# Improving Quality-Of-Service in LoRa Low-Power Wide-Area Networks through Optimized Radio Resource Management

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## Abstract

**:**

## 1. Introduction

- (i)
- definition of a mathematical optimization formulation of the problem of assigning SF and CF parameters according to the traffic characteristics of LoRa end-devices;
- (ii)
- definition of an approximation algorithm that leads to results very close to the optimal, but with an execution time that grows much slower as the number of end-devices in the network scales;
- (iii)
- approach to implement and integrate the approximation algorithm in LoRaWAN networks and analyze the imposed overhead of the radio parameter assignment scheme to ensure compatibility with the standard protocol;
- (iv)
- implementation of the proposed optimization algorithms and of other baseline policies (benchmarks to which our method is compared against in Section 6), and as well as of the ADR mechanism (not implemented in LoRaSim) in the LoRaSim open-source simulator, making our code available to the community [10]; and
- (v)
- Comparative performance analysis of six radio parameter assignment policies, showing the merit of the two proposed parameter assignment methods in relation to the other four policies that we consider as benchmarks.

## 2. Related Work

## 3. LoRa and LoRaWAN Overview

#### 3.1. Protocol Stack

#### 3.2. LoRa Physical Layer

**Bandwidth (BW)**: BW is the width of the frequencies in the transmission band. Higher BW values provide a higher data transfer rate and greater sensitivity to noise. The sets of BW in LoRa are 125, 250, and 500 kHz.

**Spreading Factor (SF)**: SF is the ratio between the symbol rate and the chip rate, which can be in the range of 7–12. Higher SF increases the SNR, transmission range, and packet airtime, therefore it decreases the data rate. SFs are imperfectly orthogonal. However, for traceability purposes in our experiments, they are considered orthogonal. If different SFs are used, the gateway can successfully decode multiple simultaneous data packets. LoRa modulation transmits the data at a chip rate equal to the programmed BW (chip-per-second-per-Hertz). The symbol rate and the bitrate are proportional to the BW. With CSS, each LoRa symbol is coded with a spreading code of ${2}^{SF}$ chips. Then, it takes ${2}^{SF}$ chips ($SF=SFbits\times {2}^{SF}$) to spread a symbol [27].

**Carrier Frequency (CF)**: CF is the center frequency and can be programmed in a range of 137 MHz to 1020 MHz according to current geographic region legislation. For example, Table 1 shows the range of frequencies for each CF parameter, sub-bands, and max-duty-cycle (per hour) according to the ETSI EN300.220 European continent standard [28].

**Transmission Power (TP)**: Due to hardware limitations, the TP in a LoRa network can be configured in steps of 1 dB with a signal power between 2 and 20 dBm and a service level of 1% from 17 dBm [29].

**Coding Rate (CR)**: LoRa modulation adds Forward Error Correction (FEC), providing protection against transmission interference by encoding 4-bit data with 5–8-bit redundancies, allowing the receiver to detect and correct errors in the message. The CR values are 4/5, 4/6, 4/7, and 4/8, proportional to the FEC. This means that, if the code rate is denoted as $k=N$, where k represents useful information, and the encoder generates N number of output bits, then $N-k$ will be the redundant bits. Higher CR values provide greater interference protection. However, it increases the air time. LoRa devices with different CR can switch to communicate with each other through an explicit header stored in the packet header [30].

#### 3.3. Class Transactions

#### 3.4. Frame Structure

#### 3.5. LoRaWAN Adaptive Data Rate

Algorithm 1: ADR-NODE [32]. |

Algorithm 2: ADR-NET [32]. |

## 4. MILP Optimization Problem

#### 4.1. Background on Mathematical Optimization

#### 4.2. Notation and Model

#### 4.3. MILP Problem Statement

## 5. Approximation Algorithm

#### 5.1. Description of the Approximation Algorithm

Algorithm 3: Approximation Algorithm. |

#### 5.2. Backward Compatibility with LoRaWAN

## 6. Evaluation

#### 6.1. Simulation Setup

#### 6.2. Evaluation Metrics

**Reception overlap:**In LoRaSim, two packets overlap when the reception intervals overlap. It is represented by $O(x,y)$.**Carrier Frequency**: It is evaluated whether transmissions with the same CF and BW parameters but different SFs can be successfully decoded. Importantly, they are available assuming two reception paths. CF collision is expressed by ${C}_{cf}(x,y)$.**Power (capture effect):**In our simulations, the capture effect was considered, which is modeled on LoRaSim to match a Semtech SX1272. It is defined when two signals occur simultaneously at the receiver and the weakest signal is suppressed by the strongest. It is determined by ${C}_{pwr}(x,y)$.**Timing:**Experiments conducted by Bor et al. [29] conclude that packages can overlap as long as there are at least five preamble symbols intact. This defines the transmission interval that two transmission packets collide within their critical section. It is represented by ${C}_{timing}$.

