As wireless communication applications evolve from traditional multipath environments to high-mobility scenarios like unmanned aerial vehicles, multiplexing techniques have advanced accordingly. Traditional single-carrier frequency-domain equalization (SC-FDE) and orthogonal frequency-division multiplexing (OFDM) have given way to emerging orthogonal timefrequency space (OTFS) and affine frequency-division multiplexing (AFDM). These approaches exploit specific channel structures—e.g., Toeplitz-structured multipath channel matrix for OFDM and SC-FDE or doubly selective channels for OTFS and AFDM—to diagonalize or sparsify the effective channel, thereby enabling low-complexity detection. However, their reliance on these structures significantly limits their robustness in dynamic, real-world environments. To address these challenges, this paper studies a random multiplexing technique that is decoupled from the physical channels, thereby enabling its application to arbitrary norm-bounded and spectrally convergent channel matrices. Random multiplexing achieves statistical fading-channel ergodicity for transmitted signals by constructing an equivalent input-isotropic channel matrix in the random transform domain. It guarantees the asymptotic replica MAP bit-error rate (BER) optimality of AMP-type detectors for linear systems with arbitrary norm-bounded, spectrally convergent channel matrices and signaling configurations, under the unique fixed point assumption. A low-complexity cross-domain memory AMP (CD-MAMP) detector is considered for random multiplexing systems, leveraging the sparsity of the time-domain channel and the input isotropy of the equivalent channel. Optimal power allocations are derived to minimize the replica MAP BER and maximize the replica constrained capacity of random multiplexing systems, respectively. The optimal coding principle and replica constrained-capacity optimality of CD-MAMP detector are investigated for random multiplexing systems. Additionally, the versatility of random multiplexing in diverse wireless applications is explored. Numerical results are presented to validate the theoretical findings.

The integration of multicarrier modulation and multiple-input-multiple-output (MIMO) is critical for reliable transmission of wireless signals in complex environments, which significantly improve spectrum efficiency. Existing studies have shown that popular orthogonal time frequency space (OTFS) and affine frequency division multiplexing (AFDM) offer significant advantages over orthogonal frequency division multiplexing (OFDM) in uncoded doubly selective channels. However, it remains uncertain whether these benefits extend to coded systems. Meanwhile, the information-theoretic limit analysis of coded MIMO multicarrier systems and the corresponding low-complexity receiver design remain unclear. To overcome these challenges, this paper proposes a multi-slot cross-domain memory approximate message passing (MS-CD-MAMP) receiver as well as develops its information-theoretic (i.e., achievable rate) limit and optimal coding principle for MIMO-multicarrier modulation (e.g., OFDM, OTFS, and AFDM) systems. The proposed MS-CD-MAMP receiver can exploit not only the time domain channel sparsity for low complexity but also the corresponding symbol domain constellation constraints for performance enhancement. Meanwhile, limited by the high-dimensional complex state evolution (SE), a simplified single-input single-output variational SE is proposed to derive the achievable rate of MS-CD-MAMP and the optimal coding principle with the goal of maximizing the achievable rate. Numerical results show that coded MIMO-OFDM/OTFS/AFDM with MS-CD-MAMP achieve the same maximum achievable rate in doubly selective channels, whose finite-length performance with practical optimized low-density parity-check (LDPC) codes is only$0.5\sim 1.8$dB away from the associated theoretical limit, and has$0.8\sim 4.4$dB gain over the well-designed point-to-point LDPC codes.

Orthogonal delay-Doppler division multiplexing (ODDM) modulation has recently been regarded as a promising technology to provide reliable communications in high-mobility situations. Accurate and low-complexity channel estimation is one of the most critical challenges for massive multiple input multiple output (MIMO) ODDM systems, mainly due to the extremely large antenna arrays and high-mobility environments. To overcome these challenges, this paper addresses the issue of channel estimation in downlink massive MIMO-ODDM systems and proposes a low-complexity algorithm based on memory approximate message passing (MAMP) to estimate the channel state information (CSI). Specifically, we first establish the effective channel model of the massive MIMO-ODDM systems, where the magnitudes of the elements in the equivalent channel vector follow a Bernoulli-Gaussian distribution. Further, as the number of antennas grows, the elements in the equivalent coefficient matrix tend to become completely random. Leveraging these characteristics, we utilize the MAMP method to determine the gains, delays, and Doppler effects of the multi-path channel, while the channel angles are estimated through the discrete Fourier transform method. Finally, numerical results show that the proposed channel estimation algorithm approaches the Bayesian optimal results when the number of antennas tends to infinity and improves the channel estimation accuracy by about 30% compared with the existing algorithms in terms of the normalized mean square error.

This paper introduces a random modulation technique that is decoupled from the channel matrix, allowing it to be applied to arbitrary norm-bounded and spectrally convergent channel matrices. The proposed random modulation constructs an equivalent dense and random channel matrix, ensuring that the signals undergo sufficient statistical channel fading. It also guarantees the asymptotic replica maximum a posteriori (MAP) bit-error rate (BER) optimality of approximate message passing (AMP)-type detectors for linear systems with arbitrary norm-bounded and spectrally convergent channel matrices when their state evolution has a unique fixed point. Then, a lowcomplexity cross-domain memory approximate message passing (CD-MAMP) detector is proposed for random modulation, leveraging the sparsity of the time-domain channel and the randomness of the random transform-domain channel. Furthermore, the optimal power allocation schemes are derived to minimize the replica MAP BER and maximize the replica constrained capacity of random-modulated linear systems, assuming the availability of channel state information (CSI) at the transceiver. Numerical results show that the proposed random modulation can achieve BER and block-error rate (BLER) performance gains of up to$2 \sim 3 \mathbf{d B}$compared to existing OFDM/OTFS/AFDM with 5G-NR LDPC codes, under both average and optimized power allocation.

The demand for accurate sensing in the complex environment, such as urban areas and indoor spaces, is critical for future wireless networks, where scattered signals become essential for sensing occluded targets under non-line-of-sight (NLOS) conditions. To reduce the demand for beam-sweeping and geometric assumptions, we propose a bistatic NLOS sensing technique that fully exploits the scattered signals. By modeling the scattering channel responses and leveraging sparsity-driven compressed sensing, our method achieves robust environmental reconstruction to estimate target positions, shapes, and orientations. The proposed algorithm is applicable for estimating the parameters of first-order and second-order scattering targets. Experimental results demonstrate its superiority in occluded target sensing and environmental mapping, thus offering an efficient solution for NLOS sensing in complex scenarios.

The utilization of data buffer in unmanned aerial vehicle (UAV) introduces a dual role in the age of information (AoI) performance. Despite the enhancement of data delivery quality resulting from flexible and efficient data transmission, buffering may also risk increasing AoI by causing data aging. Against this background, this paper investigates the AoI minimization problem in buffer-aided UAV wireless communications while incorporating the effects of UAV buffering dynamics and limited buffer size. Specifically, we formulate the problem as a partially observable Markov decision process (POMDP) and propose a deep recurrent Q-network (DRQN) -based algorithm to jointly optimize UAV trajectory planning and buffering decisions. Simulation results exhibit the superiority of the proposed algorithm in terms of reducing the average AoI. Moreover, the study sheds light on the impact of UAV buffer size on AoI optimization, yielding essential design for buffer-aided UAV communications.

