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Study of Iterative Detection and Decoding for {Mixed Near- and Far-Field} XL-MIMO Systems
Nayyab Haider, Rodrigo C. de Lamare
TL;DR
Near-field XL-MIMO offers spherical-wave channels with spatial structure that existing SIC orderings do not explicitly exploit, while near-field CSI estimation is challenging. The paper proposes WR-SIC with an LDPC-based iterative detection and decoding scheme; simulations report a 3–4 dB SNR gain at BER = 10−3 under perfect CSI and an extra 2 dB gain through IDD iterations.
Problem
Existing SIC ordering approaches do not explicitly account for near-field channel properties, and accurate distance and angle estimation makes CSI challenging.
Source: §I · p. 1Method
The paper proposes WR ordering for SIC and integrates the WR-SIC detector with LDPC coding through iterative soft-information exchange.
Source: §I · p. 1, §VII · p. 5Results
3–4 dB SNR gain over conventional ordering schemes at BER = 10−3 under perfect CSI, with an extra 2 dB gain through IDD iterations.
Source: §VII · p. 6Takeaways & Limitations
The results show that WR-SIC exploits near-field spatial degrees of freedom, with IDD iterations further improving its reported performance.
Source: §VI · p. 5, §VII · pp. 5–6
Abstract
from arXiv · showhide
Extra-large multiple-input multiple-output (XL-MIMO) systems {serving users across near-field and far-field regions} experience spherical wavefront propagation that provides enhanced spatial resolution over traditional far-field systems. In this work, we propose a novel weighted rate (WR) ordering-based successive interference cancellation (SIC) scheme that exploits the spatial degrees of freedom inherent in near-field propagation. We also develop an iterative detection and decoding (IDD) framework that integrates the proposed WR ordering with low-density parity-check (LDPC) coding and channel estimation. We then analyze the information rates and the impact of near-field channel characteristics. Numerical results show that the proposed WR-SIC and the IDD scheme outperform existing approaches.
I. INTRODUCTION
Near-field spherical-wave XL-MIMO offers enhanced spatial discrimination, but existing SIC orderings do not explicitly account for near-field structure and receivers face channel-estimation challenges. The paper proposes WR-SIC and an LDPC-based IDD framework.
I. INTRODUCTION
- Near-field propagation offers spatial discrimination, yet existing SIC orderings do not explicitly exploit its properties and accurate distance and angle estimation challenge CSI.Prior work also lacks an integrated framework combining specialized near-field ordering with interference mitigation.Source: §I · p. 1
- The proposed WR ordering weights each stream’s information rate by its squared singular value, and the IDD scheme combines WR-SIC with LDPC coding and iterative soft-information exchange.The detector and decoder exchange LLRs, with extrinsic information fed back to update a priori probabilities.Source: §I · p. 1
II. SYSTEM MODEL
- The uplink model has a base station with M receive antennas serving K users, each with NU transmit antennas and independent data streams.The BS uses a ULA with antenna spacing d = λ/2.Source: §II · p. 1
A. Near-Field and Far-Field Channel Models
- Near-field users are modeled with spherical-wave channels, while far-field users use a plane-wave approximation.Near-field channel coefficients follow a non-uniform spherical-wave model with Friis path-loss gain.Source: A. Near-Field and Far-Field Channel… · pp. 1–2, §II · p. 1
B. Signal Model and Spatial Degrees of Freedom
The signal model combines streams from near- and far-field users at the receiver. Spherical-wave propagation increases effective channel rank through distance-dependent phase variation, adding spatial degrees of freedom.
B. Signal Model and Spatial Degrees of Freedom
- The hybrid channel matrix contains KNF near-field users and KFF far-field users, with KNF + KFF = K.Each user’s channel matrix Hk has dimensions M × NU.Source: B. Signal Model and Spatial Degrees of… · p. 2
- The BS receives a vector y containing users’ transmitted symbols and additive white Gaussian noise.Each xk is a user’s transmitted-symbol vector with total power Pk.Source: B. Signal Model and Spatial Degrees of… · p. 2
- Near-field spherical waves increase expected effective channel rank relative to far-field channels, adding spatial degrees of freedom.Distance-dependent quadratic phase makes same-angle users at different distances linearly independent in the near field, whereas their far-field channel vectors are collinear.Source: B. Signal Model and Spatial Degrees of… · p. 2
III. PROPOSED WEIGHTED RATE-SIC
WR-SIC orders streams using a weighted information-rate metric that emphasizes strong singular-value gains. Its ordering is applied first across users and then across each user’s streams.