#### 6.3. Parameter Assignment Policies

**Min-airtime**: The**min-airtime**is a default assignment used by LoRa end-devices which assigns a fixed CF in CF4 (sub-band g) and SF in SF7 so that packets have the minimum air time (see Table 2).**Random**: The**random**policy dynamically assigns $\mathrm{CF},\mathrm{SF}$ pairs randomly, aiming at reducing concurrent transmissions (that cause packet collision).**Equal-distribution**: With a similar goal to**random**, the**equal-distribution**distributes the number of end-devices equally between $\mathrm{CF},\mathrm{SF}$ pairs.**Tiurlikova**: The**Tiurlikova**policy is based on the work of [16], which creates a dynamic allocation method of SF. This policy determines the number of nodes distributed in each SF ${n}_{i}$ through Equation (13), where i is the index of SF, T is the airtime (according to Table 2), and N is the nodes numbers:$$\begin{array}{c}\hfill {n}_{i}=\frac{\frac{1}{{T}_{i}}}{{\sum}_{i=S{F}_{min}}^{S{F}_{max}}\frac{1}{{T}_{i}}}\xb7N\end{array}$$**Opt-problem**: The**opt-problem**is the assignment resulting from solving the optimization problem presented using the CPLEX ILP solver (in Section 4).**Approx-alg**: The**approx-alg**policy is the result of using the Approximation Algorithm (in Section 5).

#### Analysis of Network Scalability of Assignment Policies

**opt-problem**and

**approx-alg**. This is due to the optimization to dynamically assign to each node the ($\mathrm{CF},\mathrm{SF}$) pair leading to the shortest airtime, considering the use of sub-bands g and g1. As a result, the

**opt-problem**and

**approx-alg**policies allow the best scaling of the network, with a maximum number of 353 nodes. The

**Tiurlikova**allocates 64 nodes per sub-band. Using sub-bands g and g1, the number of nodes that can be allocated is 128.

**random**policy is 353 nodes if the randomly generated CF and SF values for all nodes are the same as

**opt-problem**and

**approx-alg**policies (regardless of their ordering). However, the

**random**policy allows only six nodes to be allocated in the worst-case scenario, which is all nodes allocated in SF12 using only one of the sub-bands (g or g1).

**min-airtime**assignment policy allocates a maximum of 176 nodes, respecting the max-duty- cycle limit of 1%, with all nodes configured in SF7 using the g sub-band. Importantly, policy

**min-airtime**uses only the sub-band. If sub-band g1 is enabled, network scalability results are similar to

**opt-problem**and

**approx-alg**policies, with 353 nodes. Finally, the maximum number of nodes that can be allocated with the

**equal-distribution**policy is 66 nodes.

#### 6.4. Evaluation Results

#### 6.4.1. DER

**opt-problem**(green line) and

**approx-alg**(navy blue line) show the highest DER performance with an average increase of 7.14%, 5.19%, 3.03%, and 2.82% in relation to the

**min-airtime**(orange line),

**equal-distribution**(brown line),

**Tiurlikova**(silver line), and

**random**(red line), respectively.

**opt-problem**shows the highest DER performance with an average increase of 6.63%, 5.04%, 2.95%, 1.95%, and 0.1% in relation to the

**min-airtime**,

**equal-distribution**,

**Tiurlikova**,

**random**, and

**approx-alg**, respectively.

#### 6.4.2. Number of Collisions

**opt-problem**and

**approx-alg**cause the lowest number of collisions, being the curves represented in the graph practically equivalent. The policies

**min-airtime**,

**equal-distribution**,

**Tiurlikova**, and

**random**lead to average collision rates 13.3, 12.7, 7.8 and 7.4 times higher, respectively, in relation to

**opt-problem**and

**approx-alg**. Figure 11 demonstrates the number of collisions according to the number of nodes with gateway transmission range of 350 m.

