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## Proposed Signal Detection Scheme

In this section, we present the proposed scheme. We first present the transmitte design and the wireless channel model. We then present our method for the receiver, starting from the optimal detector formulation via the Maximum Likelihood Detector MLD), which we show has a combinatorial complexity. To overcome this limitation, we propose an algorithm that approximates the MLD with a much lower complexity based on the CEM [72]. To further reduce the computational complexity, we propose a low-complexity multiuser detector that only searches for the closest peak to the expected one. It is to be noted that the CEM-based and the low-complexity detectors will be used as references for comparison. We did not find any competitive method in the literature or theoretical bounds for a method equivalent to our NOMA proposal. The only one which would be relevant would be a pure ALOHA scheme or a perfect Time Division Multiple Access (TDMA) approach. Even if it is impractical in real networks, this latter approach will also be used as a comparison, but our scheme significantly outperforms both. In addition to that, we propose two PA schemes. The first one avoids ambiguities when two users transmit the same information at the same time. The second one distributes the powers to ensure a constant distance between the power of the selected peak and that of the nearest lower peak to improve equity.

**Transmitted signal**

To avoid the limitation due to the duty cycle, we propose to transmit N frames simultaneously, with the same SF and on the same frequency band. It is possible with Class B devices that can be synchronized and in receive mode during the same time frame. The objective is then to design a communication strategy that allows us to superimpose N users in the duration of a single packet. The idea is to generate information streams for N end-devices, modulate them using the CSS scheme, then add all signals with different allocated powers to form a single packet. A preamble and a common header are added at the packet start. The information about the number of users and the PA scheme is added in the header. At the receiver side, the receivers select and decode the signal which corresponds to their allocated power. The combined transmitted signal is: x(t) = XN i=1 q p(i) x(i)(t); (2.3) where p(i) is the power allocated to user i.

### Power considerations

The maximum transmission power in an ISM band is restricted. For LoRa (at 868 MHz), in Europe, this maximum is set to 14 dBm for uplink and 27 dBm for downlink. The noise level of a receiver at room temperature is: N0(dBm) = 174 + 10 log10(B) + NF; (2.4) where the first term is the thermal noise in 1 Hz of bandwidth and can only be affected by changing the receiver’s temperature. NF is the receiver noise figure, which depends on the hardware implementation, and a typical 6 dB noise figure is considered [21]. If we consider B = 250 kHz, the noise power density at the receiver is 114 dBm.

#### Cross-Entropy Multiuser Detector

The CEM is a flexible Monte Carlo technique, which was originally developed for rare-event probability estimation, solving combinatorial, continuous, constrained, and noisy optimization problems [73].

The basic idea is to generate a set of candidate solutions (mq in our case consisting of N integers in f0; : : : ; 2SF 1g), select the best possible candidates, update the generating rule and iterate until convergence is obtained. One important step is the possible solution generation: what distribution for mq should be chosen? Let fm(:) be the PMF of mq. The proposed cross-entropy algorithm is presented in algorithm 2.1. Steps 1 to 3 define some parameters: the number of sequences we generate at each iteration, the number of sequences we keep to update the distribution, and a parameter that controls the convergence speed. Along with two parameters chosen for the initialization of the PMF of mq, these parameters are important and could be optimized because they represent a compromise between the complexity burden and the algorithm’s accuracy. We chose parameters that ensure a good convergence rather than a reduced complexity to perform close to the true ML. Steps 4 to 9 initialize the PMF of mq. All values are possible, but we give a slightly higher probability to the dominant peaks. This reduces the necessary number of iterations. An example is seen in Fig. 2.1, where the initial fm is represented. The same PMF is used for each user. Step 10 starts the main loop. We set the end of iterations when for each user, the probability of a given value is at least 0:85. This probability is set empirically. From steps 11 to 17, we generate Nseq random sequences ~mq according to fm and the corresponding decoded vector ~Z (j) q [k]. This requires the channel estimate ^h(j). The distance with the true received sequence is also calculated. We chose Nseq = 2000 to ensure enough variety in the generated sequences and a good convergence of the algorithm. Steps 18 and 19 select the Nkeep sequences leading to the closest received vectors form the truly received one. We chose Nkeep = 100, also ensuring a good convergence of the algorithm. These sequences will be used in step 20 to update fm by reinforcing the weights on symbols that have been generated in the set of selected sequences. A parameter P is needed for this purpose and is empirically set to 0:003, which has been shown to be a good compromise. A larger value increases the convergence speed but also the number of wrong decisions. The process is illustrated in Fig. 2.2 and Fig. 2.3, where we show the CEM values of fm per user after 15 and 30 iterations.

