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Low Power Wide Area Network Analysis: Can LoRa Scale?

Orestis Georgiou, Usman Raza

arXiv:1610.04793v2cs.NI

TL;DR

LoRa’s scalability as IoT device populations grow is difficult to assess because same-spreading-factor interference is not captured by assumptions of spreading-sequence orthogonality. The paper uses stochastic geometry to model single-gateway uplink coverage under LoRa’s chirp modulation, duty-cycle constraints, ALOHA access, and interference. It finds that coverage probability decays exponentially with the number of end-devices, identifying co-spreading-factor interference as a fundamental scalability limit.

  • Problem

    LoRa’s spreading sequences are often assumed orthogonal, but same-spreading transmissions create co-spreading-factor interference that can make dense networks interference-limited.

  • Method

    The paper applies stochastic geometry to model single-gateway LoRa uplink coverage under SNR and co-spreading-factor outage conditions.

  • Results

    Coverage probability decays exponentially as the number of end-devices increases because of co-spreading-factor interference.

  • Takeaways & Limitations

    Co-spreading-factor interference provides a fundamental limiting factor for LoRa scalability despite low duty cycling and chirp orthogonality.

Abstract

from arXiv · show

Low Power Wide Area (LPWA) networks are making spectacular progress from design, standardisation, to commercialisation. At this time of fast-paced adoption, it is of utmost importance to analyse how well these technologies will scale as the number of devices connected to the Internet of Things (IoT) inevitably grows. In this letter, we provide a stochastic geometry framework for modelling the performance of a single gateway LoRa network, a leading LPWA technology. Our analysis formulates unique peculiarities of LoRa, including its chirp spread-spectrum modulation technique, regulatory limitations on radio duty cycle, and use of ALOHA protocol on top, all of which are not as common in today's commercial cellular networks. We show that the coverage probability drops exponentially as the number of end-devices grows due to interfering signals using the same spreading sequence. We conclude that this fundamental limiting factor is perhaps more significant towards LoRa scalability than for instance spectrum restrictions. Our derivations for co-spreading factor interference found in LoRa networks enables rigorous scalability analysis of such networks.

I. INTRODUCTION

LoRa combines adaptive chirp spread-spectrum communication with flexible spreading factors, low-power operation, and an ALOHA-based MAC. The paper identifies same-spreading-factor interference as a distinct scalability challenge and models its effect on coverage.

  • I. INTRODUCTION: LoRa uses adaptive chirp spread-spectrum modulation to support flexible long-range communication with low power consumption and low-cost designs.LoRaWAN supplies higher-layer architecture on top of the LoRa physical layer.
  • I. INTRODUCTION: Same-spreading-factor transmissions create co-spreading factor interference, a LoRa-specific impairment that can make dense deployments interference-limited rather than noise-limited.The paper motivates interference-related metrics tailored to LoRa networks.
  • I. INTRODUCTION: Coverage probability decays exponentially as the number of end-devices increases, despite low duty cycling and chirp orthogonality.The paper uses stochastic geometry to analyze SNR and co-spreading-factor outage conditions in a single-gateway network.
  • II. LORA BASICS: Higher spreading factors increase symbol duration exponentially while improving receiver sensitivity, communication range, and interference-free outage performance.The NetServer selects spreading factors from SF∈{7, 8, . . . , 12} in Europe, with Ts = 2^SF/BW.
  • II. LORA BASICS: LoRa gateways can receive multiple transmissions through orthogonal sub-bands and quasi-orthogonal spreading factors, but equal-spreading-factor signals remain difficult to distinguish.The MAC layer is essentially ALOHA, without collision avoidance provisions.

III. SINGLE GATEWAY: UPLINK SYSTEM MODEL

The model represents a single-gateway LoRa uplink with randomly distributed end-devices, ALOHA transmissions, duty-cycle limits, fading, path loss, and same-frequency, same-spreading-factor interference.

  • III. SINGLE GATEWAY: UPLINK SYSTEM MODEL: End-devices are distributed in a disk of radius R km according to an inhomogeneous Poisson point process with mean population ¯N = ρV.The gateway is positioned at the coordinate-system origin.
  • III. SINGLE GATEWAY: UPLINK SYSTEM MODEL: Devices transmit randomly using ALOHA and obey a maximum p0 = 1% duty-cycle policy, causing higher-spreading-factor devices to transmit less often.All transmissions are modeled in one BW = 125 kHz channel.
  • III. SINGLE GATEWAY: UPLINK SYSTEM MODEL: Spreading factors are assigned according to device distance from the gateway, while concurrent equal-spreading-factor signals can cause severe packet losses.Such losses may require retransmissions, increasing battery use, delay, and signaling overhead.
  • III. SINGLE GATEWAY: UPLINK SYSTEM MODEL: The received uplink signal includes the desired transmission, concurrent same-frequency and same-spreading-factor interferers, and additive white Gaussian noise.The channel model includes block flat Rayleigh fading and distance-dependent path loss.

IV. UPLINK OUTAGE PROBABILITY

The uplink outage model separates failures caused by insufficient SNR from failures caused by a stronger concurrent transmission using the same spreading factor.

