With the explosive growth of vehicles on road, safety has become a major concern for future intelligent transportation systems (ITS) . Statistical data show that the number of crashes in the United States is nearly million each year . Vehicle-to-Everything, abbreviated as V2X, is a promising means to cut the road toll . Through V2X, all the entities on the road (e.g., vehicles, road side units and pedestrians) are connected, hence, they can exchange safety messages and cooperate to prevent road accidents or cut down fatality and injury rates when they do occur.
Safety messages in V2X can be classified into two categories: 1) heartbeat messages. Each on-road node periodically broadcasts heartbeat messages to declare its existence, current state and environment information. Receiving nodes can then evaluate whether there are hazards from information disseminated by transmitters and data gathered from the environment. 2) event-driven messages. Safety in V2X is not limited to passive evaluation of the received heartbeats. An on-road node encountering unexpected events could actively broadcast event-driven messages so that the surrounding nodes can respond quickly. Typical events that may induce event-driven messaging include lane change, roadwork, ambulance approach, to name a few.
Among event-driven messages, life-critical warning messages (hereinafter, referred to as warning messages) deserve particular attention . Warning messages are triggered by extreme traffic emergencies that are likely to cause casualties, e.g., hard braking on the highway, imminent crash, and swerving vehicles at the opposite lane. Typically, a warning message contains the following data : node ID ( bytes), message generation time ( bytes, modulo one minute, with resolution ), message type ( bytes, e.g., braking, acceleration, steering) and message attributes ( bytes, e.g., for braking message type, the attributes could contain brake force, current vehicle speed and wheel state) for an aggregate of bytes.
Three important characteristics that distinguish warning messages from ordinary vehicular messages are as follows:
They are rare and sporadic. Statistics indicate that there are on average fatal crashes every million miles a vehicle travels .
Warning messages are short but multiple warning messages may arrive as a crowd in a batch. This is because a single emergency event can trigger multiple emergency responses from multiple nearby nodes. As a result, these emergency nodes (typically less than ) can broadcast multiple warning messages simultaneously.
They must be delivered with high certainty in short order. According to the automotive white paper from 5G-PPP , the maximum tolerable end-to-end delay of these safety-of-life messages is ms, and the maximum tolerable message loss rate within ms is .
We refer to these three message characteristics as sporadicity, crowding, and ultra-time-criticality.
In V2X, safety messages are disseminated by simple means of one-hop broadcast. Multiple access control (MAC) designs are especially crucial if the stringent delay and reliability requirements are to be met. As shown in Fig. 1, the Federal Communications Commission (FCC) in the United States allocates MHz “5.9 GHz band” for V2X communication [5, 6], based on which many MAC protocols have been proposed and developed to support safety-message broadcasting [5, 6, 7, 8, 9]. However, existing schemes are designed primarily for heartbeat messages and conventional event-driven messages. When it comes to sporadic ultra-time-critical crowd messaging, none of them can meet the stringent delay and reliability requirements.
To fill this gap, this paper puts forth a medium-access control protocol tailored for the delivery of life-critical warning messages without exclusive allocation of wireless spectrum to them. Two underpinnings of our MAC protocol are as follows:
To address sporadicity efficiently, we build our MAC protocol upon an override network architecture whereby wireless spectrum originally allocated to regular vehicular network is used to deliver warning messages only when they appear. Specifically, no wireless spectrum is dedicated exclusively to warning messages since they rarely occur. A vehicle with warning messages will first send an interrupt message to pre-empt the transmission of regular vehicular messages so that the warning message can follow after that.
To address crowding and ultra-time-criticality, we use advanced channel access techniques to ensure delivery of warning messages within the stringent delay and reliability targets. In particular, in a life-threatening situation, multiple vehicles may have life-critical messages to send. A channel access protocol that does not incur excessive hand-shaking overhead to coordinate the transmissions of these vehicles on the shared spectrum is critical if the stringent delay target is to be met.
In short, the overall MAC protocol operates by means of interrupt-and-access. For wireless interrupt, we devise an interrupt mechanism for V2X in which the interrupt signals are spread spectrum sequences. Simulation results show that the missed detection rate (MDR) of the interrupt signals can be very small provided that the interrupt sequences are long enough, e.g., when the signal-to-interference ratio (SIR) is dB, a ms sequence ( symbols, MHz) can guarantee an MDR of . For channel access, we investigate two uncoordinated channel access schemes for reliable multiple access. Targeting for a message loss rate in our set-up, a simple multi-replica ALOHA scheme can support up to nodes. If the number of transmitters exceeds , a more advanced (and more complex) coded ALOHA scheme can potentially support up to nodes while keeping the message loss rate lower than .
The remainder of this paper is organized as follows: Section II reviews the state-of-the-art MAC protocols for V2X. Section III outlines our interrupt-and-access MAC protocol tailored for life-critical warning messages. Section IV presents our wireless interrupt protocol, and the design of interrupt signals on the ISM band. Section V presents two random channel access protocols for warning messages. Section VI concludes this paper.
