This paper presents a polar-coded orthogonal frequency-division multiplexing (OFDM) system that utilizes adaptive code rate selection based on channel impulse response. In conventional OFDM systems, power levels vary across subcarriers because of channel frequency selectivity. To ensure reliable communication in polar-coded OFDM systems, it is essential to predict communication quality using estimated channel state information (CSI) and to adaptively allocate the code rate. This approach aims to meet specified reliability constraints while optimizing system performance. The estimated block error rate (BLER) serves as an indicator of communication quality and can be accurately predicted using the estimated CSI. We develop a scheme that adaptively selects the code rate according to the CSI by identifying the maximum number of information bits while ensuring that the estimated BLER stays below a specified target BLER. To assess the effectiveness of the proposed method, we perform computer simulations and analyze its performance in terms of both BLER and achievable throughput in a general retransmission framework with hybrid automatic repeat request (HARQ).

Furudoi T., Takahashi T., Ochiai H.. Discrete-Valued Signal Estimation via GAMP under Finite-Sized Highly Correlated GLMs. Proceedings of the IEEE International Conference on Communications (ICC 2026); https://doi.org/10.1109/ICC59461.2026.11587545.

Abstract In recommending songs to users, various types of relationships can be considered, such as songs liked by users with similar preferences or songs that are acoustically similar to those the target user already likes. Providing explanations for recommendations based on such relationships improves transparency and trust, but users currently have no control over which relationships are emphasized. To solve this problem, we extend an existing recommendation method based on a graph convolutional network (GCN) by representing each relationship as a separate graph layer with adjustable weights. By applying this method, we implemented a song recommender system with three types of relationships (user preference similarity, acoustic similarity, and creator commonality) on a music web service called “Kiite.” On the service, four types of recommendation results are displayed, depending on which relationships are emphasized and to what degree. The recommender system offers both transparency and controllability in that users can freely switch between the four recommendation result types. An analysis of over two years of usage logs demonstrates the effectiveness of combining transparency and controllability in music recommendation.

This paper proposes a novel Bayesian reciprocity calibration method that consistently ensures uplink and downlink channel reciprocity in repeater-assisted multiple-input multiple-output (MIMO) systems. The proposed algorithm is formulated under the minimum mean-square error (MMSE) criterion. Its Bayesian framework incorporates complete statistical knowledge of the signal model, noise, and prior distributions, enabling a coherent design that achieves both low computational complexity and high calibration accuracy. To further enhance phase alignment accuracy, which is critical for calibration tasks, we develop a von Mises denoiser that exploits the fact that the target parameters lie on the circle in the complex plane. Simulation results demonstrate that the proposed MMSE algorithm achieves substantially improved estimation accuracy compared with conventional deterministic non-linear least-squares (NLS) methods, while maintaining comparable computational complexity. Furthermore, the proposed method exhibits remarkably fast convergence, making it well suited for practical implementation.

We propose a framework to design integrated communication and computing (ICC) receivers capable of simultaneously detecting data symbols and performing over-the-air computing (AirComp) in a manner that: a) is systematically generalizable to any nomographic function, b) scales to a massive number of user equipments (UEs) and edge devices (EDs), c) supports the computation of multiple independent functions (streams), and d) operates in a multi-access fashion whereby each transmitter can choose to transmit either data symbols, computing signals or both. For the sake of illustration, we design the proposed multi-stream and multi-access method under an uplink setting, where multiple single-antenna UEs/EDs simultaneously transmit data and computing signals to a single multiple-antenna base station (BS)/access point (AP). Under the communication functionality, the receiver aims to detect all independent communication symbols while treating the computing streams as aggregate interference which it seeks to mitigate; and conversely, under the computing functionality, to minimize the distortion over the computing streams while minimizing their mutual interference as well as the interference due to data symbols. To that end, the design leverages the Gaussian belief propagation (GaBP) framework relying only on element-wise scalar operations coupled with closed-form combiners purposebuilt for the AirComp operation, which allows for its use in massive settings, as demonstrated by simulation results incorporating up to 200 antennas and 300 UEs/EDs. The efficacy of the proposed method under different loading conditions is also evaluated, with the performance of the scheme shown to approach fundamental limiting bounds in the under/fully loaded cases.

This paper proposes a novel sparse Bayesian learning (SBL) algorithm for channel estimation (CE) in multiple-input multiple-output orthogonal time frequency space (MIMO-OTFS) systems, aiming to exploit both the row and group (RG) sparsity and pseudo-sparsity inherent in practical delay– Doppler (DD)-domain channels. Conventional CE approaches model the DD-domain OTFS channel as strictly sparse; however, due to fractional delay and Doppler shifts, the DD-domain channel observed in practical bases does not exhibit strict sparsity, even if the original impulse response is sparse. Instead, it exhibits a structure characterized by numerous small but nonzero elements, with significant variations in signal strength across entries. Capturing this pseudo-sparse structure is crucial for further performance improvement. To address this, we design a new prior distribution that integrates a heavy-tailed complex t-distribution, which effectively captures pseudo-sparsity, with RG sparsity to model the clustered sparse patterns inherent in MIMO-OTFS channels. Simulation results demonstrate that the proposed method significantly outperforms state-of-the-art (SotA) sparse signal recovery (SSR)-based alternatives in terms of both CE accuracy and data detection performance.

Digital communication systems inherently operate through physical media governed by partial differential equations (PDEs). In this paper, we introduce a physics-aware decoding framework that integrates gradient descent-based error correcting algorithms with PDE-based channel modeling using differentiable PDE solvers. At the core of our approach is gradient flow decoding, which harnesses gradient information directly from the PDE solver to guide the decoding process. We validate our method through numerical experiments on both the heat equation and the nonlinear Schrödinger equation (NLSE), demonstrating significant improvements in decoding performance. The implications of this work extend beyond decoding applications, establishing a new paradigm for physicsaware signal processing that shows promise for various signal detection and signal recovery tasks.

Abstract Numerous systems have been proposed for placing songs on a map to enable music exploration, but existing systems assume that users explore alone and thus lack social interactions, which has been identified as a significant issue for these systems. In this paper, we describe “Kiite World,” a web service that enables social-aware music exploration. Kiite World has over 440,000 songs placed on a map and lets users perform the following social interactions while moving their avatars: (1) Users can publish “My Kiite World,” where songs from their created playlists are displayed on the map, and they can visit each other’s “My Kiite Worlds” to explore songs on the map. (2) The activities of all users exploring songs on Kiite World are visualized in real time, enabling users to synchronize with interested users and explore songs while listening to music together. (3) Any user can easily host music events where she listens to her favorite songs together with other users while they synchronize with her. Analysis of user behavior logs over seven months revealed several reusable insights on the usefulness of incorporating social aspects into map-based music exploration (e.g., users often like songs that are farther from their original interests as a result of exploring songs in other users’ “My Kiite Worlds.”).

