Successive Interference Cancellation (SIC)

• Successive Interference Cancellation is a detection technique that iteratively decodes and subtracts overlapping signals, enhancing receiver performance.
• Stochastic-geometry models demonstrate that SIC improves coverage probability from 13% to 20% at the cell edge, achieving a 34% relative gain.
• SIC enables network designers to nearly double the sustainable active user count and extend node density by a factor of 2.6 with minimal end-device changes.

Successive Interference Cancellation (SIC) is a detection technique that enables receivers to decode superposed or colliding signals by iteratively decoding and subtracting previously recovered signal contributions from the aggregated received waveform. This approach is integral to modern wireless communication protocols, especially in low-power wide-area networks (LPWANs) such as LoRaWAN, where uncoordinated transmissions and pure random access lead to frequent packet collisions. In the context of LoRa networks, rigorous stochastic-geometry models and closed-form coverage formulas have precisely quantified the gains from incorporating SIC at the gateway level, revealing substantial enhancements in both reliability and network capacity (Sant'Ana et al., 2020).

1. Stochastic Geometry Model for LoRa with SIC

The physical and access layer models considered for LoRa networks with SIC are constructed as follows:

• Coverage area: A disk $\mathcal{V} \subset \mathbb{R}^2$ of radius $R$, area $V = \pi R^2$.
• Node distribution: $\bar{N}$ end-devices are uniformly scattered, with spatial density $\rho = \bar{N}/V$.
• Spreading-factor rings: The cell is partitioned into six concentric rings, each ring $i$ using spreading factor $\mathrm{SF}_i$, with area $V_i = \pi(l_i^2 - l_{i-1}^2)$.
• Medium access: Pure ALOHA, with duty-cycle $p_i$ per node in ring $i$. Active nodes in ring $i$ form a Poisson point process (PPP) $\Phi_i$ of intensity $\alpha_i = 2\,p_i\,\rho\,V_i$.
• Path loss: For a node at distance $d_k$, the large-scale gain $g_k \approx d_k^{-\eta}$, where $\eta$ is the path-loss exponent.
• Small-scale fading: Rayleigh fading $|h_k|^2 \sim \mathrm{Exp}(1)$.
• Noise: AWGN with power $\sigma_w^2$ (e.g. $-117\,\mathrm{dBm}$ for a $125\,\mathrm{kHz}$ channel).
• Transmit power: Same for all nodes, $P_t$.
• SNR/capture thresholds: Each $\mathrm{SF}_i$ has a sensitivity $q_i$; capture threshold is $\gamma$ (typically 1–6 dB).

This mathematically tractable framework allows the derivation of coverage and reliability metrics incorporating the impact of SIC under real-world constraints on path loss, fading, interference, and stochastic user activity (Sant'Ana et al., 2020).

2. SIC-Enabled Decoding Probability and Coverage Formulas

2.1 Baseline (No SIC) Coverage

For a reference node at distance $d_1$ in ring $i$, coverage is only possible if both:

• The received signal-to-noise ratio (SNR) exceeds the sensitivity threshold $q_i$ (probability $H_1$).
• The signal-to-interference ratio (SIR) exceeds the capture threshold $\gamma$ against the aggregate PPP interferers in the same ring (probability $Q_1$).

The resulting baseline coverage probability is:

$C_1 \simeq H_1 Q_1$

2.2 Coverage with SIC

SIC posits that, after decoding and subtracting one interfering packet, the originally-collided reference signal may become decodable. The improved coverage probability is:

$C_1^{\mathrm{SIC}} \simeq H_1 Q_1 + H_1 Q_2$

where $Q_2$ characterizes the probability that (i) only one interferer is present, (ii) this interferer has received power $\geq \gamma$ times that of the reference, and (iii) both signals clear their respective SNR thresholds.

The explicit closed-form for $Q_2$ involves the duty cycle, path loss, and analytic evaluation over the spatial distribution:

$Q_2 = \frac{\alpha_i e^{-\alpha_i}}{l_i^2-l_{i-1}^2} \bigg[ l_i^2\,_2F_1(1,\tfrac{2}{\eta};1+\tfrac{2}{\eta};-\gamma\,l_i^\eta/d_1^\eta) - l_{i-1}^2\,_2F_1(1,\tfrac{2}{\eta};1+\tfrac{2}{\eta};-\gamma\,l_{i-1}^\eta/d_1^\eta) \bigg]$

where $_2F_1$ is the Gauss hypergeometric function.