III. PROPOSED WEIGHTED RATE-SIC
- WR weights each stream’s information rate by its own squared singular value, distinguishing it from rate-blind channel-norm and equally weighted capacity-based ordering.The metric is designed for SIC stream ordering rather than asymptotic rate-scaling analysis.Source: §III · p. 2
- The metric amplifies the score of near-field users with larger, more evenly distributed singular values, even when their total channel power matches a far-field user.In that equal-power case, channel norm cannot distinguish the users.Source: §III · p. 2
A. Ordering Algorithm and Transmission Scheme
- The ordering sorts users by descending weighted rate, sorts each user’s streams by descending singular value, then processes users’ streams in that order.Each transmitted stream is drawn from a unit-energy constellation with power Pk/NU per antenna.Source: A. Ordering Algorithm and Transmission… · p. 2
B. Proposed WR-SIC Algorithm
WR-SIC initializes the residual signal and undetected-stream set, then processes streams in the prescribed order. Its ordering targets per-user reliability by determining which streams face residual interference at each stage.
B. Proposed WR-SIC Algorithm
- The algorithm starts with the received vector as the first-stage residual and all K · NU streams in the undetected set.At each stage, it selects the highest-priority remaining stream according to the ordering.Source: B. Proposed WR-SIC Algorithm · p. 3
- For the selected stream, the receiver applies an MMSE filter, makes a nearest-constellation hard decision, subtracts the detected contribution, and removes that stream from the remaining set.The MMSE soft estimate is mapped to the nearest constellation point before cancellation.Source: B. Proposed WR-SIC Algorithm · p. 3
- Decoding order governs per-user reliability and error propagation because streams face different residual interference; under ideal cancellation, MMSE-SIC attains sum-capacity for any order.WR-SIC prioritizes streams with strong singular-value structure characteristic of near-field users.Source: B. Proposed WR-SIC Algorithm · p. 3
IV. ANALYSIS
This section analyzes WR-SIC information rates in near-field scenarios and compares its gain with the ordering overhead. It also relates the gain to prioritizing users with better channel conditions.
A. Information Rate Analysis
- The information-rate gain stems from prioritizing users with better channel conditions.The analysis associates this gain with enhanced spatial degrees of freedom and weighted-rate ordering in near-field scenarios.Source: A. Information Rate Analysis · p. 3
- WR-SIC’s 3–4 dB gain comes at about 6.3% additional cost over the MMSE cost shared by all schemes.The added ordering cost is attributed to a one-time per-user SVD.Source: A. Information Rate Analysis · p. 3
B. Outage Probability Analysis
The outage analysis gives closed-form probabilities across two weighted-rate regimes and finds that WR-SIC improves outage performance without increasing diversity order. Under equal power, decoding order changes individual-user outage probabilities but not system outage.
B. Outage Probability Analysis
- The closed-form analysis distinguishes RA, where near- and far-field weighted rates differ by more than δ_th, from RB, where their difference is at most δ_th.RB represents the region of comparable weighted rates.Source: B. Outage Probability Analysis · p. 3
- System outage decreases at rate 1/ρ, giving diversity order one; WR-SIC’s advantage is a smaller outage coefficient, not higher diversity.System failure occurs whenever any single user fails.Source: B. Outage Probability Analysis · p. 4
- CN-SIC can place a far-field user early, exposing it to strong residual interference from undecoded near-field users and degrading its individual outage performance.This early-stage assignment can yield a large threshold for a far-field user with small ηFF.Source: B. Outage Probability Analysis · p. 4
- With equal power allocation, system outage is independent of decoding order, although individual-user outage probabilities depend on the order.WR-SIC assigns near-field users with large ηπ(i) to early stages, where their large mean gains keep their outage thresholds small.Source: B. Outage Probability Analysis · p. 4
V. PROPOSED ITERATIVE DETECTION AND DECODING
The proposed IDD scheme combines soft WR-SIC-MMSE detection with LDPC decoding through iterative soft-information exchange. It also accounts for channel-estimation error in residual variance and effective gain.