This paper presents a novel wireless autoencoder (WAE) consisting of neural network (NN) modulator and probabilistic data association detector with the aid of deep unfolding (PDA-DU) in coded multi-input multi-output (MIMO) systems. When using error correction code (ECC), the signal constellation that maximizes the minimum Euclidean distance, such as quadrature amplitude modulation (QAM), is not always optimal. For example, set partitioning is often utilized in higher-order modulation schemes. On the other hand, nonlinear iterative signal detection of PDA has been shown to efficiently suppress interference and to reduce the bit error rate (BER) compared to traditional minimum mean square error (MMSE) spatial filtering. However, PDA may degrade detection performance due to outliers in the expected value of transmitted signals. To solve these complicated issues, the proposed WAE retrieves the best signal constellation using the NN modulator, and simultaneously mitigates outliers in the expected value by introducing scaling factors optimized by DU in the PDA detector.

Global navigation satellite system (GNSS) positioning, including the global positioning system (GPS), is susceptible to multipath effects in urban areas and between tall buildings, which degrade positioning accuracy. In this study, to address this issue, we complement GNSS positioning with information obtained through communication with LTE base stations and use it as features for position estimation. Using this information, we propose a long short-term memory (LSTM)-based neural network (NN) model with a parallel structure. In this model, GNSS positioning information and long term evolution (LTE) signal information are combined and input into LSTM with different structures. Features obtained from multiple information sources are used in a complementary manner to improve the accuracy of position estimation. Furthermore, the positioning accuracy of test data is evaluated to confirm the effectiveness of the proposed method. This evaluation takes into account positioning at unknown locations that are different from those used during training.

Generalized approximate message passing (GAMP) achieves near-optimal performance in detecting spatially multiplexed massive multiple-input multiple-output (MIMO) signals with significantly reduced computational complexity under independent and identically distributed (i.i.d.) measurements. However, in spatially correlated MIMO channels where the ideal assumption of large-scale uncorrelated observation does not hold, the detection capability severely deteriorates. This performance degradation can be compensated for by optimizing GAMP with embedded learnable parameters via deep unfolding (DU) techniques, i.e., data-driven tuning; however, the learning process becomes quite unstable. To address this issue, we propose a novel method that achieves stable learning by incorporating a monotonic increase constraint on the reliability of propagated messages by learning the differential (incremental) values of the learnable parameters between two consecutive iterations. The efficacy of the proposed method is confirmed through numerical results in terms of loss trajectory in the learning process and bit error rate (BER) of massive MIMO detection.

This paper proposes a novel vector similarity search (VSS)-based modulation and coding scheme (MCS) selection for massive multi-user multiple-input multiple-output orthogonal frequency division multiplexing (MU-MIMO-OFDM) systems that employ uplink multi-user detection (MUD) based on iterative signal estimation. To maximize the uplink throughput of MU-MIMO-OFDM systems, it is necessary to assign a carefully selected MCS to each user according to an accurate prediction of the mutual information (MI) that can be achieved with MUD based on the knowledge of the estimated channel state information (CSI). However, since the detection accuracy of iterative MUDs, such as expectation propagation (EP), varies depending on the convergence characteristics, it is challenging to analytically predict the achievable MI in the presence of MUD. To address this difficulty, we propose a novel method for predicting the achievable MI by creating a vector database (VDB) offline that stores feature vectors (keys) computed from CSI and the actual MI (values) achieved with iterative MUD, and then searching this VDB online using approximate nearest neighbors (ANN) search, which enables VSS at ultra-high speed. Simulation results show that the MCS selection based on the proposed MI prediction achieves higher uplink throughput than the conventional schemes in MU-MIMO-OFDM systems using the EP-based MUD.

In this paper, we propose a novel low-complexity Bayesian receiver design to jointly perform channel, CFO, and data estimation from observations subject to different CFO among users in MU-MIMO-OFDM systems. ICI due to CFO significantly reduces channel estimation accuracy under frequency-selective fading environments, making reliable communications difficult. To tackle this difficulty, a JCCE algorithm is designed based on BP. Our method uses a BG distribution as the prior distribution of the channel coefficient to capture its delay-domain sparsity, and a GM distribution as the prior distribution of the phase shift due to CFO to perform parallel search for the allowable range of CFO defined in the 3GPP standard by the number of mixture components. The proposed algorithm can further improve the accuracy of channel, CFO, and data estimation by treating the tentatively detected data symbols as extra pilots. The efficacy of the proposed method is confirmed by numerical studies, which show that the proposed method not only significantly outperforms the SotA methods with much lower computational cost but also approaches the performance of an idealized Genie-aided scheme.

We propose new schemes for joint channel and data estimation (JCDE) and radar parameter estimation (RPE) in doubly-dispersive channels, such that integrated sensing and communications (ISAC) is enabled by user equipment (UE) independently performing JCDE, and base stations (BSs) performing RPE. The contributed JCDE and RPE schemes are designed for waveforms known to perform well in doubly-dispersive channels, under a unified model that captures the features of either legacy orthogonal frequency division multiplexing (OFDM), state-of-the-art (SotA) orthogonal time frequency space (OTFS), and next-generation affine frequency division multiplexing (AFDM) systems. The proposed JCDE algorithm is based on a Bayesian parametric bilinear Gaussian belief propagation (PBiGaBP) framework first proposed for OTFS and here shown to apply to all aforementioned waveforms, while the RPE scheme is based on a new probabilistic data association (PDA) approach incorporating a Bernoulli-Gaussian denoising, optimized via expectation maximization (EM). Simulation results demonstrate that JCDE in AFDM systems utilizing a single pilot per block significantly outperforms the SotA alternative even if the latter is granted a substantial power advantage. Similarly, the AFDM-based RPE scheme is found to outperform the OTFS-based approach, as well as the sparse Bayesian learning (SBL) technique, regardless of the waveform used.

