This paper applies the Orthogonal Time-Frequency Space (OTFS) modulation to underwater mobile acoustic communications where the communication channel suffers from severe multipath and Doppler effects simultaneously. Field experiments have been conducted with acoustic transmission at a center frequency of 115 kHz and a data rate of 11.5 kilosymbols per second. We propose a new Turbo Decision Feedback Equalizer and Decoder (TDFED) for the receiver and the experimental results demonstrate the superior performance of the proposed TDFED algorithm over existing MMSE equalizers.

This paper proposes a hardware implementation of a Successive Interference Cancellation (SIC) scheme in a Turbo Equalizer for very long multipath fading channels where the Intersymbol-interference (ISI) channel length L is on the order of 100 taps. To reduce the computational complexity caused by large matrix arithmetic in the SIC, we explore the data dependencies and convolutional nature of the SIC algorithm and propose an FPGA acceleration architecture by taking advantage of the high degree of parallelism and the flexible data movements offered by FPGA. Instead of reconstructing interference in symbol-wise by matrix and vector multiplication directly for each symbol in a block, we propose a two-stage processing algorithm. The first stage is block-wise processing, where the convolution of the channel impulse response (CIR) vector and the vector consisting of the whole symbol block is computed. The second stage is symbol-wise processing but turns to the multiplication of one symbol and the CIR vector. The result shows that for a block of Nblk symbols and a channel of length L, the proposed architecture completes the SIC within 2Nblk+L clock cycles, while direct matrix multiplication requires L×Nblk clock cycles. Implemented on a Xilinx Zynq UltraScale+ MPSoC ZCU104 Evaluation Kit, the SIC and equalization in one turbo iteration based on this architecture is completed around 40 us for a 1024 symbol block and a channel length of L=100. This architecture achieves around 40× speed-up compared with the implementation on a powerful CPU platform.

This article proposes a novel deep-reinforcement learning-based medium access control (DL-MAC) protocol for underwater acoustic networks (UANs) where one agent node employing the proposed DL-MAC protocol coexists with other nodes employing traditional protocols, such as time division multiple access (TDMA) or q -Aloha. The DL-MAC agent learns to exploit the large propagation delays inherent in underwater acoustic communications to improve system throughput by either a synchronous or an asynchronous transmission mode. In the sync-DL-MAC protocol, the agent action space is transmission or no transmission, while in the async-DL-MAC, the agent can also vary the start time in each transmission time slot to further exploit the spatiotemporal uncertainty of the UANs. The deep Q -learning algorithm is applied to both sync-DL-MAC and async-DL-MAC agents to learn the optimal policies. A theoretical analysis and computer simulations demonstrate the performance gain obtained by both DL-MAC protocols. The async-DL-MAC protocol outperforms the sync-DL-MAC protocol significantly in sum throughput and packet success rate by adjusting the transmission start time and reducing the length of time slot.

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.

In this poster, we show the design of an underwater datalogger that can achieve accurate position and location estimation and tracking on the order of centimeters. The prototype of underwater datalogger utilizes a 9-axis inertial measurement unit (IMU) and a microcontroller, which is housed in a sphere with a diameter of 11 cm. A novel calibration procedure is developed to achieve the accuracy and precision which is of great importance in civil engineering experiments that measure water flow and sediment movement.

This paper designs a novel geometry-conformal antenna for Magnetic Induction (MI)-based subsea wireless communications for autonomous underwater vehicles (AUV). The designed tri-directional antennas can be wrapped directly on the surface of AUVs, such that the AUVs fluid dynamics are well maintained to ensure power efficiency of the vehicles. In addition, ferrite materials are added between the MI antenna and the metallic body surface of the AUVs to overcome the shielding effect and enhance the MI signal strength. The designed MI communication system is implemented in hardware and the effectiveness of the geometry-conformal MI antenna is demonstrated through COMSOL simulations and lab experiments.