Ii State-of-The-Art V2X MAC Protocols
Existing MAC protocols for V2X communications operate in either a distributed or a centralized manner111Some hybrid MAC designs, e.g., LTE-ProSe , support both distributed and centralized modes.. Centralized MAC designs, e.g., LTE-based MAC , have certain limitations: 1) Infrastructure could be a single point of failure. These MAC protocols may not function when infrastructure failure occurs or when vehicles are out of the coverage of the infrastructure (e.g., in blind zone, tunnels, and underground parking lots). 2) The coordination-based framework, e.g., schedule-before-transmit, does not fit delay-sensitive applications, owing to the extra delay and overhead consumed. Distributed self-organizing MAC designs are in general more suitable for ultra-delay-sensitive warning messages .
Ii-a IEEE 802.11p
Dedicated short-range communication (DSRC)  refers to the sets of standards on the 5.9 GHz band222The sets of standards in Europe are referred to as C-ITS . DSRC and C-ITS share similar PHY and MAC layers.. The MAC protocol in DSRC, i.e., IEEE 802.11p , is an amendment from IEEE 802.11a with enhanced distributed channel access (EDCA) Quality-of-Service (QoS) extension. In 802.11p, both heartbeat and event-driven messages share the MHz control channel (CCH) by means of carrier sensing multiple access (CSMA). In particular, different types of messages are assigned with different priorities: high-priority messages have smaller interframe spacing and backoff waiting time so that they have priority over low-priority messages in channel access.
There are three main reasons why 802.11p is not suitable for sporadic ultra-time-critical crowd messaging, even if we assign the highest priority to warning messages.
Delay concern – In 802.11p, messages with different priorities share the same control channel. When high-priority warning messages are generated, a low-priority message may be in the midst of occupying the channel. As a result, the warning messages must have to wait until the channel is idle. Furthermore, even if the channel is idle, multiple warning messages with the same high priority may compete for the channel simultaneously, leading to a high collision rate that may significantly increases the delay.
Lack of acknowledgment (ACK) – Warning messages are broadcasted for all vehicles in the vicinity of the warning-message generating vehicle. However, requiring an ACK from each one-hop neighbor of the broadcaster (potentially hundreds of nodes) can be highly costly. As a result, 802.11p does away with ACK for broadcast messages. This means that nodes cannot detect collisions and there is no retransmission. In other words, collisions mean packet loss, and this makes 802.11p highly unreliable. A simple calculation shows that, if we set the contention window to ( is already the maximum contention window for the access category with the highest priority ), the collision rate is as high as when there are warning-message transmitters, and this number increases to when there are transmitters.
Hidden node problem – To tackle the hidden node problem, RTS/CTS handshaking is implemented in conjunction with CSMA in IEEE 802.11a . However, in 802.11p, the hidden node problem is left unsolved, because for broadcast messages, the frequent RTS/CTS handshakes consumes too much resources. As a result, a warning broadcast message may collide with another warning broadcast message two hops away, leading to packet loss.
Ii-B TDMA-based MAC
As with IEEE 802.11p, VeMAC use the control channel (CH 178) in the 5.9 GHz band for both heartbeat and event-driven messages. This MHz channel is assumed to be time-slotted, and every slots are grouped together as a frame. In VeMAC, each node occupies at least one slot in every frame for the broadcast of its heartbeat message. If a node has an event-driven message to broadcast, it will need to acquire one more slot. In particular, the slots a node occupies must be different from the slots occupied by any of its neighbors within two hops (this guarantees that there is no hidden node problem). How nodes within two hops coordinate with each other and occupy different slots is an essence of VeMAC.
To enable sporadic ultra-time-critical crowd messaging in the context of VeMAC, all nodes can reserve one slot every ms to cater for the rare occasion when they have warning messages to broadcast. However, simple calculation indicates that this is not viable. Assuming the slot duration is , and therefore, there are slots available in ms, if there are nodes within two hops (in practice could be up to ), then all the slots are reserved by these nodes for warning messaging alone. Even if we assumed sparse nodes, reserving resources for warning messaging is quite inefficient, because warning messages are rare and sporadic.
Instead of exclusive reservation of slots, a node could attempt to acquire a slot only upon the generation of a warning message. However, slot acquisition under VeMAC takes one or more frames (a frame usually lasts for ms ), because the transmitter must wait for all its one-hop neighbors’ ACKs to make sure the new slot is free for it to use. Worse still, when there are nodes with warning messages, the interaction process for them to acquire different new slots can take an inordinate amount of time.
