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Sequential Detection-Based Iterative Blind Separation for Single-Channel Co-Frequency Signals
Heng Wang, Peng Sun, Kexian Gong, Kunheng Zou, Hua Jiang
TL;DR
Single-channel co-frequency signal separation faces trade-offs among accuracy, complexity, and robustness, while CSI estimation remains insufficiently precise. SDIS combines sequential detection, DUKF-based CSI estimation, and iterative decision feedback; simulations report gains across separation, CSI estimation, efficiency, and robustness, including a speed advantage for 8PSK-8PSK signals.
Problem
Existing SCSBS methods struggle to balance accuracy, computational efficiency, and robustness, while CSI estimation methods lack precision.
Source: §I · p. 1Method
SDIS combines sequential detection for symbol detection, DUKF-based CSI estimation, and iterative decision feedback to refine symbol decisions and CSI estimates.
Source: §I · p. 1, A. Key Innovations of SDIS · p. 2Results
SDIS outperforms benchmarks across separation, CSI accuracy, efficiency, and robustness; for 8PSK-8PSK signals below MBER 3 × 10^-4, it is at least 4.60× faster.
Source: C. Impact of Noise and Modulation on… · p. 4, §V · p. 5Takeaways & Limitations
Unlike conventional algorithms whose complexity scales as M^2L′, SDIS detaches complexity from L′, enabling L′ = 5 in practice.
Source: §V · p. 5
Abstract
from arXiv · showhide
Existing single-channel co-frequency signal blind separation (SCSBS) algorithms struggle to balance separation accuracy, computational complexity, and robustness, while current channel state information (CSI) estimation methods lack precision. To address these limitations, we propose a sequential detection (SD)-based iterative separation (SDIS) algorithm. SDIS incorporates a delayed unscented Kalman filter (DUKF) into an iterative decision feedback framework, jointly enhancing signal separation and CSI estimation. Simulation results show that SDIS outperforms benchmarks in separation accuracy, CSI estimation accuracy, computational efficiency, and robustness. Notably, when the mean bit error rate (MBER) drops below $10^{-4}$, SDIS can tolerate at least $0.8$ dB more noise than the benchmarks.
I. INTRODUCTION
Scarce spectrum and resource reuse have made co-frequency signals more prevalent, motivating blind recovery of their constituent sub-signals. The paper introduces SDIS to address separation and CSI-estimation limitations, then specifies the two-signal model and its assumptions.
I. INTRODUCTION
- As spectrum resources become scarce and time-frequency reuse grows, independent sub-signals increasingly share a band, motivating blind recovery from a single-channel co-frequency signal.The paper identifies a gap in balancing separation accuracy, efficiency, and robustness, alongside insufficiently accurate CSI estimation.Source: §I · p. 1
- PSP-based methods outperform SIC- and PF-type approaches, but PSPL, PCP, and TVD become computationally costly for higher-order modulation.SDS was proposed as a low-complexity alternative; PSP-based methods and SDS are sensitive to CSI pre-estimation errors.Source: §I · p. 1
- SDIS combines sequential detection with DUKF-based CSI estimation and iterative decision feedback to refine symbol decisions and CSI estimates.The paper reports benchmark gains in separation accuracy, CSI-estimation accuracy, computational efficiency, and robustness, increasing with modulation order.Source: §I · p. 1
II. SYSTEM MODEL
- The system model forms two pulse-shaped, independent PSK sub-signals with equal symbol rates and closely spaced carriers, then superimposes them and adds complex AWGN.It assumes equal modulation orders, equiprobable symbols, identical raised-cosine pulse shaping, and CSI parameters constant over the observation interval.Source: §II · pp. 1–2
III. THE SDIS ALGORITHM
SDIS makes sequential detection practical by truncating the pulse-support calculation and refining its decision metric through iterative feedback. A delayed UKF tracks CSI alongside symbol decisions, with delayed updates and averaging used in the estimation process.
