This paper presents an innovative movable antenna (MA)-enhanced multi-user multiple-input multiple-output (MIMO) downlink system. We aim to maximize the energy efficiency (EE) under statistical channel state information (S-CSI) through a joint optimization of the precoding matrix and the antenna position vectors (APVs). To solve the resulting stochastic problem, we first resort to deterministic equivalent (DE) tecnology to formulate the deterministic minorizing function of the system EE and the deterministic function of each user terminal (UT)’s average achievable rate w.r.t. the transmit variables (i.e., the precoding matrix and the transmit APV) and the corresponding receive APV, respectively. Then, we propose an alternating optimization (AO) algorithm to alternatively optimize the transmit variables and the receive APVs to maximize the formulated deterministic objective functions, respectively. Finally, the above AO algorithm is tailored for the single-user scenario. Our numerical results reveal that, the proposed MA-enhanced system can significantly improve the system EE compared to several benchmark schemes based on the S-CSI and the optimal performance can be achieved with a finite size of movement regions for MAs.

A wiretap channel is served as the fundamental model of physical layer security techniques, where the secrecy capacity of the Gaussian wiretap channel is proven to be achieved by Gaussian input. However, there remains a gap between the Gaussian secrecy capacity and the secrecy rate with conventional uniformly distributed discrete constellation input, e.g. amplitude shift keying (ASK) and quadrature amplitude modulation (QAM). In this paper, we propose a probabilistic shaped multilevel polar coding scheme to bridge the gap. Specifically, the input distribution optimization problem for maximizing the secrecy rate with ASK/QAM input is solved. Numerical results show that the resulting sub-optimal solution can still approach the Gaussian secrecy capacity. Then, we investigate the polarization of multilevel polar codes for the asymmetric discrete memoryless wiretap channel, and thus propose a multilevel polar coding scheme integration with probabilistic shaping. It is proved that the scheme can achieve the secrecy capacity of the Gaussian wiretap channel with discrete constellation input, and satisfies the reliability condition and weak security condition. A security-oriented polar code construction method to natively satisfies the leakage-based security condition is also investigated. Simulation results show that the proposed scheme achieves more efficient and secure transmission than the uniform constellation input case over both the Gaussian wiretap channel and the Rayleigh fading wiretap channel.

This paper investigates asynchronous multiple-input multiple-output (MIMO) massive unsourced random access (URA) in an orthogonal frequency division multiplexing (OFDM) system over frequency-selective fading channels, with the presence of both timing and carrier frequency offsets (TO and CFO) and non-negligible codeword collisions. The proposed coding framework segregates the data into two components, namely, preamble and coding parts, with the former being tree-coded and the latter LDPC-coded. By leveraging the dual sparsity of the equivalent channel across both codeword and delay domains (CD and DD), we develop a message-passing-based sparse Bayesian learning algorithm, combined with belief propagation and mean field, to iteratively estimate DD channel responses, TO, and delay profiles. Furthermore, by jointly leveraging the observations among multiple slots, we establish a novel graph-based algorithm to iteratively separate the superimposed channels and compensate for the phase rotations. Additionally, the proposed algorithm is applied to the flat fading scenario to estimate both TO and CFO, where the channel and offset estimation is enhanced by leveraging the geometric characteristics of the signal constellation. Extensive simulations reveal that the proposed algorithm achieves superior performance and substantial complexity reduction in both channel and offset estimation compared to the codebook enlarging-based counterparts, and enhanced data recovery performances compared to state-of-the-art URA schemes.

This paper investigates the multiple-input-multiple-output (MIMO) massive unsourced random access in an asynchronous orthogonal frequency division multiplexing (OFDM) system, with both timing and frequency offsets (TFO) and non-negligible user collisions. The proposed coding framework splits the data into two parts encoded by sparse regression code (SPARC) and low-density parity check (LDPC) code. Multistage orthogonal pilots are transmitted in the first part to reduce collision density. Unlike existing schemes requiring a quantization codebook with a large size for estimating TFO, we establish a graph-based channel reconstruction and collision resolution (GB-CR2) algorithm to iteratively reconstruct channels, resolve collisions, and compensate for TFO rotations on the formulated graph jointly among multiple stages. We further propose to leverage the geometric characteristics of signal constellations to correct TFO estimations. Exhaustive simulations demonstrate remarkable performance superiority in channel estimation and data recovery with substantial complexity reduction compared to state-of-the-art schemes.

This paper investigates the transmitter and receiver beamforming (TB and RB) for over-the-air computation (AirComp) in massive multiple-inputs and multiple-outputs (MIMO) systems. First, we propose a two-phase hybrid beamforming algorithm to design TB and hybrid RB. In the first phase, we adopt a projected gradient descent with momentum (PGDM) algorithm to search for the optimal fully-digital TB matrices. Compared with the benchmarks on the mean square error (MSE) performances, PGDM can achieve up to 5 dB gain in signal-to-noise ratio (SNR) with less algorithm execution time when fully-digital RB is assumed. In the second phase, we plug the TB matrices obtained in PGDM as well as the optimal baseband RB (BBRB) matrix into the MSE objective, and adopt gradient descent to search for the optimal radio-frequency RB (RFRB) matrix. Compared with the state-of-the-arts, the proposed two-phase algorithm reduces up to 30% of the algorithm execution time and 18% of the MSE. Second, we propose a statistical TB algorithm to reduce the communication overheads, in which TB completely depends on statistical channel state information (CSI) and thus does not rely on the feedback from the base station (BS). We prove that orthonormal matrices are asymptotically optimal for statistical TB when uncorrelated Rayleigh channels are assumed and the number of receiving antennas approaches to infinity. For correlated channels, experimental results show that the proposed statistical TB can achieve about 5 dB gain in SNR compared with orthonormal matrices in terms of the MSE performance. Third, a large scale system analysis is made in this paper. As the number of the receiving antennas approaches to infinity, asymptotically optimal choices for TB and RB are provided, and upper bounds of MSE are derived in terms of the number of clients and receiving antennas. For hybrid RB, an upper bound of the squared distance between the optimal hybrid RB and the optimal fully-digital RB is also derived.

In this paper, the analysis of excess distortion exponent for joint source-channel coding (JSCC) in semantic-aware communication systems is presented. By introducing an unobservable semantic source, we extend the classical results by Csiszar to semantic-aware communication systems. Both upper and lower bounds of the exponent for the discrete memoryless source-channel pair are established. Moreover, an extended achievable bound of the excess distortion exponent for MIMO systems is derived. Further analysis explores how the block fading and numbers of antennas influence the exponent of semantic-aware MIMO systems. Our results offer some theoretical bounds of error decay performance and can be used to guide future semantic communications with joint source-channel coding scheme.

In this paper, we investigate a joint device activity detection (DAD), channel estimation (CE), and data decoding (DD) algorithm for multiple-input multiple-output (MIMO) massive unsourced random access (URA). Different from the state-of-the-art slotted transmission scheme, the data in the proposed framework is split into only two parts. A portion of the data is coded by compressed sensing (CS) and the rest is low-density-parity-check (LDPC) coded. In addition to being part of the data, information bits in the CS phase also undertake the task of interleaving pattern design and CE. The principle of interleave-division multiple access (IDMA) is exploited to reduce the interference among devices in the LDPC phase. Based on the belief propagation (BP) algorithm, a low-complexity iterative message passing (MP) algorithm is utilized to decode the data embedded in these two phases separately. Moreover, combined with successive interference cancellation (SIC), the proposed joint DAD-CE-DD algorithm is performed to further improve performance by utilizing the belief of each other. Additionally, based on the energy detection (ED) and sliding window protocol (SWP), we develop a collision resolution protocol to handle the codeword collision, a common issue in the URA system. In addition to the complexity reduction, the proposed algorithm exhibits a substantial performance enhancement compared to the state-of-the-art in terms of efficiency and accuracy.

This paper investigates the unsourced random access (URA) scheme to accommodate numerous machine-type users communicating to a base station equipped with multiple antennas. Existing works adopt a slotted transmission strategy to reduce system complexity; they operate under the framework of coupled compressed sensing (CCS) which concatenates an outer tree code to an inner compressed sensing code for slot-wise message stitching. We suggest that by exploiting the MIMO channel information in the angular domain, redundancies required by the tree encoder/decoder in CCS can be removed to improve spectral efficiency, thereby an uncoupled transmission protocol is devised. To perform activity detection and channel estimation, we propose an expectation-maximization-aided generalized approximate message passing algorithm with a Markov random field support structure, which captures the inherent clustered sparsity structure of the angular domain channel. Then, message reconstruction in the form of a clustering decoder is performed by recognizing slot-distributed channels of each active user based on similarity. We put forward the slot-balanced$ K $-means algorithm as the kernel of the clustering decoder, resolving constraints and collisions specific to the application scene. Extensive simulations reveal that the proposed scheme achieves a better error performance at high spectral efficiency compared to the CCS-based URA schemes.

Federated learning (FL) is a popular distributed learning paradigm, in which a global model at a server learns private data of clients without data shared among clients or the server. In this paper, we consider FL over a noisy fading multiple access channel (MAC) via over-the-air computation (AirComp). Benefiting from waveform-superposition propriety of wireless signals, AirComp is able to achieve fast aggregations in FL and improve spectral efficiency. However, most of the schemes exploiting AirComp require intensive channel estimations as the demands from precoders, which results in considerable communication overheads. For this reason, we propose two novel FL schemes with statistical channel state information (FL-SCSI-A and FL-SCSI-B) to reduce the efforts required by channel estimations. In FL-SCSI-A, precoders adjust phases of transmitted signals with phases of instant channel state information (CSI), and scale transmitted signal powers based on statistical CSI. The precoder design has the following two advantages. First, phases of instant CSI can be easier to estimate than complete instant CSI. Second, since clients only need to estimate phases of their own instant CSI (instead of CSI of all clients), with channel reciprocity, this can be easily achieved by letting the server broadcast pilots to all clients. The server in FL-SCSI-A is also efficient. It only needs to estimate the sum of channel gains of all clients, which can be easily achieved by letting clients transmit pilots simultaneously. To further reduce the communication overhead, FL-SCSI-B is proposed. The precoders in FL-SCSI-B are similar to FL-SCSI-A, while the server does not require any knowledge of instant CSI, which reduces the demands of channel estimations. For both schemes, we prove that the distortion caused by the noisy fading MAC is bounded, and the convergences of the learning processes are guaranteed for strongly smooth losses with heterogeneous data assumptions. Experimental results show that the proposed schemes perform better than benchmark schemes while reducing efforts required by channel estimation.

Massive multiple-input and multiple-output (MIMO) enables ultra-high throughput and low latency for tile-based adaptive virtual reality (VR) 360° video transmission in wireless network. In this paper, we consider a massive MIMO system where multiple users in a single-cell theater watch an identical VR 360° video. Based on tile prediction, base station (BS) deliveries the tiles in predicted field of view (FoV) to users. By introducing practical supplementary transmission for missing tiles and unacceptable VR sickness, we propose the first stable transmission scheme for VR video. we formulate an integer non-linear programming (INLP) problem to maximize users’ average quality of experience (QoE) score. Moreover, we derive the achievable spectral efficiency (SE) expression of predictive tile groups and the approximately achievable SE expression of missing tile groups, respectively. Analytically, the overall throughput is related to the number of tile groups and the length of pilot sequences. By exploiting the relationship between the structure of viewport tiles and SE expression, we propose a multi-lattice multi-stream grouping method aimed at improving the overall throughput for VR video transmission. Moreover, we analyze the relationship between QoE objective and number of predictive tile. We transform the original INLP problem into an integer linear programming problem by setting the predictive tiles groups as some constants. With variable relaxation and recovery, we obtain the optimal average QoE. Extensive simulation results validate that the proposed algorithm effectively improves QoE.

Internet of Things (IoT) devices often transmit very short message blocks without strong error correction coding or pilots for channel equalization. When the transmitted signals encounter a severe multipath channel, the receiver is often unable to equalize the resulting inter-symbol interference (ISI) via traditional methods, leading to a high retransmission rate. This paper proposes a joint channel equalization and symbol detection scheme for this scenario by utilizing the preamble sequence as a training pilot for equalization and the relatively weak cyclic redundancy check (CRC) 8-Dallas code for error correction. By assuming a sparse channel impulse response, the proposed joint channel equalization and symbol detection scheme formulates an l1norm constrained optimization problem and solves it by a saddle-point algorithm. The proposed algorithm is applied to a set of real-world underwater animal tracking IoT data, and the results show improvement of correct message detection rate from 21.5% (direct symbol decisions) to 41.6% (equalization and decoding).