Iii An Override Architecture
Let us consider a typical V2X scenario where on-road nodes are communicating with each other on the 5.9 GHz band in an ad-hoc manner. Each node is equipped with two sets of half-duplex transceivers TRX and TRX. TRX is aligned to the MHz control channel (CH 178), on which nodes exchange heartbeat or conventional event-driven messages to get an overall perception of the environment. TRX is aligned to the MHz service channels (CH 175 and 181), on which nodes exchange non-safety messages, e.g., infotainment messages.
As illustrated in Fig. 2, an accident suddenly happens: a runaway vehicle violates the traffic light and runs to an opposite lane. This accident triggers the urgent reactions of nearby nodes, and each of them generates a life-critical warning message to warn its nearby nodes. For example, node brakes hard, triggering a warning message informing its neighbors (e.g., nodes and ) of its emergency braking caused by the runaway node , so that they could react in time to avoid further crashes.
These life-critical warning messages have stringent delay and reliability requirements. In this sense, we may need to assign them sufficient time-frequency resources, so that the stringent QoS requirements can be met. On the other hand, warning messages are sporadic and arrive once in a long while, hence, assigning them exclusive resources is highly inefficient, because these resources are wasted most of the time in the absence of life-critical events. This motivates us to build the warning-message MAC protocol upon an override network architecture, where life-critical warning messages share the MHz service channels with non-safety messages. In non-emergency situations, non-safety messages are the primary users on the service channels. When emergency arises, high-priority warning messages will override non-safety messages and seize the service channels333In practice, warning messages can override the whole MHz bandwidth or part of the bandwidth of the service channels, e.g., override only the MHz channel 181, so that non-safety messages would not be totally deprived of services..
As shown in Fig. 3, our override architecture operates by means of interrupt-and-access: nodes with incoming warning messages send interrupt signals to nodes transmitting non-safety messages to pre-empt them so that the nodes with warning messages can broadcast on the service channels. Sections IV and V provide the details of wireless interrupt and channel access, respectively.
Iv Wireless Interrupt
Interrupt is a technique widely used in computer systems for multitasking with different priorities. Specifically, an incoming high-priority task triggers an interrupt signal to the central processor, so that the processor can suspend the currently ongoing low-priority task and process the high-priority task immediately. Interrupt is rarely used in conventional wireless communication systems. It is, however, useful for our application scenario.
Iv-a Interrupt in V2X
In the vehicular network, if a node wants to broadcast a warning message successfully on the service channels, a prerequisite is that all its one-hop and two-hop neighbors are silent on these channels. The objective of wireless interrupt in V2X is to silent these neighbors (i.e., neighbors within two hops) in case they are halfway transmitting on the service channels.
To this end, two interrupt signals, a primary interrupt signal (PIS) and a secondary interrupt signal (SIS), are defined. For our MAC protocol, interrupts proceed as follows:
A node with a warning message to transmit first broadcasts a PIS.
Any node detecting the PIS then broadcasts a SIS.
Any node detecting a PIS or a SIS (except for nodes in iv) below) keeps silent on the service channels for ms, including nodes that are halfway transmitting on a service channel when the PIS or SIS is detected444For any neighbor within two hops of an emergency node, interrupt is successful as long as at least one interrupt signal is detected, whether it is PIS or SIS..
Any node that issues PIS, regardless of whether it receives a PIS/SIS from another node, then transmits its warning message during the channel access period following the interrupt period.
An example is given in Fig. 4, where the emergency node sends a PIS to pre-empt other nodes from using the service channels. The one-hop neighbors of are , and, the two-hop neighbors of are . First, node broadcasts the PIS. The instant ’s one-hop neighbors detect the PIS, they keep silent on the service channels. Further, the detection of PIS triggers each of them to broadcast an SIS, so that ’s two-hop neighbors can detect the SIS and keep silent on the service channels as well. Once they have received a PIS or a SIS, node A’s one-hop and two-hop neighbors will be silent on the service channels in the next ms, and node can broadcast the warning message in the channel access period safely.
Note that multiple overlapped PISs and SISs may be broadcasted simultaneously (e.g., when there are multiple warning-message transmitters). A node may detect the multiple PIS and SIS separately, and respond to each of the interrupt signal following rule iii).
Iv-B Interrupt signal design
We now present our designs for the PIS and SIS. Potentially, there are two alternatives: in-band interrupt and out-of-band interrupt. We could interrupt in-band555Another alternative to realize in-band interrupt is full duplex communication. However, full duplex communication requires dedicated full duplex transceivers, i.e., tailor-made RF chips with self-interference cancellation. Interrupt via full-duplex techniques is overkill, because unlike the receiver of a full-duplex link, the receiver of an interrupt does not need to receive a data stream in the reverse direction; it only needs to be able to detect the presence of an interrupt signal. by exploiting special features of non-safety signal on the service channels. For instance, assuming the non-safety messages are carried by OFDM signals, we could transmit the interrupt signal on the guard-band subcarriers.