Reservoir computing (RC) is a class of neuromorphic computing approaches that deals particularly well with time-series prediction tasks. It significantly reduces the training complexity of recurrent neural networks and is also suitable for hardware implementation whereby device physics are utilized in performing data processing. In this paper, the RC concept is applied to detecting a transmitted symbol in multiple-input multiple-output orthogonal frequency division multiplexing (MIMO-OFDM) systems. Due to wireless propagation, the transmitted signal may undergo severe distortion before reaching the receiver. The nonlinear distortion introduced by the power amplifier at the transmitter may further complicate this process. Therefore, an efficient symbol detection strategy becomes critical. The conventional approach for symbol detection at the receiver requires accurate channel estimation of the underlying MIMO-OFDM system. However, in this paper, we introduce a novel symbol detection scheme where the estimation of the MIMO-OFDM channel becomes unnecessary. The introduced scheme utilizes an echo state network (ESN), which is a special class of RC. The ESN acts as a black box for system modeling purposes and can predict nonlinear dynamic systems in an efficient way. Simulation results for the uncoded bit error rate of nonlinear MIMO-OFDM systems show that the introduced scheme outperforms conventional symbol detection methods.

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, 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 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.

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 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.

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.

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, we study the design of frequency domain turbo equalization (FDTE) in single carrier (SC) multiple-input multiple-output (MIMO) systems, and prove the equivalence of two typical FDTE schemes under constant-modulus modulation. In the design of FDTE schemes, received signals and soft decision symbols obtained at the previous iteration are utilized to recover the transmitted symbols under the minimum mean squared error (MMSE) criterion. Frequency domain equalization with frequency domain decision feedback (FDE- FDDF), and frequency domain equalization with parallel interference cancellation (FDE-PIC) are presented with details. Under constant-modulus modulation, the FDE-FDDF scheme and the FDE-PIC scheme are proved to be equivalent mathematically. The equivalence of the two FDTE schemes under constant-modulus modulation has also been verified through numerical simulations.

This paper proposes an online resource allocation algorithm for weighted sum rate maximization in energy harvesting downlink multiuser multiple-input multiple-output (MIMO) systems. Taking into account the discrete nature of the modulation and coding rates (MCRs) used in practice, we formulate a stochastic dynamic programming (SDP) problem to jointly design the MIMO precoders, select the MCRs, assign the subchannels, and optimize the energy consumption over multiple time slots with causal and statistical energy arrival information and statistical channel state information. Solving this high-dimensional SDP entails several difficulties: the SDP has a nonconcave objective function, the optimization variables are of mixed binary and continuous types, and the number of optimization variables is on the order of thousands. We propose a new method to solve this NP-hard SDP by decomposing the high-dimensional SDP into an equivalent three-layer optimization problem and show that efficient algorithms can be used to solve each layer separately. The decomposition reduces the computational burden and breaks the curse of dimensionality.

This paper presents theoretical modeling and circuit analysis of magneto-inductive communication channels where receivers use multiple coils to improve the spatial sensitivity patterns and communication range. The mutual coupling among the multi-coils at receiver and between transmit and receive coils is derived for general configurations in 3D space. The equivalent circuit of induced voltage for receive coils is analyzed which provides a guide for the design of matching circuits for optimal performance. The methodology developed in this paper can also be applied to other sensor network scenarios where MI communications are used.

In this paper, we propose a low-complexity single- carrier frequency-domain iterative receiver for triply-selective underwater acoustic (UWA) fading channels, which combines frequency domain decision feedback equalization (FD-DFE) with iterative channel estimation. Due to long multipath channels, frequency domain turbo equalization has to use large block size to achieve low computational complexity and high data efficiency, but UWA channel coherence time is often much shorter than block length. We utilize pilots or soft decision symbols obtained at the previous iteration to re-estimate channel at each turbo iteration, thus achieving satisfactory performance. Although having slightly inferior bit error performance to time-domain turbo equalizers, the proposed FDE scheme reduces the complexity by three orders of magnitude, making it affordable for real-time implementation. The proposed iterative receiver has been verified through both numerical simulations and undersea experiment data collected in the Surface Processes and Acoustic Communications Experiment 2008 (SPACE08).

