Activity-Aware SIC for mMTC Uplinks

• AA-MF-SIC is a detection strategy that integrates user activity probabilities to enhance successive interference cancellation in sparse, grant-free CDMA uplinks.
• It employs an activity-aware MMSE filter with ℓ₁ regularization and a dynamic shadow area constraint to mitigate error propagation.
• Performance evaluations reveal up to a 3 dB gain over conventional methods and robustness even under imperfect CSI conditions.

Activity-aware Multiple Feedback Successive Interference Cancellation (AA-MF-SIC) is a low-complexity detection strategy for massive machine-type communications (mMTC), specifically targeting grant-free code division multiple access (CDMA) uplinks in scenarios where user activity is sparse and random. AA-MF-SIC incorporates a priori activity probabilities into both its filter design and its decision logic, thereby achieving robustness and performance improvements over conventional SIC-based approaches while maintaining computational efficiency (Renna et al., 2019).

1. System and Signal Model

AA-MF-SIC is designed for under-determined grant-free CDMA uplinks with $N$ machine-type devices (MTCDs) and a spreading factor $M$ at the receiver. Each active device transmits one symbol per signaling interval, drawn from a finite constellation $\mathcal{A}$, while inactive devices transmit zero. The augmented transmit vector is

$$\mathbf{x} = [x_1, \dots, x_N]^T, \qquad x_n \in \mathcal{A}_0, \;\; \mathcal{A}_0 = \mathcal{A} \cup \{0\},$$

and the received signal is modeled as

$\mathbf{y} = \mathbf{H}\,\mathbf{x} + \mathbf{n},$

where $\mathbf{H} \in \mathbb{C}^{M \times N}$ combines spreading sequences with flat Rayleigh-fading coefficients, and $$\mathbf{n} \sim \mathcal{CN}(\mathbf{0},\,\sigma_n^2\mathbf{I})$$ is circular complex Gaussian noise.

The activity pattern is sparse: each $x_n$ is nonzero (active) with probability $p_n \ll 1$, otherwise $x_n = 0$, with user activity assumed independent across devices.

2. Detection Problem Formulation

The optimal maximum a posteriori (MAP) rule selects

$M$0

where

$M$1

and $M$2 is the indicator function. This cost augments least-squares detection with an activity-related penalty term, enforcing sparsity in the estimated signal.

Direct minimization is intractable for large $M$3, motivating the use of low-complexity SIC, where users are detected sequentially. At each step, interference from previously detected users is cancelled, and the activity prior ($M$4) shapes both the detection and reliability assessment.

3. Algorithmic Structure and Innovations

3.1 MMSE Filter with Activity-aware $M$5 Regularization

At stage $M$6 of SIC, the residual is

$M$7

with $M$8 a possibly permuted version of $M$9. The filter $\mathcal{A}$0 is chosen to minimize

$\mathcal{A}$1

where $\mathcal{A}$2-regularization is used to account for sparsity and is approximated by a weighted quadratic

$\mathcal{A}$3

Setting the derivative to zero yields the activity-aware MMSE filter

$\mathcal{A}$4

with

$\mathcal{A}$5

where $\mathcal{A}$6 consists of columns $\mathcal{A}$7 to $\mathcal{A}$8. The soft symbol estimate is $\mathcal{A}$9, followed by hard quantization $$\mathbf{x} = [x_1, \dots, x_N]^T, \qquad x_n \in \mathcal{A}_0, \;\; \mathcal{A}_0 = \mathcal{A} \cup \{0\},$$0 over $$\mathbf{x} = [x_1, \dots, x_N]^T, \qquad x_n \in \mathcal{A}_0, \;\; \mathcal{A}_0 = \mathcal{A} \cup \{0\},$$1.