This paper proposes a novel content-centric framework for joint content update, push, and delivery in wireless caching networks. We employ a two-stage transmission strategy by grouping users based on their distribution locations and content caching status of the content server (CS). Users can be served either by the base station (BS) through multicast transmission or by the CS covering them and caching the requested contents. The content update scheme is designed based on the caching function that takes the request popularity and file size into account. Afterwards, the content push and delivery process is conducted in two stages. In the first stage, the requested and updated contents for multicast groups and the CS are delivered, while the CS harvests energy by employing the function of simultaneous wireless information and power transfer (SWIPT). In the second stage, the CS serves its covering users utilizing non-orthogonal multiple access (NOMA) transmission. Based on the proposed caching and transmission designs, we formulate the sum rate optimization problem, which is challenging due to its non-convexity. Thereafter, we convert it into a convex second-order cone programming problem using semi-definite relaxation (SDR), successive convex approximation (SCA), and other approximation techniques, and solve it with CVX solvers. Simulation results exhibit the fast convergence property of the proposed algorithm and demonstrate the advantages of our twostage content transmission approach, particularly in terms of the content hit rate and the sum rate.

Initial random access is a crucial process in wireless communication networks, which sets up reliable connections between the base station (BS) and multiple active users. In this procedure, useful connection information can be naturally obtained to achieve user positioning, and the channel state information (CSI) of multiple users can be further exploited to realize environment sensing. On the other hand, environment sensing is highly related to user positioning as it requires user-specific CSI and benefits from multi-view observations from different user positions. Therefore, in this paper, we propose a joint initial random access, environment sensing, and user positioning framework. Specifically, oversampled cyclic prefixes (CPs) in orthogonal frequency division multiplexing (OFDM) systems, which contain rich environmental information, can be exploited to achieve enhanced channel estimation. Environment sensing and user positioning are further implemented based on the channel estimation results, and the scatter points are then clustered to reconstruct the environment objects. The simulation results show that the proposed framework can achieve a decimeter-level accuracy and a reconstruction ratio of about 89% for user positioning and environment sensing.

Conventional wireless communication receivers guided by Bayesian inference methods need to know the exact statistical relationship among variables, which is hard to obtain accurately in wireless contexts, thus limiting the system performance. The recently emerging artificial intelligence (AI)-empowered algorithms have shown striking performances in exploring the implicit relationship among variables with specially designed Neural Networks (NNs). Therefore, it is preferable to integrate NNs with BPs in receiver design. Such approaches also leverage NNs’ lack of reasoning ability in large state spaces and traditional BPs’ lack of reasoning depth. However, conventional receiver modules are usually designed based on explicit mathematical derivations, which cannot be easily substituted with data-driven NNs as they may break the overall inner relationship of the algorithm. In this paper, we investigate how to beneficially incorporate NNs into the existing Belief Propagation (BP)-based framework, taking the traditional semi-blind estimation problem in an Orthogonal Frequency-Division Multiplexing (OFDM) receiver as an example. Unlike existing deep-unfolding approaches, we simply utilize NNs as embedded functional units rather than duplicate denoising modules. Through qualitative discussions and numerical results, we illustrate the characteristics, principles, and differences of our proposed architecture compared to the traditional BP framework and show the dramatic performance improvements brought by incorporating NNs with BP in this well-investigated problem. Recalling that the state evolution of NNs is different from that of traditional BP methods, we give some new insights and design principles which are somehow counterfactual. We also raise some open issues on the incorporated framework.

Orthogonal delay-Doppler division multiplexing (ODDM) modulation has recently been considered a promising technology for enhancing communication system performance in high-mobility scenarios. Accurate and low-complexity channel estimation is one of the most significant challenges for massive multiple-input multiple-output (MIMO) ODDM systems, mainly due to the massive antenna arrays and high-mobility environments. In this paper, we focus on the downlink massive MIMO-ODDM communication systems, and propose a two-stage low-complexity channel estimation algorithm. Specifically, we first derive the effective channel model of the massive MIMO-ODDM systems, where the elements of the channel matrix do not follow a Bernoulli-Gaussian distribution, but their magnitudes do. Utilizing this characteristic, we employ the memory approximate message passing method to estimate the gains, delay, and Doppler of the multi-path channel, while the angles of the channel are estimated using the discrete Fourier transform method, achieving low-complexity Bayes-optimal results. Finally, numerical results demonstrate that the proposed algorithm can achieve improved estimation results, surpassing existing algorithms by approximately 2 dB.

Approximate Message Passing (AMP) type algorithms are widely used for signal recovery in high-dimensional noisy linear systems. Recently, a principle called Memory AMP (MAMP) was proposed. Leveraging this principle, the gradient descent MAMP (GD-MAMP) algorithm was designed, inheriting the strengths of AMP and OAMP/VAMP. In this paper, we first provide an overflow-avoiding GD-MAMP (OA-GD-MAMP) to address the overflow problem that arises from some intermediate variables exceeding the range of floating point numbers. Second, we develop a complexity-reduced GD-MAMP (CR-GD-MAMP) to reduce the number of matrix-vector products per iteration by 1/3 (from 3 to 2) with little to no impact on the convergence speed.

High-resolution mmWave radar imaging plays an important role in applications such as autonomous driving. Beam-based imaging methods often require scanning the scene of interest with a sufficiently small angular stepsize to achieve high-resolution, thus leading to a large computational and storage burden. Compressive sensing (CS) is a promising strategy to reconstruct high-dimensional yet sparse signals from low-dimensional measurements with random sampling. Therefore in this paper, we conduct random space sampling by adding random phase shifts on the transmit antennas of a frequency modulated continuous wave (FMCW)-based radar system. We prove that the sensing model can be formulated as a CS problem and solved by Expectation-Maximization Gaussian-Mixture Approximate Message Passing (EMGMAMP)-based approaches. Simulation results show that the model has excellent imaging performance even with very few sensing measurements. To further improve the imaging quality, we consider a multi-view sensing scenario in which sensing results from different positions are fused by proper occlusion processing and coordinate transformation. Finally, appropriate evaluation metrics are proposed for target sensing results to validate the effectiveness of the proposed sensing model and algorithm.

Recently , over-the-air computation (OAC) has shown potential in realizing computation tasks over wireless transmission. Through proper transmit and receive beamforming design, multiple-input multiple-output (MIMO)-based OAC systems can even realize partial functions of neural networks (NNs). In this paper, we propose an OAC-NN with reconfigurable intelligent surface (RIS)-aided MIMO, in which the NN computation task can be realized through updating the RIS reflection matrix. In the proposed structure, the communication system can complete the overall simple NN-based tasks only through multiple rounds of transmissions without introducing any additional computing resources. Numerical results reflect the effectiveness of the proposed scheme and the tradeoff between communication costs and computing performance.