2.3 Step-by-Step SIC Operation at the Gateway

1. The gateway receives a superposition of colliding signals $s_1$ (reference), $s_2$ (interferer).
2. Compute instantaneous received powers $G_j = P_t |h_j|^2 g(d_j)$.
3. If $\max(G_1, G_2)/\min(G_1, G_2) \geq \gamma$, decode strongest.
4. Subtract reconstructed waveform of the decoded signal from the received sum.
5. Compute the residual SNR for the weaker packet.
6. If residual SNR $\geq q_i$, declare successful decode (Sant'Ana et al., 2020).

3. Numerical Results and Network Gains from SIC

• Worst-case reliability: At the cell edge ($d_1=3\,\mathrm{km}$), baseline worst-case coverage is $C_1\approx 13\%$; with SIC, $C_1^{\mathrm{SIC}}\approx 20\%$, a $34\%$ relative improvement.
• Capacity scaling: For a target worst-case reliability of $80\%$, the maximum per-ring load $\alpha_i$ increases from $0.20$ (no SIC) to $0.52$ (SIC). This translates to increasing the maximum sustainable node count from $4,689$ to $12,191$ at fixed duty cycle, a $159\%$ user-serving gain at the same reliability.
• Sustainable density: SIC extends the node density support by a factor of roughly $2.6$ for a given reliability.

These numerical findings were obtained by Monte Carlo simulations that validate the tightness of the analytic formulas over $10^5$ random placements and fading realizations (Sant'Ana et al., 2020).

4. Design Implications and Practical Considerations

• Gateway complexity: All SIC logic is implemented at the gateway; end devices require no hardware or protocol change.
• Duty-cycle/user-count tradeoff: At fixed duty cycle per end-device, SIC enables increased user density; at fixed user count, it permits higher per-user duty cycle.
• Spreading-factor (SF) allocation: Rings with higher SF (cell edges) see the largest relative benefits from SIC since their near-far suppression is worst under pure capture. Optimizing SF ring boundaries $l_i$ can balance network loads when SIC is present.
• Capture threshold tuning: Lowering the capture threshold $\gamma$ by improving receiver design increases $Q_2$ (the SIC term), further enhancing gains.
• Incremental deployment: Even single-step SIC (decode up to one interferer) yields large gains; deeper (multi-level) SIC may have diminishing marginal improvement due to the rapidly decaying probabilities of multiple independent decodable overlaps in realistic ALOHA loads.

5. Analytical Framework and Formula Table

Key coverage probability components in the LoRa SIC setting are summarized:

Probability Term	Mathematical Definition	Physical Meaning
$H_1$	$P[\mathrm{SNR}_1 \ge q_i \mid d_1]$	Reference node SNR above sensitivity
$Q_1$	$P[\mathrm{SIR}_1 \ge \gamma \mid d_1]$	Captured against all interferers
$C_1 = H_1 Q_1$	Baseline coverage probability	Without any SIC
$Q_2$	Probability of one strong interferer, both above SNR	SIC-enabled two-packet decoding event
$C_1^{\mathrm{SIC}}=H_1 Q_1 + H_1 Q_2$	Total coverage probability with single-step SIC	Baseline plus single interferer SIC

The contextually relevant deployment parameters (cell radius, ALOHA duty cycle, SF allocation) and precise stochastic-geometry treatment of capture and interference ensure these results are directly implementable by LoRaWAN network designers (Sant'Ana et al., 2020).

6. Interpretation and Domain-Specific Impact

Theoretical modeling and simulation establish that in LoRa networks operating under pure ALOHA, the integration of single-step SIC at the gateway can:

• Significantly increase the worst-case delivery reliability,
• More than double the supported active user population,
• Substantially improve the robustness of cell-edge devices,
• Allow for higher per-user duty cycles or support densified deployments,
• Be realized with minimal impact to end-device cost or complexity.

These properties, rigorously demonstrated in the referenced stochastic-geometry analysis, motivate the adoption of SIC-capable receivers as a low-cost, high-impact method of enhancing LoRaWAN/LPWAN systems (Sant'Ana et al., 2020).