This paper considers out-of-band interrupt. Specifically, we transmit interrupt signals on the 5.8 GHz ISM band. PIS and SIS are designed as spread-spectrum sequences  on this MHz band, so that they can be detected in the presence of interference.
Iv-B1 Interference on the 5.8 GHz band
The GHz ISM band (- GHz) is a free radio band centered on GHz, the channel characteristics of which is similar to that of the GHz vehicular band. The primary traffic on the 5.8 GHz band is Wi-Fi signal, and Wi-Fi are commonly deployed indoors.
To evaluate the interference of indoor Wi-Fi signal to our outdoor interrupt signal, we conducted an experiment over our campus to capture GHz Wi-Fi signal using USRP X310 (with BasicTX daughter board). The experimental data indicates that in the outdoor environment, 1) most of the time, the GHz band was calm and quiet, and nothing can be detected; 2) when Wi-Fi signal was detected on the GHz band, the signal power was much lower than the indoor power.
In one experiment, an access point (AP, Linksys EA6900) was deployed indoors. The AP used Wi-Fi channel 153 (5.765 GHz) with MHz channel bandwidth. We measured the received Wi-Fi signal intensities from the AP at two locations. The first location was indoor ( meters from the AP, LOS), and the second location was outdoor (straight distance meters from the AP, NLOS).
The Power Spectral Densities (PSDs) of the received signals captured indoors and outdoors are plotted in Fig. 5. As can be seen, there is a
-dB gap between them. In particular, for the outdoor signal, the signal-to-noise ratio (SNR) is aboutdB over the MHz ISM band.
Remark: The PIS and SIS designed in this paper are spread spectrum signals over the MHz ISM band. As will be shown later, the interference from the Wi-Fi captured in the experiment is negligible for the designed PIS/SIS signal as far as missed detection rate and false alarm rate are concerned.
Iv-B2 Interrupt signal design
This subsection presents the design of PIS and SIS on the GHz ISM band. We only explain the generation and detection of PIS in the following, SIS is generated and detected similarly.
The PIS consists of -point Zadoff-Chu (ZC) sequences  embedded in a -point maximum-length sequence (m-sequence ), for a total of samples. Denote the m-sequence by . Let be a ZC sequence given by
where , and is a positive integer coprime to . For our application, we set (the reason for choosing will be explained later).
Then, the -point PIS is generated by
where is the Kronecker product, and each element in is given by
for . In (2), the ZC sequence acts like a spread spectrum sequence with rate MHz, thereby spreading the power of the m-sequence over the MHz band.
The receiver computes two cross-correlations to detect the PIS. Given the received sequence (i.e., the MHz samples after ADC), the receiver first cross-correlates and as follows:
Note that the target interrupt signal is embedded in . Thus, in the presence of an interrupt signal, the operation in (3) produces peaks if we look at the absolute values of the resulting sequence , thanks to the correlation property of ZC sequences. Then, we make use of the m-sequence modulated on the ZC sequence, and accumulate the power of all peaks, yielding
Finally, a sharp peak emerges from the absolute values of sequence . The capture of this peak results in successful detection of PIS.
For the SIS, the same ZC sequence is used, but in place of , another -point m-sequence is used.
Remark: ZC sequences have a nice correlation property: the periodic autocorrelation function of a ZC sequence is zero everywhere except at a single maximum per period . However, when we modulate m-sequence onto ZC sequence, this nice correlation property no longer holds. To be specific, let us consider the first two ZC sequences in PIS.
If these two ZC sequences are modulated by same values or , then for , because a ZC sequence is orthogonal to its cyclic shift.
If these two ZC sequences are modulated by opposite values and , we show in Appendix A that
As can be seen, when the two adjacent ZC sequences in PIS are modulated by opposite values, the resulting cross-correlated signal is in general nonzero at . The cross-correlated signals for and are shown in Fig. 6. Among all possible , we found that setting minimizes the maximal interference as well as the overall interference . Thus, is set to to generate the ZC sequence.
Iv-C Performance evaluation
There are three components in the received sequence : the target interrupt signal, the Wi-Fi signal on the 5.8 GHz band as interference, and noise. If we fix the noise power, then the successful detection of interrupt signal depends on the amount of interference, or more precisely, the signal-to-interference ratio (SIR).
To evaluate the detection performance of our scheme under various SIR, we simulated the following single interrupter case: an interrupt node broadcasts a PIS, and this PIS triggers three SISs by one-hop neighbors of . For node ’s one-hop neighbors, detection of the PIS peak means a successful interrupt; for node ’s two-hop neighbors, detection of at least one SIS peak means a successful interrupt.
Performance metrics in our simulation are missed detection rate (MDR) and false alarm rate (FAR) . We set a threshold commensurate with the PIS (SIS) length (longer sequence corresponds to higher thresholds). Any entry in sequence above is considered as a peak. Moreover, the real data we collected outdoors only contains one Wi-Fi signal (SNR dB). For the simulation, we deliberately added additional Wi-Fi signal so that we can vary the SIR, and show the robustness of our system under even stronger interferences from Wi-Fi signals.
The MDR versus SIR (dB) are shown in Fig. 7, where we fix the received power of PIS and SIS to be equal to the noise power666In practice, a transmitter can evaluate the nearby Wi-Fi signal intensity before transmission, and adjust its transmitted power accordingly. (that is, dBm/Hz MHz dBm), and set different interference power to obtain the target SIR (e.g., for SIR dB, we set dBm).
Two observations from Fig. 7 are as follows: 1) The MDR of the interrupter ’s two-hop neighbors outperforms that of ’s one-hop neighbors, given the same PIS (SIS) length. This is intuitive because each of ’s two-hop neighbors has three chances to capture the SIS, while ’s one-hop neighbors only have one chance to capture the PIS777A caveat here is that if a one-hop neighbor did not detect the PIS, it is possible for it to detect SIS sent by another one-hop neighbor who detected the PIS, if and are within transmission range of each other. Thus, the MDR of a one-hop neighbor presented here is conservative.. 2) If we set as the required MDR, then setting can meet the requirement when SIR dB; setting can meet the requirement when SIR dB. Moreover, when , the number of symbols in PIS (SIS) is , and the overall time consumed by interrupt is about ms (the signal processing time is ignored).
We now evaluate the FAR versus interference power with the same simulation set-up as for Fig. 7. In this simulation, there is no interrupt signal, and the received sequence contains only interference and noise. The noise power is fixed to dBm as in Fig. 7, and the interference powers are set as in Fig. 7 (e.g., for SIR dB, we set dBm; for SIR dB, we set
dBm). FAR is defined as the probability that we detect a false alarm within a sample sequence of PIS (SIS) length (i.e.,samples). Thus, given a FAR, we can calculate the number of false alarms per hour by FAR MHz.
The FAR versus interference power under different thresholds are shown in Fig. 8. As can be seen, higher threshold yields better FAR performance. If we set , , the number of false alarms per hour is less than when dBm (corresponding to SIR dB in Fig. 7). Note that the consequence of a false alarm is only to keep silent on the service channel for ms.
Remark: If we use a long -point ZC sequence instead of our design in this paper (i.e., cascaded -point ZC sequences), the detection performance will be the same. However, long ZC sequences greatly increases the computational complexity. Specifically, 1) for our design, the two-step cross-correlation takes multiplication and addition; 2) for a long -point ZC sequence, one -point cross-correlation is needed, and it takes multiplication and addition.
V Channel Access
After interruption, the service channels are set aside for ultra-time-critical crowd messaging. The next problem is the channel access of multiple emergency nodes. Overall, we can summarize the problem as follows:
There are (out of ) active nodes. Typically, and .
All the active nodes intend to transmit a message ( Bytes) within ms, where is the time consumed by interrupts.
The available bandwidth is MHz. In practice, we may override only MHz so that the primary traffic of the service channels would not be clipped suddenly, and can still transmit on the other MHz channels.
Schedule-based channel access protocols, e.g., TDMA, FDMA, CDMA, OFDMA, requires pre-allocating orthogonal resources for the overall nodes . Let us take CDMA for instance. When operated with CDMA, all the nodes within two hops are pre-assigned different spread spectrum codes, e.g., PN codes, so that the spread spectrum signals from distinct nodes will not interfere with each other. For one thing, a background coordinator must run in all time to guarantee all the nodes within two hops use different PN codes; for another, since there is no prior information on the potential transmitters, a receiving node must despread the received signal using all the potential PN codes (up to a few thousands). This poses great challenges to the processing capacity of the receiver. In this context, random channel access protocols are preferable in our framework.
V-a Multi-replica ALOHA
A simple random-access protocol is ALOHA . However, ALOHA requires ACK to inform the transmitter whether the previous transmission is successful or not. As stated in the introduction, ACK is not viable for the broadcast scenario, because each broadcast requires feedback from all one-hop neighbors, incurring excessive overhead when the network is dense, hence compromising the ability to meet the critical time constraint.
One alternative is multi-replica ALOHA. The basic idea is that, since transmitters cannot determine whether their transmissions are successful or not given the lack of ACK, they can replicate their warning packet times and randomly broadcasts these replicas within ms. If one or more replicas from a node are broadcasted without any collision, then the delivery of the warning message is considered successful. An example is given in Fig. 9, in which , and three transmitters , and broadcast four replicas, respectively. In this example, only replica is clean. Thus, only node successfully broadcasts its warning message while nodes and fail.
V-A1 Message loss rate
To analyze the performance, we first derive a probability : for any two nodes and , is defined as the probability that a particular ’s replica, say , does not collide with any of ’s replicas. For multi-replica ALOHA, as follows is derived in Appendix B:
is the probability that is clean with respect to ’s messages. By our independence assumption, is also the probability that is clean with respect to any other node’s messages and that is the probability that is clean with respect to all other node’s messages.