Index modulation (IM) is one of the key enabling technologies for beyond fifth generation (B5G) and sixth generation (6G) wireless systems, attracting attention for its inherent energy and spectral efficiency resulting from conveying information through the indexation of the resources utilized in during signal transmission. However, a remaining critical bottleneck for large-scale IM is the consequently infeasible detection complexity of combinatoric order. Therefore in this article, in order to maximally reap the advantages of IM in large scenarios, we propose a novel message passing (MP) decoder designed under the Gaussian belief propagation (GaBP) framework exploiting a novel unit vector decomposition (UVD) of IM signals with purpose-derived novel probability distributions. The proposed method enjoys a low decoding complexity that is independent of previously prohibitive combinatorial factors, while still approaching the performance of unfeasible state-of-the-art (SotA) search-based methods. The effectiveness of the proposed approach is demonstrated via complexity analysis and numerical results for the exemplary piloted generalized quadrature spatial modulation (GQSM) systems of truly massive sizes (up to 96 antennas).

In high-speed mobile communication environments, an orthogonal time frequency space (OTFS) scheme with robustness to doubly-selective fading channels by spreading symbols in the frequency-time (FT) domain has attracted much attention. However, typical pilot-based channel estimation schemes cause system performance degradation due to the increased overhead of channel state information (CSI) acquisition, and large-scale matrix operations based on the size of OTFS equivalent channels are also problematic in terms of the computational cost. To address this issue, in this paper, we focus on the fact that joint channel and data estimation (JCDE) in the delay-Doppler (DD) domain OTFS systems can be formulated as a large-scale parametric bilinear inference problem, and solve it via Gaussian belief propagation (GaBP) to design a novel low-complexity and high-accuracy JCDE algorithm with the use of relatively short pilot sequences. From computer simulations, we confirm that the proposed method significantly outperforms the conventional two-stage channel and data estimation, and asymptotically approaches the idealized scheme given perfect CSI knowledge.

This paper proposes a novel Bayesian receiver design for uplink signal detection in overloaded massive multi-user multi-input multi-output (MU-MIMO) systems. Iterative detection schemes are roughly classified into two types: iterative detection and decoding (IDD), in which log-likelihood ratios (LLRs) are exchanged between the detector and the channel decoder, and self-iterative detection (SID), in which a message passing algorithm (MPA) is operated without involving the channel decoder. In either scheme, the most vital mechanism of iterative signal detection is to decouple the self-feedback across iterations and propagate extrinsic values. As a receiver design to achieve an excellent performance-complexity trade-off while adhering to this mechanism, a concatenated structure of SID based on expectation propagation (EP) and IDD based on turbo equalization is proposed. Numerical simulations show that the proposed method outperforms the state-of-the-art alternatives in terms of bit error rate (BER) performance in coded systems, especially when the overloading ratio is high. In addition, the iterative behavior is analyzed by extrinsic information transfer (EXIT) chart to verify the efficacy of extrinsic value exchange.

This paper proposes deep unfolding (DU)-aided blind signal separation (BSS) for short data block communications of multi-user multi-input multi-output (MU-MIMO) transmission. Independent component analysis (ICA) is a BSS technique that does not require a pilot signal for channel estimation. However, when applying ICA to short data length, inaccurate non-Gaussianity evaluations deteriorate the performance of BSS. To compensate for this drawback, we design a novel DU-aided BSS algorithm as trainable ICA (TICA) that incorporates a data-driven design based on deep learning and learning optimization of internal trainable parameters. Considering that the weight matrix obtained as the outcome of ICA does not converge to an appropriate value for short data length, we introduce two trainable parameters: one for correcting the non-Gaussian evaluation and the other for damping to suppress oscillations. Numerical results show that the proposed algorithm substantially improves the bit error rate (BER) performance with trainable parameter optimization using DU techniques.

Intelligent reflecting surface (IRS) has emerged as a promising communication technology to increase throughput and facilitate communication in non-line-of-sight scenarios. While existing studies primarily focus on the application of IRS in communication tasks, its unique capability to precisely control radio frequency ($\mathbf{R F}$) signal reflections offers untapped potential for non-communication purposes. This paper ventures into an innovative domain and explores the application of IRS properties for image processing tasks conducted over the air. We introduce a novel scheme called “single antenna imaging”, a proof-of-concept scheme for over-the-air image processing. This approach leverages analog modulation and compressed sensing techniques to reconstruct high-quality images from a limited number of transmissions between multiple transmit antennas and a single receive antenna. Evaluations using the Kodak image dataset show that the proposed scheme can retrieve the same quality images with over 40% reduction in traffic compared to the simple minimum norm solution (MNS) and linear minimum mean square error (LMMSE) schemes.

This paper proposes a novel precoder design for time-varying millimeter-wave (mmWave) multiple-input multiple-output (MIMO) signal detection based on expectation propagation (EP). In mmWave wireless communications, millisecond-scale fluctuations in the surrounding environment cause significant changes in the wireless channel, and the channel aging over time causes a mismatch between the beam and actual channel. The proposed precoder attempts to maximize detection performance by adjusting information propagated across iterations when employing the EP-based iterative algorithm to suppress interference components due to channel aging at the receiver. Simulation results show that the precoders that impose heterogeneity in quality among streams of MIMO spatial multiplexing minimize the bit error rate (BER). We conjecture that this phenomenon is due to the improved detection accuracy in the early iterations caused by the heterogeneity among streams, and discuss appropriate precoder design criteria by quantitatively evaluating the performance improvement.

This paper proposes a novel beam-domain channel estimation (CE) algorithm based on sparse Bayesian learning (SBL) using complex t-prior for massive multi-user multiple-input multiple-output (MU-MIMO) systems. Due to the sidelobe leakage and insufficient observation resolution, the equivalent channel after digital beamforming at the receiver does not have a sparse structure strictly consisting of zero/non-zero elements, but has a structure characterized by differences in signal intensity consisting of a large number of small non-zero elements and a few large elements. To fully capture this pseudo-sparse structure, a complex t-distribution with appropriate degrees of freedom (DoF) is incorporated into the SBL algorithm as a hierarchical Bayesian model. This heavy-tailed prior allows for efficient beam-domain CE accounting for small but non-negligible elements, which is verified by the analysis of regularization based on an equivalent optimization problem. Simulation results show that the proposed method significantly outperforms the state-of-the-art (SotA) sparse signal recovery (SSR)-based alternatives in sub-6 GHz wireless communication scenarios.