Approximate message passing (AMP) algorithms are iterative methods for signal recovery in noisy linear systems. In some scenarios, AMP algorithms need to operate within a distributed network. To address this challenge, the distributed extensions of AMP (D-AMP, FD-AMP) and orthogonal/vector AMP (D-OAMP/D-VAMP) were proposed, but they still inherit the limitations of centralized algorithms. In this letter, we propose distributed memory AMP (D-MAMP) to overcome the IID matrix limitation of D-AMP/FD-AMP, as well as the high complexity and heavy communication cost of D-OAMP/D-VAMP. We introduce a matrix-by-vector variant of MAMP tailored for distributed computing. Leveraging this variant, D-MAMP enables each node to execute computations utilizing locally available observation vectors and transform matrices. Meanwhile, global summations of locally updated results are conducted through message interaction among nodes. For acyclic graphs, D-MAMP converges to the same mean square error performance as the centralized MAMP.

This paper investigates the generalized linear system (GLS), widely employed to evaluate the impact of nonlinear preprocessing on wireless transceivers. Two state-of-the-art signal recovery algorithms, namely generalized approximate message passing (GAMP) and generalized orthogonal/vector AMP (GOAMP/GVAMP), are comparatively studied. They have demonstrated Bayesian optimality for independently and identically distributed (IID) Gaussian matrices and unitary matrices, respectively. However, Bayesian optimality does not inherently guarantee error-free signal recovery. For coded GLS, the information-theoretic (i.e., achievable rate) limit of GAMP remains unknown, and there are still no analytical comparisons between GAMP and GOAMP/GVAMP in terms of the mean-square error and information-theoretic limit. To address these issues, we present the achievable rate analysis and optimal coding principle for GAMP with IID Gaussian matrices, as well as provide comprehensive comparisons with GOAMP/GVAMP with unitary matrices. Specifically, based on the celebrated I-MMSE lemma and the preconditions for state evolution (SE) to hold, the simplified variational SEs of GAMP and GOAMP/GVAMP are derived, leveraging the IID and unitary matrix properties to analyze the achievable rate and optimal coding principle, respectively. On this basis, it is proven that GOAMP/GVAMP outperforms GAMP in terms of asymptotic MSE and maximum achievable rate while requiring less complexity. Furthermore, two common nonlinear functions, clipping and quantization, are used as examples to demonstrate the theoretical comparisons and practical low-density parity-check (LDPC) code design for GAMP and GOAMP/GVAMP. Numerical results show that GAMP and GOAMP/GVAMP with optimized LDPC codes can approach the theoretical limits within 0:3 dB and overcome the decoding deterioration and even divergence of the existing state-of-the-art methods, particularly under low-resolution quantization.

This paper investigates a large unitarily invariant system (LUIS) involving a unitarily invariant sensing matrix, an arbitrarily fixed signal distribution, and forward error control (FEC) coding. A universal Gram-Schmidt orthogonalization is considered for constructing orthogonal approximate message passing (OAMP), enabling its applicability to a wide range of prototypes without the constraint of differentiability. We develop two single-input-single-output variational transfer functions for OAMP with Lipschitz continuous local estimators, facilitating an analysis of achievable rates. Furthermore, when the state evolution of OAMP has a unique fixed point, we reveal that OAMP can achieve the constrained capacity predicted by the replica method of LUIS based on matched FEC coding, regardless of the signal distribution. The replica method is rigorously validated for LUIS with Gaussian signaling and certain sub-classes of LUIS with arbitrary signal distributions. Several area properties are established based on the variational transfer functions of OAMP. Meanwhile, we present a replica constrained capacity-achieving coding principle for LUIS. This principle serves as the basis for optimizing irregular low-density parity-check (LDPC) codes specifically tailored for binary signaling in our simulation results. The performance of OAMP with these optimized codes exhibits a remarkable improvement over the unoptimized codes and even surpasses the well-known Turbo-LMMSE algorithm. For quadrature phase-shift keying (QPSK) modulation, we observe bit error rates (BER) performance near the replica constrained capacity across diverse channel conditions.

To support complex communication scenarios in next-generation wireless communications, this paper focuses on a generalized MIMO (GMIMO) with practical assumptions, such as massive antennas, practical channel coding, arbitrary input distributions, and general right-unitarily-invariant channel matrices (covering Rayleigh fading, certain ill-conditioned and correlated channel matrices). The orthogonal/vector approximate message passing (OAMP/VAMP) receiver has been proved to be information-theoretically optimal in GMIMO, but it is limited to high-complexity linear minimum mean-square error (LMMSE). To solve this problem, a low-complexity memory approximate message passing (MAMP) receiver has recently been shown to be Bayes optimal but limited to uncoded systems. Therefore, how to design a low-complexity and information-theoretically optimal receiver for GMIMO is still an open issue. To address this issue, this paper proposes an information-theoretically optimal MAMP receiver and investigates its achievable rate analysis and optimal coding principle. Specifically, due to the long-memory linear detection, state evolution (SE) for MAMP is intricately multi-dimensional and cannot be used directly to analyze its achievable rate. To avoid this difficulty, a simplified single-input single-output (SISO) variational SE (VSE) for MAMP is developed by leveraging the SE fixed-point consistent property of MAMP and OAMP/VAMP. The achievable rate of MAMP is calculated using the VSE, and the optimal coding principle is established to maximize the achievable rate. On this basis, the information-theoretic optimality of MAMP is proved rigorously. Furthermore, the simplified SE analysis by fixed-point consistency is generalized to any two iterative detection algorithms with the identical SE fixed point. Numerical results show that the finite-length performances of MAMP with practical optimized low-density parity-check (LDPC) codes are 0.5 ~ 2.7 dB away from the associated constrained capacities. It is worth noting that MAMP can achieve the same performances as OAMP/VAMP with 4‰ of the time consumption for large-scale systems.

This paper considers a generalized multiple-input multiple-output (GMIMO) with practical assumptions, such as massive antennas, practical channel coding, arbitrary input dis-tributions, and general right-unitarily-invariant channel matrices (covering Rayleigh fading, certain ill-conditioned and corre-lated channel matrices). Orthogonal/vector approximate message passing (OAMP/VAMP) has been proved to be information-theoretically optimal in GMIMO, but it is limited to high complexity. Meanwhile, low-complexity memory approximate message passing (MAMP) was shown to be Bayes optimal in GMIMO, but channel coding was ignored. Therefore, how to design a low-complexity and information-theoretic optimal receiver for GMIMO is still an open issue. In this paper, we propose an information-theoretic optimal MAMP receiver for coded GMIMO, whose achievable rate analysis and optimal coding principle are provided to demonstrate its information-theoretic optimality. Specifically, state evolution (SE) for MAMP is intricately multi-dimensional because of the nature of local memory detection. To this end, a fixed-point consistency lemma is proposed to derive the simplified variational SE (VSE) for MAMP, based on which the achievable rate of MAMP is calcu-lated, and the optimal coding principle is derived to maximize the achievable rate. Subsequently, we prove the information-theoretic optimality of MAMP. Numerical results show that the finite-length performances of MAMP with optimized LDPC codes are about 1.0 ~ 2.7 dB away from the associated constrained capacities. It is worth noting that MAMP can achieve the same performance as OAMP/VAMP with 4%o of the time consumption for large-scale systems.