A. Key Innovations of SDIS
- Because path metrics depend on a pulse contribution spanning L symbols, SDIS truncates the calculation and partitions the raised-cosine support into interval types.The partition uses the pulse’s sharp main-lobe property; the text identifies truncation, compensation, and residual regions.Source: A. Key Innovations of SDIS · p. 2
- Iterative decision feedback estimates compensation terms in real time, improving β_n accuracy when approximate terms fail to compensate their effects.The method uses the exact form of β_n and current symbol estimates in later iterations.Source: A. Key Innovations of SDIS · p. 2
- CSI pre-estimation errors make channel estimates unreliable, so SDIS replaces benchmark LMS tracking with a delayed unscented Kalman filter.The DUKF tracks the CSI parameters; its state update is delayed to align with the sequential-detection search.Source: A. Key Innovations of SDIS · p. 2
- Final estimates of channel gain, CFO, carrier phase offset, and symbol timing offset average converged samples to mitigate stochastic fluctuations and support asymptotic consistency.The state update uses a short delay because one timing component is estimated independently, and the text says this barely affects convergence.Source: A. Key Innovations of SDIS · p. 2
B. Workflow of SDIS
SDIS combines DUKF-based CSI estimation with iterative decision feedback to refine symbol decisions and CSI estimates. Its workflow initializes candidate paths, extends and updates them, and outputs decisions over repeated iterations.
B. Workflow of SDIS
- SDIS integrates DUKF-based CSI estimation with iterative decision feedback to progressively refine both CSI estimates and symbol decisions.Source: B. Workflow of SDIS · p. 3
- The algorithm initializes a stack of at least M^2 rows, each storing a windowed candidate path with up to K symbol pairs.Source: B. Workflow of SDIS · p. 3
- Each path tracks its path metric and output count, while the selected paths begin with CSI state estimates from pre-estimation.Source: B. Workflow of SDIS · p. 3
- Path extension and DUKF state updates feed cyclic decision output, followed by CSI updates and another iteration unless the iteration limit is reached.The algorithm reports the average loop count when it terminates.Source: B. Workflow of SDIS · p. 3
IV. NUMERICAL RESULTS AND ANALYSIS
The numerical evaluation compares SDIS with five listed benchmark algorithms.
IV. NUMERICAL RESULTS AND ANALYSIS
- The evaluated methods are PSPL, PCP, TVD, SDS, and FPJE, alongside SDIS.Source: §IV · p. 3
A. Experimental Setup
The experiments define averaged error metrics and CSI pre-estimation errors, then evaluate the methods using repeated MATLAB simulations under stated signal and algorithm settings.
A. Experimental Setup
- MBER and MNMSE denote BER and CSI-estimate NMSE averaged over the two received sub-signals, respectively.The passage also defines normalized gain, CFO, and phase CSI pre-estimation errors.Source: A. Experimental Setup · p. 3
- Results are averaged over 100 Monte Carlo trials, with each terminal transmitting 24,000 bits per trial.Simulations use MATLAB R2020a on Windows 10 with an Intel Core i5-12400F and 16 GB DDR4 RAM.Source: A. Experimental Setup · p. 3
- The QPSK setup uses p = 1, α = 0.35, and Es/N0 = 19 dB, with specified channel-gain, timing, CFO, phase, and pre-estimation-error settings.Source: A. Experimental Setup · p. 4
- For SDIS and SDS, the stated settings include U = 2, L′′1 = 1, L′′1 = 2, λ = 1.5, K = 12, and D = 16M^2.Other benchmarks use stated LMS, traceback, and search settings; PSPL with L′0 = 2 is denoted PSPL4, FPJE uses p = 4, and PCP is assumed to attain CFO estimation accuracy of 10^-5.Source: A. Experimental Setup · p. 4
B. Computational Complexity Analysis
SDIS has lower stated per-sample complexity scaling than the benchmarks, and its runtime advantage increases with modulation order and L′.
B. Computational Complexity Analysis
- M^2 versus M^2L′: SDIS scales as M^2, while the benchmarks scale as M^2L′.The conventional methods’ per-stage costs are dominated by M^2L′ branch-metric computations and 2M^(2L′−2) LMS updates.Source: B. Computational Complexity Analysis · p. 4
- Each SDIS iteration performs approximately QM^2/2 DUKF operations alongside its branch-metric computations.Source: B. Computational Complexity Analysis · p. 4
- The running-time advantage of SDIS increases with M and L′.Source: B. Computational Complexity Analysis · p. 4
C. Impact of Noise and Modulation on Separation
SDIS improves separation across modulation schemes, with decision feedback boosting accuracy and a reported noise-tolerance advantage over benchmarks. Its performance gains depend on iteration count, with little additional improvement beyond U = 2 under mutual interference.