**opt-problem**and

**approx-alg**have the smallest number of collisions, with equivalent results. The policies

**min-airtime**,

**equal-distribution**,

**Tiurlikova**, and

**random**have average collision rates 15.4, 11.7, 8.3 and 2.5 times higher, respectively, in relation to

**opt-problem**and

**approx-alg**.

#### 6.4.3. Network Energy Consumption

**equal-distribution**has a three times higher energy consumption rate as

**opt-problem**and it is 2.94 greater than

**approx-alg**. The

**random**policy resulted in an average energy consumption 2.84 and 2.76 times higher than

**opt-problem**and

**approx-alg**, respectively.

**Equal-distribution**and

**random**achieved similar energy consumption, being 5.5% greater for

**equal-distribution**. The difference in the average energy consumption between

**opt-problem**and

**approx-alg**is 2.7%.

**Tiurlikova**achieved energy consumption similar to

**opt-problem**and

**approx-alg**. Both obtained an average consumption 2.9 times greater in relation to the

**min-airtime**. Using this policy, SF is set to SF7, which has the lowest energy consumption, as reported in Section 3. However, in

**opt-problem**and

**approx-alg**, dynamic values of SF are assigned to the network nodes.

**opt-problem**and

**approx-alg**—proved to be better than policies

**random**,

**min-airtime**,

**Tiurlikova**, and

**equal-distribution**in relation to DER and number of collisions. The results show that

**opt-problem**and

**approx-alg**obtained DER values above 0.98 and 0.83 for the 99 m and 350 m scenarios, respectively. The number of collisions was minimal in relation to

**random**,

**min-airtime**,

**Tiurlikova**, and

**equal-distribution**. In addition, the energy consumption of the proposed optimization schemes is similar to

**Tiurlikova**and lower when compared to other methods of dynamic assignment of values of SF and CF:

**random**and

**equal-distribution**.

#### 6.4.4. ADR Analysis and Comparison in **approx-alg** and **random** Policies

**random**and

**approx-alg**dynamic assignment policies, using, according to the DER, number of collisions and Network Energy Consumption evaluation metrics.

**random**policy with the ADR mechanism is 1.43% compared to without ADR. The difference in

**approx-alg**was smaller, only 0.23%. Therefore, it was the

**random**policy that obtained the highest gain of DER with ADR mechanism.

**random**and 1.89% in the

**approx-alg**.

**random**. Therefore, the NEC value in was very close in

**approx-alg**with and without ADR. The results demonstrate that the

**random**policy benefited from the ADR mechanism. However, the ADR mechanism difference in

**approx-alg**is only noticeable in the collision rate.

#### 6.4.5. Analysis of Overheads Inferred by the Optimization Proposed in the Standard LoRa Protocol

- (i)
**Computation Time**: The Approximation Algorithm (Algorithm 3) has a linear complexity time O(n) = $111n+57$, in the worst-case. Thus, since the Approximation Algorithm is expected to run in the LoRaWAN Application Layer and end-devices with a time complexity that is similar to the ADR mechanism (Algorithms 1 and 2), our optimization scheme causes no significant computation (time) overhead, neither in the end-devices nor in the LoRa Server.- (ii)
**Storage space**: The most significant part of the (optimization) algorithm runs in the LoRa Server, accounting for approximately 70 lines of code, while the extra code in the end-devices is around 60 lines. Overall, the implementation of our algorithm takes less than 20 kB of storage space (4 kB in average, 20 kB worst-case, considering different situations), which is not significant considering that most commercial off-the-shelf nodes have at least 128 kB of programming/non-volatile memory (minimum requirements for a LoRaWAN microcontroller [49]);- (iii)
**Energy consumption**: The proposed optimization scheme achieves lower Network Energy Consumption compared to other dynamic allocation policies. The way the Approximation Algorithm assigns end-devices pairs of ($\mathrm{CF},\mathrm{SF}$), ordered from lowest to highest airtime, results in an improved network scalability (maximum number of nodes) ratio for lower power consumption. Regarding the**min-airtime**policy, which has shorter airtime due to using the SF parameter fixed in SF7, the simulation results show that the Approximation Algorithm consumed on average three times more energy.- (iv)
**Communications**: Considering with Approximation Algorithm input an array of valid (SF, CF) pairs, end-devices only receive the (SF and CF) parameter values once (generated by the Approximation Algorithm). Our simulations show that the proposed optimization has a lower network packet send rate, as well as number of collisions, compared to the assignment policies**min-airtime**,**equal-distribution**, and**random**. Therefore, the proposed optimization method causes no additional communication overhead.