As a result, the probability that node can broadcast its warning message successfully, denoted by , is equal to the probability that one or more replicas from node are clean. That is,
wherein an approximating assumption is made that all replicas from node A have independent collision probabilities. This approximation is valid when .
We note that is the “message success rate” , defined as the number of successful nodes over the number of all emergency nodes. Thus, the “message loss rate” is
V-A2 Numerical results
To evaluate the multiple-access performance of Multi-replica ALOHA, we consider a specific OFDM-based PHY layer, the parameters of which are given in Table I . In particular, 1) we assume warning messages override half of the service channels, i.e., MHz, so that the non-safety messages would not be totally deprived of services. 2) A typical Byte warning message occupies two OFDM symbols, leading to a warning packet at the PHY layer (each OFDM symbol is and the preamble is ). 3) The time for interruption is ms, hence, the available time for channel access is ms.
|available data subcarriers|
|channel code rate|
|OFDM symbol duration|
|warning message size||Bytes|
|warning packet duration|
|Overall TTL of warning messages||ms|
|Time consumed by interruption||ms|
|Time left for channel access||ms|
Following (8), the numerical results of is plotted in Fig. 10. We also simulate a system to verify the accuracy of given by (8). It turns out that the simulated matches with Fig. 10 very well, and the approximation in (7) is very accurate in our set-up.
Two observations from Fig. 10 are as follows:
For different numbers of emergency nodes , Fig. 10 shows that the optimal performance (i.e., the minimum ) is obtained by different duplication factors . For example, when , the optimal , and when , the optimal . We show in Appendix C that the optimal can be approximated by
Given as the target performance, the maximal number of sustainable nodes in multi-replica ALOHA is . More generally, given a target message loss rate , the maximal number of sustainable nodes in multi-replica ALOHA can be approximated by
The derivations and insights are presented in Appendix C.
Remark: Appendix C also draws an analogy between classical ALOHA and our problem using Multi-replica ALOHA. In classical ALOHA, the transmission attempt rate involves the offered load (i.e., new arrivals) and the retransmissions. The optimal is given by for unslotted ALOHA, in which case the optimal throughput is . In our problem, however, the objective is to lower the loss probability rather than maximizing the throughput. In particular, the offered load in our problem is fixed to , and we allow attempts per node to jack up the transmission attempt rate to lower the loss probability. The effective is therefore (i.e., number of attempts per packet duration). Assuming large so that , equation (9) and imply that we have to achieve an effective to obtain the minimum message loss rate. Note that the expression is independent of and under the adoption of the optimal for the given . This expression in turn implies that we need to modify the optimal transmission attempt rate of classical ALOHA, , by a factor of in order to arrive at as the optimal transmission attempt rate for our problem.
Overall, multi-replica ALOHA is a simple channel-access technique. Compared with other advanced techniques (e.g., the coded ALOHA introduced below), simplicity is its most attractive property. In particular, the signal processing of multi-replica ALOHA will not consume much additional time. Thus, for a target , if the number of transmitters is no more than given in (10), we would recommend Multi-replica ALOHA for reliable channel access with message loss rate less than . On the other hand, for the target , if exceeds in (10), we need to resort to more advanced techniques using more complex signal processing. In subsection V-B below, we explore the use of coded ALOHA to increase the sustainable .
V-B Coded ALOHA
At the transmitter, as with the multi-replica approach, each emergency node repeats its broadcast for times to increase the success rate. At the receiver, successive interference cancellation (SIC)  can be used to boost performance. In this paper, by Coded ALOHA, we means that the SIC technique is used at the receiver to extract messages. This includes the same set-up that we studied in subsection V-A where a transmitter just repeats its message time (i.e., repetitive code is used), with the difference that SIC is used at the receiver to reduce message loss rate.
Consider the example in Fig. 9 again. Only can be decoded with the previous multi-replica reception mechanism. With coded ALOHA, the receiver stores all the signal received during the ms, and make use of SIC to recursively cancel the interference caused by the decoded nodes. First, the clean replica can be used to cancel other replicas of node , i.e., , , and . As a result, the interference from node to other nodes is removed. Moreover, this interference cancellation process creates a new clean replica , and all node ’s replicas can be removed accordingly. Finally, only replicas from node is left, and they are all clean and decodable.
This scheme, multi-replica ALOHA with SIC (or for simplicity, coded ALOHA), is similar to coded slotted ALOHA [20, 21], except for the absence of the concept of slotted time in the former. Practically, a time-slotted system causes two problems in our application: 1) The slot must be short, e.g., as short as . However, small slot duration means larger overhead on slot alignment/synchronization among nodes. The required guard time between slots will eat up a large portion of the slot time. 2) Alignment and synchronization of slots in the slotted system must be maintained all the time since we cannot predict the arrival of emergencies. That is, nodes will need to participate in the slot synchronization process whether they currently have urgent messages to transmit, in preparation for possible arrivals of urgent messages – performing synchronization only after the arrivals of messages will likely to cause unacceptable latency.