The generalized linear system (GLS) has been widely used in wireless communications to evaluate the effect of nonlinear preprocessing on receiver performance. Generalized approximation message passing (AMP) is a state-of-the-art algorithm for the signal recovery of GLS, but it was limited to measurement matrices with independent and identically distributed (IID) elements. To relax this restriction, generalized orthogonal/vector AMP (GOAMP/GVAMP) for unitarily-invariant measurement matrices was established, which has been proven to be replica Bayes optimal in uncoded GLS. However, the information-theoretic limit of GOAMP/GVAMP is still an open challenge for arbitrary input distributions due to its complex state evolution (SE). To address this issue, in this paper, we provide the achievable rate analysis of GOAMP/GVAMP in GLS, establishing its information-theoretic limit (i.e., maximum achievable rate). Specifically, we transform the fully-unfolded state evolution (SE) of GOAMP/GVAMP into an equivalent single-input single-output variational SE (VSE). Using the VSE and the mutual information and minimum mean-square error (I-MMSE) lemma, the achievable rate of GOAMP/GVAMP is derived. Moreover, the optimal coding principle for maximizing the achievable rate is proposed, based on which a kind of low-density parity-check (LDPC) code is designed. Numerical results verify the achievable rate advantages of GOAMP/GVAMP over the conventional maximum ratio combining (MRC) receiver based on the linearized model and the BER performance gains of the optimized LDPC codes (0.8 ~ 2.8 dB) compared to the existing methods.

The widely applied orthogonal frequency division multiplexing (OFDM) system naturally contains oversampled cyclic prefixes (CP) in the generation process, which provide a wealth of environmental information and higher distance resolution for integrated sensing and communication (ISAC) but is underutilized. Therefore, we develop a compressed sensing (CS) model with oversampled CP, reaching the higher distance resolution limit corresponding to the sample rate of the analog-to-digital converter (ADC) than the fixed signal bandwidth. Since the measurement matrix formed by shifting adjacent oversampled CP pairs is ill-conditioned, we proposed random modulation and random extraction from multiple oversampled CP to increase the validity of the observations. To exploit the channel fading characteristics and sparsity of scattering points, we propose an element-by-element demodulator based on the orthogonal approximate message passing (OAMP) algorithm, called the element-wise OAMP (E-OAMP) algorithm. The simulation results validate the outstanding performance of the proposed algorithm over traditional CS algorithms.

Approximate Message Passing (AMP) is an efficient iterative parameter-estimation technique for certain high-dimensional linear systems with non-Gaussian distributions, such as sparse systems. In AMP, a so-called Onsager term is added to keep estimation errors approximately Gaussian. Orthogonal AMP (OAMP) does not require this Onsager term, relying instead on an orthogonalization procedure to keep the current errors uncorrelated with (i.e., orthogonal to) past errors. In this paper, we show the generality and significance of the orthogonality in ensuring that errors are “asymptotically independently and identically distributed Gaussian” (AIIDG). This AIIDG property, which is essential for the attractive performance of OAMP, holds for separable functions. We present a simple and versatile procedure to establish the orthogonality through Gram-Schmidt (GS) orthogonalization, which is applicable to any prototype. We show that different AMP-type algorithms, such as expectation propagation (EP), turbo, AMP and OAMP, can be unified under the orthogonal principle. The simplicity and generality of OAMP provide efficient solutions for estimation problems beyond the classical linear models. As an example, we study the optimization of OAMP via the GS model and GS orthogonalization. More related applications will be discussed in a companion paper where new algorithms are developed for problems with multiple constraints and multiple measurement variables.

In this paper, we consider a reconfigurable intelligent surface (RIS) aided uplink multiuser multi-input multi-output (MIMO) orthogonal frequency division multiplexing (OFDM) system, where the receiver is assumed to conduct low-complexity iterative detection. We aim to minimize the total transmit power by jointly designing the precoder of the transmitter and the passive beamforming of the RIS. This problem can be tackled from the perspective of information theory. But this information-theoretic approach may involve prohibitively high complexity since the number of rate constraints that specify the capacity region of the uplink multiuser channel is exponential in the number of users. To avoid this difficulty, we formulate the design problem of the iterative receiver under the constraints of a maximal iteration number and target bit error rates of users. To tackle this challenging problem, we propose a groupwise successive interference cancellation (SIC) optimization approach, where the signals of users are decoded and canceled in a group-by-group manner. We present a heuristic user grouping strategy, and resort to the alternating optimization technique to iteratively solve the precoding and passive beamforming sub-problems. Specifically, for the precoding sub-problem, we employ fractional programming to convert it to a convex problem; for the passive beamforming sub-problem, we adopt successive convex approximation to deal with the unit-modulus constraints of the RIS. We show that the proposed groupwise SIC approach has significant advantages in both performance and computational complexity, as compared with the counterpart approaches.

With the complication of future communication scenarios, most conventional signal processing technologies of multi-user multiple-input multiple-output (MU-MIMO) become unreliable, which are designed based on ideal assumptions, such as Gaussian signaling and independent identically distributed (IID) channel matrices. As a result, this paper considers a generalized MU-MIMO (GMU-MIMO) system with more general assumptions, i.e., arbitrarily fixed input distributions, and general unitarily-invariant channel matrices. However, there is still no accurate capacity analysis and capacity optimal transceiver with practical complexity for GMU-MIMO under the constraint of coding. To address these issues, inspired by the replica method, the constrained sum capacity of coded GMU-MIMO with fixed input distribution is calculated by using the celebrated mutual information and minimum mean-square error (MMSE) lemma and the MMSE optimality of orthogonal/vector approximate message passing (OAMP/VAMP). Then, a capacity optimal multi-user OAMP/VAMP receiver is proposed, whose achievable rate is proved to be equal to the constrained sum capacity. Moreover, a design principle of multi-user codes is presented for the multi-user OAMP/VAMP, based on which a kind of practical multi-user low-density parity-check (MU-LDPC) code is designed. Numerical results show that finite-length performances of the proposed MU-LDPC codes with multi-user OAMP/VAMP are about 2 dB away from the constrained sum capacity and outperform those of the existing state-of-art methods.

Approximate message passing (AMP) type algorithms have been widely used in the signal reconstruction of certain large random linear systems. A key feature of the AMP-type algorithms is that their dynamics can be correctly described by state evolution. However, state evolution does not necessarily guarantee the convergence of iterative algorithms. To solve the convergence problem of AMP-type algorithms in principle, this paper proposes a memory AMP (MAMP) under a sufficient statistic condition, named sufficient statistic MAMP (SS-MAMP). We show that the covariance matrices of SS-MAMP are L-banded and convergent. Given an arbitrary MAMP, we can construct the SS-MAMP by damping, which not only ensures the convergence, but also preserves the orthogonality, i.e., its dynamics can be correctly described by state evolution.