This paper studies the impact of distance measurement error on node localization in large scale Underwater Wireless Sensor Networks (UWSNs) where only a small percent of nodes are anchor nodes with accurate location information and a large percent of ordinary nodes are to be localized. The recursive localization algorithm is re-evaluated under realistic assumptions that low-cost underwater sensor node may experience large system errors and random errors of distance measurement. Our results show that the errors indeed cause severe performance degradation in localization coverage and normalized localization errors. The sources of distance measurement errors are also identified and their remedies are suggested.

This letter presents a new sparsity basis selection compressed sensing method (SBSCS) for improving signal reconstruction from compressed sensing (CS) measurements. Based on the observation that different classes of transform cause different sparsity expressions and better sparsity expression leads to better signal recovery, the proposed SBSCS method searches the best class of transform and basis in a set of redundant tree-structured dictionaries by nesting sparsity maximization within the CS minimization. The SBSCS method adaptively selects the class of transform and basis with the best sparsity measure at each ℓ1iteration and converges quickly to the final class of transform and basis. Numerical experiments show that the proposed SBSCS method improves the quality of signal recovery over the existing best basis compressed sensing method (BBCS) proposed by Peyré in 2010.

This paper proposes an online resource allocation algorithm for weighted sum rate maximization in energy harvesting downlink multiuser multiple-input-multiple-output (MIMO) systems, where the base station transmitter is powered by both a regular energy source and an energy buffer that is connected to an energy harvester. Taking into account the discrete nature of the modulation and coding rates (MCRs) used in practice, we formulate a stochastic dynamic programming (SDP) problem to jointly design the MIMO precoders, select the MCRs, assign the subchannels, and optimize the energy consumption over multiple time slots with causal and statistical energy arrival information and statistical channel state information. Solving this high-dimensional SDP entails several difficulties: the SDP has a nonconcave objective function, the optimization variables are of mixed binary and continuous types, and the number of optimization variables is on the order of thousands. We propose a new method to solve this NP-hard SDP by decomposing the high-dimensional SDP into an equivalent three-layer optimization problem and develop efficient algorithms to solve each layer separately. The decomposition reduces the computational burden and breaks the curse of dimensionality successfully. We analyze the complexity of the proposed algorithm and demonstrate the performance gains based on numerical examples.

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.

A low complexity detection algorithm based on list sphere decoding (LSD) is proposed for under-determined multiple-input multiple-output (UD-MIMO) systems with N transmit antennas and M <; N receive antennas. The proposed algorithm utilizes the unique structure of UD-MIMO systems by dividing the N detection layers into two groups. Group 1 contains layers 1 to M that have similar structures as a symmetric MIMO system; while Group 2 contains layers M + 1 to N that contribute to the rank deficiency of the channel Gram matrix. Tree search algorithms are used for both groups, but with different search radii. A new method is proposed to adaptively adjust the tree search radius of Group 2 based on the statistical properties of the received signals. The employment of the adaptive tree search can significantly reduce the computational complexity. Simulation results show that the proposed algorithm can reduce the complexity by one orders of magnitude with less than 0.01 dB degradation in the Bit-Error-Rate (BER) performance.

This paper presents an accurate approximation of the frame error rate (FER) of coded wireless communication systems with receiver diversity, such as single-input multiple-output (SIMO) systems with maximum ratio combining (MRC) or hybrid automatic repeat request (HARQ) systems with Chase combining. The signals at different diversity branches experience independent but non-identically distributed Rayleigh fading. The FER approximation is obtained with a threshold-based method. Specifically, the threshold value, which is critical to the FER approximation accuracy, is modeled as a linear function of the frame length in the log-domain, with the slope and intercept of the linear function determined by the underlying modulation and channel coding schemes. The analytical FER approximation is expressed as an explicit function of parameters related to modulation, coding, frame length, number of diversity branches, and the power distribution across the diversity branches. Such an FER approximation summarizes the complex physical layer operations into a few parameters, and it provides the parametric flexibility that is not available in most existing FER approximations. Simulation results show that the proposed FER approximation can accurately predict the FER performance of a wide range of receiver diversity systems.