Conventional point cloud delivery schemes employ tree-based or graph-based digital compression techniques to stream three-dimensional (3D) points and their associated attributes over wireless multiple-input multiple-output (MIMO) channels for 3D scene reconstruction. However, these digital-based delivery methods suffer from the cliff and leveling effects. Moreover, in MIMO communication environments, poor quality in some spatial layers, i.e., subchannels, can lead to point cloud quality degradation. We propose a novel point cloud delivery scheme that addresses both effects simultaneously. Our approach leverages a k-dimensional tree (k-d tree)-based graph Fourier transform (GFT) for energy compaction, a subchannel assignment mechanism to fully utilize subchannel diversity in MIMO links, and analog modulation with non-uniform power allocation for error-resilient and fluctuation-resilient transmission. Evaluation results demonstrate that the proposed scheme delivers superior 3D reconstruction quality compared to conventional digital-based point cloud delivery schemes, such as geometry-based point cloud compression (G-PCC), in noisy MIMO channels.

In this paper, considering its application in Bluetooth low energy (BLE), we propose a novel self-interference (SI) cancellation method for in-band full-duplex (IBFD) communications in the presence of fractional delay paths. Traditional SI cancellation methods, such as the active SI canceller (ASIC), generate and subtract a replica of the SI signal from the received signal. However, generating this replica requires accurate channel state information (CSI), which increases communication overhead and reduces spectral efficiency. Therefore, the differential active SI canceller (DASIC) has been proposed, which does not require prior CSI information. Nonetheless, the presence of fractional delay paths results in residual SI, making cancellation insufficient. In this paper, we propose a method to generate a replica of the residual SI from DASIC outputs, resolving the residual SI issue. The efficacy of the proposed method is confirmed through computer simulations by comparing its bit error rate (BER) performance with that of ASIC.

This paper proposes an outer loop link adaptation (OLLA) algorithm for massive multi-user multi-input multi-output (MIMO) systems that employs uplink multi-user detection (MUD) based on generalized approximate message passing (GAMP). The contribution aims to improve uplink system throughput performance for future beyond-fifth-generation mo-bile communication systems by designing a novel scheduler that can select spatially multiplexed user equipment (UE) devices and their modulation and coding schemes (MCSs), considering the high detection accuracy provided by the GAMP-based MUD. To achieve this, we propose an OLLA algorithm that accu-rately predicts the signal-to-interference and noise power ratio (SINR) that each UE can achieve after the GAMP-based MUD. Specifically, the proposed method can dynamically optimize the scheduler according to the iterative detection characteristics of GAMP by introducing a mechanism to correct the predicted SINR separately for each combination of spatially multiplexed UEs. System-level simulation results indicate that adjusting our OLLA algorithm achieves a 50% higher throughput than the conventional OLLA algorithm when applied to GAMP.

We propose a novel joint channel and data estimation (JCDE) algorithm via bilinear Gaussian belief propagation (BiGaBP) for massive multi-user MIMO (MU-MIMO) systems with non-orthogonal pilot sequences. The contribution aims to reduce significantly the communication overhead required for channel acquisition by enabling the use of short non-orthogonal pilots, while maintaining multi-user detection (MUD) capability. Bilinear generalized approximate message passing (BiGAMP), which is systematically derived by extending approximate message passing (AMP) to the bilinear inference problem (BIP), provides computationally efficient approximate implementations of large-scale JCDE via sum-product algorithm (SPA); however, as the pilot length decreases, the estimation accuracy is severely degraded. To tackle this issue, the proposed BiGaBP algorithm generalizes BiGAMP by relaxing its dependence on the large-system limit approximation and leveraging the belief propagation (BP) concept. In addition, a novel belief scaling method complying with the data detection accuracy for each iteration step is designed to avoid the divergence behavior of iterative estimation in the early iterations due to the use of non-orthogonal pilots, especially in insufficient large-system conditions. Simulation results show that the proposed method outperforms the state-of-the-art schemes and approaches the performance of idealized (genie-aided) scheme in terms of mean square error (MSE) and bit error rate (BER) performances.

We propose a novel joint channel tracking and data detection (JCTDD) scheme to combat the channel aging phenomenon typical of millimeter-wave (mmWave) multiple-input multiple-output (MIMO) communication systems in high-mobility scenarios. The contribution aims to significantly reduce the communication overhead required to estimate time-varying mmWave channels by leveraging a Bayesian message passing framework based on Gaussian approximation, to jointly perform channel tracking (CT) and data detection (DD). The proposed method can be interpreted as an extension of the Kalman filter-based two-stage tracking mechanism to a Bayesian bilinear inference (BBI)-based joint channel and data estimation (JCDE) framework, featuring the ability to predict future channel state information (CSI) from both reference and payload signals by using an auto-regressive (AR) model describing the time variability of mmWave channel as a state transition model in a bilinear inference algorithm. The resulting JCTDD scheme allows us to track the symbol-by-symbol time variation of channels without embedding additional pilots, leaving any added redundancy to be exploited for channel coding, dramatically improving system performance. The efficacy of the proposed method is confirmed by computer simulations, which show that the proposed method not only significantly outperforms the state-of-the-art (SotA) but also approaches the performance of an idealized Genie-aided scheme.

We propose a wireless localization algorithm based on complex-domain super multidimensional scaling (CD-SMDS) augmented with a self-localization (SL) component, whereby each target tracks its own motion by incorporating bearing information, obtained e.g., from integrated inertial sensors. The proposed method improves localization accuracy by simultaneously using the time series information of distance and angle associated to the SL information in order to construct the SMDS rank-one edge kernel matrix, maximizing the noise reduction effect of the low-rank truncation via singular value decomposition (SVD). The efficacy of the proposed method over the original CD-SMDS is confirmed via software simulations, and compared with an SL-aware Cramér-Rao lower bound (CRLB).

This paper proposes a novel angle-of-arrival (AoA) estimation-aided Bayesian joint channel and data estimation (JCDE) algorithm for uplink signal detection in millimeter-wave (mmWave) massive multi-user MIMO (MU-MIMO) systems with short non-orthogonal pilots. In the proposed method, the prior distribution of mmWave channels in the angular domain after digital beamforming is approximated by a Bernoulli-Gaussian (BG) distribution, and the mismatch with the actual distribution is corrected based on AoA estimation by low-complexity angle rotation (AR) method. The resultant beam-domain JCDE algorithm has an inherent mechanism to update path gains of the channels estimated based on AoA for every iteration. This receiver design allows us to take the advantage of both stochastic (i.e., Bayesian) and deterministic (i.e., AR) approaches. Efficacy of the proposed method over the state-of-the-art is confirmed via computer simulations in terms of bit error rate (BER) performance compared to the state-of-the-art alternatives.