Underwater acoustic communication often suffers from extended channel impulse response (CIR) and large Doppler spread such that signals become difficult to detect and decode. For the underwater Internet-of-Things (IoT) applications, the challenges are even bigger, because the IoT devices usually transmit very short messages due to severe power constraints, and the length of pilots are often shorter than that of CIR. Therefore, conventional pilot-assisted channel estimation and equalization approaches are incapable of detecting the information data. Moreover, the existing blind channel equalization algorithms, which do not require pilots, are not able to detect information data either, because the number of transmitted symbols is too small to approximate the expected loss with empirical loss, where the loss refers to as the error of estimated signal envelopes. In this article, a new equalization and decoding algorithm is proposed for the underwater IoT devices under harsh communication environments. Inspired by the recent blind deconvolution and compressive sensing techniques, we construct an optimization problem with the objective function rewarding sparsity of the estimated CIR using l4-norm and convexify the feasible set of the problem while guarantee the same solution. Then, we develop a pruned tree search initialization method and use gradient descent to find an optimal solution efficiently. The new algorithm is first verified by simulations, which show that the proposed algorithm outperforms conventional methods, such as the linear minimum mean square error (LMMSE) equalizer and a constant modulus algorithm (CMA). The proposed algorithm, along with a practical procedure for compensating large Doppler spread and carrier frequency offset, is further employed to process the real-world underwater IoT data collected in a fish-tag project. It shows that the proposed algorithm can equalize and detect the IoT data which were corrupted by channels whose lengths are longer than that of pilots, but the existing algorithms, such as LMMSE equalizer and CMA-based blind equalizer are not able to accomplish. It also shows that the proposed algorithm can provide a very impressive improvement compared to raw detection (no equalization or decoding) and decoding-only approaches.

We investigate the multicast precoding design in multicell massive multiple-input multiple-output (MIMO) systems with finite-alphabet inputs. Focusing on the multicast transmission with only statistical channel state information at the base station, we derive a lower bound on the achievable ergodic rate for finite-alphabet inputs, from which we utilize the concave-convex procedure (CCCP) to devise a CCCP-based algorithm maximizing the minimum weighted achievable ergodic rate lower bound. The CCCP-based algorithm is proven to converge to a local optimum. Furthermore, exploiting the channel characteristic in massive MIMO systems, we prove that the optimal precoding vectors should be linear combination of columns of eigenmatrix of transmit correlation matrices in order to maximize the minimum weighted rate lower bound with lower computational complexity. Then, a relation-based algorithm is developed to obtain the optimal solution of the weighted max-min fairness (MMF) problem by using the duality between the MMF and quality of service problem. Numerical results demonstrate the tightness of the achievable ergodic rate lower bound and the significant performance of the proposed algorithms.

This paper investigates the hybrid precoding design for millimeter wave (mmWave) multiple-input-multiple-output (MIMO) systems with finite-alphabet inputs. The mmWave MIMO system employs partially-connected hybrid precoding architecture with dynamic subarrays, where each radio frequency (RF) chain is connected to a dynamic subset of antennas. We consider the design of analog and digital precoders utilizing statistical and/or mixed channel state information (CSI), which involve solving an extremely difficult problem in theory: First, designing the optimal partition of antennas over RF chains is a combinatorial optimization problem, whose optimal solution requires an exhaustive search over all antenna partitioning solutions; Second, the average mutual information under mmWave MIMO channels lacks closed-form expression and involves prohibitive computational burden; and Third, the hybrid precoding problem with given partition of antennas is nonconvex with respect to the analog and digital precoders. To address these issues, this paper first presents a simple criterion and the corresponding low complexity algorithm to design the optimal partition of antennas using statistical CSI. Then, it derives the lower bound and its approximation for the average mutual information, in which the computational complexity is greatly reduced compared to calculating the average mutual information directly. In addition, it also shows that the lower bound with a constant shift offers a very accurate approximation to the average mutual information. This paper further proposes utilizing the lower bound approximation as a low-complexity and accurate alternative for developing a manifold-based gradient ascent algorithm to find near-optimal analog and digital precoders. Several numerical results are provided to show that our proposed algorithm outperforms the existing hybrid precoding algorithms.

Due to the lack of explicit expression of instantaneous mutual information (IMI), online throughput optimization for energy harvesting (EH) MIMO systems with finite alphabet inputs suffers from heavy computation burden and large feedback overhead. We propose a two-layer predictive strategy with the aid of context information, by constructing a precoding codebook offline at both the transmitter and receiver, to relax the time pressure for the online strategy. Two schemes were provided to accelerate the codebook construction. One is to estimate IMI during optimization by using a reference function. The other is by starting the optimization of each precoder from an adjacent precoder. With the channel distribution information (CDI), the feedback overhead is reduced by minimizing the codebook size. By the methods above, the building speed of the precoding codebook can be up to two orders of magnitude faster than no accelerating strategies. Meanwhile, through topology analysis, we propose a higher layer predictive strategy, which determines the index of allocated energy at each slot within a frame. The higher layer strategy takes full advantage of the constructed precoding codebook and context information when estimating the future throughput. Simulation results demonstrate the effectiveness and practicality of the proposed two-layer strategy.

In this paper, the design of robust linear precoders for the massive multi-input-multi-output (MIMO) downlink with imperfect channel state information (CSI) is investigated. The imperfect CSI for each UE obtained at the BS is modeled as statistical CSI under a jointly correlated channel model with both channel mean and channel variance information, which includes the effects of channel estimation error, channel aging, and spatial correlation. The design objective is to maximize the expected weighted sum-rate. By combining the minorize-maximize (MM) algorithm with the deterministic equivalent method, an algorithm for robust linear precoder design is derived. The proposed algorithm achieves a stationary point of the expected weighted sum-rate maximization problem. To reduce the computational complexity, two low-complexity algorithms are then derived. One for the general case, and the other for the case when all the channel means are zeros. For the later case, it is proved that the beam domain transmission is optimal, and thus the precoder design reduces to the power allocation optimization in the beam domain. Simulation results show that the proposed robust linear precoder designs apply to various mobile scenarios and achieve high spectral efficiency.

Hybrid precoding provides a tradeoff between spectral efficiency and power consumption in millimeter wave (mmWave) multiple-input multiple-output (MIMO) systems. In this paper, we investigate the partially-connected hybrid precoding design for mmWave MIMO broadcast channels with finite alphabet inputs. To enhance the spectral efficiency, a new algorithm is proposed to dynamically optimize the mapping strategy from radio frequency (RF) chains to transmit antennas such that the weighted sum of channel gains is maximized. Then we adopt the inexact alternating minimization method to design hybrid precoding matrices with given optimal mapping strategy and finite-alphabet inputs. Simulation results demonstrate the good performance of our proposed algorithm.

The unprecedented growth in the number of mobile data and connected machines ever-fast approaches limits of fourth generation technologies to address this enormous data demand. Therefore, the development of the fifth generation (5G) wireless communication technologies is a priority issue currently. The evolution towards 5G wireless communications will be a cornerstone for realizing the future human-centric and connected machine-centric networks, which achieve near-instantaneous, zero distance connectivity for people and connected machines. On the other hand, wireless networks have been widely used in civilian and military applications and become an indispensable part of our daily life. People rely heavily on wireless networks for transmission of important/private information, such as credit card information, energy pricing, e-health data, command, and control messages. Therefore, security is a critical issue for future 5G wireless networks. Physical layer security techniques can be used to either perform secure data transmission directly or generate the distribution of cryptography keys for conventional cryptography techniques in the 5G networks. With careful management and implementation, physical layer security can be used as an additional level of protection on top of the existing security schemes. As such, they will formulate a well-integrated security solution together that efficiently safeguards the confidential and privacy communication data in 5G wireless networks. The main goal of this IEEE JSAC Special Issue on “Physical Layer Security for 5G Wireless Networks” is to bring together leading researchers in both academia and industry from diversified backgrounds to advance the theory and practice of physical layer security for 5G wireless networks.

Physical layer security which safeguards data confidentiality based on the information-theoretic approaches has received significant research interest recently. The key idea behind physical layer security is to utilize the intrinsic randomness of the transmission channel to guarantee the security in physical layer. The evolution toward 5G wireless communications poses new challenges for physical layer security research. This paper provides a latest survey of the physical layer security research on various promising 5G technologies, including physical layer security coding, massive multiple-input multiple-output, millimeter wave communications, heterogeneous networks, non-orthogonal multiple access, full duplex technology, and so on. Technical challenges which remain unresolved at the time of writing are summarized and the future trends of physical layer security in 5G and beyond are discussed.

The unprecedented growth in the number of mobile data and connected machines ever-fast approaches limits of fourth generation technologies to address this enormous data demand. Therefore, the development of the fifth generation (5G) wireless communication technologies is a priority issue currently. The evolution towards 5G wireless communications will be a cornerstone for realizing the future human-centric and connected machine-centric networks, which achieve near-instantaneous, zero distance connectivity for people and connected machines. On the other hand, wireless networks have been widely used in civilian and military applications and become an indispensable part of our daily life. People rely heavily on wireless networks for transmission of important/private information, such as credit card information, energy pricing, e-health data, command, and control messages. Therefore, security is a critical issue for future 5G wireless networks. Physical layer security techniques can be used to either perform secure data transmission directly or generate the distribution of cryptography keys for conventional cryptography techniques in the 5G networks. With careful management and implementation, physical layer security can be used as an additional level of protection on top of the existing security schemes. As such, they will formulate a well-integrated security solution together that efficiently safeguards the confidential and privacy communication data in 5G wireless networks. The main goal of this IEEE JSAC Special Issue on “Physical Layer Security for 5G Wireless Networks” is to bring together leading researchers in both academia and industry from diversified backgrounds to advance the theory and practice of physical layer security for 5G wireless networks.

Provides an overview of the technical articles and features presented in this issue. Our regular papers this month focus on 5G related topics such as multipleinput– multipleoutput transmission using finite input signals, and achieving ultrareliable and low-latency wireless communication.

Multiple antennas have played an essential role in spatial multiplexing and diversity transmission for a wide range of communication applications. Most advances in the design of high-speed wireless multiple-input-multiple-output (MIMO) systems have been based on information-theoretic principles that demonstrate how to efficiently transmit signals conforming to Gaussian distribution. However, although the Gaussian signal is capacity-achieving, practical systems transmit signals belonging to finite and discrete constellations. Therefore, capacity-achieving transceiver processing based on a Gaussian input signal can be quite suboptimal for practical MIMO systems with discrete constellation input signals. To address this shortcoming, this paper aims to provide a comprehensive overview of MIMO transmission design with finite input signals. It first summarizes existing fundamental results for MIMO systems with finite input signals. Next, focusing on basic point-to-point MIMO systems, it examines transmission schemes based on the three most important criteria for communication systems: mutual-information-driven designs, mean-square-error-driven designs, and diversity-driven designs. In particular, a unified framework is developed for the design of low-complexity transmission schemes applicable to massive MIMO systems in forthcoming 5G wireless networks for the first time. Furthermore, adaptive transmission designs are proposed that switch among these criteria based on channel conditions to formulate the best transmission strategy. A survey is then given of transmission designs with finite input signals for multiuser MIMO scenarios, including MIMO uplink transmission, MIMO downlink transmission, MIMO interference channel, and MIMO wiretap channel. Additionally, transmission designs with finite input signals are discussed for other multi-antenna systems. Finally, a number of technical challenges that remain unresolved at the time of writing are highlighted, and future trends in transmission design with finite input signals are discussed.

This paper investigates the hybrid precoding design for millimeter wave multiple-input multiple-output systems with finite-alphabet inputs. The precoding problem is a joint optimization of analog and digital precoders, and we treat it as a matrix factorization problem with power and constant modulus constraints. This paper presents three main contributions. First, we present a sufficient condition and a necessary condition for hybrid precoding schemes to realize unconstrained optimal precoders exactly when the number of data streams Nssatisfies Ns= min{rank(H), Nrf}, where H represents the channel matrix and Nrfis the number of radio frequency chains. Second, we show that the coupled power constraint in our matrix factorization problem can be removed without loss of optimality. Third, we propose a Broyden-Fletcher-Goldfarb-Shanno-based algorithm to solve our matrix factorization problem using gradient and Hessian information. Several numerical results are provided to show that our proposed algorithm outperforms existing hybrid precoding algorithms.

