--- title: Imperfect SIC in Wireless Systems url: https://www.emergentmind.com/topics/imperfect-successive-interference-cancellation-ipsic type: topic --- # Imperfect SIC in Wireless Systems Imperfect Successive Interference Cancellation (ipSIC) refers to the scenario where interference cancellation at a multiuser receiver is non-ideal and leaves residual interference due to channel estimation errors, decoder misdetections, hardware limitations, quantization or algorithmic imperfections. The ipSIC phenomenon is fundamental to the analysis and design of contemporary wireless systems, including power-domain non-orthogonal multiple access (NOMA), multi-carrier code-division systems, spatial-multiplexing multiple-input multiple-output (MIMO), rate-splitting, relay-aided, and reconfigurable intelligent surface (RIS) networks. The mathematical modeling of ipSIC incorporates a nonzero interference residual (often parametrized by factors such as ε, β, η, or Ξ) into SINR expressions, simulation setups, and closed-form performance metrics. This treatment allows for precise quantification of its degrading effects on outage, bit error rate, diversity, and throughput. ## 1. Mathematical Models and Mechanisms of ipSIC In canonical downlink NOMA, the received signal at each user is a superposition of $L$ user symbols, and SIC proceeds by decoding the higher-power layers in sequence. Under ipSIC, if the $l$-th user fails to decode and subtract the signals of users $k=1,\dots,l-1$ perfectly, residual interference proportional to their power and detection error accumulates. The post-SIC observation model becomes: $$ \tilde{r}_l = \sqrt{\alpha_l P} h_l x_l + \sum_{n=l+1}^L \sqrt{\alpha_n P} h_l x_n + \underbrace{\sum_{k=1}^{l-1} \sqrt{\alpha_k P} h_l \Delta_k}_{\text{ipSIC residuals}} + n_l, $$ where $\Delta_k = x_k - \hat{x}_k$ models the symbol error for user $k$ [1804.03847]. The same structure recurs in uplink RSMA [2501.19019], cooperative relay NOMA [2103.12418], RIS-NOMA [2509.19383], ISAC [2405.00109], DS-CDMA [1102.5442], and spatial MIMO [1610.01426]. In many frameworks, the net residual is abstracted as an additive term scaled by an imperfection coefficient (e.g., $\varepsilon$ or $\eta$) in the SINR denominator, capturing the fraction of power or raw interference that remains after cancellation. Imperfect CSI, hardware distortion, timing errors, and quantization further compound ipSIC residuals. For instance, in quantized ARIS-NOMA, ADC quantization noise, residual hardware impairments, and ipSIC are aggregated in the SINR denominator [2509.19383]. In MIMO, transmitter and receiver error-vector magnitudes (EVMs) and channel estimation dispersion jointly impact the post-SIC SINDR [1610.01426]. ## 2. Analytical Performance Metrics and Diversity Behavior The principal performance metrics impacted by ipSIC are pairwise error probability (PEP), outage probability (OP), bit error rate (BER), and system throughput. Closed-form expressions for these quantities under ipSIC are available for a range of scenarios: - **PEP in downlink NOMA:** For user $l$, $$ \mathrm{PEP}(x_l \to \hat{x}_l) = \frac{L!}{\sigma_h^2 (l-1)!(L-l)!} \sum_{j=0}^{l-1} (-1)^{l-1-j} \binom{l-1}{j} (L-l+j+1) \left[1 - \frac{\beta_l \sigma_h}{\sqrt{\beta_l^2 \sigma_h^2 + (L-l+j+1)\upsilon^2}}\right], $$ where $\beta_l$ includes ipSIC residual terms [1804.03847]. - **Outage probability and floors:** In cooperative NOMA-relay networks, ipSIC yields a high-SNR error floor in closed form; the dominant term is a function of residual coefficients $\varepsilon_{X}$ and link powers, and does not vanish as SNR $\to \infty$ [2103.12418]. In ARIS-NOMA with quantization, asymptotic OP approaches a constant for any $\varepsilon>0$ [2509.19383]. - **Diversity order:** Under ipSIC, diversity order often collapses (e.g., $d_{k}=0$ for any $\varepsilon>0$ in high-SNR ARIS-NOMA [2509.19383]; $d_l = l$ in downlink NOMA [1804.03847], but with error-rate floors dominating in practice). The table below summarizes diversity effects in several paradigms: | System | Perfect SIC Diversity | ipSIC Diversity (any $\varepsilon>0$) | |----------------------|--------------------------|-------------------------------------------------| | Downlink NOMA | $l$ (user order) | $l$ (theoretical), but with prominent floor | | MIMO ZF-SIC | $n - m + i$ | 0 (hard floor) | | MMSE-SIC | $n - m + i$ (if $\kappa_R=0$) | 0 (otherwise) | | ARIS-NOMA | $(\mu_0+1)/2$ | 0 | In all cases, ipSIC induces either a nonvanishing probability of error ("error floor") or a severe reduction in coding gain [1804.03847, 2103.12418, 1610.01426, 2509.19383]. ## 3. Algorithmic Mitigation and Optimal ipSIC Strategies Several techniques can mitigate ipSIC effects: - **Partial/Weighted Cancellation:** Instead