This paper proposes a novel blind self-interference (SI) canceller with adaptive differential delay for in-band full duplex (IBFD) communications, even in the presence of a fractional delay path. As an SI cancellation method, active SI canceller (ASIC) that generates and subtracts a replica of the SI signal from the received signal has been proposed. However, the replica generation requires accurate and periodic channel state information (CSI) acquisition, causing system performance degradation due to increased communication overhead. To avoid this inconvenience, differential active SI canceller (DASIC) without prior channel estimation of SI has been proposed. However, due to the effects of a fractional delay path, DASIC cannot completely cancel SI, resulting in residual SI. The proposed method adaptively controls the differential delay to eliminate the residual SI, according to the occurrence pattern of its own transmission signal. In addition, an appropriate maximum a-posteriori probability (MAP) detector is designed based on the DASIC outputs. Finally, computer simulations confirm the efficacy of the proposed method with and without error correction code (ECC) in terms of bit error rate (BER) performance.

We propose a novel joint channel and data estimation (JCDE) scheme to combat the rate limitation in fronthaul links of cell-free massive MIMO (CF-mMIMO) systems introduced by the use of analog-to-digital converters (ADCs) at access points (APs), which makes channel estimation and multi-user detection at the central AP (CAP) challenging. The latter problem is solved here via the new JCDE scheme which differs from state-of-the-art (SotA) alternatives due to two contributions. The first is the design and incorporation of de-quantization (DQ) step which relies only on scalar Gaussian approximation (SGA) assumptions in conformity with mild central limit theorem (CLT), in contrast to the much harder asymptotic conditions required by the classic bilinear generalized approximate message passing (BiGAMP) algorithm. The second is a modification of bilinear Gaussian belief propagation (BiGaBP), whereby quantized outputs are linearized via the Bussgang decomposition enabling tractable signal processing. The resulting DQ-aided JCDE method achieves both low-complexity and high-accuracy by exploiting both the spatial degrees of freedom (DoF) obtained from, and the observations at the CAP to compensate for the low-resolution distortion introduced by, the distributed APs. The efficacy of the proposed method over the SotA is confirmed via computer simulations.

This paper proposes a look-up table (LUT)-based multi-user detection (MUD) scheme imitating approximate message passing (AMP) for uplink signal detection in large multi-user multi-input multi-output (MU-MIMO) systems. When AMP is implemented with double-precision arithmetic, the increase in power consumption and memory occupation becomes a major obstacle to practical application as the system scale expands. To tackle this issue, we design a novel referential AMP detector composed by hierarchically cascading many small LUTs, where only informative integer-valued messages are exchanged on a factor graph. The quantization thresholds of LUTs are sequentially computed by tracking the discrete distribution of the LUT outputs at each layer to minimize the performance degradation owing to quantization errors. Based on the distribution at each layer, the thresholds are optimized by clustering with the Lloyd-Max algorithm using the initial values given by the k-means++ method. Simulation results demonstrate the efficacy of the proposed method in terms of the bit error rate (BER) performance and memory usage. Notably, we show that the referential AMP is robust to changes in communication environments, and then clarify the reason in terms of the algorithmic structure.

In this paper, we propose a novel joint activity and channel estimation (JACE) algorithm for grant-free extra large MIMO (XL-MIMO) systems subject to spatial non-stationarity phenomena by means of a Bayesian bilinear inference framework. In XL-MIMO systems, the signal from each user is visible only by a small portion of its antenna arrays, which are typically distributed over the surface of a certain structure. The sporadic user activity due to grant-free access, as well as the spatial non-stationarity, jointly imposes a challenging JACE problem involving a nested Bernoulli-Gaussian random variable. In order to address this issue, we decompose the latter into a bilinear inference problem of two independent random quantities, deriving novel message passing rules based on Gaussian approximation and bilinear inference. Performance evaluation via software simulations is offered to demonstrate the effectiveness of the proposed algorithm, which achieves the Genie-aided ideal estimation performance.

This paper deals with uplink multi-user detection (MUD) via generalized approximate message passing (GAMP) in highly correlated large multi-user multi-input multi-output (MUMIMO) systems. The most vital mechanism of GAMP is Onsager correction for decoupling the self-noise feedback of beliefs across iterations; this makes it possible to exchange extrinsic values. First, we show that by introducing the belief scaling method proposed in the context of Gaussian belief propagation (GaBP) for adjusting the convergence speed into GAMP, the Onsager correction works properly even under spatial fading correlation, which significantly improves detection capability. Surprisingly, the performance is much better compared to that of the GaBP with belief scaling, and even asymptotically approaches that of computationally expensive expectation propagation (EP) detectors. Based on the results, we clarify why such a dramatic performance improvement is possible only for GAMP in terms of the suppression mechanism of self-noise feedback.

Linear minimum mean square error (LMMSE) filters are often utilized to achieve low-complexity multi-user detection (MUD) in uplink large multi-input multi-output (MIMO) systems. As the scale and density of MIMO systems grow towards truly massive setups, however, the LMMSE detection requiring high-dimensional matrix inversion operations becomes computationally expensive. As a promising approach to tackle this issue, the local LMMSE (LLMMSE) detector was proposed, where a contiguous block of beams can be selected for each user to construct the reduced beam-domain channels, assuming the use of digital beamforming at a base station (BS). A main issue is the performance degradation according to the angular spread of the received signal, due to the information loss induced by an excessive dimensionality reduction aiming at the computational reduction. To alleviate this issue, this paper proposes to selectively combine the information from the overlapped LLMMSE filters in the log-likelihood ratio (LLR) domain. In addition, this method is extended to probabilistic data association (PDA)-based iterative detection scheme for further enhancement of communication reliability. The efficacy of the proposed methods is demonstrated by simulation results in terms of the bit error rate (BER) performance and the computational cost.