3.2 Activity-aware Shadow Area Constraint (SAC)

Decision reliability at each user is dynamically set according to activity priors. The minimum distance to the nearest constellation point is

$$\mathbf{x} = [x_1, \dots, x_N]^T, \qquad x_n \in \mathcal{A}_0, \;\; \mathcal{A}_0 = \mathcal{A} \cup \{0\},$$2

The reliability threshold is

$$\mathbf{x} = [x_1, \dots, x_N]^T, \qquad x_n \in \mathcal{A}_0, \;\; \mathcal{A}_0 = \mathcal{A} \cup \{0\},$$3

If $$\mathbf{x} = [x_1, \dots, x_N]^T, \qquad x_n \in \mathcal{A}_0, \;\; \mathcal{A}_0 = \mathcal{A} \cup \{0\},$$4, the hard decision is accepted; otherwise, AA-MF-SIC enters a multi-feedback (MF) stage.

3.3 Multi-feedback (MF) Stage

A candidate set $$\mathbf{x} = [x_1, \dots, x_N]^T, \qquad x_n \in \mathcal{A}_0, \;\; \mathcal{A}_0 = \mathcal{A} \cup \{0\},$$5 of the $$\mathbf{x} = [x_1, \dots, x_N]^T, \qquad x_n \in \mathcal{A}_0, \;\; \mathcal{A}_0 = \mathcal{A} \cup \{0\},$$6 nearest symbols (including $$\mathbf{x} = [x_1, \dots, x_N]^T, \qquad x_n \in \mathcal{A}_0, \;\; \mathcal{A}_0 = \mathcal{A} \cup \{0\},$$7) is established around $$\mathbf{x} = [x_1, \dots, x_N]^T, \qquad x_n \in \mathcal{A}_0, \;\; \mathcal{A}_0 = \mathcal{A} \cup \{0\},$$8. For each candidate $$\mathbf{x} = [x_1, \dots, x_N]^T, \qquad x_n \in \mathcal{A}_0, \;\; \mathcal{A}_0 = \mathcal{A} \cup \{0\},$$9, a trial-path is constructed: $\mathbf{y} = \mathbf{H}\,\mathbf{x} + \mathbf{n},$0 is cancelled from the residual, and standard SIC is executed for subsequent users, producing a trial estimate $\mathbf{y} = \mathbf{H}\,\mathbf{x} + \mathbf{n},$1. The final decision for $\mathbf{y} = \mathbf{H}\,\mathbf{x} + \mathbf{n},$2 is selected as

$\mathbf{y} = \mathbf{H}\,\mathbf{x} + \mathbf{n},$3

with $\mathbf{y} = \mathbf{H}\,\mathbf{x} + \mathbf{n},$4.

This mechanism injects alternative hypotheses only for uncertain decisions, thereby suppressing error propagation at a modest complexity.

3.4 Algorithm Pseudocode

The high-level workflow is $$\mathbf{n} \sim \mathcal{CN}(\mathbf{0},\,\sigma_n^2\mathbf{I})$$8 This structure maintains per-stage low complexity, with additional MF branches invoked only as required.

4. Computational Complexity

The computational costs of AA-MF-SIC and comparative detectors are summarized below:

Detector	Complexity Order	Notable Features
MMSE	$\mathbf{y} = \mathbf{H}\,\mathbf{x} + \mathbf{n},$5	-
SA-SIC	$\mathbf{y} = \mathbf{H}\,\mathbf{x} + \mathbf{n},$6	No ordering
K-Best	$\mathbf{y} = \mathbf{H}\,\mathbf{x} + \mathbf{n},$7	Number of survivors $\mathbf{y} = \mathbf{H}\,\mathbf{x} + \mathbf{n},$8, alphabet size
Ordered SA-SIC	$\mathbf{y} = \mathbf{H}\,\mathbf{x} + \mathbf{n},$9	A-SQRD, etc.
AA-MF-SIC	$\mathbf{H} \in \mathbb{C}^{M \times N}$0, adds $\mathbf{H} \in \mathbb{C}^{M \times N}$1 at low SNR	Modest per-symbol MF branch overhead

At high SNR, the multi-feedback branch is rarely needed, so complexity remains limited by the cubic scaling of conventional SIC. At low SNR, the number of MF paths increases, adding a quadratic term. These characteristics ensure scalability for large-scale mMTC scenarios (Renna et al., 2019).