The simulation results for coded ALOHA are plotted in Fig. 11, where the PHY-layer parameter settings are given in Table I, and we assume perfect interference cancellation at the PHY layer. For different number of active nodes , , and , the message loss rate is simulated. As can be seen, when , the requirement is satisfied for all .
To measure the maximal number of sustainable nodes in coded ALOHA systems, we keep increasing the number of active nodes and simulate given different degree . Fig. 12 shows the when . Approximately, the maximal number of sustainable nodes in coded ALOHA systems is given a target performance .
Remark (The optimal degree distribution): The performance of coded (unslotted) ALOHA is analytically intractable due to the lack of mathematical tools to characterize the embedded SIC process. On the other hand, in coded slotted ALOHA, the SIC decoding process can be analytically described by iterative message passing (i.e., the evolution of the erasure probabilities) on a bipartite graph [22, 20]. The bipartite graph consists of Burst Nodes (BNs), Sum Nodes (SNs) and edges. For example, a BN is a warning message transmitter, a SN is a slot, and an edge connects a BN and a SN if and only if a replica of the BN is transmitted in the SN/slot. The number of edges connected to a BN is referred to as the BN degree. Graphs for which the BN degree is constant are referred to as regular graphs; otherwise, the graphs are referred to as irregular graphs.
An important insight from the graph analyses of coded slotted ALOHA is that, the optimal throughput performance is often achieved by irregular graphs, whereas regular graphs usually lead to a performance loss [23, 22].
For our problem, instead of using a fixed degree (transmitting a fixed number of replicas), we let each emergency node sample a degree from a degree distribution , where is the probability that the node chooses degree . The polynomial representation of the degree distributions is given by
The problem is then to discover the optimal degree distribution to minimize the message loss rate .
The degree distributions simulated in Fig. 11 and 12 are regular distributions for fixed . It is shown that the regular distribution has already met the reliability requirements of warning messages. However, for the problem itself, the optimal degree distribution is yet unknown due to the lack of mathematical tools for coded unslotted ALOHA.
We note that our problem is different from the problem studied previously in the context of coded slotted ALOHA . The most obvious difference is that ours is an unslotted system while  studied a slotted system. A more subtle difference is that the degree distribution obtained in  is one that optimizes the throughput in the asymptotic limit when the number of active nodes goes to infinity. For our problem set-up, is finite, and the offered load (therefore the target throughput) is low. For a given and offered load , our problem is to find the optimal degree distribution that minimizes . For example, with and , the offered load is only . In essence, we are trying to achieve low latency (low ) and high reliability (low ) with a finite node population (finite ); whereas in , the aim is to study the asymptotic throughput in the limit that (and therefore ) goes to infinity. Because of these fundamental differences, it is not clear that the degree distribution optimal for the problem set-up in  is also optimal in the context of high reliability with low latency such as in our problem set-up. As we will see, the answer in no.
Additional simulations are performed by us to verify if the optimal degree distributions designed for coded slotted ALOHA can be applied to our problem of coded unslotted ALOHA. The simulation results are presented in Table II, in which . The first three rows of Table II are irregular distributions (with maximal degrees , , and ) designed for coded slotted ALOHA . With greater maximal degree, higher asymptotic threshold of throughput, denoted by , can be achieved (if the offered load is smaller than , the messages can be recovered from the SIC process with a probability close to in the asymptomatic limit when ). The last two rows in Table II are regular distributions used in Fig. 11. As shown, the regular distributions outperforms irregular distributions by much.
This paper studies the problem of life-critical warning messaging in V2X. Our main contributions are as follows.
We put forth an interrupt-and-access MAC protocol for warning messaging that takes into account the three characteristics of warning messages: sporadicity, crowding, and ultra-time-criticality requirement. The idea is to interrupt the regular wireless services only when warning messages arrive so as to acquire usage of the spectrum ordinarily allocated to the regular services. In this way, precious wireless spectrum does not have to be pre-allocated to warning messaging, which occurs only once in a long while in a sporadic manner.
For wireless interrupt, we devised an interrupt mechanism for V2X and presented an out-of-band interrupt signal design where the interrupt signals are spread spectrum sequences on the ISM band. Simulation results validate the nice detection performance of our design, e.g., for a ms ( symbols, MHz) sequence, the missed detection rate can be kept lower than when SIR dB.
For wireless access, we investigated different uncoordinated channel access schemes to meet the stringent delay and reliability requirements of warning message. A simple multi-replica ALOHA scheme can support up to nodes in our set-up with message loss rate lower than . If the number of transmitters in the system exceeds , a more advanced coded ALOHA scheme with successive interference cancellation can support up to nodes in our set-up while keeping the message loss rate lower than .
Appendix A Deriving the cross-correlation results
In this Appendix, we derive the cross-correlation results when the two adjacent ZC sequences in PIS are modulated by distinct values.
As with (3), at the receiver, we cross-correlate PIS with the conjugate of ZC sequence , yielding
Given sequence , we find peak in its modulus . Without loss of generality, we now focus on the first two ZC sequences in PIS.
If these two ZC sequences are modulated by same values, then
where . Eq. (12) follows since a ZC sequence is orthogonal to its cyclic shift.
If these two ZC sequences are modulated by distinct values, say and , respectively. We have
Notice that and are two strings of a unit circle on the complex plane. According to the Law of cosines, we have
Thus, (14) can be written as
Appendix B Deriving for multi-replica aloha
This appendix derives the probability of multi-replica ALOHA in (6). For any two nodes and , is the probability that one of ’s replicas, say , does not collide with ’s replicas .
Let us consider a simple case where , and is the probability that does not collide with . Denote by the transmission start time of packet , and the transmission start time of packet . To avoid collisions, and must satisfy the following constraints:
Fig. 13 illustrates these constraints, wherein the shaded regions are the regions that satisfy the constraints. is then the proportion of the shaded area to the total area, giving,
Next, we consider the case , and is the probability that does not collide with and . To avoid collisions, the transmission start times , and must satisfy
In particular, the condition is met by default because node will not transmit two overlapping packets. can be derived as
Fig 14 illustrates the regions associated with the numerator and denominator of (15). As can be seen, the region associated with the numerator of (15) is essentially a cube with side length . On the other hand, the region associated with the denominator of (15) is a cuboid with length (-axis), width (-axis) and height (-axis). As a result,
In general, for the general case where node transmit replicas, we have
where the numerator represents a ()-dimensional regular polyhedron with side length , and the denominator represents a ()-dimensional polyhedron with side length , , …, , (i.e., only one side is of length ). Thus, we have
Appendix C Approximating the optimal degree and the maximal number of sustainable nodes in Multi-replica ALOHA
Consider the situation faced by one particular node, say, node . On a line of length , there are points corresponding to the beginnings of the replicas of the other nodes. We denote this set of points by . To the extent that is large, approximately the points in
form a Poisson process on the line. In other words, the inter-point distance is exponentially distributed with mean
C-a The optimal degree for a given
Consider a replica of node A, say , that is randomly placed on the line of length . Refer to the beginning of this packet as point . Ignoring the edge effects at the two ends of the line, the probability that the distance of point to the next point of to the right is more than is . Similarly, the probability the distance of point to the next point of to the left is more than is . The probability of no collision is therefore is . Thus, is approximately given by
Differentiating with respect to and setting the derivative to zero gives us the following equation:
This is satisfied by , which gives
From (C-A), the optimal is given by
For our experiments where , we have
More importantly, the above analysis reveals a fundamental relation between and in (17). That is, the optimal is inversely proportional to .
C-B On the optimal transmission rate
In classical ALOHA, is the the number of transmission attempts by all nodes per packet duration (including both the new arrivals and the retransmissions). The throughput of ALOHA is packets per packet duration. Thus, the optimal to maximize throughput is , and the corresponding optimal throughput is . The study of classical ALOHA is to achieve this optimal throughput. If packets can be retransmitted indefinitely after back-offs until success, then there is no loss in the system as long as the offered load is less than (subject to a proper backoff method). This may incur excessive delay, however.
In our problem, the offered load is fixed to , and we allow attempts per node. In other words, the effective in our problem is . Assuming large so that is approximately , equation (17) implies that we have to achieve to minimize the message loss rate. That is, we need to modify the optimal transmission attempt rate of classical Aloha, , by a factor of .
Note that, in our problem set-up, we do not adjust the offered load to try to meet the maximum throughput – our offered load is already fixed (in fact smaller than the best sustainable offered load). We try to reduce the loss probability for a fixed offered load lower than the sustainable offered load of ALOHA, while bounding the delay to within . The optimal will therefore be different.
C-C The maximal number of sustainable nodes
As far as one of the replicas is concerned, its success rate is given by in the optimal setting – i.e., half chance of success for each trial. Note that this success rate for a replica is independent of and because and have been optimized to give . Thus, regardless of , under the optimal setting, the failure rate after attempts of the replicas is . Of course, for a fixed , the larger the , the smaller the . For a given , the minimum message loss rate is given by
Eq. (19) gives us an insight on how the minimum message loss rate depends on with the optimized . In the log scale, we have
Given a target message loss rate , the maximum is
For our settings where , the maximum is . This is consistent with the numerical results in Fig. 10.
From (6), we have
where the approximation follows because .
As , we have
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