γ. In fact, an increase of the data traffic (e.g., higher vehicle density, larger packets, more frequent packet generation), which corresponds to an increase of the net CBR γ usually degrades the communication performance. Moreover, if the channel is not congested (lower values of γ), an increase of the repetitions can benefit the performance (i.e., ψ N +1 (γ) > ψ N (γ) for lower values of γ). Differently, under a higher channel load, a further increase of repetitions can degrade the performance (i.e., ψ N +1 (γ) < ψ N (γ) for higher values of γ). The value of γ where ψ N +1 (γ) and ψ N (γ) intersect thus represents a threshold below which N + 1 repetitions are preferable than N and above which the opposite is true.
Based on such considerations, we divide the net CBR domain [0, 1] into N max + 1 intervals, where N max is the maximum number of repetitions. Specifically, if the CBR falls within the i th interval, the best option is to mostly use i − 1 repetitions. The i th interval is defined as [γ * i , γ * i−1 ), with the threshold γ * i defined as: where we define x [ H L max (L, min (x, H)) to simplify the notation, and where γ * 0 1, γ * Nmax 0, and Equation (4) guarantees that the thresholds are correctly ordered. If γ * i = γ * i−1 , it simply means that transmitting i − 1 repetitions is not convenient.
Deterministic strategy. In the deterministic strategy, the station transmits an average number of repetitions that is a step function of γ, i.e.
and i = 0, 1, . . . , N max . The average number of repetitions for the deterministic strategy is exemplified in Fig. 2. The number of repetitions N rep is then deterministic and equal to N rep (γ).
Probabilistic strategy. In the probabilistic strategy, the average number of repetitions N rep (γ) follows a piece-wise linear function. Specifically, the station transmits an average number of repetitions equal to Nmax Nmin (7) where N min = 0 and . The average number of repetitions for the probabilistic strategy is exemplified in Fig. 2.
The vehicle then determines N rep as a random variable equal to where δ(γ) is a Bernoulli random variable equal to 1 with probability p(γ) = N rep (γ) − N rep (γ) . This definition implies that δ(γ) = 1 with probability p(γ) = 0.5 when the CBR value γ equals any of the thresholds γ * i (the orange points in Fig. 2). When the CBR is between two thresholds, such probability varies linearly with γ. The piecewise function for γ below γ * Nmax and above γ * Nmin+1 maintains the slope of the adjacent intervals until reaching the maximum (N max ) and minimum (N min ) values, respectively. As an example, when γ = γ * 2 , the average number of repetitions is 1.5, i.e. the station sets 1 repetition with probability 0.5 and 2 repetitions otherwise.

IV. RESULTS AND DISCUSSION
In this section, we first assess the impact of repetitions assuming that all nodes adopt the same number of repetitions, and considering different modeling of the preamble detection and propagation models. Then, we show the effect of both the proposed strategies assuming a fully distributed decision. A modified version of the open source simulator WiLabV2Xsim is used [6]. 2 Table I shows the main simulation settings.

A. On the impact of preamble detection
As described in Section II, the packet consists of preamble and data field. The receiver tries to decode the data field only if it first detects the preamble. Otherwise, the packet is treated as noise. This means that the receiver is not always able to store all the copies, as assumed in related work where the preamble detection process is not taken into account. This is especially true with a small difference between the min. power to detect the preamble and the min. power to decode the packet. 3 Fig . 3 shows the effect of preamble detection when the vehicle density is 5 veh./km. The solid and dashed lines are obtained with or without considering the preamble detection, respectively. When the distance is large (e.g., 700 m), even if more repetitions would in principle increase the overall SINR thanks to MRC (as shown by the dashed curves), the received power is mostly insufficient to detect the preamble and therefore the real improvement due to multiple transmissions is limited (solid curves). The results show that the preamble detection has a notable impact on the performance.

B. Threshold setting
With the aim to determine the thresholds, the performance when all the vehicles adopt the same number of repetitions times chose by all vehicles at the same time is investigated in Fig. 4, where the range, defined as the maximum distance to have PRR > 0.90, is shown varying the net CBR γ. In Fig. 4, two different propagation models are adopted to verify the generality of the derived results. In particular, in addition to the WINNER+, scenario B1 model, which is normally adopted for these kind of studies and used in the rest of the paper, also the modified ECC Report 68 rural described in [10] is here considered. By comparing dashed and solid curves, results show that, apart from a scale factor on the distance, the impact of repetitions is similar for the two propagation models when looking at the net CBR. This means that the applicability of the derived thresholds and the performance trends that follow are not limited to the specific settings adopted in this work.
As expected, Fig. 4 confirms that in a low load scenario the transmission of more repetitions improves the performance, whereas it has a negative impact when the channel load is higher. For example, if we focus on the case of net CBR larger than approximately 0.09, we note that it is preferable that all stations do not use any repetitions compared to the case where all the stations transmit one repetition (the two cases have the same net CBR by definition).
Given these results and adopting the interval setting process explained in Sec. III, the three thresholds are set as γ * 1 = 0.09, γ * 2 = 0.05, γ * 3 = 0.03. C. Performance of the proposed strategies Fig. 5 shows the range varying the vehicle density, assuming either all the stations adopt the same and fixed number of repetitions, or all the stations adopt one of the strategies detailed in Sec. III. Please note that in the simulations the stations are completely unsynchronized and the intervals of duration T CBR used to calculate the CBR are independent among the stations. It can be noted that both the deterministic and probabilistic strategies, for any value of the density, approximately provide the same performance as the best solution with a fixed number of repetitions, therefore demonstrating the validity of the proposed approach.
Even if both strategies are effective to optimize the network performance, the probabilistic strategy allows a better distribution of the number of repetitions. This is shown through Fig. 6, which illustrates the impact of the two repetition strategies over time and space in a sample simulated interval. The two bottom-side subfigures are zooms of the upper-side ones. In each subfigure, the y-axis represents the location of the stations and the x-axis the time; the colors indicate the number of repetitions set by the station located in that position at that time. The figure shows that with the deterministic strategy the vehicles tend to maintain the same number of repetitions for longer intervals than with the probabilistic strategy; for example, looking at magnified parts in the lower subfigures, with the deterministic strategy all stations keep using 2 repetitions except a single one, which keeps using only 1 and is therefore penalized; a variable and thus fairer number of repetitions is instead selected by all stations in the probabilistic case.

V. CONCLUSION
Considering the possibility added by IEEE 802.11bd to transmit more than one replica of the same packet to improve the reliability of V2X communications, in this paper we proposed two strategies to let each station set the number of repetitions in a fully distributed way based on local measurements of the channel load, with the objective to maximize the network performance. The effectiveness of the proposed strategies is validated through network-level simulations performed in complex scenarios where each station autonomously performs the selection under variable conditions.