This paper investigates a large unitarily invariant system (LUIS) involving a unitarily invariant sensing matrix, an arbitrary fixed signal distribution, and forward error control (FEC) coding. Several area properties are established based on the state evolution of orthogonal approximate message passing (OAMP) in an un-coded LUIS. Under the assumptions that the state evolution for joint OAMP and FEC decoding is correct and the replica method is reliable, we analyze the achievable rate of OAMP. We prove that OAMP reaches the constrained capacity predicted by the replica method of the LUIS with an arbitrary signal distribution based on matched FEC coding. Meanwhile, we elaborate a constrained capacity-achieving coding principle for LUIS, based on which irregular low-density parity-check (LDPC) codes are optimized for binary signaling in the simulation results. We show that OAMP with the optimized codes has significant performance improvement over the un-optimized ones and the well-known Turbo linear MMSE algorithm. For quadrature phase-shift keying (QPSK) modulation, constrained capacity-approaching bit error rate (BER) performances are observed under various channel conditions.

In this article, we investigate an unsourced random access scheme for massive machine-type communications (mMTC) in the sixth-generation (6G) wireless networks with sporadic data traffic. First, we establish a general framework for massive unsourced random access based on a two-layer signal coding, i.e., an outer code and an inner code. In particular, considering Rician fading in the scenario of mMTC, we design a novel codeword activity detection algorithm for the inner code of unsourced random access based on the distribution of received signals by exploiting the maximum-likelihood (ML) method. Then, we analyze the performance of the proposed codeword activity detection algorithm exploiting Fisher Information Matrix, which facilitates the derivative of the approximated distribution of the estimation error of the codeword activity vector when the number of base station (BS) antennas is sufficiently large. Furthermore, for the outer code, we propose an optimization algorithm to allocate the lengths of message bits and parity check bits, so as to strike a balance between the error probability and the complexity required for outer decoding. Finally, extensive simulation results validate the effectiveness of the proposed detection algorithm and the optimized length allocation scheme compared with an existing detection algorithm and a fixed-length allocation scheme.

Conventional multi-user multiple-input multiple-output (MU-MIMO) mainly focused on Gaussian signaling, independent and identically distributed (IID) channels, and a limited number of users. It will be laborious to cope with the heterogeneous requirements in next-generation wireless communications, such as various transmission data, complicated communication scenarios, and unprecedented massive user access. Therefore, this paper studies a generalized MU-MIMO (GMU-MIMO) system with more generalized and practical constraints, i.e., practical channel coding, non-Gaussian signaling, right-unitarily-invariant channels (covering Rayleigh fading channel matrices, certain ill-conditioned and correlated channel matrices, etc.), and massive users and antennas. These generalized assumptions bring new challenges in theory and practice. For example, there is no accurate constrained capacity region analysis for GMU-MIMO. In addition, it is unclear how to achieve constrained-capacity-optimal performance with practical complexity. To address these challenges, a unified framework is proposed to derive the constrained capacity region of GMU-MIMO and design a constrained-capacity-optimal transceiver, which jointly considers encoding, modulation, detection, and decoding. Group asymmetry is developed to group users according to their rates, which makes a tradeoff between user rate allocation and implementation complexity. Specifically, the constrained capacity region of group-asymmetric GMU-MIMO is characterized by using the minimum mean-square error (MMSE) optimality of orthogonal/vector approximate message passing (OAMP/VAMP) and the relationship between mutual information and MMSE. Furthermore, a theoretically optimal multi-user OAMP/VAMP receiver and practical multi-user low-density parity-check (MU-LDPC) codes are proposed to achieve the constrained capacity region of group-asymmetric GMU-MIMO. Numerical results demonstrate that the proposed MU-LDPC coded GMU-MIMO systems achieve asymptotic performance within 0.2 dB from the theoretical sum capacity. Moreover, their finite-length performances are about 1~2 dB away from the associated sum capacity of GMU-MIMO.

Approximate message passing (AMP) is a low-cost iterative parameter-estimation technique for certain high-dimensional linear systems with non-Gaussian distributions. AMP only applies to independent identically distributed (IID) transform matrices, but may become unreliable (e.g., perform poorly or even diverge) for other matrix ensembles, especially for ill-conditioned ones. To solve this issue, orthogonal/vector AMP (OAMP/VAMP) was proposed for general right-unitarily-invariant matrices. However, the Bayes-optimal OAMP/VAMP (BO-OAMP/VAMP) requires a high-complexity linear minimum mean square error (MMSE) estimator. This prevents OAMP/VAMP from being used in large-scale systems. To address the drawbacks of AMP and BO-OAMP/VAMP, this paper offers a memory AMP (MAMP) framework based on the orthogonality principle, which ensures that estimation errors in MAMP are asymptotically IID Gaussian. To realize the required orthogonality for MAMP, we provide an orthogonalization procedure for the local memory estimators. In addition, we propose a Bayes-optimal MAMP (BO-MAMP), in which a long-memory matched filter is used for interference suppression. The complexity of BO-MAMP is comparable to AMP. To asymptotically characterize the performance of BO-MAMP, a state evolution is derived. The relaxation parameters and damping vector in BO-MAMP are optimized based on state evolution. Most crucially, the state evolution of the optimized BO-MAMP converges to the same fixed point as that of the high-complexity BO-OAMP/VAMP for all right-unitarily-invariant matrices, and achieves the Bayes optimal MSE predicted by the replica method if its state evolution has a unique fixed point. Finally, simulations are provided to verify the theoretical results’ validity and accuracy.

Approximate message passing (AMP) is a low-cost iterative parameter-estimation technique for certain high-dimensional linear systems with non-Gaussian distributions. However, AMP only applies to independent identically distributed (IID) transform matrices, but may become unreliable for other matrix ensembles, especially for ill-conditioned ones. To handle this difficulty, orthogonal/vector AMP (OAMP/VAMP) was proposed for general right-unitarily-invariant matrices. However, the Bayes-optimal OAMP/VAMP requires high-complexity linear minimum mean square error estimator. To solve the disadvantages of AMP and OAMP/VAMP, this paper proposes a memory AMP (MAMP), in which a long-memory matched filter is proposed for interference suppression. The complexity of MAMP is comparable to AMP. The asymptotic Gaussianity of estimation errors in MAMP is guaranteed by the orthogonality principle. A state evolution is derived to asymptotically characterize the performance of MAMP. Based on the state evolution, the relaxation parameters and damping vector in MAMP are optimized. For all right-unitarily-invariant matrices, the optimized MAMP converges to OAMP/VAMP, and thus is Bayes-optimal if it has a unique fixed point. Finally, simulations are provided to verify the validity and accuracy of the theoretical results.

This paper studies a large random matrix system (LRMS) model involving an arbitrary signal distribution and forward error control (FEC) coding. We establish an area property based on the approximate message passing (AMP) algorithm. Under the assumption that the state evolution for AMP is correct for the coded system, the achievable rate of AMP is analyzed. We prove that AMP achieves the constrained capacity of the LRMS with an arbitrary signal distribution provided that a matching condition is satisfied. We provide related numerical results of binary signaling using irregular low-density parity-check (LDPC) codes. We show that the optimized codes demonstrate significantly better performance over unmatched ones under AMP. For quadrature phase shift keying (QPSK) modulation, bit error rate (BER) performance within 1 dB from the constrained capacity limit is observed.