An efficient hardware implementation scheme is proposed for iterative multi‐input–multi‐output orthogonal frequency‐division multiplexing receiver which includes an MMSE‐IC (minimum‐mean‐square error interference cancellation) detector, a channel estimator, a low‐density parity‐check (LDPC) decoder and other supporting modules. The proposed implementation uses the QR decomposition (QRD) of the complex‐valued matrices with four coordinate rotation digital computer (CORDIC) cores and a back substitution to solve the MMSE‐IC equations while the existing systolic array architectures require 15–38 CORDIC cores to achieve a similar throughput. The proposed 4‐CORDIC QRD architecture can be configured as a 16‐matrix or a 64‐matrix pipelining by using a different number of multipliers combined with one‐dimensional (1D) or 2D arrays of the back substitution, respectively. The channel estimator implements a commonly‐used frequency domain least squares channel estimation with the canonic‐signed‐digits method, thanks to the character of the Zadroff‐Chu sequence used as the pilot. In the LDPC decoder, the min‐sum algorithm is implemented for the quasicyclic LDPC decoding. The two schemes for the MMSE‐IC detector with different throughput and resource usages have been implemented in a Field Programmable Gate Array for a complete baseband turbo receiver. Their resource usages, throughputs and latencies are compared with the classic systolic array architectures, which demonstrate that the proposed receiver architecture achieves the best tradeoff between the throughput and the resource usage.

The optimum energy efficient and spectral efficient designs for type-I automatic-repeat-request (ARQ) systems in Rayleigh flat fading channels are studied in this paper. Three optimum designs are considered: the first scheme maximizes the energy efficiency (EE), or equivalently, minimizes the total energy per information bit without considering the spectral efficiency (SE); the second scheme minimizes a new metric, the energy per information bit normalized by the SE; and the third scheme maximizes the EE under the constraint of a minimum SE. For given physical and link layer parameters, such as hardware power consumption, coding rate, modulation, bit rate, number of overhead bits, and communication distance, the three schemes are optimized with respect to the average transmission energy and the number of information bits per frame. The fundamental EE-SE tradeoff curve is analytically identified via the optimization of the third scheme, and it is shown that the optimum EE is quansiconcave in SE in a type-I ARQ system. The optimum solutions to the first two schemes are special operating points on the EE-SE tradeoff curve. Computer simulation results verify the analytical solutions.

A low-resource implementation of QR decomposition (QRD) is proposed for MIMO-OFDM systems that employ turbo MMSE-IC (Minimum mean square error interference cancellation) detector. The proposed implementation uses only four CORDIC cores for QR decomposition of complex-valued matrices while existing systolic array architecture requires 15 to 38 CORDIC cores to achieve similar throughput. For 4-by-4 MIMO with 1024 subcarrier OFDM, the turbo MMSE-IC requires 1024 QRD of 4-by-4 complex matrices followed by back substitution. Each matrix QRD is accompanied by rotations of four vectors for the second and subsequent turbo iterations. The proposed architecture implements the multiple vector rotation by multipliers rather than CORDIC cores, thus saving resources. When combined with a 2-dimensional array of back substitution, the proposed QRD architecture can achieve 64-matrix pipelining and a throughput of seven clocks per matrix for MMSE-IC calculation. The proposed MMSE-IC architecture has been implemented in Altera Stratix IV FPGA with LDPC decoding and other baseband receiver components.

Energy efficiency (EE) and spectral efficiency (SE) feature one of the most fundamental tradeoffs in communication systems. In this paper, we propose an optimum transmission scheme for coded Type-I automatic repeat request (ARQ) systems to balance the EE-SE tradeoff. The optimization is performed with respect to a new design metric, the normalized EE (NEE), which is defined as the energy per bit normalized by the SE. Minimizing NEE means either reducing the energy per bit or increasing the SE, it thus yields a balanced tradeoff between the two. The system design incorporates a wide range of practical system parameters, such as circuit power, modulation, coding, and detection errors in the physical layer, and frame length and protocol overhead in the media access control layer. Under the constraints of fixed modulation level and data rate, the optimum transmission energy and frame length are identified as closed-form expressions of the system parameters. Simulation results show that minimizing the NEE instead of energy per bit almost doubles the SE with less than 1 dB loss in EE.