  • 1) Outage Condition 1:: An uplink transmission is in outage when its received SNR falls below the spreading-factor-specific threshold q_SF.The threshold is a piecewise constant function of the device distance from the gateway.
  • 1) Outage Condition 1:: The instantaneous SNR is SNR = P_1|h_1|^2g(d_1)/N, combining transmit power, channel gain, path loss, and receiver noise.The channel gain |h_i|^2 is modeled as an exponential random variable with mean one.
  • 1) Outage Condition 1:: The first outage condition measures the probability that a signal from distance d_1 fails to satisfy its required SNR threshold.This condition is distinct from the co-spreading-factor interference condition.

2) Outage Condition 2:

The second outage condition evaluates whether the strongest concurrent transmission using the desired signal’s spreading factor is sufficiently weaker than that desired signal.

  • 2) Outage Condition 2:: The model identifies the strongest interfering received signal among concurrent transmissions sharing the desired signal’s spreading factor.Time dependence is omitted under an ergodic-system assumption, and equal-spreading-factor devices use equal transmit powers.
  • 2) Outage Condition 2:: Q1 quantifies when same-spreading-factor collisions become significant and is expected to decrease as the mean number of end-devices ¯N increases.This metric isolates the interference-related outage condition.
  • 2) Outage Condition 2:: The joint outage probability is J1 = 1 − H1Q1, combining the SNR and co-spreading-factor success probabilities.The complementary outage probability provides a system-level performance metric for the single-gateway LoRa network.

3) Coverage Probability:

Coverage probability is defined for a randomly selected end-device and obtained by averaging its complementary outage probability over the deployment region, yielding a system-level metric for a single-gateway network.

  • Coverage probability measures whether a randomly selected end-device is not in outage at a particular time.
  • Averaging over the deployment region removes the selected device’s specific position and produces system-level coverage for X = {H1, Q1, H1Q1}.
  • The resulting metric describes a single-gateway LoRa network with approximately N̄ end-devices.

1) Outage Condition 1:

The first outage condition is the SNR-based connection failure, whose complementary probability follows from Rayleigh channel fading and remains independent of deployment density apart from the distance-dependent threshold.

  • The SNR outage probability is obtained by rearranging the SNR condition for an exponentially distributed channel gain |h1|^2.
  • The complementary outage probability H1 is a standard point-to-point result modified by the distance-dependent threshold qSF.
  • H1 is independent of the end-device deployment density ρ = N̄/V.

2) Outage Condition 2:

The second outage condition models co-spreading-factor interference by deriving the strongest same-spreading-factor interferer from spatial, fading, and random-transmission distributions, with an easier approximation that preserves the general trend but is crude.

  • Co-spreading-factor outage analysis uses order statistics to model the maximum among independently distributed interfering signals.The maximum represents the strongest interfering signal Xk* among same-spreading-factor interferers.
  • For uniformly deployed devices, the interfering signal variable Xi combines Rayleigh channel gain with distance-dependent path loss within the same-spreading-factor annulus.
  • The number of concurrently transmitting interferers is Poisson distributed with mean v = p0ρ|V̂(d1)|.
  • Equation (11) requires numerical computation, whereas its Taylor approximation in (12) provides a closed-form alternative for small z ≪ 1.
  • The approximation Q1 has piecewise-constant distance dependence and is very crude, although simulations confirm that it captures the general trend.
  • Figure 2 evaluates the derived coverage and outage expressions across distance and mean device counts using numerical integration and Monte Carlo markers.

B. Numerical Simulations and Discussion

Monte Carlo simulations verify the analytical derivations and reveal distinct distance-dependent behavior for SNR and co-spreading-factor interference, including a regime where interference limits scalability.

  • 10^5 random deployment realizations produce excellent agreement between the derived results and Monte Carlo simulations, except for the crude Q1 approximation.
  • The SNR outage condition H1 exhibits a saw-tooth boost when devices transition into regions assigned higher spreading factors.This effect follows from the distance-dependent SNR threshold qSF.
  • Co-spreading interference reverses the saw-tooth behavior because the number of interferers in adjacent spreading-factor regions varies geometrically with distance.
  • A vertical line in Fig. 2b identifies when co-spreading-factor interference becomes the dominant outage cause and therefore a scalability limit.The boundary depends strongly on the propagation environment and transmission-scheme details.

V. CONCLUSION

The study models interference in a single-gateway LoRa network and finds that co-spreading sequence interference limits scalability. Coverage degrades exponentially as end-device numbers increase, despite mitigation measures and low duty cycling.

  • LoRa performance was analyzed in a single-gateway network using stochastic geometry and two link-outage conditions.The conditions were based on SNR and co-spreading sequence interference.
  • Signals colliding in time, frequency, and spreading factor create interference in LoRa networks.
  • Co-spreading sequence interference causes performance to decay exponentially as the number of end-devices increases.This occurs despite available interference mitigation measures.
  • The resulting interference limits LoRa network scalability despite the communication range provided by adaptive CSS modulation without interference.
  • If cumulative interference is present, the reported qualitative scalability results are optimistic upper bounds.
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