This paper proposes a high reliable demodulation method via phase-noise-aware log-likelihood ratios (LLRs) in millimeter-wave (mmWave) multi-user multi-input multi-output (MU-MIMO) systems with higher-order quadrature amplitude modulation (QAM). When using high-order QAM schemes in mmWave wide-band wireless communication systems, the phase noise severely degrades the demodulation performance at the operating point in the high signal-to-noise ratio (SNR) region. Typical two-stage processing, which consists of MIMO signal separation (i.e., multi-user detection (MUD)) and phase noise compensation via LLR calculation, cannot properly solve this inherent problem, because the spatial fading correlation in mmWave channels causes phase noise enhancement during MUD. To circumvent this issue, we formulate an approximate probability density function (PDF) of the received signals including phase noise, which enables us to jointly perform MUD and phase noise compensation; this makes it possible to compute reliable LLRs to be input to the channel decoder, without phase noise enhancement. Numerical results demonstrate the efficacy of the proposed method in terms of the bit error rate (BER) performance in coded mmWave MIMO systems.

We propose two full-digital receive beamforming (BF) methods for low-complexity and high-accuracy uplink signal detection via Gaussian belief propagation (GaBP) at base stations (BSs) adopting massive multi-input multi-output for open radio access network. In such scenarios, it is vital to reduce the cost of the BSs by limiting the bandwidth of fronthaul (FH) links, and the dimensionality reduction of the received signal based on receive BF at a radio unit is a well-known strategy to reduce the amount of data transported via the FH links. We clarify appropriate criteria for designing a BF weight considering the subsequent GaBP signal detection with the proposed methods: singular-value-decomposition-based BF and QR decomposition-based BF with the aid of discrete-Fourier-transformation-based spreading. Both methods enable dimensionality reduction without compromising the desired signal power by taking advantage of a null space of the channels. BF reduces correlations between the received signals in the BF domain, which improves the robustness of GaBP against spatial fading correlation. Simulation results indicate that the proposed methods improve detection capability while significantly reducing computation.

Extra large MIMO (XL-MIMO) systems are subject to spatial non-stationarity forming visibility regions (VRs), which leads to a sub-array-wise sparse structure of the channel matrix. When XL-MIMO systems operate in grant-free access mode, in which only a fraction of the potential users are active during a given time slot, it follows that the channel matrix possesses a doubly-sparse and user-specific structure such that the activity of each user and each sub-array can be jointly modeled by a nested Bernoulli-Gaussian distribution. This article considers the joint activity and channel estimation (JACE) problem in XL-MIMO systems subject to this so-defined spatial non-stationarity, tackling this challenging inference problem. Our main contributions are 1) to introduce the novel Bernoulli-Gaussian model to simultaneously capture the aforementioned two distinct structured sparsities, and 2) a new bilinear Bayesian inference algorithm capable of jointly estimating the associated channel coefficients, user activity patterns, sub-array activity patterns ($a.k.a$. spatial non-stationarity), boosted by expectation maximization (EM)-based auto-parameterization. In addition, to shed light on a realistic modeling of VRs, we also introduce a Matérn-cluster point process (MCPP)-based approach to imitate the clustered activity pattern due to spatial non-stationarity. The efficacy of the proposed bilinear JACE algorithm is confirmed by numerical simulations, which show that the proposed method not only significantly outperforms the state-of-the-art (SotA) but also can reach the performance of a genie-aided scheme over wide signal-to-noise-ratio (SNR) ranges, in both uniformly-random and MCPP-based sub-array activity scenarios.

In large multi-user multi-input multi-output systems, the computational cost and circuit scale of base stations (BSs) are effectively reduced using two-stage signal processing consisting of a slow varying outer beamformer (OBF) based on long-term channel statistics and group-specific multi-user detection for instantaneous channel variations. However, the dimensionality reduction of the group-specific beam-domain channel based on the OBF causes significant performance degradation in the subsequent spatial-filtering detection. To compensate for this drawback, this paper introduces a novel layered belief propagation (BP) detector with a concatenated structure of beam- and antenna-domain BP layers for post-stage OBF processing. The proposed detector is designed for improving the convergence of iterative detection by suppressing intra- and inter-group interference in stages. The layered structure provides the advantages of both beam and antenna domains while maintaining low signal-processing complexity. Numerical results show the validity of our proposed method in terms of the bit error rate performance in both the uncoded and coded cases and the computational complexity.

Ryuji Kano, Takumi Takahashi, Toru Nishino, Motoki Taniguchi, Tomoki Taniguchi, Tomoko Ohkuma. Proceedings of the 16th Conference of the European Chapter of the Association for Computational Linguistics: Main Volume. 2021.

We consider large multi-user detection (MUD) via deep unfolding-aided belief propagation (BP) in coded multi-user MIMO (MU-MIMO) systems. A BP detector optimized (trained) by data-driven-tuning of embedded internal parameters achieves low-complexity and high-accuracy MUD while compensating practical imperfections. However, in actual implementation, these parameters should be optimized according to system parameters, e.g., modulation and coding scheme (MCS). In particular, when channel coding is used, it is vital not only to minimize the mean square error (MSE) but also to enhance the Gaussianity of the output log-likelihood ratio (LLR), in order to maximize the error correction capability of the subsequent soft-decision decoder. To that end, a novel loss function based on a weighted average of negentropy, which is a key measure to evaluate the Gaussianity, and MSE of the detector output is proposed. Simulation results show that the trainable Gaussian BP (T-GaBP) detector optimized with the proposed negentropy-aware loss function significantly improves the bit error rate (BER) performance of the decoder output and substantially outperforms the T-GaBP optimized with the typical MSE loss function.

We propose a novel joint channel and data estimation (JCDE) scheme for highly-correlated large multi-user multi-input multi-output (MIMO) systems with short non-orthogonal pilots. Bayesian JCDE via scalar-wise tensor products is a solid strategy for achieving multi-user detection (MUD) with extremely low computational cost, but the convergence property is significantly degraded in practical MIMO systems assuming spatially correlated fading channels. When using ultra-short pilots aiming at significant overhead reduction, the reliable MUD via JCDE becomes increasingly challenging. To address this issue, the proposed method estimates channel coefficients via a maximum a-posteriori (MAP)-like approach with the aid of long-term channel statistics. Furthermore, while the data detection is performed via probabilistic data association (PDA) to suppress the observation correlation, the channel estimation is performed via Gaussian belief propagation (GaBP) by leveraging the pseudo-orthogonality of the pilot-plus-data sequences, which makes it possible to realize low-complexity and high-accuracy Bayesian JCDE for highly-correlated MUD. Computer simulation demonstrates the validity of our proposed method in terms of bit error rate (BER) performance and computational cost.