This paper investigates the hybrid precoding design for millimeter wave (mmWave) multiple-input multiple- output(MIMO) systems with finite alphabet inputs. The precoding problem is a joint optimization of analog and digital precoders,and it imposes nonconvex constant modulus constraints on the analog precoder. We treat this problem as a matrix factorization problem with constant modulus constraints. The main contributions of our work are listed as follows: First, we propose sufficient and necessary conditions for hybrid precoding schemes to realize any unconstrained optimal precoders exactly when the number of data streams is equal to the number of radio frequency chains. Second, we show that the power constraint in the hybrid precoding problem can be removed without loss of optimality. Third, we present a trust region Newton method to solve our problem using gradient and Hessian information, and the proposed algorithm converges to a stationary point satisfying the first and second order necessary optimality conditions. Several numerical examples are provided to show that the proposed algorithm outperforms existing hybrid precoding algorithms.

In this paper, we investigate secure transmission over the large-scale multiple-antenna wiretap channel with finite alphabet inputs. First, we show analytically that a generalized singular value decomposition (GSVD) based design, which is optimal for Gaussian inputs, may exhibit a severe performance loss for finite alphabet inputs in the high signal-to-noise ratio (SNR) regime. In light of this, we propose a novel Per-Group-GSVD (PG-GSVD) design which can effectively compensate the performance loss caused by the GSVD design. More importantly, the computational complexity of the PG-GSVD design is by orders of magnitude lower than that of the existing design for finite alphabet inputs in \cite{Wu2012TVT} while the resulting performance loss is minimal. Numerical results indicate that the proposed PG-GSVD design can be efficiently implemented in large-scale multiple-antenna systems and achieves significant performance gains compared to the GSVD design.

In this paper, the design of linear precoders for simultaneously wireless information and power transfer (SWIPT) over multi-input multi-output (MIMO) broadcast channels with discrete input signals is investigated. The considered system model consists of one base station (BS), one information receiver (IR) and one energy receiver (ER). The design objective is to maximize the input-output mutual information of the IR subject to the harvested energy requirement for the ER. The structure of the optimal precoder is derived by using the methods of manifold optimization, and an algorithm is proposed to find the optimal precoder. Simulation results show that the proposed algorithm can achieve better performance than the time sharing scheme and the optimal precoder designed for Gaussian inputs.

In this paper, we investigate the mutual information maximization for a multiple-input multiple-output (MIMO) system with simultaneous wireless information and power transfer (SWIPT), where perfect channel state information (CSI) is known at the transmitter. We formulate an optimization problem under the constraints of transmit power and harvested energy. Different from previous work, we assume the input signals to be taken from finite-alphabet inputs instead of Gaussian signals. The formulated problem is NP-hard, so a global optimal solution can not be found with polynomial time complexity. However, by exploiting the structure of the problem, this optimization problem can be transformed into a semidefinite programming (SDP) problem, and then a near optimal algorithm based on semidefinite relaxation (SDR) technique is developed. Simulation results show the efficacy of the proposed algorithm.

In this paper, we investigate the design of linear precoders for simultaneously wireless information and power transfer (SWIPT) in a multi-input multi-output (MIMO) broadcasting system with discrete input signals. The considered system model consists of one base station (BS), one information receiver (IR), and one energy receiver (ER). The design objective is to maximize the input-output mutual information of the IR subject to the power constraint and the harvested energy requirement for the ER. We derive the structure of the optimal linear precoder by using manifold optimization, and propose an algorithm to find the optimal precoder. Simulation results show that the proposed algorithm can achieve better performance than the time sharing scheme and the Gaussian optimal precoder when Gaussian inputs are replaced by discrete input signals.

In this paper, we investigate secure transmission over the large-scale multiple-antenna wiretap channel with finite alphabet inputs. First, we investigate the case where instantaneous channel state information (CSI) of the eavesdropper is known at the transmitter. We show analytically that a generalized singular value decomposition (GSVD)-based design, which is optimal for Gaussian inputs, may exhibit a severe performance loss for finite alphabet inputs in the high signal-to-noise ratio regime. In light of this, we propose a novel Per-Group-GSVD (PG-GSVD) design, which can effectively compensate the performance loss caused by the GSVD design. More importantly, the computational complexity of the PG-GSVD design is by orders of magnitude lower than that of the existing design for finite alphabet inputs while the resulting performance loss is minimal. Then, we extend the PG-GSVD design to the case where only statistical CSI of the eavesdropper is available at the transmitter. Numerical results indicate that the proposed PG-GSVD design can be efficiently implemented in large-scale multiple-antenna systems and achieves significant performance gains compared with the GSVD design.

This paper investigates a new class of nonconvex optimization, which provides a unified framework for linear precoder design. The new optimization is called generalized quadratic matrix programming (GQMP). Due to the non-deterministic polynomial time (NP)-hardness of GQMP problems, we provide a polynomial time algorithm that is guaranteed to converge to a Karush-Kuhn-Tucker (KKT) point. In terms of application, we consider the linear precoder design problem for spectrum-sharing secure broadcast channels. We design linear precoders to maximize the average secrecy sum rate with finite-alphabet inputs and statistical channel state information (CSI). The precoder design problem is a GQMP problem and we solve it efficiently by our proposed algorithm. A numerical example is also provided to show the efficacy of our algorithm.

This paper investigates the linear precoder design for cognitive multiple-access wiretap channel (CMAC-WT), where two secondary-user transmitters (STs) communicate with one secondary-user receiver (SR) in the presence of an eavesdropper and subject to interference threshold constraints at primary-user receivers (PRs). It designs linear precoders to maximize the ergodic secrecy sum rate for multiple-input multiple-output (MIMO) CMAC-WT under finite-alphabet inputs and statistical channel state information (CSI). For this non-convex problem, a two-layer algorithm is proposed by embedding the convex-concave procedure into an outer approximation framework. The key idea of this algorithm is to reformulate the approximated ergodic secrecy sum rate as a difference of convex (DC) functions, and then generate a sequence of simpler relaxed sets to approach the non-convex feasible set. In this way, near optimal precoding matrices are obtained by maximizing the approximated ergodic secrecy sum rate over a sequence of relaxed sets. Numerical results show that the proposed precoder design provides a significant performance gain over the Gaussian precoding method in the medium and high SNR regimes.

This paper considers the precoder optimization for secure cognitive radios. Different from existing works, we consider multiple antennas at each node, instead of assuming only particular node/nodes having multiple antennas; we use finite-alphabet inputs as the signaling, instead of ideal Gaussian-input assumption; we exploit statistical channel state information (CSI), instead of instantaneous CSI at the transmitter. We maximize the secrecy rate of the secondary user, while controlling the transmit power and the power leakage to primary receivers that share the same frequency spectrum. We reformulate the precoder design problem and propose a branch-and-bound based algorithm, which provides a solution asymptotically converging to the global maximum of the secrecy rate. We illustrate the tradeoff between the performance and complexity of the proposed algorithm and demonstrate the performance gains comparing with other approaches.

Wireless communication systems with energy harvester are attracting much attention due to their ability to improve the system operation time. Extensive research has been carried out on how to maximise the sum of mutual information over multiple time slots (i.e. the throughput). However, most research focuses on the energy harvesting transmitter with Gaussian inputs and single antenna. This study considers the throughput maximisation problem for an energy harvesting transmitter with causal energy constraint over multiple‐input multiple‐output (MIMO) channels. Different from existing works, the authors consider the MIMO system with finite‐alphabet inputs and partial instantaneous channel state information (CSI). Specifically, the transmitter knows the statistical CSI of the entire channel frame as well as the instantaneous CSI of current time slot. The precoder design in this scenario is an intractable optimisation problem with respect to multiple precoding matrices. The authors’ analysis shows that this difficult precoding problem can be equivalently transformed into a set of scalar optimisation subproblems with respect to the transmit power. To solve these subproblems, an efficient algorithm based on the dynamic programming is proposed. The authors analyse the performance of the proposed algorithm, and simulation results validate its effectiveness.

We consider a low complexity polynomial expansion (PE) detector in a massive multiple-input multiple-output (MIMO) uplink channel. In contrast to most massive MIMO systems in the literature, where single antenna user equipments (UEs) are assumed, multiple antenna UEs are employed in this paper. Moreover, the channel between a base station (BS) and a UE is a jointly correlated Rician fading channel. The PE detector reduces the computational complexity of the minimum mean square error (MMSE) detector by replacing the matrix inversion with an approximate matrix polynomial. The coefficients of the approximate matrix polynomial are computed from the deterministic equivalents of the moments of the channel Gram matrix. We use operator-valued free probability, which is a more general version of free probability, to derive the deterministic equivalents. In particular, we use the operator-valued moment-cumulant formula. The proposed low complexity PE detector is easy to compute. Simulation results show that the proposed detector can achieve performance close to the MMSE detector.

In this paper, a free deterministic equivalent is proposed for the capacity analysis of the multi-input multi-output (MIMO) multiple access channel (MAC) with a more general channel model compared to previous works. In particular, a MIMO MAC with one base station (BS) equipped with several distributed antenna sets is considered. Each link between a user and a BS antenna set forms a jointly correlated Rician fading channel. The analysis is based on operator-valued free probability theory, which broadens the range of applicability of free probability techniques tremendously. By replacing independent Gaussian random matrices with operator-valued random variables satisfying certain operator-valued freeness relations, the free deterministic equivalent of the considered channel Gram matrix is obtained. The Shannon transform of the free deterministic equivalent is derived, which provides an approximate expression for the ergodic input-output mutual information of the channel. The sum-rate capacity achieving input covariance matrices are also derived based on the approximate ergodic input-output mutual information. The free deterministic equivalent results are easy to compute, and simulation results show that these approximations are numerically accurate and computationally efficient.

In this paper, we investigate secure and reliable transmission strategies for multi-cell multi-user massive multiple-input multiple-output systems with a multi-antenna active eavesdropper. We consider a time-division duplex system where uplink training is required and an active eavesdropper can attack the training phase to cause pilot contamination at the transmitter. This forces the precoder used in the subsequent downlink transmission phase to implicitly beamform toward the eavesdropper, thus increasing its received signal power. Assuming matched filter precoding and artificial noise (AN) generation at the transmitter, we derive an asymptotic achievable secrecy rate when the number of transmit antennas approaches infinity. For the case of a single-antenna active eavesdropper, we obtain a closed-form expression for the optimal power allocation policy for the transmit signal and the AN, and find the minimum transmit power required to ensure reliable secure communication. Furthermore, we show that the transmit antenna correlation diversity of the intended users and the eavesdropper can be exploited in order to improve the secrecy rate. In fact, under certain orthogonality conditions of the channel covariance matrices, the secrecy rate loss introduced by the eavesdropper can be completely mitigated.

This paper considers the precoder design for multiantenna secure cognitive radio networks. We use finite-alphabet inputs as the signaling and exploit statistical channel state information (CSI) at the transmitter. We maximize the secrecy rate of the secondary user and control the transmit power and the power leakage to the primary receivers that share the same frequency spectrum. The secrecy rate maximization is important for practical systems, but challenging to solve, mainly due to two reasons. First, the secrecy rate with statistical CSI is computationally prohibitive to evaluate. Second, the optimization over the precoder is a nondeterministic polynomial-time hard (NP-hard) problem. We utilize an accurate approximation of the secrecy rate to reduce the computational effort and then propose a global optimization approach based on branch-and-bound method. The idea is to define a simplex and transform the secrecy rate into a concave function. The derived concave function converges to the secrecy rate when the defined simplex shrinks down. Using this feature, we solve a sequence of concave maximization problems over iteratively shrinking simplices and eventually attain the globally optimal solution that maximizes the approximation of the secrecy rate. When the complexity is concerned, a low-complexity variant with limited number of iterations can be used in practice. We demonstrate the performance gains when compared with others through numerical examples.

In this paper, a low complexity polynomial expansion (PE) detector for massive multi-input multi-output (MIMO) uplink transmissions is proposed. In contrast to most massive MIMO systems in the literature, where single-antenna user equipments (UEs) are assumed, multiple-antenna UEs are employed in this paper. Furthermore, each link between a user and the base station forms a jointly correlated Rician fading channel. The PE detector reduces the complexity of the minimum mean square error (MMSE) detector by replacing the matrix inversion with an approximate matrix polynomial. In the design of the low complexity PE detector, the approximations of the moments of the channel Gram matrix are needed. We use operator- valued free probability to derive these approximations. The low complexity PE detector is easy to compute. Simulation results show that it can achieve performance close to the MMSE detector.