of subtracting the entire reconstructed interference, the receiver applies an optimized weighting $\alpha$ to the estimated signal. The optimal factor is $$ \alpha^{\rm opt} = \frac{R_x}{P_x(1+\sigma_h^2)}, $$ where $R_x=\mathbb{E}\mathrm{Re}(x_u\hat{x}_u^*)$, $P_x=\mathbb{E}|\hat{x}_u|^2$, and $\sigma_h^2$ is the normalized channel estimation MSE [1111.3163]. This minimizes the normalized residual interference. Partial SIC yields substantial SNR gains (up to 3 dB at BER $=10^{-4}$) for moderate channel error. - **Adaptive Blind Cancellation:** MC DS-CDMA receivers employing constant-modulus adaptive despreaders generate data-driven scaling for cancellation and achieve superior BER versus conventional matched filter or classical SIC [1102.5442]. - **Deep Learning-Aided SIC:** Data-driven designs (e.g., SICNet) replace hard decision-based cancellation with DNN blocks trained to output soft probabilities for each interfering symbol, directly learning to invert ipSIC effects and CSI mismatch [2207.14468]. Such receivers significantly reduce the error floor associated with ipSIC. - **Power Allocation and User Pairing:** Joint optimization of user power coefficients subject to ipSIC-aware error probability thresholds balances fairness and overall BER. Closed-form bounds (e.g., on $\delta_s$ in two-user NOMA) dictate feasible regions for maintaining rate gains under increasing residuals [2201.09204]. - **Protocol Adaptation:** STBC-CNOMA reduces the number of SIC steps compared to classical cooperative-NOMA, lowering cumulative ipSIC exposure [2007.03497]. In full-duplex ISAC, ordering of successive detection/decoding should be dynamically selected based on target distance and residual self-interference fraction [2405.00109]. ## 4. Fundamental Impact on Link-Level and System-Level Performance Imperfect SIC systematically degrades performance across wireless architectures: - **Error Floors and Coding Gain Loss:** Analytical and simulation results for NOMA, spatial multiplexing MIMO, RSMA, and ARIS-NOMA agree that ipSIC introduces error floors at high SNR, which cannot be eliminated by code or modulation refinements [1804.03847, 2509.19383, 2103.12418, 1610.01426, 2501.19019]. - **Throughput Saturation:** In ARIS-NOMA, quantized and ipSIC-impaired systems have throughput ceilings below the maximal user rate as SNR increases, while perfect SIC enables throughput to approach theoretical maxima [2509.19383]. - **Uplink vs. Downlink Sensitivity:** For uplink RSMA, at low SNR, channel estimation error dominates, but at high SNR, ipSIC dictates outage and throughput limits [2501.19019]. RSMA is more robust than NOMA to ipSIC due to its message-splitting structure. - **Ordering and Scheduling:** In ISAC networks, the optimal order for joint comm-radar successive decoding is contingent on the ipSIC level, as even minuscule residuals (e.g., $\zeta \sim 10^{-6}$) can render radar detection infeasible at longer ranges [2405.00109]. ## 5. System Design and Engineering Guidelines under ipSIC Constraints Key design principles synthesized from analytical and empirical studies include: - **Power Allocation:** For fairness-oriented objectives, far-user power must be sufficiently large to overcome ipSIC-induced error floors, but not so large as to starve near-users or violate maximum error constraints [1804.03847, 2201.09204, 2103.12418]. - **Hardware Quality:** Receiver hardware impairment (quantized ADCs, nonzero EVM, analog cancellation leakage) must be tightly controlled to avoid irreducible performance floors—in MIMO SIC, receiver RF chain EVM is especially critical [1610.01426, 2509.19383]. - **Adaptive Protocols:** In full-duplex sensing-communication, system-initiated switching of decoding order, or selection of protocol phases (e.g., when to transition from detect-first to decode-first strategies), should be implemented as a function of ipSIC parameters and operational region [2405.00109, 2103.12418]. - **System Load and User Number:** The maximum simultaneous user load in spread-spectrum Aloha with ipSIC is inversely proportional to $(1-\varepsilon)$, and must be scaled down as ipSIC worsens [1610.09215]. - **Advanced Coding/Iterative Approaches:** For MAI-heavy, channel-impaired links, joint iterative channel estimation, partial cancellation and modern codes (e.g., turbo, LDPC) assist in minimizing ipSIC impact, particularly when pilot densities are limited [1111.3163, 1102.5442]. ## 6. Comparative Assessment of ipSIC Impact across Architectures A cross-section of results is instructive: | Architecture | Residual term in SINR/OP | Dominant effect of ipSIC | |---------------------------------|-------------------------------------------------------|------------------------------------| | Downlink NOMA | $\sum_{k