V. PROPOSED ITERATIVE DETECTION AND DECODING
- The IDD scheme exchanges soft information between a WR-SIC-MMSE detector and an LDPC decoder, feeding decoder extrinsic information back to update detector a priori probabilities.The detector generates LLRs, while the decoder refines symbol estimates using belief propagation.Source: §V · p. 4
- With channel estimation, the residual variance includes an additional term ε_est arising from channel-estimation error.The estimated channel is modeled as the true channel plus an error vector.Source: §V · p. 4
- Channel-estimation error perturbs the effective gain of the stream detected at stage i.The passage denotes this perturbation by Δμπ(i).Source: §V · p. 4
A. LLR Computation and LDPC Decoding
This subsection describes bit-LLR computation for QPSK with Gray mapping and the LDPC decoder’s log-domain belief-propagation updates. Decoder extrinsic information is fed back to the detector.
A. LLR Computation and LDPC Decoding
- For QPSK with Gray mapping, the detector computes an LLR for each bit of a symbol.The passage introduces the bit LLR through its computation expression.Source: A. LLR Computation and LDPC Decoding · p. 4
- Decoder extrinsic LLRs are fed back to the detector as a priori information.The passage identifies LC(bl) as the decoder’s extrinsic LLR for bit bl.Source: A. LLR Computation and LDPC Decoding · p. 4
- The LDPC decoder uses standard log-domain belief propagation with variable-node and check-node updates..Source: A. LLR Computation and LDPC Decoding · p. 4
B. Iterative Algorithm with Channel Estimation
The channel-estimated IDD algorithm iterates between SIC detection and LDPC decoding, updating soft information until its convergence condition is met. Channel-estimation errors add uncertainty to detector LLRs, which LDPC extrinsic information helps mitigate through iterative refinement.
B. Iterative Algorithm with Channel Estimation
- IDD initializes uniform priors and performs initial SIC, then iteratively updates priors, recomputes the residual, calculates detector LLRs, and runs LDPC decoding.The decoder supplies extrinsic LLRs and symbol estimates for subsequent iterations.Source: B. Iterative Algorithm with Channel… · p. 4
- The algorithm terminates when all parity checks pass and the decoder-message norm falls below 10^-3.The maximum number of IDD iterations is T_IDD.Source: B. Iterative Algorithm with Channel… · p. 4
- With estimated channels, IDD uses the estimated channel in place of H; LDPC extrinsic information helps mitigate estimation-induced LLR uncertainty through iterative refinement.This benefit is described despite the degradation introduced by channel estimation.Source: B. Iterative Algorithm with Channel… · p. 5
VI. SIMULATION RESULTS
Simulations report that WR-SIC improves BER performance over conventional ordering and achieves the highest sum rate under perfect CSI, while retaining an advantage with estimated CSI. IDD adds gains for WR-SIC, and near-field users outperform far-field users across schemes.
VI. SIMULATION RESULTS
- WR-SIC gains 3–4 dB SNR over CN-SIC and SINR-SIC at BER = 10−3 under perfect CSI, and achieves the highest sum-rate across SNR values.The conclusion also reports an extra 2 dB gain through IDD iterations.Source: Figure 1 · p. 5, §VI · p. 5, §VII · p. 6
- Under PD-OMP, near-field users outperform far-field users across schemes, and WR-SIC has the most pronounced sum-rate gap.The reported comparison validates rank enhancement and WR-SIC's exploitation of near-field channel structure.Source: Figure 2 · p. 5, §VI · p. 5
- With PD-OMP estimation, WR-SIC gains an extra 2 dB from IDD, converges faster to a lower BER floor, and captures most available gain within the first few iterations.WR-SIC achieves the largest absolute gain from iterative processing among the compared schemes.Source: Figure 3 · p. 5, §VI · p. 5
VII. CONCLUSION
- The conclusion describes WR-SIC as weighting achievable rates by squared singular values to exploit near-field spatial degrees of freedom, with IDD integrating SIC and LDPC through soft information exchange.The reported gains are 3–4 dB over conventional ordering under perfect CSI, with an extra 2 dB through IDD iterations.Source: §VII · pp. 5–6