This paper investigates the precoder design in multiple-input multiple-output (MIMO) systems with energy harvester. The objective is to maximize the sum of mutual information (MI) over multiple time slots with causal knowledge of energy arrivals. Different from existing works, the system is considered with finite-alphabet inputs, and the transmitter is assumed to know not only the statistical channel state information (CSI) but also the instantaneous CSI of the current time slot at the beginning of each time slot. The optimal precoder design leads to an intractable multi- dimensional matrix optimization problem. We show that this difficult optimization problem can be transformed into an equivalent scalar optimization problem with respect to the transmit power. By doing this, the computational complexity of the precoder design is significantly reduced without any performance loss. Furthermore, we provide an efficient algorithm to solve the equivalent problem based on the dynamic programming. Simulation results verify the effectiveness of the proposed algorithm.

In this paper, we propose a free deterministic equivalent for the capacity analysis of multi-input multi-output (MIMO) multiple access channel (MAC) with distributed antenna sets. In the analysis, we use the operator-valued free probability framework, which is much more straightforward than the widely used methods, i.e., the Bai and Silverstein method and the Gaussian method. By replacing independent random Gaussian variables with freely independent circular entries, we obtain the free deterministic equivalent of our channel model. To evaluate the capacity, we use the Shannon transform of the free deterministic equivalent to approximate that of the channel model. The free deterministic equivalent results are easy to compute, and simulation results show that these approximations are numerically accurate and computationally efficient.

We study a multiuser multicarrier downlink communication system in which the base station (BS) employs a large number of antennas. By assuming frequency-division duplex operation, we provide a beam domain channel model as the number of BS antennas grows asymptotically large. With this model, we first derive a closed-form upper bound on the achievable ergodic sum-rate before developing necessary conditions to asymptotically maximize the upper bound, with only statistical channel state information at the BS. Inspired by these conditions, we propose a beam division multiple access (BDMA) transmission scheme, where the BS communicates with users via different beams. For BDMA transmission, we design user scheduling to select users within non-overlapping beams, work out an optimal pilot design under a minimum mean square error criterion, and provide optimal pilot sequences by utilizing the Zadoff-Chu sequences. The proposed BDMA scheme reduces significantly the pilot overhead, as well as, the processing complexity at transceivers. Simulations demonstrate the high spectral efficiency of BDMA transmission and the advantages in the bit error rate performance of the proposed pilot sequences.

In this paper, we investigate secure and reliable transmission strategies for multi-cell multi-user massive multipleinput multiple-output (MIMO) systems in the presence of an active eavesdropper. We consider a time-division duplex system where uplink training is required and an active eavesdropper can attack the training phase to cause pilot contamination at the transmitter. This forces the precoder used in the subsequent downlink transmission phase to implicitly beamform towards the eavesdropper, thus increasing its received signal power. We derive an asymptotic achievable secrecy rate for matched filter precoding and artificial noise (AN) generation at the transmitter when the number of transmit antennas goes to infinity. For the achievability scheme at hand, we obtain the optimal power allocation policy for the transmit signal and the AN in closed form. For the case of correlated fading channels, we show that the impact of the active eavesdropper can be completely removed if the transmit correlation matrices of the users and the eavesdropper are orthogonal. Inspired by this result, we propose a precoder null space design exploiting the low rank property of the transmit correlation matrices of massive MIMO channels, which can significantly degrade the eavesdropping capabilities of the active eavesdropper.

This study presents a low‐complexity soft‐interference cancellation equaliser (SICE) for the turbo detection of multiple‐input–multiple‐output systems operating in time dispersive channels. The SICE contains three time‐invariant linear filters: a feedforward filter, a causal feedback filter and an anti‐causal feedback filter. The feedforward filter is designed to suppress the intersymbol interference because of channel time dispersion and the multiplexing interference from multiple transmit antennas. The causal (or anti‐causal) feedback filter is developed to remove the residual interference caused by the symbols transmitted before (or after) the symbol under detection. The filters are designed by analysing the statistical properties of soft decisions. The performance of the proposed SICE is verified through both extrinsic information transfer (EXIT) chart analysis and computer simulations. The EXIT chart analysis shows that, because of the inclusion of the anti‐causal soft decision, the SICE performance approaches the ideal matched filter bound as the iteration progresses. Consequently, the proposed SICE achieves significant performance gains over conventional equalisers.

We study multicarrier multiuser multiple-input multiple-output (MU-MIMO) systems, in which the base station employs an asymptotically large number of antennas. We analyze a fully correlated channel matrix and provide a beam domain channel model, where the channel gains are independent of sub-carriers. For this model, we first derive a closed-form upper bound on the achievable ergodic sum-rate, based on which, we develop asymptotically necessary and sufficient conditions for optimal downlink transmission that require only statistical channel state information at the transmitter. Furthermore, we propose a beam division multiple access (BDMA) transmission scheme that simultaneously serves multiple users via different beams. By selecting users within non-overlapping beams, the MU-MIMO channels can be equivalently decomposed into multiple single-user MIMO channels; this scheme significantly reduces the overhead of channel estimation, as well as, the processing complexity at transceivers. For BDMA transmission, we work out an optimal pilot design criterion to minimize the mean square error (MSE) and provide optimal pilot sequences by utilizing the Zadoff-Chu sequences. Simulations demonstrate the near-optimal performance of BDMA transmission and the advantages of the proposed pilot sequences.

This work investigates the design of linear precoders in cooperative multi-cell MIMO downlink coverage for finite-alphabet source signals. Traditional design of multi-cell MIMO downlink precoder relies on Gaussian input assumption, which may lead to performance loss when true data inputs consist of discrete non-Gaussian symbols. This work presents optimized precoders for finite-alphabet input by maximizing the sum rate under per-base station power constraints. Specifically, we propose two distributed algorithms: a finite-alphabet signal Gaussian interference gradient projection algorithm and a block diagonalization alternating optimization algorithm while supporting interference cancellation. Our numerical results demonstrate considerable performance gain in terms of approximate transmission data rate as well as decoded bit error rate over precoding schemes designed by using the non-realistic Gaussian input assumption.

In this paper, we investigate the design of linear precoders for the multiple-input-multiple-output (MIMO) multiple access channel (MAC). We assume that statistical channel state information (CSI) is available at the transmitters and consider the problem under the practical finite alphabet input assumption. First, we derive an asymptotic (in the large system limit) expression for the weighted sum rate (WSR) of the MIMO MAC with finite alphabet inputs and Weichselberger's MIMO channel model. Subsequently, we obtain the optimal structures of the linear precoders of the users maximizing the asymptotic WSR and an iterative algorithm for determining the precoders. We show that the complexity of the proposed precoder design is significantly lower than that of MIMO MAC precoders designed for finite alphabet inputs and instantaneous CSI. Simulation results for finite alphabet signaling indicate that the proposed precoder achieves significant performance gains over existing precoder designs.

This paper considers the online multi-antenna pre-coder design for energy harvesting transmitter with emphasis on finite-alphabet inputs and statistical channel state information (CSI). It formulates the problem by maximizing the sum of average mutual information of multiple time slots with causal energy constraint. This formulation leads to a 2 N2t-dimensional stochastic dynamic programming (SDP) problem with a non-concave objective function, where Ntis the number of transmit antennas. The 2Nt2-dimensional SDP problem is prohibitively difficult to solve and prevents the development of efficient online solver. We provide an equivalence between the multidimensional SDP problem and a one-dimensional power choice problem. Solving the one-dimensional equivalence decreases the computational burden extraordinarily without loss of optimality. We also demonstrate the performance gains offered by the proposed method when compared with other algorithms.

This work studies the design of linear precoders for cooperative multi-cell MIMO downlink systems with finite alphabet inputs. Traditionally, multi-cell MIMO downlink precoder designs rely on Gaussian input assumption, which may lead to performance loss when the true inputs admit discrete non-Gaussian symbols. In this work, we present optimized precoders by maximizing weighted sum rate (of finite-alphabet-input) under a set of single base station power constraints. Specifically, we propose a simple gradient algorithm for general multi-cell MIMO downlink channel and a block diagonalization gradient algorithm while supporting interference cancellation.

In this paper, we investigate the design of linear precoders for multiple-input multiple-output (MIMO) multiple access channels (MAC). We assume that statistical channel state information (CSI) is available at the transmitters and consider the problem under the practical finite alphabet input assumption. First, we derive an asymptotic (in the large-system limit) weighted sum rate (WSR) expression for the MIMO MAC with finite alphabet inputs and general jointly-correlated fading. Subsequently, we obtain necessary conditions for linear precoders maximizing the asymptotic WSR and propose an iterative algorithm for determining the precoders of all users. In the proposed algorithm, the search space of each user for designing the precoding matrices is its own modulation set. This significantly reduces the dimension of the search space for finding the precoding matrices of all users compared to the conventional precoding design for the MIMO MAC with finite alphabet inputs, where the search space is the combination of the modulation sets of all users. As a result, the proposed algorithm decreases the computational complexity for MIMO MAC precoding design with finite alphabet inputs by several orders of magnitude. Simulation results for finite alphabet signalling indicate that the proposed iterative algorithm achieves significant performance gains over existing precoder designs, including the precoder design based on the Gaussian input assumption, in terms of both the sum rate and the coded bit error rate.

This paper presents a low complexity soft-interference cancellation equalizer (SICE) for the turbo detection of multiple-input multiple-output (MIMO) systems operating in time dispersive channels. The SICE contains three time-invariant linear filters: a feedforward filter, a causal feedback filter and an anti-causal feedback filter. The feedforward filter is designed to suppress the intersymbol interference (ISI) due to time dispersive channels and the multiplexing interference from multiple transmit antennas. The causal (or anti-causal) feedback filter is developed to remove the residual interference caused by the symbols transmitted before (or after) the symbol under detection. The performance of the proposed SICE is verified through both extrinsic information transfer chart (EXIT) analysis and computer simulations. The analytical and simulation results demonstrated that the inclusion of the anti-causal soft decision during SICE is critical to the system performance. The EXIT chart analysis shows that the SICE performance approaches the ideal matched filter bound as the iteration progresses.

This paper investigates the linear precoder design for multiple-input multiple-output (MIMO) K-user interference channels with finite alphabet inputs. We first obtain the general explicit expressions of the achievable rate of each user in MIMO interference channel systems. We study optimal transmission strategies in both high signal-to-noise ratio (SNR) and low SNR regions. We show that given finite alphabet inputs, a simple power allocation design can achieve optimal performance. In contrast, the well-known interference alignment technique for Gaussian input scenarios, only utilizes a partial interference-free signal space for transmission and leads to a constant performance loss when it is applied to finite-alphabet input scenarios. We determine this constant rate loss at high SNR. Moreover, we establish necessary conditions for the linear precoder design of the weighted sum-rate maximization. We also develop an efficient iterative algorithm for determining precoding matrices of all the users. Our numerical results show that for the practical digital modulated signals from discrete constellations, the proposed iterative algorithm achieves considerably higher sum-rate than the existing methods.

A low complexity precoding method is proposed for practical multiple‐input multiple‐output (MIMO) orthogonal frequency‐division multiplexing (OFDM) systems. Based on the two‐step optimal precoder design algorithm that maximises the lower bound of the mutual information with finite‐alphabet inputs, the proposed method simplifies the precoder design by fixing the right singular vectors of the precoder matrix, eliminating the iterative optimisation between the two steps, and discretising the search space of the power allocation vector. For a 4 × 4 channel, the computational complexity of the proposed precoder design is reduced to 3 and 6% of that required by the original two‐step algorithm with quadrature phase shift keying (QPSK) and 8 phase‐shift keying ( 8PSK ), respectively. The proposed method achieves nearly the same mutual information as the two‐step iterative algorithm for a large range of signal‐to‐noise ratio (SNR) region, especially for large MIMO size and/or high constellation systems. The proposed precoding design method is applied to a 2 × 2 MIMO‐OFDM system with 2048 subcarriers by designing 1024 precoders for extended channel matrices of size 4 × 4. A transceiver test bed implements these precoding matrices in comparison with other existing precoding schemes. Indoor experiments are conducted for fixed‐platform non‐line‐of‐sight channels, and the data processing results show that the proposed precoding method achieves the lowest bit error rate compared with maximum diversity, classic water‐filling and channel diagonalisation methods.