## 7. Conclusions and Future Work

## Author Contributions

## Funding

## Conflicts of Interest

## Abbreviations

ADR | Adaptive Data Rate |

BW | Bandwidth |

CF | Carrier Frequency |

CPU | CPU – Central Processing Unit |

CR | Coding Rate |

CSS | Chirp Spread Spectrum |

DER | Data Extraction Rate |

FEC | Forward Error Correction |

IoT | Internet of Things |

LoRa | Low Range |

LoRaSim | LoRa Simulator |

LPWAN | Low Power Wide Area Network |

QoS | Quality of Service |

MAC | Medium Access Control |

MILP | Mixed Integer Linear Programming |

PHY | Physical Layer |

SF | Spreading Factor |

SNR | Signal to Noise Ratio |

TP | Transmission Power |

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**Figure 1.**Mapping radio coverage vs. bandwidth of wireless technologies [8].

CF | Frequency | Sub-Band | Max-Duty-Cycle |
---|---|---|---|

CF1 | 868.1 MHz | g1 | 1% |

CF2 | 868.3 MHz | g1 | 1% |

CF3 | 868.5 MHz | g1 | 1% |

CF4 | 867.1 MHz | g | 1% |

CF5 | 867.3 MHz | g | 1% |

CF6 | 867.5 MHz | g | 1% |

CF7 | 867.7 MHz | g | 1% |

CF8 | 867.9 MHz | g | 1% |

SF | Chirps/Symbol | SNR | Airtime ^{a} | Bitrate |
---|---|---|---|---|

7 | 128 | −7.5 | 56.5 ms | 5469 bps |

8 | 256 | −10 | −103 ms | 3125 bps |

9 | 512 | −12.5 | 185.3 ms | 1758 bps |

10 | 1024 | −15 | 371 ms | 977 bps |

11 | 2048 | −17.5 | 741 ms | 537 bps |

12 | 4096 | −20 | 1318.9 ms | 293 bps |

Parameter | Value |
---|---|

Code Rate (CR) | 4/5 |

Bandwidth (BW) | 125 kHz |

Sub-band | g and g1 |

Transmission Power (TP) | 14 dBm |

Number of base stations | 1 |

Transmission range | 99 and 350 m |

Payload size $\xi $ | 20 bytes |

Average packet transmission period | 16.6 min |

Scenario run time | 1 year |

Node distribution | Randomly distributed |

Traffic Model | Poisson distribution model |

Propagation Model | Log-distance path loss model |

End-device operating voltage | 3 V |

Device Class | Class A |

Policy | Sub-Bands | Maximum Number of Nodes |
---|---|---|

Tiurlikova | g or g1 | 66 nodes |

equal-distribution | g and g1 | 72 nodes |

min-airtime | g or g1 | 176 nodes |

random | g and g1 | 353 nodes in best-case |

opt-problem/approx-alg | g and g1 | 353 nodes |

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**MDPI and ACS Style**

Sallum, E.; Pereira, N.; Alves, M.; Santos, M.
Improving Quality-Of-Service in LoRa Low-Power Wide-Area Networks through Optimized Radio Resource Management. *J. Sens. Actuator Netw.* **2020**, *9*, 10.
https://doi.org/10.3390/jsan9010010

**AMA Style**

Sallum E, Pereira N, Alves M, Santos M.
Improving Quality-Of-Service in LoRa Low-Power Wide-Area Networks through Optimized Radio Resource Management. *Journal of Sensor and Actuator Networks*. 2020; 9(1):10.
https://doi.org/10.3390/jsan9010010

**Chicago/Turabian Style**

Sallum, Eduardo, Nuno Pereira, Mário Alves, and Max Santos.
2020. "Improving Quality-Of-Service in LoRa Low-Power Wide-Area Networks through Optimized Radio Resource Management" *Journal of Sensor and Actuator Networks* 9, no. 1: 10.
https://doi.org/10.3390/jsan9010010