In the following, we will focus on the approach proposed in this paper to provide the required reliability. To this aim, we exploit the DL communication scheme provided by standard LoRaWAN: DL packets are sent by a Network Server to only one ED through one or more GWs. To elaborate, in the proposed system a remote central LoRaWAN server shown in
Figure 7 is capable of performing various tasks such as reception of data from the EDs forwarded by GWs, exploitation of the collected data with further processing, and more importantly scheduling of DL messages to the EDs for enabling coordinated transmissions. We describe each aspect in detail in the following subsections.
4.2. Coordination of ED Transmissions through Downlink Control Packets (DCPs)
We refer to the Class A DL operation in which the Network Server transmits a DL packet to an ED after the reception of an UP packet precisely at the beginning of one of two possible receiving windows. More precisely, the ED opens Class A RX1 and RX2 receiving windows after RECEIVE_DELAY1 and RECEIVE_DELAY2 secs respectively. The DL data rate for RX1 depends on the corresponding UL whereas RX2 uses a fixed data rate depending on the region.
In the considered scenario, each node transmits RPs periodically every predetermined (long) time intervals (e.g., several minutes) in UNCONF mode. We program the server in such a way that for every received RP a corresponding DCP is scheduled. Specifically, the DCP message is intended to control the eventual transmission of UPs. The adopted control mechanism, which is discussed in detail in the next section, acts independently on each cluster since it is highly unlikely that in the considered scenario EDs of different clusters have to transmit an UP at the same time (the potentially dangerous event is local and infrequent).
Hence, upon the necessity of delivering an UP to the system, the ED transmits according to the control information specified in the last received DCP. More specifically, we opted to choose the UNCONF mode also for UPs. The rationale for this choice will be given in the next section.
One of the important aspects that has to be taken into consideration while designing any LoRaWAN system is to comply with the duty cycle regulations as discussed in
Section 3. This poses some stringent constrains in the process of allocating the resources to the EDs. Owing to the per sub-band duty cycle regulations, we have various possibilities to assign the resources to the EDs for the next UPs. In particular, one of the feasible choice is to differentiate the sub-bands for the two types of packets, i.e., allocating fixed non-overlapping sub-bands for the RPs and UPs. Indeed, this not only allow the isolation in terms of frequencies but also address the issue of duty cycling in the case when it is necessary to transmit an UP when the time elapsed form the last RP is lower than the minimum time established by duty cycling restrictions. In particular, the server assign different sub-bands for RPs and UPs so that duty cycling restrictions are independently established for the two kinds of transmissions. An illustrative example is given in
Figure 9, where 5 EDs in close proximity, i.e., belonging to the same cluster, are allocated sub-band g (Channel (Ch0-4) with frequencies 867.1, 867.3, 867.5, 867.7, 867.9 MHz) and g1 (Channel (Ch5-7) with frequencies 868.1, 868.3, 868.5 MHz) for UPs and RPs respectively. To elaborate, each EDs transmit RPs by randomly selecting one of the available frequencies from g1 whereas the UPs are transmitted using different frequencies in sub-band g to avoid collisions. Such frequencies can be selected by each ED according to the last DCP received from the server which is in charge of isolating the UP transmissions of the same cluster. Considering 5 channels in sub-band g, it is worth noting that we can allocate a maximum of 5 different channels to 5 EDs in each cluster. However, we also have the possibility to accommodate more users in the cluster by assigning different SFs as shown in the next section.
4.3. The Problem of DL Priority
In standard LoRaWAN, the GWs work in half duplex mode only, i.e., they cannot receive and transmit simultaneously. Moreover, in commercial GWs, if there is the need to send a DL message, the reception of any incoming signal is interrupted, i.e., the concurrent UL packet is lost. Accordingly, the mechanism proposed in this paper for coordinating simultaneous UL UPs, which is based on periodic delivery of DCPs, could dramatically affect the PLR of UPs.
It is then of paramount importance to evaluate the PLR due to GW transmissions. To this aim, it is worth noting that the UL packet is lost by the concurrent DL transmission either when the DL packet is ongoing at the UL packet arrival time, or if it is started during the reception of the UL packet, since the GW gives priority to transmission anyway. Accordingly, denoting by and D the durations of a DCP and of an UP, respectively, the PLR of UPs is equal to the probability that at least one DCP is generated in the interval . To elaborate, in the considered setting DCPs are created as a response of RPs transmitted in the UL by each node. Accordingly, the DCPs arrival process statistics is equivalent to that of RPs generation process. Let then denote by T the rescheduling period set by each ED. Owing to inevitable clock drifts, the actual rescheduling time can be modeled as a random variable (rv) , where is the clock error.
In the considered scenario we deal with internal clocks which are natively embedded inside the ED microcontroller. This choice allows to save cost, energy, and complexity with respect to external clocks. In this case, it is shown in [
30] that the clock errors are unbiased and that they can be reasonably modeled as independent and identically distributed (IID) Gaussian rvs, i.e.,
. Accordingly, also the interarrival times
r are IID rvs, i.e., the arrival process of DCPs belong to the class of renewal processes [
31]. More specifically, we have
.
From the theory of renewal processes, it is possible to evaluate the time asymptotic density
for the the time elapsed from a generic time till the next arrival, i.e.,
where
is the cdf of
r. In the following, we are interested in evaluating the probability that an UP does not experience any collision with DCPs. To this aim, it is reasonable to assume that different nodes are characterized by independent clocks and independent time delays, and, hence, the probability
that the an UP does not experience any collision can be evaluated as the product of individual probabilities of all independent events. To elaborate, let us denote by
N the number of EDs and by
the DCP time duration of each node. Such terms depends on the SF used by the correspondent nodes to transmit DCPs, i.e., the higher SF the longer
. Since the adopted SFs in the UL depend on the channel conditions of each ED, e.g., the distance from the GW, it is reasonable to consider
as a set of i.i.d. rvs with individual pdf
. Similarly, also
D depends on the SF adopted by the ED to transmit an UP and, hence, it can be characterized by a given pdf
.
Accordingly, the probability
that the an UP does not experience any collision with DCPs for given
and
D is:
and the marginal probability is:
with
.
In the interesting case where
, the expression in (
3) can be manipulated to get an easy to understand approximation of the PLR. To elaborate, when
(i.e., small PLR), we have
thus yielding: