This paper studies asynchronous repetition slotted ALOHA (a-ReSA) for massive random access. Each user’s packet is repeated and allocated to randomly selected slots. Then, the users transmit simultaneously and arrive at the base station (BS) receiver with different delays, i.e., without user-synchronization. The BS receiver carries out an over-sampling-based operation, yielding an over-sampled signal space. We show that owing to user-asynchrony, the channel state information (CSI) can be acquired even when some users utilize an identical pilot sequence, i.e., pilot collision happens. Further, we develop an iterative soft cancellation detection and decoding that exploits the interference structure of the over-sampled signal for powerful multi-user decoding. Afterwards, packet cancellation for a-ReSA is utilized to solve packet collision. To characterize the performance of a-ReSA, we analyze the achievable channel parameter region (ACPR) and outage probability. Our analysis shows that the ACPR of the user-asynchronous scenario is considerably larger than that of user-synchronous scenarios. Further, we present an asymptotic analysis of the throughput of a-ReSA system. It is demonstrated that the normalized throughput of a-ReSA exceeds that of traditional ReSA by about 20% ~ 80%. We also show that the a-ReSA scheme is more robust than traditional ReSA in imperfect CSI scenarios. Numerical results are verified to agree with the analyzed results.

This paper studies a downlink cell-free MIMO (cf-MIMO) system consisting ofKusers, a central unit (CU), andNdistributed base stations (BSs). The CU is connected to theNBSs viaNindependent fronthaul (FH) links, which collectively serve theKusers. We put forth a new distributed integer-forcing approach. The CU selects some integer coefficients and carries out amessage-level precoding(MLP) over theKusers’ message sequences. The resultant MLP streams are forwarded to the BSs via the FH links. Then, the BSs performsignal-level precodingfor the streams usingdistributed integer forcing(d-IF). The resultant signals of theNBSs are broadcast to theKusers simultaneously. Each user’s receiver attempts to compute an integer linear combination (ILC) of the incoming encoded streams, which turns out to be its desired message. For ample FH scenario, we develop a concatenate-split method and a bisection interior point algorithm method to construct precoding matrices that collectively form integer-valued effective channels to theKusers. For stringent FH scenario, we develop a new adaptive stream allocation method, which utilizes the carefully selected shortest independent vectors w.r.t. the lattice basis vectors for allNBS. We derive the achievable rate of d-IF, and then formulate a joint optimization problem for the d-IF precoding and integer coefficient matrices. A particle swarm optimization (PSO) with bisection interior point algorithm based method is presented to solve this problem. Numerical results show that the gap to the sum-capacity upper bound is about 0.5-2.5 dB for various cf-MIMO configurations, while d-IF exhibits an improvement of more than 5 dB over existing distributed zero-forcing.

This paper studies asynchronous repetition slotted ALOHA (a-RSA) for massive random access. Each user’s packet is repeated and allocated to randomly selected slots. Then, the users transmit simultaneously and arrive at the base station (BS) receiver with different delays, i.e., without user-synchronization. The BS receiver carries out an over-sampling-based operation, yielding an over-sampled signal space. We develop an iterative soft cancellation detection and decoding that exploits the interference structure of the over-sampled signal for powerful multi-user decoding. Afterwards, packet cancellation for a-RSA is utilized to solve packet collision. To characterize the performance of a-RSA, we analyze the achievable channel parameter region (ACPR) and outage probability. Further, we present an asymptotic analysis of the throughput of a-RSA system. It is demonstrated that the normalized throughput of a-RSA exceeds that of traditional RSA by about 20% ~ 30%.

We study a downlink cell-free MIMO (cf-MIMO) system consisting of K users, a central unit (CU), and N distributed base stations (BSs). The CU is connected to N BSs via N independent fronthaul (FH) links, which collectively serve K users. We put forth a distributed integer-forcing approach. The CU selects some integer coefficients and carries out a message-level precoding (MLP) over the K users’ message sequences. The resultant MLP streams are forwarded to the BSs via the FH links. Then, the BSs perform signal-level precoding for the streams using distributed integer forcing (d-IF). The resultant signals of the N BSs are broadcast to the K users simultaneously. We derive the achievable rate of d-IF. Numerical results show that and the gap between the proposed d-IF and the capacity upper bound of the cf-MIMO is almost closed, while d-IF exhibits an improvement of more than 5 dB over existing distributed zero-forcing.

Rainfall impacts daily activities and can lead to severe hazards such as flooding. Traditional rainfall measurement systems often lack granularity or require extensive infrastructure. While the attenuation of electromagnetic waves due to rainfall is well-documented for frequencies above 10 GHz, sub-6 GHz bands are typically assumed to experience negligible effects. However, recent studies suggest measurable attenuation even at these lower frequencies. This study presents the first channel state information (CSI)-based measurement and analysis of rainfall attenuation at 2.8 GHz. The results confirm the presence of rain-induced attenuation at this frequency, although classification remains challenging. The attenuation follows a power-law decay model, with the rate of attenuation decreasing as rainfall intensity increases. Additionally, rainfall onset significantly increases the delay spread, and slight Doppler effects were also observed following the onset of precipitation. Building on these insights, we propose RainGaugeNet, the first CSI-based rainfall classification model in the sub-6GHz band that leverages multipath and temporal features. Two variants are developed: RainGaugeNet-R using ResNet1D and RainGaugeNet-T using a Transformer encoder. Using only 20 seconds of CSI data, RainGaugeNet-R achieves up to 95% an average classification accuracy in line-of-sight(LoS) scenarios and 85% in non-line-of-sight(NLoS) conditions. RainGaugeNet-T attains 90% accuracy in LoS and 99% in NLoS settings, demonstrating superior robustness. Both models significantly outperform state-of-the-art baselines while maintaining low computational complexity.

It was shown that by operating over the integer linear combinations (ILCs) ofKusers’ messages, lattice-code based multiple-access (LCMA) offers increased system load and improved error-rate performance over non-lattice based schemes. This paper advances the existing LCMA system in two aspects. 1) We formulate the spreading sequences optimization problem based on the achievable symmetric rate of LCMA. To solve this problem, we develop three new methods, namely target-switching steepest descent (TS-SD), particle swarm (PS) optimization, and Hadamard concatenation (HC). The TS-SD method always targets on the ILC with the lowest computation rate in the SD process. The PS method treats the spreading matrix as a particle and iteratively updates a swamp of particles’ positions and velocities, based on the relative distance to the best position that are currently known. To further reduce the complexity, we first obtain a solution in a lower dimension, and then apply Hadamard concatenation (HC) which yields a solution for the required dimension. The PS and HC methods are shown to approach the capacity of the MA channel. 2) We put forth a new multi-stage LCMA receiver. In each stage, the receiver attempts to compute as many ILCs as possible. Then, from these ILCs, generalized matrix inversion (GMI) is introduced to recover a subset ofKusers’ messages. These recovered messages are cancelled from the original received signal, yielding an equivalent system with less users for the next stage. Such operation continues successively until allKusers’ messages are recovered. System loads of up to 400% and near capacity performance are demonstrated for various MA models.

Terahertz (THz) communication is regarded as a key technology for 6G and beyond wireless systems due to its broad continuous bandwidth. However, the THz band suffers from a considerable propagation loss which limits the communication distance. Thanks to the submillimeter wavelength, ultra-massive multi-input multi-output (UM-MIMO) beamforming is able to enhance the received power and overcome the distance limitation. Nevertheless, hardware imperfections especially at THz frequencies, can lead to significant beamforming gain loss and degrade spectral efficiency, which are imperative to address in practical communication systems. In this paper, a user-by-user block-diagonalization (UBU-BD) algorithm in dynamic array-of-subarrays (DAoSA) architecture for multi-user UM-MIMO systems is firstly proposed under the ideal hardware assumption. Then, power losses as results of four kinds of critical hardware imperfectness, including digital-to-analog converter (DAC), analog-to-digital converter (ADC), phase shifter and switch, are modeled and evaluated. To overcome the spectral efficiency loss caused by hardware imperfectness, a switch-power algorithm is developed and assessed. Simulation results show that combinations of extra switches and transmit power are helpful to fully compensate for the spectral efficiency losses.

This paper studies a lattice-based broadcasting (LBC) scheme for a single-cell downlink system. The base station (BS) has N antennas and the K user-equipments (UEs) have a single-antenna. The system is referred to as massive-user MIMO (mU-MIMO) when K is very large. At the transmitter side, the BS encodes the messages for the UEs with state-of-the-art channel codes and q-PAM modulation. We suggest a codeword-level precoding, which transforms the K UEs’ coded sequences by an invertible integer matrix$\mathbf {A}^{-1}$over$\mathbb {Z}_{q}$, resulting in K codeword-level precoded (CLP) streams. Then, the CLP streams undergo a linear signal-level precoding (SLP) with regularized integer-forcing, and the resultant signals are transmitted via the N antennas of BS. The operations of CLP and SLP are both linear. At the receiver side, each UE attempts to compute an integer-combination (ICB) of the K CLP streams w.r.t. the integer matrix A, which turns out to be its desired message thanks to the CLP. For computing the ICB, we put forth new soft detection algorithms, which efficiently calculate the a posteriori probability of ICB over the lattice. The complexity is shown to be (much) less than$O(Kq)$, which is suited for large values of K. Further, we develop a particle swarm based approach that jointly optimizes A and the power allocation matrix. Numerical results demonstrate dramatically enhanced performance over baseline schemes including regularized zero-forcing and vector perturbation precoding, for both slow and fast fading channels.

This paper studies a cell-free MIMO (cf-MIMO) system that consists of a central unit (CU),Ndistributed base stations (BSs) andKusers. The BSs are connected to CU viaNindependent backhaul (BH) links of finite capacities. The BSs are uncoordinated, i.e. each one is ignorant of the others. We study a lattice network coding (LNC) scheme for cf-MIMO. In the uplink, theKusers encode their messages with a practical 2m-ary channel code mapped to 2m-PAM, belonging to the ensemble oflattice codes, and transmit simultaneously. Each BS computes independent streams of integer-combinations of the users’ messages, referred to asnetwork coding(NC) streams. The NC streams are forwarded to the CU via BH. The CU aggregates all NC streams from theNBSs, and recoversKusers’ messages. We derive the achievable symmetric rate of the LNC scheme. Further, we solve a “bounded independent vectors problem” (BIVP) which identifies a near-optimal set of NC coefficient vectors. The solution maximizes the number of correctly computed NC streams at each BS. For practical implementation, we develop new soft detection algorithms for LNC decoding. The per-user complexity is proved to be no greater thanO(K), suitable for cf-MIMO with a large number of users. Our developed LNC based cf-MIMO exhibits superior frame error rate (FER) and spectral efficiency over existing non-LNC based schemes. Such advances are achieved with low-cost parallel processing and efficient usage of the BH.

This paper proposes a pilot-free repetition-based slotted ALOHA (PF-RSA) scheme for a massive random access system. The users utilize coded differential modulation and transmit with the repetition-based SA (RSA) protocol. The base station employs non-coherent detection and cancellation for recovering all users' messages. We develop a belief propagation (BP) based non-coherent detection and estimation which offers improved performance. It is demonstrated that the PF-RSA scheme can achieve almost the identical throughput of the conventional pilot-aided RSA while relaxing the need of pilots. We also show that the PF-RSA is applicable to massive access with asynchrony.

Orthogonal time-frequency-space (OTFS) modulation is able to improve the performance of the wireless communication system in a high-speed environment. This paper proposes an iterative soft cancellation receiver with element-wise extrinsic information for coded OTFS system. In calculating the soft estimates that are fed back to the iterative soft cancellation, the existing full extrinsic information based method subtracts the entire a priori information from the a posteriori probability (APP) outputs from the decoder. In the proposed element-wise extrinsic information method, only the a priori information w.r.t the specific path (a single-element from the observation) in OTFS system is subtracted from the decoder's APP outputs. We show that the proposed approach outperforms existing a posteriori probability and full extrinsic information based iterative detection by 2 dB and 1 dB, respectively. Further, we apply extrinsic information transfer chart curve-fitting technique to optimize the code profile of the proposed scheme. We demonstrate that the proposed scheme performs within 0.5 dB of the capacity limit of OTFS.

This paper studies a lattice-code based multiple-access (LCMA) system. In the uplink,$K$users encode their messages with the same 2m-ary ring code mapped to 2m- PAM, belonging to the ensemble of lattice codes. All users transmit simultaneously. The receiver attempts to compute$K$independent streams of integer-combinations (ICBs) of the users' messages. For this, 1) we establish and solve a new “bounded independent vectors problem” (BIVP) which identifies a near-optimal set of coefficient vectors w.r.t. the ICBs, outperforming existing LLL and HKZ lattice reduction methods; 2) we put forth new LCMA soft detection algorithms, which calculate the a posteriori probability w.r.t. the ICB over the lattice. The per-user complexity is of order less than O(K), suitable for massive access of$K$being large. The soft detection outputs are forwarded to$K$ring-code decoders to recover the messages. With our developed techniques, LCMA is shown to support a significantly higher load of users and exhibits an improved frame error rate over state-of-the-art IDMA and SCMA schemes. Such advanced functionality are achieved with just parallel processing and$K$single-user decoding operations.

This paper concerns with efficient communication over Gaussian and fading multiple-access channels (MACs). Existing orthogonal multiple-access (OMA) and power-domain nonorthogonal-OMA (NOMA) cannot achieve all rate-tuples in the MAC capacity region. Meanwhile, code-domain NOMA schemes usually require big-loop receiver-iterations for multi-user decoding, which is subject to high implementation cost and latency. This paper studies a linear physical-layer network coding multiple access (LPNC-MA) scheme that is capable of achieving any rate-tuples in the MAC capacity region without receiver iterations. For deterministic Gaussian MACs with$M$users, we propose to utilize$q$-ary irregular repeat accumulate (IRA) codes over finite integer fields/rings and$q$-ary pulse amplitude modulation ($q$-PAM) as the underlying coded-modulation. The receiver sequentially computes$M$network coded (NC) messages of the$M$users. All users’ messages are then recovered by solving the computed$M$NC messages via the inverse of the NC coefficient matrix. A joint nested code construction and extrinsic information transfer (EXIT) chart based code optimization method is developed, yielding near-capacity performance (within 0.7 and 1.1 dB the capacity limits for two and three users respectively). For fading MAC, we study the symmetric rate of LPNC-MA, and propose a pragmatic method for identifying the mutual information (MI) maximizing network coding coefficient matrix. Numerical results demonstrate that the frame error rate (FER) of the optimized LPNC-MA is within a fraction of dB the outage probability of fading MAC capacity. LPNC-MA remarkably outperforms NOMA-SIC and IDMA while avoiding the big-loop receiver iteration.

This paper studies a linear physical-layer network coding multiple access (LPNC-MA) scheme that is capable of achieving any rate-tuples in the MAC capacity region without receiver-iterations or time-sharing. We propose to utilize q-ary irregular repeat accumulate (IRA) codes over finite integer field-s/rings and q-PAM as the underlying coded-modulation. The receiver sequentially computes M network coded (NC) message sequences, where the previously computed message sequence is used as side information in computing subsequent ones. All users’ messages are then recovered by solving the computed M NC messages via the inverse of the NC coefficient matrix. A joint nested code construction and EXIT chart based code optimization method is developed, yielding near-capacity performance (within 1.1 dB the capacity limit for three users). For fading MAC, we propose a pragmatic method for identifying the network coding coefficient matrix that maximizes the mutual information. Numerical results demonstrate that the frame error rate (FER) of LPNC-MA is within a fraction of dB the outage probability of fading MAC capacity. For a relatively large number of users, it is shown that LPNC-MA remarkably outperforms NOMA-SIC and IDMA in the high spectral efficiency regime, while avoiding the big-loop receiver iteration.

Terahertz (THz) band communication is a promising pillar technology to satisfy the demands of intelligent information society. The ultra-broad bandwidth in the THz band provides a great potential of a plethora of applications and services. However, THz wireless communication systems encounter stringent challenges, including more severe Doppler effects and more strict peak-to-average power ratio (PAPR) requirements. In this work, a discrete Fourier transform spread orthogonal time frequency space (DFT-s-OTFS) modulation scheme is proposed to address these issues of THz communications. The proposed DFT-s-OTFS can improve the bit error rate (BER) performance by two orders of magnitude compared to orthogonal frequency division multiplexing (OFDM) in presence of high Doppler spread, and reduce the PAPR by approximately 3 dB in contrast with OTFS.

Hybrid beamforming for Terahertz (THz) ultra-massive MIMO (UM-MIMO) systems is a promising technology for 6G networks, which can overcome huge propagation loss and offer unprecedented data rates. With ultra-wide band-width in THz band, the beam squint becomes one of critical problems which could reduce the array gain and degrade the data rate. However, the traditional phase-shifters-based hybrid beamforming architectures cannot tackle this issue due to the frequency-flat property of the phase shifters. In this paper, to combat this beam squint yet with reduced power consumption, a novel dynamic-subarray with fixed-true-time-delay (DS-FTTD) architecture is proposed. Furthermore, a low-complexity row-decomposition (RD) algorithm is developed for the DS-FTTD architecture. Extensive simulation results show that, by using the RD algorithm, the DS-FTTD architecture achieves signifi-cantly higher array gain and spectral efficiency than the phase-shifters-based architectures. Meanwhile, the energy efficiency is substantially improved thanks to the low-cost FTTDs.

Physical-layer network coding (PNC) is able to boost the error probability performance or throughput of a set of multi-source and multi-hop wireless networks. In this paper, we put forth a new asymmetric linear PNC (A-LPNC) scheme for the setup where the users are subject to non-identical power and modulation schemes. For deterministic channel, we show that given any unequal average symbol energy, the effective minimum distance of A-LPNC constellation can be made to be identical to the single-user minimum distance lower bound, translated into optimal error probability performance at a medium to high SNR. For fading channels, we show that the optimized network coding coefficients can be found and employed such that the effective minimum distance of A-LPNC is equal to the single-user minimum distance lower bound for integer channel gains. For real-valued channel gains, we present the optimal NC coefficients selection that minimizes the error probability of A-LPNC. These results are verified via simulations.

This paper investigates a cache-aided cloud radio access network (C-RAN), comprising a central unit, K base stations (BSs) each with NTantennas, and M users each with NRantennas, where each BS and user have local caches to store some popular contents from the central unit. For this cache-aided network, we propose the linear network coded (NC) wireless caching that consists of linear wireless network coding assisted cache placement phase and signal-space alignment (SSA) enabled content delivery phase. In the cache placement phase, we design a joint NC caching function at the BSs to store linear combinations of messages from the central unit, as a form of linear wireless network coding. In the content delivery phase, we design the SSA pattern based on the NC caching to guide the precoding designs at BSs. Then, each user can reliably decode its requested messages by receiver shaping and reverse NC operation. The primary contribution of this work is to achieve the coding gain induced by the integration of linear wireless network coding and SSA, which has been not exploited in the field of wireless coded caching. In particular, to deal with high temporal variability of user requests, we show that the proposed cache placement is invariant to different user requests in the worst-case caching, without any shared caching messages at different BSs. Furthermore, we verify that the proposed scheme is also compatible with the insufficient caching scenario at the BSs. In addition, we analyze the achievable sum degrees of freedom (DoF) for the proposed caching network. Both analytical and numerical results verify that the proposed caching scheme achieves a higher sum DoF than the existing related works.

This paper considers a multiuser communication network, where a receiver is set to compute functions of the messages from K users. All user nodes and the receiver are equipped with multi-antenna. We propose a space-time (ST) coded multiple-input multiple-output (MIMO) linear physical-layer network coding (LPNC) scheme that promises full-rate and full-diversity, while achieving the maximum coding gain of LPNC. In the proposed framework, the users' messages are encoded by the same linear dispersion ST code and transmitted simultaneously. The receiver exploits the MIMO LPNC mapping in reconstructing an arbitrary number of linearly network-coded (NC) messages. We derive the NC generator matrix that leads to the greatest coding gain and minimized error probability at the receiver. On top of that, we analytically show that the proposed ST coded LPNC scheme guarantees the full-diversity and full-rate transmission. The proposed method applies to a wide range of network configurations. Two case studies on: (1) MIMO two-way relay network and (2) MIMO multiple-access relay network are presented in this paper. For both case studies, numerical results are shown to demonstrate the performance improvement of the proposed scheme over conventional schemes by more than 4 dB, while the full-rate and full-diversity behaviors are in line with our analysis.

In multiple-input multiple-output (MIMO) two-way relay networks (TWRN), linear physical-layer network coding (LPNC) was proposed to boost the throughput by using spatial multiplexing at source nodes. How to design optimal LPNC for full-rate full-diversity MIMO TWRN is still an open problem. In this paper, we propose a full-rate full-diversity (FRFD) LPNC scheme. In this scheme, two source nodes, each with two antennas, transmit full-rate universal space-time codes to a two-antenna relay simultaneously. Then, the relay applies LPNC to compute multiple network-coded (NC) messages. In particular, we explicitly solve the optimal LPNC mapping to minimize decoding errors of NC messages in the FRFD LPNC scheme. Our analytical results verify that the optimal FRFD LPNC scheme guarantees the full-diversity and full-rate transmission at the same time. Simulation results are consistent with the analytical results and further demonstrate that our optimal FRFD LPNC scheme outperforms the conventional MIMO LPNC scheme.

In this paper, we investigate the design and analysis of coded slotted ALOHA (CSA) schemes in the presence of channel erasure. We design the code probability distributions for CSA schemes with repetition codes and maximum distance separable codes to maximize the expected traffic load, under both packet erasure channels and slot erasure channels. We derive the extrinsic information transfer (EXIT) functions of CSA schemes over erasure channels. By optimizing the convergence behavior of the derived EXIT functions, the code probability distributions to achieve the maximum expected traffic load are obtained. Then, we derive the asymptotic throughput of CSA schemes over erasure channels. In addition, we validate that the asymptotic throughput can give a good approximation to the throughput of CSA schemes over erasure channels.

In this paper, we investigate channel estimation and multiuser downlink transmission of a time division duplex massive multiple-input multiple-output (MIMO) system in millimeter wave (mmWave) channels. We propose a tone-based linear search algorithm to facilitate the estimation of angle-of-arrivals (AoAs) of the strongest line-of-sight (SLOS) channel component as well as the scattering components of the users at the base station. Based on the estimated AoAs, we reconstruct the SLOS component and scattering components of the users for downlink transmission. We then derive the achievable rates of maximum-ratio transmission (MRT) and zero-forcing (ZF) precoding based on the SLOS component and the SLOS-plus-scattering components (SLPS), respectively. Taking into account the impact of pilot contamination, our analysis and simulation results show that the SLOS-based MRT can achieve higher data rate than that of the traditional pilot-aided-CSI-based (PAC-based) MRT, under the same mean square errors of channel estimation. As for ZF precoding, the achievable rates of the SLPS-based and the PAC-based are identical. Furthermore, we quantify the achievable rate degradation of the SLOS-based MRT precoding caused by phase quantization errors in the large number of antennas regime. We show that the impact of phase quantization errors on the considered systems cannot be mitigated by increasing the number of antennas and therefore the resolutions of radio frequency phase shifters is critical for the design of efficient mmWave massive MIMO systems.

We study a downlink distributed MIMO system where a central unit (CU) broadcasts messages to K' users through K distributed BSs. The CU is connected to the BSs via K independent rate-constrained fronthaul (FH) links. The distributed BSs collectively serve the users through the air. We propose a new network coding based distributed MIMO broadcasting scheme, using reverse compute-and-forward and signal-space alignment. At the CU, a network coding generator matrix is employed for pre network coding of the users' messages. The network coded messages are forwarded to the BSs, where the FH rate-constraint determines the actual number of network-coded messages forwarded to the BSs. At the BSs, linear precoding matrices are designed to create a number of bins, each containing a bunch of spatial streams with aligned signal-spaces. At each user, post physical-layer network coding is employed to compute linear combinations over the NC messages with respect to the bins, which reverses the prenetwork coding and recovers the desired messages. We derive an achievable rate of the proposed scheme based on the existence of NC generator matrix, signal-space alignment precoding matrices, and nested lattice codes. Improved rate and degrees of freedom over existing interference alignment and compress-and-forward schemes are shown. Numerical results demonstrate the performance improvement, e.g., by as much as 70% increase in throughput over benchmark schemes.

This paper studies non-orthogonal transmission over a K-user fading multiple access channel. We propose a new reliable physical-layer network coding and cascade-computation decoding scheme. In the proposed scheme, K single-antenna users encode their messages by the same practical channel code and QAM modulation, and transmit simultaneously. The receiver chooses K linear coefficient vectors and computes the associated K layers of finite-field linear message combinations in a cascade manner. Finally, the K users' messages are recovered by solving the K linear equations. The proposed can be regarded as a generalized onion peeling. We study the optimal network coding coefficient vectors used in the cascade computation. Numerical results show the performance of the proposed approaches that of the iterative maximum a posteriori probability detection and decoding scheme, but without using receiver iteration. This results in considerable complexity reduction, processing delay, and easier implementation. Our proposed scheme significantly outperforms the iterative detection and decoding scheme with a single iteration, for example, by 1.7 dB for the two user case. The proposed scheme provides a competitive solution for non-orthogonal multiple access.

We propose a new linear physical-layer network coding and information combining scheme for the K-user fading multiple-access relay network (MARN), which consists of K users, one relay and one destination. The relay and the destination are connected via a rate-constraint backhaul link. In the proposed scheme, the K users transmit signals simultaneously. The relay and the destination receive the superimposed signals distorted by fading and noise. The relay reconstructs L linear combinations of the K users' messages, referred to as L network coded (NC) messages, and forwards them to the destination. The destination then attempts to recover all K users' messages by combining its received signals and the NC messages obtained from the relay. We develop an explicit expression on the selection of the coefficients of the NC messages at the relay that minimizes the end-to-end error probability at a high signal to noise ratio. We demonstrate that our proposed scheme outperforms the benchmark scheme significantly in an MARN.

In this paper we investigate the coded slotted ALOHA (CSA) schemes with repetition codes and maximum distance separable (MDS) codes over erasure channels. We derive the extrinsic information transfer (EXIT) functions of the CSA schemes over erasure channels, which allow an asymptotic analysis of the packet recovering process. Moreover, we define a traffic load threshold provided that the recovered probability is more than a given recovery ratio. The optimal distribution of the codes chosen by users in the CSA schemes is then designed to maximize the peak throughput and traffic load threshold. By performing the asymptotic analysis, we show that our optimal distributions improve the traffic load threshold by 60% for ε = 0.1 and 86% for ε = 0.135 compared to the optimal distribution for collision channels. Using repetition codes as an example, simulation results show that the obtained distributions enhance the peak throughput for erasure channels when both packet erasure channels and slot erasure channels are considered.

In this paper, we investigate uplink channel estimation and multiuser downlink transmission of a massive MIMO time-division duplex system in the presence of pilot contamination, where the base station (BS) with M antennas communicates with N single-antenna users in a cell. We assume that all channels are affected by Rician fading. We also assume that angles of arrival from users to the BS are different. We first analyze the impact of pilot contamination on the channel estimation, based on which we derive a tight sum-rate approximation. We also obtain the asymptotic sum-rate for large Rician K-factor in the large signal to noise ratio regime. Furthermore, we examine the impact of the Rician K-factor on the sum-rate of the system, showing that the sum-rate increases as K-factor increases.

In this paper, we propose a new linear physical- layer network coding (NC) scheme for the fading Y- channel, assuming that the channel state information (CSI) is not available at transmitters. In this scheme, each user transmits one message to a relay and intends to obtain both other two users' messages. Based on the receiver- side CSI, the relay determines two NC generator vectors for linear network coding, and reconstructs the associated two linear NC codewords. For the case when there is one time- slot in the uplink phase, we present an explicit solution for the generator vectors that minimizes the error probability at a high SNR, and a lower bound of the error performance of the proposed scheme using our optimized generator vectors. Extending to multiple time-slots in the uplink, two typical scenarios are discussed. Numerical results show that the proposed scheme significantly outperforms existing schemes, and match well with our analytical results.

We propose a new linear physical-layer network coding (LPNC) and information combining scheme for the K-user fading multiple-access relay network (MARN), which consists of K users, one relay, and one destination. The relay and the destination are connected by a rate-constraint wired or wireless backhaul. In the proposed scheme, the K users transmit signals simultaneously. The relay and the destination receive the superimposed signals distorted by fading and noise. The relay reconstructs L linear combinations of the K users' messages, referred to as L network-coded (NC) messages, and forwards them to the destination. The destination then attempts to recover all K users' messages by combining its received signals and the NC messages obtained from the relay. We develop an explicit expression on the selection of the coefficients of the NC messages at the relay that minimizes the end-to-end error probability at a high signal-to-noise ratio. We develop a channel-coded LPNC scheme by using an irregular repeat-accumulate modulation code over GF(q). An iterative belief-propagation algorithm is employed to compute the NC messages at the relay, while a new algorithm is proposed for the information combining decoding at the destination. We demonstrate that our proposed scheme outperforms benchmark schemes significantly in both un-channel-coded and channel-coded MARNs.

In this paper, we propose a new linear physical-layer network coding scheme for spatial-multiplexing MIMO two-way relay channels (TWRCs), where the transmitters lack the channel state information (CSI). In the uplink, each user transmits independent signal streams from its multiple antennas, and the two users transmit simultaneously. The relay selects a finite-field coefficient matrix based on its receiver CSI. It then jointly computes the associated linear combinations of all messages. In the downlink, the resultant message-combinations are forwarded to the users, which recover their desired messages. We derive an asymptotic expression for the coefficient matrix used by the relay that minimizes the error probability. We show by numerical results that for Rayleigh fading channel, the proposed linear PNC scheme outperforms existing schemes by up to 4.5 dB and that the proposed scheme approaches an interference-free lower bound at a sufficiently high SNR.

A distributed multiple-input-multiple-output (MIMO) system consists of M users served by L distributed base stations (BSs), where the BSs are connected to a central unit (CU) via L independent backhaul (BH) links. In this paper, we consider the design of an uplink distributed MIMO system where 1) the channel state information is not available at the transmitters and 2) the BH links are rate constrained. We propose a new linear network coding (LNC)-based protocol: the M users transmit simultaneously. Each BS generates N linear functions of the M users' messages, based on a preassigned LNC coefficient matrix. The CU collects N · L linear functions from the L BSs and recovers all M users' messages by solving these linear functions. The decoding becomes successful if the linear functions has full rank M and fails if the linear functions are rank deficient. We derive the preassigned LNC coefficient matrix that minimizes the probability of rank deficiency. We then analyze the outage probability (OP) of the proposed scheme over a Rayleigh fading channel. We analytically show that as long as the BH rate is greater than the individual data rate of one user, the OP of the proposed scheme decays like 1/SNRLat high SNR. This is in contrast to the existing scheme whose OP decays like 1/SNR. As the BH rate constraint approaches M times the data rate of one user, the performance of the proposed scheme is 10/L log10(L!) dB away from that of the full MIMO scenario at high SNR. We also develop a structured way to efficiently construct the preassigned LNC coefficient matrix that yields the optimized OP performance. Numerical results show that the proposed scheme has significantly improved performance over existing schemes.

In this paper, we propose a new linear vector physical-layer network coding (NC) scheme for spatial multiplexing multiple-input multiple-output (MIMO) two-way relay channel (TWRC) where the channel state information (CSI) is not available at the transmitters. In this scheme, each user transmits M independent quadrature amplitude modulation signal streams respectively from its M antennas to the relay. Based on the receiver-side CSI, the relay determines a NC generator matrix for linear vector network coding, and reconstructs the associated M linear combinations of all messages. We present an explicit solution for the generator matrix that minimizes the error probability at a high SNR, as well as an efficient algorithm to find the optimized solution. We propose a novel typical error event analysis that exploits a new characterization of the deep fade events for the TWRC. We derive a new closed-form expression for the average error probability of the proposed scheme over a Rayleigh fading MIMO TWRC. Our analysis shows that the proposed scheme achieves the optimal error rate performance at a high SNR. Numerical results show that the proposed scheme significantly outperforms existing schemes, and match well with our analytical results.

We propose and design a practical modulation-coded (MC) physical-layer network coding (PNC) scheme to approach the capacity limits of Gaussian and fading two-way relay channels (TWRCs). In the proposed scheme, an irregular repeat-accumulate (IRA) MC over GF(q) with the same random coset is employed at two users, which directly maps the message sequences into coded PAM or QAM symbol sequences. The relay chooses appropriate network coding coefficients and computes the associated finite-field linear combinations of the two users' message sequences using an iterative belief propagation algorithm. For a symmetric Gaussian TWRC, we show that, by introducing the same random coset vector at the two users and a time-varying accumulator in the IRA code, the MC-PNC scheme exhibits symmetry and permutation-invariant properties for the soft information distribution of the network-coded message sequence (NCMS). We explore these properties in analyzing the convergence behavior of the scheme and optimizing the MC to approach the capacity limit of a TWRC. For a block fading TWRC, we present a new MC linear PNC scheme and an algorithm used at the relay for computing the NCMS. We demonstrate that our developed schemes achieve near-capacity performance in both Gaussian and Rayleigh fading TWRCs. For example, our designed codes over GF(7) and GF(3) with a code rate of 3/4 are within 1 and 1.2 dB of the TWRC capacity, respectively. Our method can be regarded as a practical embodiment of the notion of compute-and-forward with a good nested lattice code, and it can be applied to a wide range of network configurations.

The design of a reliable physical-layer network coding (PNC) scheme for practical fading two-way relay channels is a challenging task. This is because the signals transmitted by two users arrive at the relay with varied amplitudes and a relative carrier-phase offset, which will impair the performance of PNC. This paper studies a linear PNC scheme for fading two-way relay channels where the transmitters lack the channel state information. In this scheme, the relay computes and broadcast some finite-set integer combinations of two users' messages. The coefficients for the integer combinations used at the relay are carefully designed to minimize the error probability. This scheme can be viewed as a practical embodiment of the compute-and-forward concept. We develop a new LPNC design criterion called minimum set-distance maximization. Using this criterion, we derive an explicit expression for the optimized integer coefficients that minimizes the error probability of LPNC. The optimized integer coefficients turn out to resemble the fading channel coefficients. We further derive a closed-form expression on the average error probability performance over a complex-valued Rayleigh fading two-way relay channel, which shows that our designed LPNC scheme approaches the optimal error performance at a high SNR. Numerical results show that our designed LPNC outperforms existing schemes by more than 5 dB at a medium-to-high SNR regime.

We investigate a linear physical-layer network coding (LPNC) scheme for fading two-way relay channels, where the transmitters cannot track the channel. In this scheme, the relay computes and forwards integer combinations of the two users' messages. We develop a design criterion for adaptively choosing the integer coefficients at the relay, which minimizes the high-SNR error probability of the LPNC scheme. We derive an explicit expression for the optimized integer coefficients, and show that the crucial factor is the ratio between the two users' fading channel coefficients. We also extend the LPNC scheme to the complex-valued model and derive the optimized integer coefficient vectors. Numerical results show that our designed LPNC scheme outperforms existing schemes by more than 5 dB.

We propose a novel space-division based network-coding scheme for multiple-input multiple-output (MIMO) two-way relay channels (TWRCs), in which two multi-antenna users exchange information via a multi-antenna relay. In the proposed scheme, the overall signal space at the relay is divided into two subspaces. In one subspace, the spatial streams of the two users have nearly orthogonal directions, and are completely decoded at the relay. In the other subspace, the signal directions of the two users are nearly parallel, and linear functions of the spatial streams are computed at the relay, following the principle of physical-layer network coding (PNC). Based on the recovered messages and message-functions, the relay generates and forwards network-coded messages to the two users. We show that, at high signal-to-noise ratio (SNR), the proposed scheme with optimized precoding achieves the asymptotic sum-rate capacity of MIMO TWRCs within 1/2 log(5/4) ≈ 0.161 bit per user-antenna, for any antenna configuration and any channel realization.

Generating and feeding back beamforming vector are very challenging tasks in distributed transmit beamforming (DTB) systems. Phases of DTB nodes may vary rapidly due to residual carrier frequency offset and hence frequent updating of beamforming vector is required. Existing iterative training schemes that only require one bit training and one or two bits feedback in each iteration have low convergence speed and are not robust in noisy channels due to the lack of structure in the training sequences. In this paper, we consider a DTB system where the number of training bits N sent from each node is no more than the number of source nodes M, and propose a concatenated training scheme based on optimal design of training sequences in this case. For spatially uncorrelated channels, we show that the concatenated training scheme can optimally combine the N latest training signals and achieve beamforming gain approximately proportional to N/M. An algorithm which can adaptively determine the length of the combination in time-varying channels is also proposed. Simulation results demonstrate the proposed scheme can work efficiently even at very low signal-to-noise ratio, with the total feedback bits much less than those required in the iterative schemes.

This paper addresses the design of irregular repeat accumulate (IRA) codes for coded physical-layer network coding (PNC) for the binary-input Gaussian two-way relay channel, assuming perfect synchronization and equal received power at the relay. The design is based on a nontrivial extension of EXIT-chart based design. Specifically, we analyze the components of the IRA-PNC scheme and propose an approach to model the soft information exchanged between these components. Then, we develop upper and lower bounds on the extrinsic information transfer functions to characterize the iterative process of computing the network-coded information. Based on that, we construct optimized IRA codes to minimize the computation error at the relay. The optimized IRA-PNC has considerable performance improvement over the existing regular RA coded PNC. For a rate 3/4 code, as an example, we observed improvements of 2.6 dB, and the optimized IRA-PNC scheme is only about 1.7 dB away from the capacity upper bound of the Gaussian two-way relay channel.

We investigate efficient communication over multiple-input multiple-output (MIMO) two-way relay channels (TWRCs), where two multi-antenna users exchange information via a multi-antenna relay. We propose a new MIMO physical-layer network coding (PNC) scheme that includes novel eigen-direction alignment (EDA) precoding. The proposed EDA precoding efficiently aligns the two-user's eigen-modes into the same set of orthogonal directions, and multiple independent PNC streams are implemented over the aligned eigen-modes. We derive an achievable rate-pair of the proposed scheme, for given EDA precoding parameters, over a MIMO TWRC. To maximize the achievable rate-region, we formulate a design criterion for the EDA precoding parameters, and present solutions to the formulation. Closed-form bounds on the sum-rates of the designed EDA-PNC schemes are derived. Numerical results show that there is only a small gap between the achievable rate of the proposed scheme and the capacity upper bound of the MIMO TWRC. It is shown that the proposed scheme can significantly outperforms existing schemes in the literature.

We propose a novel space-division-based network-coding scheme for multiple-input multiple-output (MIMO) two-way relay channels (TWRCs), in which two multiantenna users exchange information via a multiantenna relay. In the proposed scheme, the overall signal space at the relay is divided into two subspaces. In one subspace, the spatial streams of the two users have nearly orthogonal directions and are completely decoded at the relay. In the other subspace, the signal directions of the two users are nearly parallel, and linear functions of the spatial streams are computed at the relay, following the principle of physical-layer network coding. Based on the recovered messages and message-functions, the relay generates and forwards network-coded messages to the two users. We show that, at high signal-to-noise ratio, the proposed scheme achieves the asymptotic sum-rate capacity of the MIMO TWRC within [ 1/ 2]log(5/4) ≈ 0.161 bits per user-antenna, for any antenna configuration and any channel realization. We perform large-system analysis to derive the average sum-rate of the proposed scheme over Rayleigh-fading MIMO TWRCs. We show that the average asymptotic sum-rate gap to the capacity is at most 0.053 bits per relay-antenna. It is demonstrated that the proposed scheme significantly outperforms the existing schemes.

Distributed transmit beamforming (DTB) can significantly boost the signal-to-noise ratio (SNR) of a wireless communication system. To realize the benefits of DTB, generating and feeding back beamforming vector are very challenging tasks. Existing schemes have either enormous overhead or weak robustness in noisy channels. In this paper, we investigate the design of training sequences and beamforming vector estimators in DTB systems. We consider an under-determined case, where the length of training sequence N sent from each node is smaller than the number of source nodes M. We derive the optimal estimation of the beamforming vector that maximizes the beamforming gain and show that it can be well approximated as the linear minimum mean square error (LMMSE) estimator. Based on the LMMSE estimator, we investigate the optimal design of training sequences and propose efficient DTB schemes. We analytically show that these schemes can achieve approximately N times increased SNR in uncorrelated channels, and even higher gain in correlated ones. We also propose a concatenated training scheme which optimally combines the training signals over multiple frames to obtain the beamforming vector. Simulation results demonstrate that the proposed DTB schemes can yield significant gains even at very low SNRs, with total feedback bits much less than those required in the existing schemes.

In this paper, we investigate the error probability and the diversity order of physical-layer network coding (PNC) in the two-way relay channel (TWRC), where two users communicate with the help of a relay. Each user has one antenna and the relay has two antennas. The system operates in a half-duplex mode with binary phase shift keying (BPSK) modulation. All the channels are Rayleigh faded. In particular, we consider a general asymmetric case, where two users have different average signal-to-noise ratio (SNR) to the relay. The upper and lower bounds on the instantaneous and average error probability of the uplink channel are derived based on the maximum-likelihood (ML) criterion. We also investigate the diversity order of the uplink channel. Numerical result demonstrates that the bounds are much tighter than other existing work, especially at low SNR, and the analytical result shows that the diversity is two for the asymmetric uplink channel.

We propose a new reduced-dimension (RD) eigen-direction alignment (EDA) precoder for MIMO two-way relay channels (TWRCs) with nR>; nT, where nRdenotes the number of antennas at the relay, and nTis that at each of the two users. The RD-EDA precoder can efficiently create aligned eigen-modes for the two users, enabling independent streams of physical-layer network coding. We investigate the design of the RD-EDA and develop a simple suboptimal solution. It is shown that the proposed RD-EDA scheme performs close to the sum-capacity upper bound of the MIMO TWRC. Moreover, it is shown that the proposed scheme can significantly outperform other existing schemes in the literature.

We investigate a channel-coded physical-layer network coding (CPNC) scheme for binary-input Gaussian two-way relay channels. In this scheme, the codewords of the two users are transmitted simultaneously. The relay computes and forwards a network-coded (NC) codeword without complete decoding of the two users' individual messages. We propose a new punctured codebook method to explicitly find the distance spectrum of the CPNC scheme. Based on that, we derive an asymptotically tight performance bound for the error probability. Our analysis shows that, compared to the single-user scenario, the CPNC scheme exhibits the same minimum Euclidean distance but an increased multiplicity of error events with minimum distance. At a high SNR, this leads to an SNR penalty of at most ln2 (in linear scale), for long channel codes of various rates. Our analytical results match well with the simulated performance.

We investigate efficient communications over MIMO two-way relay channels (TWRCs) of nTR, where nTdenotes the number of antennas at each user and nRdenotes that at the relay. We propose a new reduced-dimension (RD) cooperative precoding scheme. In the proposed scheme, the two users cooperatively create nTaligned eigen-modes, supporting nTstreams of physical-layer network coding. We investigate the design of the RD cooperative precoder and derive an asymptotically optimal solution. We analytically show that, in the worst case, the proposed scheme is within ½ bit per transmit antenna of the asymptotic sum-capacity of the MIMO TWRC. For fading MIMO TWRCs with i.i.d. Gaussian coefficients, we derive a closed-form expression of the average sum-rate of the proposed scheme using large system analysis. Our analytical result shows that, for a large system with nT/nR= ½, the proposed scheme is less than 0.16 bit per transmit antenna away from the capacity. Furthermore, this gap reduces as nT/nRincreases, and vanishes as nT/nRtends to 1. It is demonstrated that the proposed scheme can significantly outperform other existing schemes in the literature.

We investigate a slotted incremental decode-and-forward (SIDF) protocol for cooperative communication in wireless networks. In the proposed scheme, each user allocates only a portion of its time-resource to incrementally relay its partner's information, thus to improve the bandwidth efficiency of the cooperative transmission. To analyze the performance, we derive the diversity-multiplexing tradeoff (DMT) of the SIDF protocol and show the optimal time-allocation. It is shown that the SIDF achieves the DMT upper bound for low and high multiplexing gain regions whereas it is slightly away from the upper bound at a medium multiplexing gain region. The superiority of the DMT of SIDF protocol is translated into significant improved outage probability, as compared with other well-known user-cooperation protocols.

We investigate joint channel and physical layer network coding (CPNC) for Gaussian two-way relay channels. The two users' messages are encoded using the same binary linear code and are transmitted simultaneously with equal power. At the relay node, the network-coded message is recovered directly from the received signal sequence, and is then broadcast to the users. We propose a new methodology to explicitly find the distance spectrum of the coding scheme. Based on that, we analyze the error probability at the relay and derive an asymptotically tight performance bound (for high SNRs). We show that, with a general binary linear code, the CPNC scheme is subject to an asymptotic SNR loss of approximately ln 2 relative to the single-user case, regardless of the coding rate. Numerical results show that our analysis matches very well with the performance of the CPNC scheme.

We propose a new joint channel coding and physical layer network coding (CPNC) scheme for multiple-input multiple-output (MIMO) two-way relay channels (TWRCs). At the heart of the scheme lies a key technique referred to as eigen-direction alignment (EDA) precoding. This technique efficiently creates multiple aligned parallel channels which facilitates the deployment of multi-stream CPNC. Our analysis shows that the achievable rate of the scheme can approach the capacity upper bound in the median to high signal-to-noise (SNR) region when nT> nR, where nTand nRdenote the number of antennas of each user and that of relay, respectively. The gap to the capacity upper bound diminishes as nT/nRincreases. Numerical results demonstrate that the proposed scheme significantly outperform other well-known schemes in the literature.

We consider an uplink communication in a wireless network where each source-user is assisted by M half-duplex relays. The source users and relays are equipped with single-antenna whereas the destination has N antennas. We show that the degree of freedom (d.o.f.) of this network is limited by the links from the source to the collection of relays and destination. This phenomenon is referred to as a "d.o.f. bottleneck problem" which compromise the cooperative multiplexing gain (CMG) and the achievable rate of the system. To improve the CMG, we propose an auxiliary frequency bands (AFBs)-based approach to tackle the d.o.f. bottleneck problem. Information theoretic analysis and numerical results show that the proposed scheme can achieve a CMG of min(M+1,N) when the number of AFBs is sufficiently large. As compared with conventional cooperative communications, the improved multiplexing gain of the proposed scheme is translated into tremendously increased achievable rate at a relatively high SNR.

In this paper, we propose a new superposition modulation-based cooperative scheme and investigate receivers with iterative detection and decoding (IDD), where we focus on an interference cancellation (IC) detector. For quasi-static fading environment, we analyze the bit-error-probability (BEP) of the proposed scheme and analytically show the optimal power allocation in the superposition modulation. It is demonstrated that the proposed scheme performs about 2-3.5 dB better than the system previously proposed in the literature and simulation results are shown to be very close to the analytical results. In addition, the receiver with IC detectors achieves the MAP detection performance in the scheme.

In this paper, we develop a rate allocation scheme for interleave-division multiple-access (IDMA) systems with iterative decoding. We use a fully-analytical approach to predict the performance of the scheme and propose a modified linear programming method to design the rate profile. Numerical results show that with just repetition coding and rate allocation, the performance of the scheme is only about 5 dB away from the capacity for a wide range of SNR, provided that the number of users is sufficiently large. Compared with power allocation schemes for IDMA, the proposed rate allocation scheme achieves a similar performance at a moderate spectral efficiency and the requirement of sophisticated power amplifiers can be relaxed.

We propose a new superposition modulation-based cooperative diversity scheme and investigate receivers with iterative detection and decoding for the scheme, where we focus on a interference cancellation (IC) detector. We analyze the bit-error-probability (BEP) of the scheme and find the optimal power allocation. Simulation results are shown to be very close to the analytical results for a wide range of signal-to-noise ratios (SNRs). It is also demonstrated that the proposed scheme is about 2-3.5 dB better than the system previously proposed in the literature.

In this letter, we develop a rate allocation scheme for interleave-division multiple-access (IDMA) systems with iterative decoding. We use a fully-analytical approach to predict the performance of the scheme. Then, we propose a modified linear programming method to find the best rate profile for the scheme. Numerical results show that with just repetition coding and optimal rate allocation, the performance of the scheme is only about 5 dB away from the capacity for a wide range of SNR, provided that the number of users is sufficiently large. Compared with power allocation schemes for IDMA, the proposed rate allocation scheme achieves a similar performance at a moderate spectral efficiency and the requirement of sophisticated power amplifiers can be relaxed.

In this paper, we propose a new superposition- modulation based cooperative multiple-access scheme. In this scheme, each user only superimpose the information from the previous user, where the full diversity is achieved by cooperative spatial-interleaving. Focusing on interference cancellation with minimum mean square error filtering at the destination, we derive a lower bound on the frame error probability of the scheme. We show that the bound can be used to predict the frame error rate of the scheme. Moreover, we show that full diversity gain is achieved and the detection complexity is reduced as compared to the previous scheme.

In this letter, we propose a new multi-stage LLR combining (MLC) algorithm in an iterative receiver for MIMOBICM systems. This algorithm combines the soft information from different receive antennas in a multi-stage fashion, where the combining factors are derived based on the joint likelihood function of bivariate Gaussian random variables. The variance transfer (VT) function of the proposed scheme is derived for performance analysis. For slow fading channels, we show that the proposed MLC algorithm can achieve almost the same performance as the linear minimum mean square error (LMMSE) filtering approach, whereas the computation-demanding matrix inverse for LMMSE can be avoided.

In this paper, we propose a new linear detector for the iterative receiver for MIMO-BICM systems. Instead of performing vector matched filtering after the interference cancellation, the proposed detector successively combines the soft information from different receive antennas, where the combining factors are computed based on the joint likelihood function of multivariate Gaussian random variables. Numerical results show that significant performance improvement can be achieved and the additional complexity is negligible.