We propose a novel joint activity, channel and data estimation (JACDE) scheme for multiple-input multiple-output (MIMO) systems. The contribution aims to allow significant overhead reduction of MIMO systems by enabling grant-free access, while maintaining moderate throughput per user. To that end, we extend the conventional MIMO transmission framework so as to incorporate activity detection capability without resorting to spreading informative data symbols, in contrast with related work which typically relies on signal spreading. Our method leverages a Bayesian message passing scheme based on Gaussian approximation, which jointly performs active user detection (AUD), channel estimation (CE), and multi-user detection (MUD), incorporating also a well-structured low-coherence pilot design based on frame theory, which mitigates pilot contamination, and finally complemented with a detector empowered by bilinear message passing. The efficacy of the resulting JACDE-based grant-free access scheme in the cell-free MIMO system setup compliant with fifth generation (5G) new radio (NR) orthogonal frequency-division multiplexing (OFDM) signaling is demonstrated by simulation results. The results are shown to outperform the current state-of-the-art and approach the performance of an idealized (genie-aided) scheme in which user activity and channel coefficients are perfectly known.

This paper proposes bilinear Gaussian belief propagation (BiGaBP) for joint channel and data estimation (JCDE) in large multi-user multi-input multi-output (MU-MIMO) systems. JCDE is a well-known strategy for realizing a high-precision MU detection (MUD) with short pilots by utilizing the orthogonality of data sequences. For massive MIMO scenarios, the JCDE via bilinear generalized approximate message-passing (BiGAMP), which is systematically derived by extending AMP to the bilinear inference problem (BIP), achieves extremely low computational cost. However, the use of short non-orthogonal pilots to reduce the channel acquisition overhead significantly degrades the convergence property of BiGAMP. To resolve the lack of an appropriate JCDE scheme based on insufficient pilots, we design a novel MP rule based on GaBP, which is given by relaxing the large-system approximation from AMP. Furthermore, the belief scaling complying with the detection state in each iteration step is introduced to suppress the negative impact of non-orthogonal pilots even in the insufficient large-system conditions. Numerical results show the validity of our proposed method in terms of bit error rate (BER) and mean square error (MSE) performances.

This paper proposes a deep unfolding-aided belief propagation (BP) for large multi-user multi-input multi-output (MU-MIMO) detection under correlated fading channels. A BP-based detector is a well-known strategy for realizing large-scale MU detection (MUD) with low-complexity and high-accuracy. However, its convergence property is severely degraded under insufficient large-system conditions and spatial fading correlation among RX antenna elements. To compensate for this drawback, we design a trainable Gaussian BP (T-GaBP) having well-organized trainable internal parameters based on the BP structure. These parameters are optimized by the deep learning techniques in the signal-flow graph of unfolded GaBP; this approach is referred to as data-driven tuning. By training the parameters according to the system model, T-GaBP can maintain the high detection capability even in practical system configurations that differ from the ideal uncorrelated massive MIMO assumption. Numerical results show that the proposed detector improves the convergence property and achieves a comparable detection performance to the cutting-edge expectation propagation (EP) detector in correlated MUD, with a lower computational cost.

This paper deals with mmWave overloaded multiuser multi-input multi-output (MU-MIMO) detection, where the number of receive antennas is less than that of transmitted streams. Belief propagation (BP) is well known strategy for achieving large-scale MU detection (MUD) with low-complexity and high-accuracy. However, in mmWave massive MUD, the BP-based signal detector is subject to ill convergence behavior of iterative detection due to under-determined problem induced by spatial overloading and strong correlation among user channels induced by narrow angular spread of receive signal and line-of-sight (LOS) environments. To alleviate these impairments, we propose a novel iterative MUD approach based on beam-domain subspace marginalized BP (SMBP). Exploiting the approximate sparsity of beam-domain channels, the maximum likelihood (ML) principle is used to combine the strongly correlated signal subspace with reduced dimension while the BP-based detection is used for the remaining complementary subspace. The space partitioning criterion is adaptively determined based on channel state information (CSI) so that the two subspaces are as orthogonal as possible. Numerical results show that the proposed method is able to serve a massive number of wireless connections with low computational complexity even in the LOS environment, while providing excellent BER performance.

In this paper, we propose a novel soft interference cancellation scheme considering processing delay for uplink ultra-reliable and low latency communication (URLLC). For URLLC, repetition transmission was specified to satisfy a requirement of reliability. In a conventional scheme, the performance is improved by combining bit log-likelihood ratios (LLRs) at each repetition transmission. Although it is ordinal to secure radio resources for single URLLC user equipment (UE) to avoid severe inter-UE interference (IUI), it is effective to share a radio resource among plural UEs to increase spectrum efficiency. By introducing the soft interference cancelation, the proposed scheme can efficiently suppress the negative impact of IUI while keeping the similar processing delay as the conventional scheme.

This paper proposes low-complexity beam-domain channel estimation using long-term channel statistics in belief propagation (BP) based large multi-input multi-output (MIMO) detection. When the channel correlation matrix between the base station (BS) and each user equipment (UE) is available and used as prior information, maximum a-posteriori probability (MAP) estimation provides the optimal estimation performance. However, it requires undesirably complex large-scale matrix operations at any time the channel statistics is changed. By appropriately selecting beam-domain angular bins for each UE, the proposed method allows us to significantly reduce the computational cost while maintaining the near-optimal performance in terms of the mean square error (MSE) of estimated channel. The selection threshold is adaptively determined based on the prior information such as the channel correlation matrix, statistical beam, and receive SNR. For the subsequent BP-based signal detection, an appropriate covariance matrix is designed while considering the detrimental impact of channel estimation errors. Numerical results show that the proposed method can reduce the computational cost to less than 4% as compared to the MAP estimation, while providing similar MSE performance.

This paper proposes a novel layered belief propagation (BP) detector with a concatenated structure of two different BP layers for low-complexity large multi-user multi-input multi-output (MU-MIMO) detection based on statistical beams. To reduce the computational burden and the circuit scale on the base station (BS) side, the two-stage signal processing consisting of slow varying outer beamformer (OBF) and group-specific MU detection (MUD) for fast channel variations is effective. However, the dimensionality reduction of the equivalent channel based on the OBF results in significant performance degradation in subsequent spatial filtering detection. To compensate for the drawback, the proposed layered BP detector, which is designed for improving the detection capability by suppressing the intra- and inter-group interference in stages, is introduced as the poststage processing of the OBF. Finally, we demonstrate the validity of our proposed method in terms of the bit error rate (BER) performance and the computational complexity.