Recently, it was found that clipping can significantly improve the section error rate (SER) performance of sparse regression (SR) codes if an optimal clipping threshold is chosen. In this paper, we propose irregularly clipped SR codes, where multiple clipping thresholds are applied to symbols according to a distribution, to further improve the SER performance of SR codes. Orthogonal approximate message passing (OAMP) algorithm is used for decoding. Using state evolution, the distribution of irregular clipping thresholds is optimized to minimize the SER of OAMP decoding. As a result, optimized irregularly clipped SR codes achieve a better tradeoff between clipping distortion and noise distortion than regularly clipped SR codes. Numerical results demonstrate that irregularly clipped SR codes achieve 0.4 dB gain in signal-to-noise-ratio (SNR) over regularly clipped SR codes at code length ≈2.5 × 104and SER ≈10−5. We further show that irregularly clipped SR codes are robust over a wide range of code rates.

We address the joint device activity detection and channel estimation (JACE) problem in a massive MIMO connectivity scenario in which a large number of mobile devices are connected to a base station (BS), while only a small portion are active at any given time. The main objective is to provide an efficient transmission and detection scheme with both spatial and temporal correlations. We formulate JACE as a multiple measurement vector (MMV) problem with correlated entries in the vectors to be estimated. We propose an MMV form of the orthogonal approximate message passing algorithm (OAMP-MMV). We derive a group Gram-Schmidt orthogonalization (GGSO) procedure for the realization of OAMP-MMV. We outline a state evolution (SE) procedure for OAMP-MMV and examine its accuracy using numerical results. We also compare OAMP-MMV with existing alternatives, including AMP-MMV and GTurbo-MMV. We show that OAMP-MMV outperforms AMP-MMV when pilot sequences are generated using Hadamard pilot matrices. Such a pilot design is attractive due to the low-cost signal processing technique using the fast Hadamard transform (FHT). We also show that OAMP-MMV outperforms GTurbo-MMV in correlated channels.

Approximate message passing (AMP) is an iterative signal recovery algorithm for compressed sensing (CS) applications. In this letter, we present an integral-based orthogonal AMP (IB-OAMP) technique that avoids the requirements of AMP (and also the original form of OAMP) on differentiable and separable denoisers. The orthogonality in IB-OAMP can be established using a Monte Carlo method similar to the training stage in a machine-learning algorithm. These features make IB-OAMP attractive to be used in conjunction with some well-studied denoising algorithms.

This paper studies a large random matrix system (LRMS) model involving an arbitrary signal distribution and forward error control (FEC) coding. We establish an area property based on the approximate message passing (AMP) algorithm. Under the assumption that the state evolution for AMP is correct for the coded system, the achievable rate of AMP is analyzed. We prove that AMP achieves the constrained capacity of the LRMS with an arbitrary signal distribution provided that a matching condition is satisfied. As a byproduct, we provide an alternative derivation for the constraint capacity of an LRMS using a proved property of AMP. We discuss realization techniques for the matching principle of binary signaling using irregular low-density parity-check (LDPC) codes and provide related numerical results. We show that the optimized codes demonstrate significantly better performance over un-matched ones under AMP. For quadrature phase shift keying (QPSK) modulation, bit error rate (BER) performance within 1 dB from the constrained capacity limit is observed.

With recent advances on the dense low-Earth orbit (LEO) constellation, the LEO satellite network has become one promising solution for providing global coverage for Internet-of-Things (IoT) services. Confronted with the sporadic transmission from randomly activated IoT devices, we consider the random access (RA) mechanism and propose a grant-free RA (GF-RA) scheme to reduce the access delay to the mobile LEO satellites. A Bernoulli–Rician message passing with expectation–maximization (BR-MP-EM) algorithm is proposed for this terrestrial–satellite GF-RA system to address the user activity detection (UAD) and channel estimation (CE) problem. This BR-MP-EM algorithm is divided into two stages. In the inner iterations, the Bernoulli messages and Rician messages are updated for the joint UAD and CE problem. Based on the output of the inner iterations, the expectation–maximization (EM) method is employed in the outer iterations to update the hyperparameters related to the channel impairments. Finally, simulation results show the UAD and CE accuracy of the proposed BR-MP-EM algorithm, as well as the robustness against the channel impairments.

This paper aims at shedding light on the impact of unsaturated traffic on the performance of uplink non-orthogonal multiple access (NOMA) transmissions. Nevertheless, the unsaturated traffic gives rise to the discontinuous interference and the inherent interaction of queues, which in turn highly complicates the performance evaluation. By utilizing tools from queuing theory, we first explicitly characterize the stable throughput region, which represents the region of traffic arrival rates on the condition that the queuing delay converges in distribution to a bounded random variable. In light of this, the critical condition under which NOMA can extend the stable throughput region of orthogonal multiple access (OMA) is derived. Then, we propose an algorithmic solution to evaluate the average delay incurred from both queuing and transmission. It is interestingly found that the superiority of NOMA over OMA in terms of average delay heavily hinges on the temporal traffic dynamics of each user. In particular, NOMA enjoys a clear advantage when the traffic arrival rate of the user with stronger channel condition considerably exceeds the traffic arrival rate of the user with weaker channel condition. The derived results can provide helpful guidance to fully leverage the comparative advantages of NOMA under various traffic conditions.

This paper considers a low-complexity Gaussian message passing (GMP) Multi-User Detection (MUD) scheme for a coded massive multiple-input multiple-output (MIMO) system with non-orthogonal multiple access (massive MIMO-NOMA), in which a base station with$N_{s}$antennas serves$N_{u}$sources simultaneously in the same frequency. Both$N_{u}$and$N_{s}$are large numbers, and we consider the overloaded cases with$N_{u}>N_{s}$. The GMP for MIMO-NOMA is a message passing algorithm operating on a fully-connected loopy factor graph, which is well understood to fail to converge due to the correlation problem. The GMP is attractive as its complexity order is only linearly dependent on the number of users, compared to the cubic complexity order of linear minimum mean square error (LMMSE) MUD. In this paper, we utilize the large-scale property of the system to simplify the convergence analysis of the GMP under the overloaded condition. We prove that thevariancesof the GMP definitely converge to the mean square error (MSE) of the LMMSE multi-user detection. Second, themeansof the traditional GMP will fail to converge when$N_{u}/N_{s}< (\sqrt {2}-1)^{-2}\approx 5.83$. Therefore, we propose and derive a new convergent GMP called scale-and-add GMP (SA-GMP), which always converges to the LMMSE multi-user detection performance for any$N_{u}/N_{s}>1$, and show that it has a faster convergence speed than the traditional GMP with the same complexity. Finally, the numerical results are provided to verify the validity and accuracy of the theoretical results presented.