This paper investigates the linear precoder design for K-user interference channels of multiple-input multiple-output (MIMO) transceivers under finite alphabet inputs. We first obtain general explicit expressions of the achievable rate for users in the MIMO interference channel systems. We study optimal transmission strategies in both low and high signal-to-noise ratio (SNR) regions. Given finite alphabet inputs, we show that a simple power allocation design achieves optimal performance at high SNR whereas the well-known interference alignment technique for Gaussian inputs only utilizes a partial interference-free signal space for transmission and leads to a constant rate loss when applied naively to finite-alphabet inputs. Moreover, we establish necessary conditions for the linear precoder design to achieve weighted sum-rate maximization. We also present an efficient iterative algorithm for determining precoding matrices of all the users. Our numerical results demonstrate that the proposed iterative algorithm achieves considerably higher sum-rate under practical QAM inputs than other known methods.

ABSTRACT A low‐complexity turbo detection scheme is proposed for single‐carrier multiple‐input multiple‐output (MIMO) underwater acoustic (UWA) communications using low‐density parity‐check (LDPC) channel coding. The low complexity of the proposed detection algorithm is achieved in two aspects: first, the frequency‐domain equalization technique is adopted, and it maintains a low complexity irrespective of the highly dispersive UWA channels; second, the computation of the soft equalizer output, in the form of extrinsic log‐likelihood ratio, is performed with an approximating method, which further reduces the complexity. Moreover, attributed to the LDPC decoding, the turbo detection converges within only a few iterations. The proposed turbo detection scheme has been used for processing real‐world data collected in two different undersea trials: WHOI09 and ACOMM09. Experimental results show that it provides robust detection for MIMO UWA communications with different modulations and different symbol rates, at different transmission ranges. Copyright © 2011 John Wiley & Sons, Ltd.

Recent works have established that MIMO systems optimized for Gaussian source signals may suffer unexpected performance loss when practical inputs are in fact discrete QAM sources. There is a practical need in the optimization of MIMO related systems of various networking scenarios to specifically target source signals of finite QAM alphabet. In this work, we investigate the precoding optimization of wireless two-hop non-regenerative three-node MIMO relay networks driven by finite-alphabet inputs. Exploiting a known optimal structure for the precoder at relay and a special convexity property, we propose an iterative two-step numerical optimization algorithm. This algorithm is a general solution, not only for arbitrary source signals but also for cooperative networks with or without direct link. Simulation results demonstrate substantial performance improvement by the new precoder over precoders optimized under the Gaussian input assumption.

We investigate the design of linear transmit precoding for multiple-input multiple-output (MIMO) broadcast channels (BC) with finite alphabet input signals. We derive an explicit expression for the achievable rate region of the MIMO BC with discrete constellation inputs, which is generally applicable to cases involving arbitrary user number and arbitrary antenna configurations. For the case where all the users employ the same modulation scheme, we further present a weighted sum rate upper-bound of the MIMO BC with identical transmit precoding matrices. The resulting bound demonstrates a serious performance loss due to multi-user interference for MIMO BC with finite alphabet inputs in high signal-to-noise ratio (SNR) region, which motivates the use of simple precoding to combat this multiuser interference. Based on a constrained optimization problem formulation, we apply the Karush-Kuhn-Tucker analysis to derive necessary conditions for MIMO BC precoders to maximize the weighted sum-rate. We then propose an iterative gradient descent algorithm with backtracking line search to optimize the linear precoders for each user. Numerical results illustrate that our proposed algorithm provides significant gains over other conventional precoding schemes including the traditional iterative water-filling (WF) design for the Gaussian input assumption.

In this paper, we investigate the secrecy rate of finite alphabet communications over multiple-input, multiple-output, multiple-antenna eavesdropper (MIMOME) systems. Traditional precoder designs at the transmitter for achieving secrecy capacity (maximum secrecy rate) for MIMOME systems are developed according to the assumption of Gaussian input signals. Such designs may risk substantial secrecy rate loss when Gaussian inputs are replaced by practical finite alphabet inputs. To address this issue, we propose a linear precoding design to directly maximize the secrecy rate for MIMOME systems under the constraint of finite alphabet input. Exploiting convex optimization and matrix calculus, we present necessary conditions required of the optimal precoding design and develop an iterative algorithm for finding an efficient precoder. With finite alphabet input signals, maximum transmission power no longer corresponds to maximum secrecy rate as in the case of Gaussian input. We further derive closed-form results on the optimal transmission design for maximizing secrecy rate in low signal-to-noise ratio (SNR) region and near-optimal transmission power in a high SNR region.

This paper investigates the interference-aware linear precoder design with finite-alphabet inputs. It maximizes the mutual information between the transmitter and intended receiver while controlling the interference power caused to unintended receivers. For this nonconcave problem, this work proposes a global optimization approach, which is based on two key observations: 1) the interference-aware precoding problem can be reformulated to the problem minimizing a function with bilinear terms over the intersection of multiple co-centered ellipsoids; 2) these bilinear terms can be relaxed by their convex and concave envelopes. In this way, the global optimal solution is obtained by solving a sequence of relaxed problems over shrinking feasible regions. The proposed algorithm calculates the optimal precoder and the theoretical limit of the transmission rate with interference constraints. Thus, it offers an important benchmark for performance evaluation of interference constrained networks.

This paper investigates the linear precoder design for spectrum sharing in multi-antenna cognitive radio networks with finite-alphabet inputs. It formulates the precoding problem by maximizing the constellation-constrained mutual information between the secondary-user transmitter and secondary-user receiver while controlling the interference power to primary-user receivers. This formulation leads to a nonlinear and nonconvex problem, presenting a major barrier to obtain optimal solutions. This work proposes a global optimization algorithm, namely Branch-and-bound Aided Mutual Information Optimization (BAMIO), that solves the precoding problem with arbitrary prescribed tolerance. The BAMIO algorithm is designed based on two key observations: First, the precoding problem for spectrum sharing can be reformulated to a problem minimizing a function with bilinear terms over the intersection of multiple co-centered ellipsoids. Second, these bilinear terms can be relaxed by its convex and concave envelopes. In this way, a sequence of relaxed problems is solved over a shrinking feasible region until the tolerance is achieved. The BAMIO algorithm calculates the optimal precoder and the theoretical limit of the transmission rate for spectrum sharing scenarios. By tuning the prescribed tolerance of the solution, it provides a trade-off between desirable performance and computational complexity. Numerical examples show that the BAMIO algorithm offers near global optimal solution with only several iterations. They also verify that the large performance gain in mutual information achieved by the BAMIO algorithm also represents the large gain in the coded bit-error rate.

This work investigates the effect of finite-alphabet input constraint on the secrecy rate of a multi-antenna wiretap channel. Most existing works have characterized maximum achievable secrecy rate or secrecy capacity for single and multiple antenna systems based on Gaussian source signals and secrecy code. For practical considerations, we study the effect of finite discrete-constellation on the achievable secrecy rate of multiple-antenna wire-tap channels. Our proposed precoding scheme converts the underlying multi-antenna system into a bank of parallel channels. Based on this precoding strategy, we develop a decentralized power allocation algorithm based on dual decomposition to maximize the achievable secrecy rate. In addition, we analyze the achievable secrecy rate for finite-alphabet inputs in low and high SNR regions. Our results demonstrate substantial difference in secrecy rate between systems given finite-alphabet inputs and systems with Gaussian inputs.

This work investigates the optimization of power allocation for hybrid-ARQ (H-ARQ) retransmissions of non-Gaussian inputs over a bank of independent parallel Gaussian channels. We establish a general solution for maximizing generic transceiver objective utility functions that are monotonically non-decreasing and concave function with respect to the accumulated signal to noise ratio (SNR). Specifically, we investigate optimized solutions under two performance metrics, namely, the mutual information (MI) and the union bound of symbol error rate (UBSER) under maximal ratio combining (MRC) reception. We establish that efficient utilization of parallel channels in H-ARQ retransmissions requires sequential updating of signal-channel pairing as well as optimizing power allocation. Applying geometric analysis of power loading for H-ARQ retransmission, we show that for i.i.d. inputs that are not necessarily Gaussian, the optimum pairing policy should match signals of the lowest cumulative signal-to-noise ratio with channels of the best quality in each transmission, which is consistent with a similar result of , for Gaussian input signals. We further propose a generalized mercury/waterfilling algorithm for the optimal power assignment problem in H-ARQ. Simulation results illustrate substantial improvements over designs based on Gaussian input assumptions.

This paper investigates communication over multiple-input multiple-output Rayleigh-product channels in the presence of both co-channel interference and thermal noise. We first present exact expressions for the marginal ordered eigenvalue distributions of the channel Gram matrix when multichannel beamforming is employed, from which we obtain exact results on the outage probability on each eigenmode. Our results are applicable to an extensive class of multichannel systems with generic system configurations. For particular scenarios of single-input multiple-output, keyhole, and multiple-input single-output channels, simplified closed-form expressions for the asymptotic distributions of the non-zero eigenvalue of the channel Gram matrix are derived. These results indicate that the diversity order is only determined by the second largest value among the number of transmit antennas, scatterers, and receive antennas. For these scenarios, we also derive concise closed-form expressions for the moments of the output signal-to-interference-plus-noise ratio, from which an explicit relationship to the moments in Rayleigh fading channels is revealed. These results are also used to investigate the impact of the number of channel scatterers on the bandwidth requirements for a given transmission rate and power, at low signal-to-noise ratios.

We investigate the design of linear transmit precoder for multiple-input multiple-output (MIMO) broadcast channels (BC) with finite alphabet input signals. We first derive an explicit expression for the achievable rate region of the MIMO BC with discrete constellation inputs, which is generally applicable to cases involving arbitrary user number and arbitrary antenna number. We further present a weighted sum rate upper bound of the MIMO BC with identical transmit precoding matrices. The resulting bound exhibits a serious performance loss because of the non-uniquely decodable transmit signals for MIMO BC with finite alphabet inputs in high signal-to-noise ratio (SNR) region. This performance loss motivates the use of a simple precoding to combat the non-unique decodability. Based on a constrained optimization problem formulation, we apply the Karush-Kuhn-Tucker analysis to derive necessary conditions for MIMO BC precoders to maximize the weighted sum-rate. We then propose an iterative gradient descent algorithm with backtracking line search to optimize the linear precoders for each user. Our { simulation} results under the practical transmit symbols of discrete constellations demonstrate significant gains by the proposed algorithm over other precoding schemes including the traditional iterative water-filling (WF) design for the Gaussian input signals. For the low-density parity-check coded systems, our precoder provides considerably coded BER improvement through iterative decoding and detection.

In this paper, we study linear precoding for multiple-input multiple-output (MIMO) multiple access channels (MAC) with discrete-constellation inputs. We derive the constellation-constrained capacity region for the MIMO MAC with an arbitrary number of users. Due to the non-concavity of the objective function, we obtain the necessary conditions for the weighted sum rate (WSR) maximization problem through Karush-Kuhn-Tucker (KKT) analysis. To find the optimal precoding matrices, we propose an iterative algorithm utilizing alternating optimization strategy and gradient descent update. Numerical results show that when inputs are digital modulated signals and the signal-to-noise ratio (SNR) is in the medium range, our proposed algorithm offers significantly higher sum rate than non-precoding and the traditional method which maximizes Gaussian-input sum capacity. Furthermore, the bit error rate (BER) results of a low-density parity-check (LDPC) coded system also indicate that the system with the proposed linear precoder achieves significant gains over other methods.

This paper studies the eigenvalue distributions of multiple-input multiple-output (MIMO) Rayleigh-product channels in the presence of both co-channel interference and thermal noise. We first present exact expressions for the marginal ordered eigenvalue distributions of the channel Gram matrix when multichannel beamforming is employed, from which we obtain exact results of the outage probability on each eigenmode. Our results apply to a wide class of multichannel systems which transmit on the eigenmodes of the MIMO channel, allowing for transmission on any numbers of eigensubchannels, with any numbers of antennas, any numbers of scatterers in the environment, and any numbers of interferers with arbitrary powers. Also, for the particular case of keyhole channels, simplified closed-form expressions for the asymptotic distributions of the non-zero eigenvalue of the channel Gram matrix are derived, which indicate that the diversity order is only determined by the minimum of the number of transmit and receive antennas.

This paper investigates the linear precoder design that maximizes the average mutual information of multiple-input multiple-output channels with finite-alphabet inputs and statistical channel state information known at the transmitter. This linear precoder design is an important open problem and is extremely difficult to solve: First, average mutual information lacks closed-form expression and involves complicated computations; Second, the optimization problem over precoder is nonconcave. This study explores the solution to this problem and provides the following contributions: 1) A closed-form lower bound of average mutual information is derived. It achieves asymptotic optimality at low and high signal-to-noise ratio regions and, with a constant shift, offers an accurate approximation to the average mutual information; 2) The optimal structure of the precoder is revealed, and a unified two-step iterative algorithm is proposed to solve this problem. Numerical examples show the convergence and the efficacy of the proposed algorithm. Compared to its conventional counterparts, the proposed linear precoding method provides a significant performance gain.

We study the design optimization of linear precoders that maximize the mutual information in complex-valued vector Gaussian channels under finite alphabet inputs. It is well known that mutual information of a vector channel with discrete constellation source is a highly nonlinear and no concave function of the linear precoder matrix G, thereby complicating the precoder design optimization. In this paper, we show that the mutual information is a concave function of W = GhHhHG, where H is the complex-valued channel matrix and superscript "h" represents conjugate transpose. We further propose an iterative algorithm for solving the globally optimal linear precoder G. Illustrative results show that the proposed iterative algorithm is very robust and efficient for global convergence.

We investigate the multiple-input multiple-output broadcast channel with channel distribution information available at the transmitter. The so-called fading-paper model is considered with Nttransmit antennas, and each user having Nrreceive antennas. Near-optimal designs are proposed for the inflation factor matrix under general fading conditions, based on maximizing the approximation of linear assignment capacity. It is proved that for Nt≤ Nr, this matrix has a similar structure and achieves a similar interference elimination effect as dirty-paper coding. Also, low complexity iterative algorithms are proposed for Nt>; Nrcase, which yield a good choice for the inflation factor matrix numerically. Based on the obtained inflation factor matrix, we provide efficient approaches to evaluate the linear assignment achievable rate region for some popular statistical channel models.

In this paper, we investigate the optimal precoding scheme for relay networks with finite-alphabet constraints. We show that the previous work utilizing various design criteria to maximize either the diversity or the transmission rate with the Gaussian inputs assumption may lead to significant loss for a practical system with finite constellation set constraint. A linear precoding scheme is proposed to maximize the transmission rate, i.e., the mutual information, for relay networks. We exploit the structure of the optimal precoding matrix, and develop a unified two-step iterative algorithm utilizing the theory of convex optimization and optimization on the complex Stiefel manifold. Numerical examples show that this novel iterative algorithm achieves significant gains compared to its conventional counterpart.

Many communication systems today encounter the problem of data transmission over a channel with inter-symbol interference (ISI). The purpose of this paper is to develop a low-complexity, iterative soft-decision feedback equalization (SDFE) receiver for severe, frequency selective ISI channels. The proposed SDFE algorithm offers a novel approach to combat error propagation. In addition, its computational complexity grows only linearly with the number of equalizer coefficients, compared to the quadratic complexity of minimum mean square error-based linear turbo equalizer with time-varying coefficients. Performance of the proposed detection scheme is verified through simulations using different signal constellations. Simulation results show that our proposed algorithm has a significant improvement over the low complexity linear turbo equalizer. Moreover, we show that the performance of the proposed equalization scheme improves significantly when higher order constellations are used for digital modulation.

In this paper, we study linear precoding for multiple-input multiple-output (MIMO) multiple access channels (MAC) with finite discrete inputs. We derive the constellation-constrained capacity region for the MIMO MAC with an arbitrary number of users and find that the boundary can be achieved by solving the problem of weighted sum rate maximization with constellation and individual power constraints. Due to the non-concavity of the objective function, we obtain a set of necessary conditions for the optimization problem through Karush-Kuhn-Tucker analysis. To find the optimal precoding matrices for all users, we propose an iterative algorithm utilizing alternating optimization strategy. In particular, each iteration of the algorithm involves the gradient descent update with backtracking line search. Numerical results show that when inputs are digital modulated signals and the signal-to-noise ratio is in the medium range, our proposed algorithm offers considerably higher sum rate than non-precoding and the traditional method which maximizes Gaussian-input sum capacity. Furthermore, a low-density parity-check coded system with iterative detection and decoding for MAC is presented to evaluate the bit error rate (BER) performance of precoders. BER results also indicate that the system with the proposed linear precoder achieves significant gains over the non-precoding system and the precoder designed for Gaussian inputs.

In this paper, we investigate the optimal power allocation scheme for relay networks with finite-alphabet constraints. It has been shown that the previous work utilizing various design criteria with the Gaussian inputs assumption may lead to significant loss for a practical system with finite constellation set constraint, especially when signal-to-noise ratio (SNR) is in medium-to-high regions, or when the channel coding rate is medium to high. An optimal power allocation scheme is proposed to maximize the mutual information for the relay networks under discrete-constellation input constraint. Numerical examples show that significant gain can be obtained compared to the conventional counterpart for nonfading channels and fading channels. At the same time, we show that the large performance gain on the mutual information will also represent the large gain on the bit-error rate (BER), i.e., the benefit of the power allocation scheme predicted by the mutual information can indeed be harvested and can provide considerable performance gain in a practical system.

In this paper, we investigate the relaying scheme for multi-antenna cooperative networks without channel state information at the transmitters. It is shown that the classic opportunistic relaying scheme, which allows only one relay node to forward the message, may lead to significant loss when it is extended to the corresponding multi-antenna relay scenarios. A generalized opportunistic relaying approach, which selects more transmit antennas distributed on multiple relay nodes to transmit data simultaneously, is proposed to maximize the network throughput via balancing the source-relay and the relay-destination channels. Numerical examples show the large impact of multiple antennas and relays on the network throughput, and the significant gains obtained through the proposed opportunistic cooperation scheme.

We propose an enhanced linear minimum mean square error (LMMSE) turbo equalization scheme for multiple-input multiple-output (MIMO) communication systems. The turbo equalizer employs soft interference cancellation (SIC), where tentative soft decisions of the interfering symbols are subtracted from the received samples before the LMMSE filtering. The enhanced LMMSE turbo equalization with SIC introduces two improvements over existing methods. First, unlike existing methods that completely rely on the a priori soft decisions at the equalizer input for SIC, the new scheme performs SIC by continuously updating the soft decisions with the a posteriori information of the symbols that have just been equalized. The a posteriori soft decision has a better quality than the a priori soft decision, thus it leads to a better SIC performance. Second, since the a posteriori soft decision of an equalized symbol will affect the SIC operation of all the subsequent symbols to be equalized, the order in which the symbols are equalized and detected plays a critical role on the overall performance. We propose a reliability-based detection ordering scheme, where symbols with more "reliable" soft input will be equalized before those less "reliable" symbols. The reliability information is extracted from the symbol a priori probability, which is a unique byproduct of turbo equalization and can be obtained with minimum extra cost. Simulation results demonstrate that the proposed scheme achieves considerable performance gain over the conventional turbo equalization methods.

It is a great honor and huge responsibility to serve as the new Editor-in-Chief of IEEE Transactions on Wireless Communications (TWireless). Since its inception in 2002, TWireless has undergone phenomenal growth, both in terms of size and prestige. It has become one of the most prestigious journals in the communications area. It received 576 submissions in 2002 when the journal published its first volume. The submission number grew to 1626 manuscripts in 2008 and reached 1827 manuscripts as of December 18, 2009. Its current acceptance rate is below 30%, and its current citation index (or impact factor, which is an important measure in the ranking of journals) is 2.18, which is higher than nearly all other journals that publish papers in the communications area.

A low-complexity, near-optimal transmit antenna selection algorithm is proposed for multi-relay networks where all nodes are equipped with multiple antennas. We first establish a system model and a unified capacity maximization framework for a two-hop opportunistic relaying scheme where the source node (S) transmits signals to multiple relay nodes (R) in the first time slot, and the selected relay antennas and their corresponding relay nodes receive, decode and forward the messages to the destination (D) in the second time slot. Based on the system model, we develop a transmit antenna selection algorithm that maximizes the network capacity assuming that the channel state information is available at the receivers but not available at the transmitters, and total transmit power constraints are imposed on source/relay transmitters. The proposed algorithm first constructs a sorted list of relay antennas with decreasing S-R capacities, then iteratively maximizes the R-D capacity over a candidate antenna set using a low-complexity, near-optimal antenna selection scheme. The candidate set is reduced in the next iteration according to the selected antenna set of the current iteration. The overall network capacity is computed for the selected antenna sets of all iterations, and the set yielding the highest S-R-D capacity is the solution to the maximization problem. We show that this novel iterative algorithm achieves near-optimal solution and has a polynomial-time complexity. We also derive the lower and upper bounds of the achievable network capacity for both average capacity and outage capacity. Numerical examples show the significant performance gains obtained via the proposed scheme compared to its conventional counterparts.

In this paper, we consider the transmit linear precoding problem for MIMO systems with discrete-constellation inputs. We assume that the receiver has perfect channel state information (CSI) and the transmitter only has partial CSI, namely, the channel covariance information. We first consider MIMO systems over frequency-flat fading channels. We design the optimal linear precoder based on direct maximization of mutual information over the MIMO channels with discrete-constellation inputs. It turns out that the optimal linear precoder is a non-diagonal non-unitary matrix. Then, we consider MIMO systems over frequency selective fading channels via extending our method to MIMO-OFDM systems. To keep reasonable computational complexity of solving the linear precoding matrix, we propose a sub-optimal approach to restrict the precoding matrix as a block-diagonal matrix. This approach has near-optimal performance when we integrate it with a properly chosen interleaver. Numerical examples show that for MIMO systems over frequency flat fading channels, our proposed optimal linear precoder enjoys 6-9 dB gain compared to the same system without linear precoder. For MIMO-OFDM systems, our reduced-complexity sub-optimal linear precoder captures 3-6 dB gain compared to the same system with no precoding. Moreover, for those MIMO systems employing a linear precoder designed based on Gaussian inputs with gap approximation technique for discrete-constellation inputs, significant loss may occur when the signal-to-noise ratio is larger than 0 dB.

In this paper, a new algorithm is proposed to estimate mobile speed for broadband wireless communications, which often encounter large number of fading channel taps causing severe intersymbol interference. Different from existing algorithms, which commonly assume that the fading channel coefficients are available for the speed estimators, the proposed algorithm is based on the received signals which contain unknown transmitted data, unknown frequency selective fading channel coefficients possibly including line-of-sight (LOS) components, and random receiver noise. Theoretical analysis is first carried out from the received signals, and a practical algorithm is proposed based on the analytical results. The algorithm employs a modified normalized auto-covariance of received signal power to estimate the speed of mobiles. The algorithm works well for frequency selective Rayleigh and Rician channels. The algorithm is very resistant to noise, it provides accurate speed estimation even if the signal-to-noise ratio (SNR) is as low as 0 dB. Simulation results indicate that the new algorithm is very reliable and effective to estimate mobile speed corresponding to a maximum Doppler up to 500 Hz. The algorithm has high computational efficiency and low estimation latency, with results being available within one second after communication is established.

In this paper, the mutual information and power allocation are discussed for vector Gaussian channels with finite discrete inputs. It is shown that the classic waterfilling and mercury-waterfilling policies, which are allocating power to a bank of independent parallel channels, may lead to significant loss compared to the original system without power allocation for finite discrete inputs. A generalized linear precoder, which is a non-diagonal and non-unitary matrix, is proposed for cross-channel power allocation to maximize the mutual information for vector channels. Numerical examples show that the new precoding-based power allocation provides significant gain for a broad region of signal-to-noise ratios.

Channel estimation for orthogonal frequency division multiplexing (OFDM) system at the presence of carrier frequency offset (CFO) and phase noise is discussed in this paper. A CFO estimation algorithm is developed by exploiting the time-frequency structure of training symbols, and it provides a very accurate estimation of CFO at the presence of both unknown frequency selective fading and phase noise. Based on the estimated CFO, the phase noise and frequency selective fading are jointly estimated by employing the maximum a posteriori (MAP) criterion. Specifically, the fading channel is estimated in the form of frequency domain channel transfer function (CTF). The estimation of CTF eliminates the requirement of the priori knowledge of channel length, and it is simpler compared to the time domain channel impulse response (CIR) estimation method in the literature. Theoretical analysis with Cramer-Rao lower bound demonstrates that the joint phase noise and CTF estimation can achieve near optimum performance.