C. Impact of Noise and Modulation on Separation
- Decision feedback (U > 1) significantly improves SDIS accuracy over U = 1, but increasing U beyond 2 yields negligible additional gain under mutual interference.Q decreases as U increases, then saturates for U ≥ 2.Source: C. Impact of Noise and Modulation on… · p. 4, Figure 3 · p. 4
- For 8PSK-8PSK, TVD degrades performance relative to PSPL4, while SDIS (U = 2) uses L′ = 5 with DUKF for accurate channel characterization.PSPL and PCP, both with L′ = 3, achieve comparable accuracy.Source: C. Impact of Noise and Modulation on… · p. 4
- For QPSK-QPSK below 10−4 MBER, SDIS requires at least 0.8 dB less Es/N0 than benchmarks; for 8PSK-8PSK below 3 × 10−4 MBER, at least 2 dB less.For 8PSK-8PSK, SDIS runs at least 4.60× faster than benchmarks.Source: C. Impact of Noise and Modulation on… · p. 4
D. Impact of CSI Pre-Estimation Errors on Separation
SDIS is more robust to CSI pre-estimation errors than the benchmarks. The comparisons cover paired CFO errors and linked channel-gain, phase, and timing errors, with SDIS showing limited sensitivity and faster convergence.
D. Impact of CSI Pre-Estimation Errors on Separation
- SDIS is barely affected by ∆(f1) and consistently outperforms benchmarks, whereas LMS-based methods’ MBER increases monotonically with ∆(f1).PCP maintains stable performance through CFO pre-compensation and LMS correction of minor residual interference.Source: D. Impact of CSI Pre-Estimation Errors… · p. 4, Figure 4 · p. 5
- At ∆(h0) = 0.02 and 0.04, LMS-based benchmarks require 6 and 12 data groups to converge, respectively; SDIS achieves faster convergence and higher accuracy.The comparison evaluates the first 20 data groups, each containing 50 symbol pairs.Source: D. Impact of CSI Pre-Estimation Errors… · pp. 4–5, Figure 4 · p. 5
- Overall, SDIS exhibits significantly better robustness to CSI pre-estimation errors than the benchmarks.Fig. 4 varies paired CFO errors in panel (a) and linked channel-gain, phase, and timing errors in panel (b).Source: D. Impact of CSI Pre-Estimation Errors… · p. 5, Figure 4 · p. 5
E. Impact of Noise on CSI Estimation
Under error-free symbol detection for FPJE, SDIS estimates all four CSI parameters more accurately than FPJE. The reported gains are about two orders of magnitude for channel gain and symbol timing offset, with a lower CFO MNMSE.
E. Impact of Noise on CSI Estimation
- SDIS accuracy for all four CSI parameters exceeds FPJE when FPJE is evaluated with error-free symbol detection.Both methods use sequence detection results as prior information for CSI estimation.Source: E. Impact of Noise on CSI Estimation · p. 5
- For CG and STO, SDIS accuracy is about two orders of magnitude higher than FPJE.FPJE uses dimension-by-dimension stepwise search in a four-dimensional parameter space and only a few dozen symbol pairs, making it prone to local optima.Source: E. Impact of Noise on CSI Estimation · p. 5
- FPJE’s CFO MNMSE is on the order of 10^-9, whereas SDIS achieves an MNMSE on the order of 10^-14.Source: E. Impact of Noise on CSI Estimation · p. 5
V. CONCLUSION
SDIS combines higher separation accuracy with lower computational complexity and improved CSI estimation precision and robustness. It also enables L′ = 5 in practice, while future work is directed toward scenarios with more than two sub-signals.
V. CONCLUSION
- For 8PSK-8PSK signals, to achieve MBER below 3 × 10−4, SDIS is at least 4.60 times faster than the benchmarks and requires at least 2 dB less Es/N0.Source: §V · p. 5
- Conventional SCSBS complexity scales as M^2L′ and typically limits L′ to 3, whereas SDIS detaches complexity from L′ and enables L′ = 5 in practice.The conclusion attributes separation-accuracy gains to combining a larger L′ with iterative decision feedback.Source: §V · p. 5
- SDIS has advantages in separation accuracy, CSI estimation precision, computational efficiency, and robustness; future work will address more than two sub-signals.Source: §V · p. 5