Linear minimum mean square error (LMMSE) estimation based turbo detection has been extensively studied for coded linear systems since the seminal work of Wang and Poor (WP). The WP algorithm operates iteratively between a linear detector (LD) and a nonlinear detector (NLD): the LD suppresses the interference based on LMMSE filtering, and the NLD decodes the data by treating the output of the LD as an observation from an additive white Gaussian noise (AWGN) channel. In WP, the messages exchanged between LD and NLD are required to beextrinsic. For the NLD, the extrinsic message comes from the constraint imposed on feedforward error correction (FEC) codes. Therefore, WP does not work in an un-coded linear system. Recently, we proposed an orthogonal approximate message passing (OAMP) algorithm, which only requires the input/output error terms of LD and NLD to beorthogonal. We conjectured that for un-coded linear systems that involve certain large random matrices, the dynamics of OAMP can be accurately characterized by state evolution (SE). In this paper, we consider a coded linear system and develop an extrinsic message aided OAMP (EMA-OAMP) algorithm. Similar to the un-coded case, EMA-OAMP relaxes the requirements on output messages to be orthogonal instead of extrinsic. We derive an SE procedure to characterize the performance of OAMP in coded systems. We conjecture that this SE procedure is accurate, which is verified by simulation results. Under this conjecture, we show that EMA-OAMP can outperform WP under certain standard assumptions for iterative decoding. Extensive simulations results are provided to verify the advantages of OAMP in coded MIMO systems.

Due to the massive number of devices in the M2M communication era, new challenges have been brought to the existing random-access (RA) mechanism, such as severe preamble collisions and resource block (RB) wastes. To address these problems, a novel sparse message passing (SMP) algorithm is proposed, based on a factor graph on which Bernoulli messages are updated. The SMP enables an accurate estimation on the activity of the devices and the identity of the preamble chosen by each active device. Aided by the estimation, the RB efficiency for the uplink data transmission can be improved, especially among the collided devices. In addition, an analytical tool is derived to analyze the iterative evolution and convergence of the SMP algorithm. Finally, numerical simulations are provided to verify the validity of our analytical results and the significant improvement of the proposed SMP on estimation error rate even when preamble collision occurs.

The common outage performance of an amplify‐and‐forward two‐hop two‐user channel is studied in the presence of multiple independent interferers at the destination. First, the exact integral form expression of the common outage probability is derived. Then, in order to decrease the computation complexity, a closed‐form approximation of the common outage probability is derived. Finally, the asymptotic analysis is performed based on the approximation expression. Numerical results demonstrate that the integral form of the common outage probability, the corresponding approximation and the asymptotic results match well with the Monte Carlo simulations.

MIMO-NOMA combines multiple-input multiple-output (MIMO) and non-orthogonal multiple access (NOMA) techniques to address heterogeneous challenges, such as massive connectivity, low latency, and high reliability in the 5G cellular communication system and beyond. In this paper, a coded MIMO-NOMA system with capacity-approaching performance and low implementation complexity is proposed. Specifically, the proposed MIMO receiver consists of a linear minimum mean-square error (LMMSE) multi-user detector and a bank of single-user message-passing decoders, which decompose the overall NOMA signal recovery into distributed low-complexity computations with iterative processing. An asymptotic extrinsic information transfer analysis is employed to model the overall performance, and a novel class of multi-user irregular repeat-accumulate channel codes that match with the LMMSE multi-user detector in the iterative decoding process are constructed for the system. As a result, the proposed coded MIMO-NOMA system achieves asymptotic performance within 0.2 dB from the theoretical capacity. Simulation results validate the reliability and robustness of the proposed system in practical settings that include different system loads, iteration numbers, code lengths, fast/block fading, and imperfect channel estimation.

Though the concept of non-orthogonal multiple access (NOMA) was proposed several years ago, the performance of uplink NOMA has only been verified in theory, but not in practice. This paper presents an over-the-air implementation of a uplink NOMA system, while providing solutions to most common practical problems, i.e., carrier frequency offset (CFO) synchronization, time synchronization, and channel estimation. The implemented CFO synchronization method adopts the primary synchronization signal (PSS) of LTE. Also, we design a novel preamble for each uplink user, and it is appended to every frame before it is transmitted through the air. This preamble will be used for time synchronization and channel estimation at the BS. Also, a low-complexity, iterative linear minimum mean squared error (LMMSE) detector has been implemented for multi- user decoding. The paper also validates the proposed architecture numerically, as well as experimentally.

In cloud radio access network (C-RAN), remote radio heads (RRHs) and users are uniformly distributed in a large area such that the channel matrix can be considered as sparse. Based on this phenomenon, RRHs only need to detect the relatively strong signals from nearby users and ignore the weak signals from far users, which is helpful to develop low-complexity detection algorithms without causing much performance loss. However, before detection, RRHs require to obtain the realtime user activity information by the dynamic grant procedure, which causes the enormous latency. To address this issue, in this paper, we consider a grant-free C-RAN system and propose a low- complexity Bernoulli-Gaussian message passing (BGMP) algorithm based on the sparsified channel, which jointly detects the user activity and signal. Since active users are assumed to transmit Gaussian signals at any time, the user activity can be regarded as a Bernoulli variable and the signals from all users obey a Bernoulli-Gaussian distribution. In the BGMP, the detection functions for signals are designed with respect to the Bernoulli-Gaussian variable. Numerical results demonstrate the robustness and effectivity of the BGMP. That is, for different sparsified channels, the BGMP can approach the mean-square error (MSE) of the genie-aided sparse minimum mean-square error (GA- SMMSE) which exactly knows the user activity information. Meanwhile, the fast convergence and strong recovery capability for user activity of the BGMP are also verified.

Low-cost message passing (MP) algorithm has been recognized as a promising technique for sparse vector recovery. However, the existing MP algorithms either focus on mean square error (MSE) of the value recovery while ignoring the sparsity requirement, or support error rate (SER) of the sparse support (non-zero position) recovery while ignoring its value. A novel low-complexity Bernoulli-Gaussian MP (BGMP) is proposed to perform the value recovery as well as the support recovery. Particularly, in the proposed BGMP, support-related Bernoulli messages and value- related Gaussian messages are jointly processed and assist each other. In addition, a strict lower bound is developed for the MSE of BGMP via the genie-aided minimum mean-square-error (GA-MMSE) method. The GA-MMSE lower bound is shown to be tight in high signal-to-noise ratio. Numerical results are provided to verify the advantage of BGMP in terms of final MSE, SER and convergence speed.

In this paper, we develop a framework using tools from stochastic geometry and queuing theory to evaluate the flow-level performance of downlink cellular networks with spatio-temporal traffic. Under this framework, we first obtain the mean service rate and the non-empty probability of a scheduled user queue by solving a fixed-point equation, which captures the inherent correlation between the interference and the queue status. By leveraging these results, we then derive closed-form expressions for the mean packet throughput and its bounds, defined as the mean number of packets that can be delivered during a given time duration. Simulation results validate the accuracy of the presented analysis, which can provide useful insight on the design of cellular networks while incorporating the spatial and temporal fluctuations of traffic.