We consider the frequency-domain channel equalization and symbol detection of multiple input multiple output (MIMO) single-carrier broadband wireless system in the presence of severe frequency-selective channel fading and multiple unknown carrier frequency offsets (CFOs). We show that the constellation of the equalized data is rotating due to multiple CFOs, therefore, the equalized data can not be reliably detected without removing the rotating phases caused by the multiple unknown CFOs. Instead of estimating the CFOs, we propose a method to estimate the rotating phases caused by multiple CFOs, remove the rotating phases from the equalized data, and perform symbol detection. Numerical example indicates that the proposed method provide very good results for a 4 times 2 wireless system with 8PSK modulation and 75-tap Rayleigh fading channels.

Optimal receiver diversity combining employing linear channel estimation is examined. Based on the statistical properties of least-squares (LS) and minimum mean square error (MMSE) channel estimation, an optimal diversity receiver for wireless systems employing practical linear channel estimation on Rician fading channels is proposed. The new receiver structure includes the conventional maximal ratio combining receiver as a special case. Exact analytical expressions for the symbol error rates (SERs) of LS and MMSE channel estimation aided optimal diversity combining are derived. It is shown that, if an optimal detector is used, an MPSK wireless system with MMSE channel estimation has the same SER when the MMSE channel estimation is replaced by LS estimation. This is an interesting counterexample to the common perception that channel estimation with smaller mean square error leads to smaller SER. Extensive simulation results validate the theoretical results.

We discuss recent results on discrete-time models for triply-selective multiple-input multiple-output (MIMO) Rayleigh fading channels. Our key finding is that a previously proposed model (Xiao et al., 2004), which allows for efficient computer simulations, is sufficiently accurate for a wide range of practical scenarios.

Turbo equalization improves communication system performance by iteratively exchanging information between soft-input soft-output (SISO) equalizer and SISO channel decoder. The trellis-based maximum a posteriori probability (MAP) algorithm serves as the optimum SISO equalizer for turbo equalization. However, MAP algorithm is unsuitable for systems with large modulation constellation size and severe inter-symbol interference (ISI) due to its prohibitively high computational complexity. In this paper, an improved SISO block decision feedback equalizer (BDFE) is proposed for low complexity turbo equalization. Unlike other sub-optimum equalizers which perform symbol by symbol detection, the proposed equalizer generates the soft output for each data bit by collecting information from a sequence of samples as in MAP algorithm. The sequence-based equalization is enabled by using not only soft a priori input from channel decoder, but also hard a priori information obtained from BDFE in previous iteration. The combination of soft a priori information and hard a priori information renders better performance with less iterations compared to other sub-optimum algorithms. In addition, the computational complexity of the proposed algorithm is on the same order as conventional SISO BDFE algorithm, and is much lower compared to the trellis-based MAP algorithm.

The ergodic capacity is investigated for triply selective MIMO Rayleigh fading channels. A mathematical formula is derived for the ergodic capacity in the case when the channel state information is known to the receiver but unknown to the transmitter. A closed-form formula is derived that quantifies the effect of the frequency-selective fading on the ergodic capacity into an intersymbol interference (ISI) degradation factor. Different from the existing conclusion that the frequency-selective fading channel has the same ergodic capacity as the frequency flat fading channel, we show that the discrete-time inter-tap correlated frequency-selective fading channel has smaller ergodic capacity than the frequency flat fading channel. Only in the special case when the fading does not have ISI inter-tap correlations will the ergodic capacity be the same as that of the frequency flat channel. Theoretical derivation and computer simulation demonstrate that the inter-tap correlations can have more significant impact on the ergodic capacity than the spatial correlations.

In this paper, we present a new Doppler spread estimation algorithm for broadband wireless orthogonal frequency division multiplexing (OFDM) systems with time-varying and frequency-selective Rayleigh fading. The algorithm is developed by analyzing the statistical properties of the power of received signals in the time domain, thus it excludes the influence of inter- carrier interference introduced by channel variation within one OFDM symbol. The operation of the algorithm doesn't require the knowledge of fading coefficients, transmitted data symbols, or signal-to-noise ratio (SNR). It works well under time-selective and frequency-selective Rayleigh fading channel with SNR as low as 0 dB. Moreover, unlike existing algorithms, the proposed algorithm takes into considerations of the discrete-time channel inter-tap correlation, as the case in practical systems. Simulation results demonstrate that this new algorithm can accurately estimate a wide range of Doppler spread with low estimation latency and high computational efficiency.

Optimal receiver diversity combining employing linear channel estimation is examined. Based on the statistical properties of pilot-assisted least-squares (LS) and minimum mean square error (MMSE) channel estimation, an optimal diversity receiver for wireless systems employing practical linear channel estimation on Rician fading channels is proposed. Exact analytical expressions for the symbol error rates of LS and MMSE channel estimation aided optimal diversity combining are derived. It is shown that an MPSK wireless system with MMSE channel estimation has the same SER when the MMSE channel estimation is replaced by LS estimation. This is an interesting counter-example to the common perception that channel estimation with smaller mean square error leads to smaller SER. Extensive simulation results validate the theoretical results.

Frequency-domain equalization (FDE) is an effective technique for high data rate wireless communication systems suffering from very long intersymbol interference. Most of existing FDE algorithms are limited to quasi-static or slow time-varying fading channels, where least mean squares (LMS) or recursive least squares (RLS) adaptive algorithms were utilized for channel estimation. In this paper, we employ interpolation method to develop channel estimation algorithm in the frequency domain. We show that the new channel estimation algorithm can significantly outperform LMS and RLS algorithms. Numerical examples demonstrate that the new algorithm can track time-varying fading channels with Doppler up to 300-400 Hz. This means, for 1.9 GHz carrier frequency band, the new algorithm can provide good bit error rate performance even if the mobile is moving at a high speed of 170-228 kilo-meters per hour, while the fading channel impulse response is 60 taps long.

In this paper, a new algorithm is proposed to estimate mobile speed for broadband wireless communications, which often encounter large number of fading channel taps causing severe intersymbol interference. Theoretical analysis is first derived and practical algorithm is proposed based on the analytical results. The algorithm employs a modified auto-covariance of received signal power to estimate the speed of mobiles. The algorithm is based on the received signals which contain unknown transmitted data, unknown frequency selective multipaths possibly including line-of-sight (LOS) component, and random receiver noise. The algorithm works well for frequency selective Rayleigh and Rician channels. The algorithm is very resistant to noise, it provides accurate speed estimation even if the signal-to-noise (SNR) is as low as 0dB. Simulation results indicate that the new algorithm is very reliable and effective to estimation mobile speed corresponding maximum Doppler up to 500Hz. The algorithm has high computational efficiency and low estimation latency, with results being available within one second after communication is established.

The theoretical error performance of double space time transmit diversity (DSTTD) system with optimum combining receiver is analyzed in this paper. By employing both spatial multiplexing and transmit diversity in one system, DSTTD provides practical tradeoff between system spectral efficiency and diversity gain. We derive exact analytical expressions to describe the symbol error rate for DSTTD systems. The effects of both diversity gain and antenna interference introduced by spatial multiplexing are quantified in the results. In addition, the performance of DSTTD system with successive interference cancellation is also investigated. Simulation results are in excellent agreement with the theoretical results obtained in this paper.

Receiver timing phase is one of the essential factors defining the performance of wireless communication systems. In this paper, we investigate the effects of timing phase offset, which is introduced by the phase difference between the transmitter clock and receiver clock, on the performance of wireless systems over frequency selective fading. With frequency domain analysis, the instantaneous signal-to-noise ratio (SNR) observed by the communication receiver is expressed as an explicit function of system timing phase offset and receiver oversampling factor. A tight performance lower bound, which corresponds to the best possible system performance under particular system configuration, is then derived by examining the statistical properties of the receiver SNR. From the analytical results, it is observed that, if the receiver sampling rate is less than the Nyquist rate of the received signal, then the system performance lower bound is a periodic function of the timing phase offset. On the other hand, the best possible performance of the oversampled system is independent of timing phase offset. Moreover, the oversampled system can use a receive filter matched to the time-invariant transmit filter instead of a statistical filter matched to the joint response of channel and transmit filter without affecting the best possible system performance. Simulation results show that the theoretical bound derived in this paper can accurately predict the performance of practical communication systems suffering from both frequency selective fading and timing phase offset

In this paper, a new algorithm is proposed for estimating mobile speed of cellular systems over frequency selective Rician fading channels. Theoretical analysis is first derived and practical algorithm is proposed based on the analytical results. The algorithm employs a modified auto-covariance of received signal power to estimate the speed of mobiles. The algorithm is based on the received signals which contain unknown transmitted data, unknown frequency selective multipaths including line- of-sight (LOS) component, and random receiver noise. The algorithm works very well for frequency selective Rician fading channels with large ranges of Rice factor and angle of arrival of the LOS component. Simulation results indicate that the new algorithm is very reliable and effective to distinguish slow speed and fast speed mobiles. The algorithm is computationally efficient. It only requires simple arithmetic operations such as multiplications, additions and subtractions.

In this paper, we consider the serial concatenation of linear time-varying (LTV) systems and its impact on the discrete-time modeling of wide-sense stationary uncorrelated scattering (WSSUS) fading channels. By deriving an expression for the composite impulse response of the overall concatenated system, we find that unlike the time-invariant case, the concatenation of LTV systems is not commutative, i.e., the order of arrangement affects the overall impulse response. This has significant impact when a digital transmission over a time-varying fading channel, which is an LTV channel, is represented by an equivalent discrete-time model that incorporates both transmitter and receiver filters. We further show that if the maximum Doppler frequency is much smaller than the system bandwidth, the concatenation of LTV systems is approximately commutative, then a convenient and efficient representation in the discrete-time domain for WSSUS fading channels is obtainable.

The statistical properties of Clarke's fading model with a finite number of sinusoids are analyzed, and an improved reference model is proposed for the simulation of Rayleigh fading channels. A novel statistical simulation model for Rician fading channels is examined. The new Rician fading simulation model employs a zero-mean stochastic sinusoid as the specular (line-of-sight) component, in contrast to existing Rician fading simulators that utilize a non-zero deterministic specular component. The statistical properties of the proposed Rician fading simulation model are analyzed in detail. It is shown that the probability density function of the Rician fading phase is not only independent of time but also uniformly distributed over [-pi, pi). This property is different from that of existing Rician fading simulators. The statistical properties of the new simulators are confirmed by extensive simulation results, showing good agreement with theoretical analysis in all cases. An explicit formula for the level-crossing rate is derived for general Rician fading when the specular component has non-zero Doppler frequency

The sampler timing (phase) sensitivity of wireless communication systems is discussed in this paper. Based on the matched filter bound technique, a tight error performance bound is derived for systems experiencing frequency selective Rayleigh fading, with the receiver timing offset being quantified in the error performance expressions. With the error performance bound, the timing phase sensitivity of systems with both symbol spaced receivers and fractionally spaced receivers is analyzed. Simulation results show that the new bound can accurately predict the performance of practical communication systems suffering both frequency selective fading and timing phase offset

An adaptive space time transmit diversity scheme with simple feedback is proposed for the next generation wireless communication systems. By combining orthogonal space time block codes with adaptive sub-group antenna encoding, this new diversity scheme can effectively exploit the diversity potential provided by multiple antenna arrays without introducing interference among the signals transmitted at different antennas. In order to reduce the amount of feedback information as well as the computational complexity, a new quadrant phase constraining method is introduced for the computation of the feedback information. With simple operations at both the transmitter and the receiver, the new adaptive diversity scheme outperforms not only open loop space time block encoding techniques, but also some closed loop transmit diversity techniques with the same amount of feedback.

Theoretical error performances of communication systems with doubly selective (time-varying and frequency-selective) fadings and fractionally spaced (oversampled) receivers are analyzed. Closed-form error probability expressions of MPSK, MASK and MQAM systems are derived as tight lower bounds of the symbol error probabilities. The effects of receiver oversampling, Doppler spread and fading power delay profile are quantified in the error probability expressions. Simulation results show that the new analytical results can accurately predict the error performances of MLSE and MAP equalizers in a wide range of SNR. Moreover, it is discovered that significant performance gain can be achieved by fractionally spaced receivers over symbol spaced receivers for systems experiencing fast time-varying fading, whereas the effects of Doppler spread are overlooked by most previous works.