**Power allocation performance**

Figs. 2.5a and 2.6a show the symbol error rate of a single user with an additive Gaussian noise, SNR= 10 and 12 dB respectively, and an increasing number (N 1) of interfering users with N = 3; : : : ; 13. In both cases, the power allocation scheme 2 (fair allocation) exhibits better performance. This is more significant in Fig. 2.6a when the SNR is smaller so that the user is in the weak users. This can be observed from Figs. 2.5b and 2.6b, where the histogram of the position of the selected user when users are ordered from the weakest channel (strongest allocated power) to the best channel. For instance, in the case with N = 12, it is seen that the mean position is between 3 and 4 in Fig. 2.6b (SNR= 12 dB) when it is between 10 and 11 in Fig. 2.5b (SNR= 10 dB). This latter case sees a larger benefit with the second power allocation scheme, which comes from the fairness approach and the fact that for the first allocation scheme, the gap between amplitudes is small for the users with the good channels.

This analysis is confirmed in Figs. 2.7 and 2.8 where the average symbol error rate is plotted for different SF (SF = 7; 8; 9, and 10) and the two power allocation schemes. These two plots also show that the proposed MUD exhibits good performance whatever the SF. As a comparison, the actual implementation of LoRa allows us to address only one user at a time. This means that we can increase by one order of magnitude the number of users that can be addressed in a single time slot.

**Table of contents :**

Acknowledgments

Résumé | Abstract

Contents

Table of Figures

List of Table

List of Algorithms

List of Abbreviations

Mathematical Notations

General Introduction

**1 Introduction **

1.1 Introduction

1.2 LoRaWAN

1.3 LoRa PHY

1.4 State of the Art: Scalability

1.4.1 Physical Layer

1.4.2 MAC Layer

**2 Downlink Communication in LoRa-like Networks **

2.1 Introduction

2.2 System Model

2.3 Proposed Signal Detection Scheme

2.3.1 Transmitted signal

2.3.1.1 Power considerations

2.3.1.2 Channel Model

2.3.2 Receiver Design

2.3.2.1 Cross-Entropy Multiuser Detector

2.3.2.2 Proposed Low-Complexity Detector

2.3.2.3 Direct Peak Detection

2.3.3 Power allocation scheme

2.3.3.1 Power Allocation 1: Suppressing ambiguities

2.3.3.2 Power Allocation 2: Fair Spacing

2.4 Results

2.4.1 Simulation setup

2.4.2 Performance of the three receivers

2.4.3 Power allocation performance

2.4.4 Fairness

2.4.5 Computational Complexity Analysis

2.4.5.1 Direct peak detection

2.4.5.2 Cross Entropy Method

2.4.5.3 Proposed Method

2.4.5.4 Comparison

2.4.6 SF Orthogonality

Conclusion .

**3 Uplink Communication in LoRa-like Networks **

3.1 Multi-user Detection: Serial Interference Cancellation

3.1.1 System Model

3.1.2 Proposed SIC Receiver

3.1.3 Results

3.1.3.1 Performance for a given selected link

3.1.3.2 Mean Performance

3.1.3.3 SF Orthogonality

3.2 Single User Detection: Deep learning-based

3.2.1 System Model

3.2.2 Deep Learning-based Receiver

3.2.2.1 Deep Feedforward Neural Network-based receiver

3.2.2.2 Convolutional Neural Networks-based receiver

3.2.3 Results

3.2.3.1 Results for Ni P()

3.2.3.2 Capture Effect – Ni = 1

3.2.3.3 Computational complexity

Conclusion .

Conclusion and Perspectives

**A Appendix related to Down-link Communication in LoRa **

A.1 Power allocation 2

**B Appendix related to Up-link Communication in LoRa-like Networks **

B.1 Chirp Formulation

B.2 Received Signal and De-chirping

B.3 Amplitudes of the Peaks

**Bibliographie**