Sparse code multiple access (SCMA) has been recently proposed for the future wireless networks, which allows nonorthogonal spectrum resource sharing and enables system overloading. In this paper, we apply SCMA into device-to-device (D2D) communication and cellular hybrid network, targeted at using the overload feature of SCMA to support massive device connectivity and expand network capacity. Particularly, we develop a stochastic geometry-based framework to model and analyze SCMA, considering underlaid and overlaid modes. Based on the results, we analytically compare SCMA with orthogonal frequency-division multiple access (OFDMA) using area spectral efficiency (ASE) and quantify closed-form ASE gain of SCMA over OFDMA. Notably, it is shown that system ASE can be significantly improved using SCMA and the ASE gain scales linearly with the SCMA codeword dimension. Besides, we endow D2D users with an activated probability to balance cross-tier interference in the underlaid mode and derive the optimal activated probability. Meanwhile, we study resource allocation in the overlaid mode and obtain the optimal codebook allocation rule. It is interestingly found that the optimal SCMA codebook allocation rule is independent of cellular network parameters when cellular users are densely deployed. The results are helpful in the implementation of SCMA in the hybrid system.

This paper considers a low-complexity Gaussian Message Passing Iterative Detection (GMPID) algorithm for Multiple-Input Multiple-Output systems with Non-Orthogonal Multiple Access (MIMO-NOMA), in which a base station with $N_r$ antennas serves $N_u$ sources simultaneously. Both $N_u$ and $N_r$ are very large numbers and we consider the cases that $N_u>N_r$. The GMPID is based on a fully connected loopy graph, which is well understood to be not convergent in some cases. The large-scale property of the MIMO-NOMA is used to simplify the convergence analysis. Firstly, we prove that the variances of the GMPID definitely converge to that of Minimum Mean Square Error (MMSE) detection. Secondly, two sufficient conditions that the means of the GMPID converge to a higher MSE than that of the MMSE detection are proposed. However, the means of the GMPID may still not converge when $ N_u/N_rN_r$ with a faster convergence speed. Finally, numerical results are provided to verify the validity of the proposed theoretical results.

This paper considers a iterative Linear Minimum Mean Square Error (LMMSE) detection for the uplink Multiuser Multiple-Input and Multiple-Output (MU-MIMO) systems with Non-Orthogonal Multiple Access (NOMA). The iterative LMMSE detection greatly reduces the system computational complexity by departing the overall processing into many low-complexity distributed calculations. However, it is generally considered to be sub-optimal and achieves relatively poor performance. In this paper, we firstly present the matching conditions and area theorems for the iterative detection of the MIMO-NOMA systems. Based on the proposed matching conditions and area theorems, the achievable rate region of the iterative LMMSE detection is analysed. We prove that by properly design the iterative LMMSE detection, it can achieve (i) the optimal sum capacity of MU-MIMO systems, (ii) all the maximal extreme points in the capacity region of MU-MIMO system, and (iii) the whole capacity region of two-user MIMO systems.

In this paper, we investigate the energy-efficient transmission problem by resource allocation in SCMA networks. We formulate it as an optimization problem to maximize the network energy efficiency (EE) subject to quality-of-service (QoS) requirements, codebook assignment, power allocation, and subcarrier reuse constraints. Due to its mixed combinatory, we separate codebook assignment and power allocation to devise suboptimal but cost- efficient algorithms. With power equally distributed, we first propose a novel scheme to assign codebooks. We then develop a derivative- bisection based algorithm to optimally solve the resultant power allocation problem by exploiting its quasiconcave structure. Simulation results exhibit the superiority of the proposed algorithms against the existing classical schemes and of SCMA over OFDMA in terms of the network EE.

Device-to-Device (D2D) communication underlaid cellular networks has been regarded as a technology with great promise to provide higher transmission rate, lower latency and better energy efficiency in services between user terminals in the future fifth generation (5G) wireless network. In this paper, we consider the resource allocation problem to enhance the system performance. Specifically, we use hypergraph to characterize the interference among cellular uplinks and D2D links when sparse code multiple access (SCMA) is applied as the multiple access strategy. Targeting at maximizing system sum rate, we propose an Interference-Aware Hypergraph based Codebook Allocation (IAHCA) algorithm. Using IAHCA, each orthogonal SCMA resource, i.e., SCMA codebook, is allowed to be shared by one cellular uplink and more than one D2D links. As a consequence, available SCMA resources can be fully exploited, thereby effectively achieving higher system throughput and activating more D2D links. Simulation results confirm that IAHCA outperforms conventional graph based algorithm and other hypergraph based algorithms.

As a promising multiple access technique for 5G wireless networks, sparse code multiple access (SCMA) has been put forward to support massive connectivity and enhance network performance. In this paper, we develop a theoretical framework using stochastic geometry to evaluate the performance of SCMA ad hoc networks. Under this framework, we first derive an explicit matrix form for the successful transmission probability. We then consider two area spectral efficiency (ASE) maximization problems without and with link reliability constraint to investigate the ASE gain of SCMA over OFDMA networks and the tradeoff between the ASE and link reliability, respectively. In particular, we obtain the optimal medium access probability (MAP) to solve both problems. Both numerical and simulation results exhibit that, compared to OFDMA networks, an asymptotically 160% gain in the ASE and a nearly 91% improvement in the transmission opportunity can be achieved by SCMA networks with typical settings.

This paper considers a low-complexity Gaussian message passing iterative detection (GMPID) algorithm for a massive multiuser multiple-input multiple-output (MU-MIMO) system, in which a base station with$M$antennas serves$K$Gaussian sources simultaneously. Both$K$and$M$are very large numbers, and we consider the cases that$K<M$. The GMPID is a message passing algorithm operating on a fully connected loopy graph, which is well understood to be non-convergent in some cases. As it is hard to analyze the GMPID directly, the large-scale property of the massive MU-MIMO is used to simplify the analysis. First, we prove that the variances of the GMPID definitely converge to the mean square error of minimum mean square error (mmse) detection. Second, we derive two sufficient conditions that make the means of the GMPID converge to those of the mmse detection. However, the means of GMPID may not converge when$ K/M\geq (\sqrt {2}-1)^{2}$. Therefore, a modified GMPID called scale-and-add GMPID, which converges to the mmse detection in mean and variance for any$K

Rate regions of a multi‐way relay channel with direct links (MWRC‐DLs), where K users exchange their messages via a relay terminal and all users can overhear each other directly, are studied in this study. Under the assumption that a restricted encoder is employed at each user, the cut‐set outer bound on the capacity region is derived first. Then, achievable rate regions of the MWRC‐DLs with decode‐and‐forward (DF) and compress‐and‐forward (CF) strategies are characterised. Meanwhile, the explicit expressions of the outer bound and the achievable rate regions for the Gaussian MWRC‐DLs are also derived. It is shown that the rate regions of the DF and CF strategies for the two‐way relay channel and the multiple‐access relay channel can be obtained from those of the MWRC‐DLs. To give more insights on the two strategies of the MWRC‐DLs system, the common rates of a symmetric Gaussian network are analysed. It is shown that the CF strategy achieves common rates within 1/2( K − 1) bits of the capacity when the relay's power is at least ( K − 1) times as large as the user power. Numerical examples are also provided to verify the theoretical analysis.