5. Performance Evaluation

AA-MF-SIC was evaluated under uncoded block-fading channels using QPSK-augmented $\mathbf{H} \in \mathbb{C}^{M \times N}$2, with $\mathbf{H} \in \mathbb{C}^{M \times N}$3 devices and spreading length $\mathbf{H} \in \mathbb{C}^{M \times N}$4. The device activation probabilities $\mathbf{H} \in \mathbb{C}^{M \times N}$5 were drawn uniformly from $\mathbf{H} \in \mathbb{C}^{M \times N}$6. Results over $\mathbf{H} \in \mathbb{C}^{M \times N}$7 Monte Carlo trials with SNR in the range $\mathbf{H} \in \mathbb{C}^{M \times N}$8–$\mathbf{H} \in \mathbb{C}^{M \times N}$9 dB are characteristic.

Key performance metric: Net Symbol Error Rate (NSER) for active devices.

Key results:

• AA-MF-SIC consistently outperforms MMSE, SA-SIC, SA-SIC+ordering (A-SQRD), Iterative Reweighted, and K-Best detectors across the entire SNR range, achieving up to $$\mathbf{n} \sim \mathcal{CN}(\mathbf{0},\,\sigma_n^2\mathbf{I})$$0 dB gain at NSER $$\mathbf{n} \sim \mathcal{CN}(\mathbf{0},\,\sigma_n^2\mathbf{I})$$1.
• At increased activity rates, AA-MF-SIC remains superior and eventually outpaces even an “Oracle MMSE” detector with perfect active set knowledge.
• Under imperfect CSI (with $$\mathbf{n} \sim \mathcal{CN}(\mathbf{0},\,\sigma_n^2\mathbf{I})$$2, $$\mathbf{n} \sim \mathcal{CN}(\mathbf{0},\,\sigma_n^2\mathbf{I})$$3), the AA-MF-SIC preserves its performance advantage, with only a slight margin lost compared to perfect CSI.

6. Key Insights and Applications

AA-MF-SIC leverages activity-awareness in two critical algorithmic junctures:

• The MMSE filter regularization is modulated by each user’s activation probability via $$\mathbf{n} \sim \mathcal{CN}(\mathbf{0},\,\sigma_n^2\mathbf{I})$$4, directly informing the aggressiveness of interference cancellation and thresholding.
• Decision confidence is governed by the activity-tuned Shadow Area Constraint (SAC), ensuring that only unreliable soft estimates trigger multi-path exploration.

This architecture suppresses error propagation, a principal source of performance degradation in standard SIC, while maintaining low additional cost per user—particularly at moderate and high SNR.

AA-MF-SIC enables efficient, near-optimal detection in mMTC settings where sparse user activity and grant-free operation preclude traditional scheduling and coordinated access. The design is naturally extensible to adaptive candidate set selection, coded transmission schemes (e.g., integration with LDPC codes), higher-order constellations, MIMO uplinks, and joint channel estimation and detection for grant-free systems (Renna et al., 2019).

7. Trade-offs and Prospects

The balance between complexity and performance is governed by the parameter $$\mathbf{n} \sim \mathcal{CN}(\mathbf{0},\,\sigma_n^2\mathbf{I})$$5 (number of multi-feedback branches). Larger $$\mathbf{n} \sim \mathcal{CN}(\mathbf{0},\,\sigma_n^2\mathbf{I})$$6 mitigates unreliability at low SNR but increases computational burden. In practice, $$\mathbf{n} \sim \mathcal{CN}(\mathbf{0},\,\sigma_n^2\mathbf{I})$$7 can be set adaptively according to SNR or empirical reliability statistics.

Potential lines of further research include:

• Optimizing MF candidate selection beyond nearest points.
• Integration with advanced channel-coding frameworks.
• Generalization to higher spectral efficiency and multi-antenna contexts.
• Joint detection and channel estimation, particularly for fully grant-free access architectures.

AA-MF-SIC thus provides a systematic, activity-informed framework for powerful, scalable detection in the emerging landscape of massive, uncoordinated, and sporadic machine-type communications (Renna et al., 2019).