New results are presented for the ergodic capacity of spatially-correlated, time-varying and frequency-selective (i.e., triply selective) MIMO Rayleigh fading channels. Simplified capacity formulas are also derived for special cases such as SIMO and MISO triply selective fading channels. A closed form formula is proposed that quantifies the effect of the frequency-selective fading on the ergodic capacity into an intersymbol interference (ISI) degradation factor. It is discovered that, in general frequency-selective MIMO channels, the ISI inter-tap correlations reduce the ergodic capacity compared to the frequency flat fading channel. Only in the special case when the fading does not have ISI inter-tap correlations will the ergodic capacity be the same as that of the frequency flat channel. The new capacity results are experimentally verified via Monte-Carlo simulations.

The performances of coherent diversity receivers with noisy channel estimation are examined. Fading channel gain estimates are modeled as sums of the true fading channel gain values plus independent Gaussian distributed estimation errors. The optimal diversity receiver for coherent reception with noisy channel state information and independent and identically distributed fading channels is derived. Exact expressions for the average error probability of optimal diversity MPSK with noisy channel estimation are derived for Rayleigh and Ricean fading channels; closed-form expressions are obtained for some special cases. Some interesting observations regarding practical diversity receiver design for higher-order modulation formats are drawn.

An adaptive transmit diversity scheme with quadrant phase constraining feedback is proposed in this paper. With simple linear operations at both transmitter and receiver, the proposed algorithm can achieve better system performances with only 2M-2 bits of feedback information for systems with M transmit antennas. Theoretical performance bounds of the proposed transmit diversity scheme are derived. Simulation examples and theoretical analyses show that the proposed transmit diversity scheme outperforms not only the conventional open-loop transmit diversity techniques, but also some closed-loop transmit diversity techniques with more information transmitted in the feedback channel.

Space-time correlation functions between the links of MIMO Rayleigh fading channels are derived using a new three-dimensional (3-D) cylinder scattering model. Closed form, mathematically tractable formulas are obtained for the space-time correlation functions for general MIMO systems where the base station and mobile station antennas may be arranged in 3-D space. It is shown that the correlation functions computed by the 3-D cylinder model are of significant difference than those of the conventional 2-D Clarke's isotropic scattering model for vertically placed antennas. The general formulas of the correlation functions includes the 2-D Clarke's model and the 3-D SIMO, MISO models as special cases.

The ergodic capacity is investigated for doubly selective (frequency selective and time varying) MIMO Rayleigh fading channels. A closed form formula is derived that quantifies the effect of the ISI fading on the ergodic capacity into an ISI degradation factor. It is discovered that, in general frequency selective MIMO channels, the inter-tap correlations of the ISI fading will reduce the ergodic capacity comparing to the frequency flat fading channel. Only in the special case when the ISI fading does not have inter-tap correlations will the ergodic capacity be the same as that of the frequency flat channel. This new formula is mathematically proved and experimentally verified via Monte-Carlo simulations.

A statistical discrete-time model is proposed for simulating wideband multiple-input multiple-output (MIMO) fading channels which are triply selective due to angle spread, Doppler spread, and delay spread. The new discrete-time MIMO channel model includes the combined effects of the transmit filter, physical MIMO multipath channel fading, and receive filter, and it has the same sampling period as that of the MIMO receiver. This leads to very efficient simulation of physical continuous-time MIMO channels. A new method is also presented to efficiently generate the MIMO channel stochastic coefficients. The statistical accuracy of the discrete-time MIMO channel model is rigorously verified through theoretical analysis and extensive simulations in different conditions. The high computational efficiency of the discrete-time MIMO channel model is illustrated by comparing it to that of the continuous-time MIMO channel model. The new model is further employed to evaluate the channel capacity of MIMO systems in a triply selective Rayleigh fading environment. The simulation results reveal some interesting effects of spatial correlations, multipaths, and number of antennas on the MIMO channel capacity.

The channel estimation and equalization for EDGE system with time-varying and frequency-selective fading channels are discussed. It is shown that the fast fading channel during a selected slot in the EDGE system can be modeled as a linear function of time, and a linear least-squares algorithm is proposed to estimate the fading channel. For typical channel profiles of the EDGE system, the channel impulse response is not in its minimum phase form, thus cannot be directly used in computationally efficient equalizers, such as delayed decision feedback sequence estimation or reduced state sequence estimation. To overcome this problem, a Cholesky decomposition-based method is introduced to transform the estimated channel impulse response into its minimum phase form. The simulation results show that the proposed algorithms can effectively combat the time-varying and frequency-selective channel fading with Doppler frequency being in a wide range up to 300 Hz.

In this paper, an accurate and computationally efficient algorithm is proposed for estimating a time-varying and frequency-selective fading channel with unequally spaced pilot symbols. By employing the time-varying coefficient polynomial interpolation method, it is proved that the time-varying channel impulse response can be estimated by the product of a constant interpolation matrix and the fading information at pilot symbol positions. Furthermore, a least square off-line training algorithm is presented to optimally calculate the constant matrix, taking into consideration the statistics of channel fading and noise. Simulation results indicate that the bit error rate performance of our new estimation algorithm is close to that of the perfect channel estimation.

New simulation models are proposed for Rayleigh and Rician fading channels. First, the statistical properties of Clarke's fading model with a finite number of sinusoids are analyzed. An improved Clarke's model is then proposed for the simulation of Rayleigh fading channels. Based on this improved Rayleigh fading model, a novel simulation model is proposed for Rician fading channels. The new Rician fading model employs a zero-mean stochastic sinusoid as the specular (line-of-sight) component, in contrast to all existing Rician fading simulators that utilize a non-zero mean deterministic specular component. The statistical properties of the proposed Rician fading model are analyzed in detail. It is shown that the probability density function of the Rician fading phase is not only independent of time but also uniformly distributed over (-/spl pi/, /spl pi/). This property is different from that of existing Rician fading models. The statistical properties of the new simulators are confirmed by extensive simulation results, finding good agreement with theoretical analysis in all cases. An explicit formula for the level crossing rate is derived for general Rician fading when the specular component has non-zero Doppler frequency.

In this paper, a statistical discrete-time model is proposed for simulating wideband MIMO channels which experience spatially and temporally correlated, widesense stationary uncorrelated scattering (WSSUS) multipath Rayleigh fading. A new method is also presented to efficiently generate the correlated MIMO channel coefficients, which can be used for accurate simulation of physical continuous-time MIMO channel. The statistic accuracy of the discrete-time MIMO channel model is rigorously verified through theoretical analysis and extensive simulations in different criteria.

Recently, a Clarke's model-based simulator was proposed for Rayleigh fading channels. However, that model, as shown in this paper, may encounter statistic deficiency. Therefore, an improved model is presented to remove the statistic deficiency. Furthermore, a new simulation model is proposed for Rician fading channels. This Rician fading simulator with finite number of sinusoids plus a zero-mean stochastic sinusoid as the specular (line-of-sight) component is different from all the existing Rician fading simulators, which have non-zero mean deterministic specular component. The statistical properties of the proposed Rayleigh and Rician fading channel models are analyzed in detail, which shows that these statistics either exactly match or quickly converge to the theoretically desired ones. Additionally and importantly, the probability density function of the Rician fading phase is not only independent from time but also uniformly distributed, which is fundamentally different from that of all the existing Rician fading models. The statistical properties of the new simulators are evaluated by numerical results, finding good agreement in all cases.

In this paper, new sum-of-sinusoids statistical simulation models are proposed for Rayleigh fading channels. These new models employ random path gain, random initial phase, and conditional random Doppler frequency for all individual sinusoids. It is shown that the autocorrelations and cross correlations of the quadrature components, and the autocorrelation of the complex envelope of the new simulators match the desired ones exactly, even if the number of sinusoids is as small as a single-digit integer. Moreover, the probability density functions of the envelope and phase, the level crossing rate, the average fade duration, and the autocorrelation of the squared fading envelope which contains fourth-order statistics of the new simulators, asymptotically approach the correct ones as the number of sinusoids approaches infinity, while good convergence is achieved even when the number of sinusoids is as small as eight. The new simulators can be directly used to generate multiple uncorrelated fading waveforms for frequency selective fading channels, multiple-input multiple-output channels, and diversity combining scenarios. Statistical properties of one of the new simulators are evaluated by numerical results, finding good agreements.

A new algorithm is modified and applied for estimating mobile velocity for EDGE (enhanced data rates for GSM evolution) cellular systems. The algorithm uses normalized autocorrelation of filtered received signals to estimate the velocity of EDGE mobiles. The algorithm works well for both non-dispersive channels and dispersive channels including typical urban and hilly terrain propagation models. Simulation results indicate that the new algorithm is very reliable and effective for distinguishing fast and slow moving mobiles in EDGE cellular systems with both 900 MHz and 1900 MHz carrier frequencies.

A new sum-of-sinusoids statistical simulation model is proposed for Rayleigh fading channels. The new model employs random path gain, random initial phase, and conditional random Doppler frequency for all individual sinusoids. It is shown that the autocorrelations and cross-correlations of the quadrature components, the autocorrelation of the complex envelope of the new simulator match the desired ones exactly even if the number of sinusoids is as small as a single-digit integer Furthermore, the probability density functions of the fading envelope and phase, the level crossing rate and the average fade duration of the new simulator asymptotically approach the desired ones as the number of sinusoids approaches infinity, while good convergence is achieved when the number of sinusoids is small. Statistical properties of the new simulator are evaluated by numerical results, finding good agreement in all cases.

An improved Jakes' fading channel simulator was proposed by Pop and Beaulieu (2001) to eliminate the stationarity problem occurring in Jakes' original design. In this paper second-order statistical properties of the improved Jakes' simulator are analyzed. Consistent with Pop and Beaulieu's caution about high-order statistics of the simulator it is proved that some second-order statistics of both the quadrature components and the envelope do not match the desired ones even if the number of sinusoids approaches infinity. Therefore, care must be taken when the simulator is employed to evaluate algorithms and systems.

We provide simple analytical results for the coefficients of a finite-impulse response (FIR) prefilter and the effective channel impulse response (IR) for use in cellular communication systems. We show that using a FIR filter with both causal and anticausal filter taps, it is possible to find the jointly optimized impulse response, such that the signal-to-noise ratio is maximized in the least-squares sense. We show via computer simulation for 8-ary phase-shift keying in Enhanced Data rates for Global Evolution (EDGE) that the joint optimization of the prefilter and IR produces results similar to the minimum mean-square error decision-feedback equalizer prefilter in thermal noise, but yields gain in colored noise.

An improved Jakes' (1994) fading channel simulator was proposed by Pop and Beaulieu (see ibid., vol.49, p.699-708, Apr. 2001) to eliminate the stationarity problem occurring in Jakes' original design. In this paper, second-order statistical properties of the improved Jakes' simulator are analyzed. Consistent with Pop and Beaulieu's caution about high-order statistics of the simulator, it is proved that some second-order statistics of both the quadrature components and the envelope do not match the desired ones even if the number of sinusoids approaches infinity. Therefore, care must be taken when the simulator is employed to evaluate algorithms and systems.

A new method for designing IIR digital filters with linear phase in the passband is proposed. This method is based on frequency-weighted least-square error optimization using the Broyden-Fletcher-Goldfarb-Shanno (BFGS) method. The gradient of the cost function with respect to the design parameters, required for the implementation of the BFGS method, is derived. The proposed method is started by obtaining an initial IIR filter design using model reduction of a linear phase FIR filter. Based on this initial design the cost function is minimized using the BFGS method. An example shows that the proposed method leads to very good filter designs.

The discrete-time bounded-real lemma is further developed for nonminimal digital systems. Based on this lemma, rigorous necessary and sufficient conditions for the existence of positive definite solutions to the Lyapunov equation for n-dimensional (n-D) digital systems are proposed. These new conditions are improvements and extensions of earlier conditions and can be applied to n-D digital systems with characteristic polynomials involving 1-D factor polynomials. Further, the results in this paper show that the positive definite solutions to the n-D Lyapunov equation of a n-D system with characteristic polynomial involving 1-D factors can be obtained from the solutions of a k-D (0/spl les/k/spl les/n) subsystem and m(1/spl les/m/spl les/n) 1-D subsystems. This could significantly simplify the complexity of solving the n-D Lyapunov equation for such cases.