This paper focuses on multi-user detection in uplink Massive multiple-input multiple-output (MIMO) systems. As a low computational complexity signal detection algorithm, matched filter (MF)-based Gaussian belief propagation (MF-GaBP) using adaptively scaled belief (ASB) has been proposed. In addition, to suppress the negative impact of spatial correlation, an MMSE detector is introduced as the prior stage processing of MF-GaBP. Through computer simulations, this algorithm exhibits high performance even in high- spatially loaded Massive MIMO scenarios. However, in actual radio environments, there is a possibility to observe an extremely high channel correlation among some antenna elements or some users due to co-located polarization antenna elements or closely deployed mobile stations (MS). The highly correlated channel results in the performance degradation of MF-GaBP using ASB because of the low reliability of initial beliefs. This paper aims to verify the performances of MF- GaBP in the actual radio environments. The predetermined parameters in MF- GaBP are also adjusted according to actual environments for improving the convergence property of the iterative detection. To obtain propagation channel data for performance evaluation in the actual environments, an indoor experimental trial using Massive MMO equipment with 32 antenna elements was carried out under a condition that 16 MSs are closely deployed. Computer simulations using the obtained propagation channel data validate that simply applying the MMSE detector before MF-GaBP with ASB suppress an error floor in the bit error rate (BER) performance even in highly correlated channel.

This paper proposes a symbol replica generation method using look-up table (LUT) based on the information bottleneck (IB) theory in matched filter Gaussian belief propagation (MF-GaBP) for massive multi-input multi-output (MIMO) detection. MF-GaBP serves as an iterative signal detection scheme with low computational complexity by utilizing massive MIMO simplification owing to the law of large numbers. However, when the internal mathematical processes in MF-GaBP are conducted in double precision, a severe processing delay is inevitable. To avoid the impairment, we propose a quantized MF-GaBP detection scheme using predesigned LUTs. The quantization threshold is designed based on the sequential IB (sIB) method for minimizing the mutual information loss. Finally, computer simulations demonstrate that the proposed method significantly reduces the memory occupancy on the basis of table-based processing while suppressing error floor level of the bit error rate (BER) performance.

This paper proposes an adaptively scaled belief (ASB) in Gaussian belief propagation (GaBP) designed for use in large multi-user multi-input multi-output (MU-MIMO) detection under higher order modulation schemes. In practical MU-MIMO systems, the dominant factor in the poor convergence of GaBP iterative detection is approximation errors arising from the fact that the law of large numbers does not work well in many such applications as a result of physical system limitations. Unfortunately, the approximation errors become more severe when there is higher correlation among typical bit-wise prior beliefs when higher order quadrature amplitude modulation schemes are used. To cope with the impairments arising from inter-bit correlation, symbol-wise beliefs can be defined for GaBP self-iterative detection, although this still does not remove approximation errors. As a simple method for mitigating the harmful effects of approximation error, this paper proposes a novel method for adaptive belief scaling while stabilizing the dynamics of random MIMO channels. Based on the functionality of ASB, we also propose a method for approximately calculating conditional expectations with lower computational complexity without sacrificing detection capability. Finally, the validity of using ASB for symbol-wise iterative detection in suppressing the bit-error-rate floor level is confirmed.

This paper introduces Augmented Jump, a backpack multirotor system for jumping ability augmentation. Augmented Jump hovers and supports users' weight by a constant upward power of thrust. Users can jump higher and stay in the air for a longer time than usual with Augmented Jump. We designed and developed our first proof-of-concept prototype that can be controlled as an octocopter and support user's weight by 50kg at maximum. In our experiments, it is found that the system enabled the user to perform jumping in simulated 75% reduced gravity. From user study, the results showed that our system was effective for extending the height and the duration of jumping.

This paper proposes a random codebook design and its constraints for Gaussian belief propagation (GaBP) in massive Sparse Code Multiple Access (SCMA). In typical SCMA, a message passing algorithm (MPA) is applicable as the detection scheme for multi-user detection (MUD) on the assumption of a predefined optimal codebook. As the number of transmit streams increases, however, it becomes quite difficult to design optimal codebook due to a large number of its candidates. To address such an inconvenient problem, we employ the structured random codebook and GaBP iterative detection, which may achieve the near-optimal performance thanks to the diversity gain in the large-scale MUD. Moreover, an abnormal noise enhancement induced in GaBP can be suppressed by appropriate constraints in random codebook design. To improve the convergence property of GaBP iterative detection, we propose a novel random codebook design and its constraints for GaBP. Finally, we demonstrate the validity of our proposed method, in terms of improvement of bit error rate (BER) performances.

The human body has unique electrical characteristics. These characteristics have been investigated in various studies in human-computer interaction (HCI) and related research fields. Such studies include applications for using the body as a conductive lead for transmission or electric field sensing and activating human muscles or organs. However, electricity is not completely safe for the human body; therefore, to avoid harming users, careful consideration is essential when developing such devices. The knowledge required for such consideration is spread throughout a large number research fields, and it can be difficult for researchers in the HCI field to comprehend all of them. The purpose of this article is to support researchers in developing systems that apply electricity to the human body and to serve as a basis for further research. This article reviews previous research pertaining to HCI in which users come into contact with electricity. In addition, considerations of how and where this type of research can be expanded, along with guidelines grounded in other fields for designing systems safely and addressing ethical concerns, are presented. An understanding of the field and of the related safety issues will enhance the understanding of limitations and potential and can clarify the design space.

This paper proposes a normalized matched filter (MF) belief in Gaussian belief propagation (GaBP) detection especially for a large multiple-input multiple-output (L-MIMO) configuration where a base station (BS) has tens of antennas. In a massive MIMO channel where the BS has hundreds of antennas, damped GaBP is known to be an effective detector in terms of low computational complexity and its detection capability. However, in L- MIMO channels, GaBP is subject to ill convergence behavior of iterative detection due to lack of channel hardening effects obtained by massive number of receive antennas. To improve the convergence property, we investigate the MF belief, instead of a traditional log likelihood ratio (LLR) belief. Then, we propose the novel normalized MF belief according to instantaneous channel state. As a side effect of the normalization, a noise variance estimator is not necessary. Finally, we demonstrate the validity of the normalized MF belief with the aid of damped processing, in terms of suppression of bit error rate (BER) floor as well as approach to maximum likelihood detection (MLD) limit.