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.

A two-stage list sphere decoding (LSD) algorithm is proposed for under-determined multiple-input multiple-output (UD-MIMO) systems that employ N transmit antennas and M<;N receive antennas. The two-stage LSD algorithm exploits the unique structure of UD-MIMO systems by dividing the N detection layers into two groups. Group 1 contains layers 1 to M that have similar structures as a symmetric MIMO system; while Group 2 contains layers M+1 to N that contribute to the rank deficiency of the channel Gram matrix. Tree search algorithms are used for both groups, but with different search radii. A new method is proposed to adaptively adjust the tree search radius of Group 2 based on the statistical properties of the received signals. The employment of the adaptive tree search can significantly reduce the computation complexity. We also propose a modified channel Gram matrix to combat the rank deficiency problem, and it provides better performance than the generalized Gram matrix used in the Generalized Sphere-Decoding (GSD) algorithm. Simulation results show that the proposed two-stage LSD algorithm can reduce the complexity by one to two orders of magnitude with less than 0.1 dB degradation in the Bit-Error-Rate (BER) performance.

A modified FSD algorithm is proposed for under-determined (UD) multiple-input multiple-output (MIMO) systems with N transmit antennas and M < N receive antennas. This paper focuses on the low-complexity detection of coded UD-MIMO systems with iterative turbo detection, where a soft-input soft-output (SISO) MIMO detector exchanges soft information with a SISO decoder. In the first iteration, a modified fixed complexity sphere decoding (FSD) method is developed by utilizing the structure of a UD-MIMO system. The modified FSD employs a new detection ordering scheme that has a lower complexity but a better performance compared to the conventional ordering scheme. From the second iteration and beyond, the MIMO detector is implemented with a generalized serial interference cancelation (GSIC) scheme and a block decision feedback equalizer (BDFE) to further reduce the complexity. Simulation results show that the newly proposed FSD-GSIC-BDFE structure can achieve significant performance gains over existing schemes, especially for systems with high level modulations.

The energy efficient design of coded automatic-repeat-request (ARQ) systems is studied in this paper. The optimization aims to minimize the energy required for the successfully delivery of one information bit from a transmitter to a receiver. The design is performed by incorporating a wide range of practical system parameters and metrics, such as hardware power consumption, modulation, channel coding, and frame error rate (FER) in the physical layer, and frame length and protocol overhead in the media access control layer. A new log-domain threshold approximation method is proposed to analytically quantify the impacts of the various system parameters on the FER, and the results are used to facilitate the system design. The optimum transmission energy and frame length that minimize the energy per information bit are identified in closed-form expressions as functions of the various practical system parameters. The analytical and simulation results demonstrate that the total energy consumption in a coded ARQ system can be reduced by increasing the transmission energy during one transmission attempt, and significant energy saving as high as 9.5 dB is achieved with the optimum system.

This paper successfully implements compressed sensing (CS) to a near-field wideband 3-D synthetic aperture radar (SAR) imaging system. SAR data are measured at a low percentage of random-selected positions on a uniform grid of planar aperture in the stripmap mode. The near-field 3-D range migration algorithm (RMA) is used in combination with the CS principle to reconstruct the 3-D image via l1regularized least-square approach. Experiments were performed with Q-band stepped-frequency monostatic stripmap SAR imaging system on a blue foam embedded with eight rubber pads and one copper square chip. The results of the experiments show near-field 3-D image of the specimen under test (SUT) can be reconstructed efficiently from low percentage of the full measurement positions, which largely lessens the data collection load. The reconstructed image was better focused and denoised.

This paper presents optimum multi-hop transmission strategies (MHTS) for energy constrained wireless sensor networks (WSNs). Nodes in a multi-hop WSN need to transmit their own information and to relay each other's information to a base station (BS), and there are usually multiple available paths between a node and the BS. The optimum MHTS derived in this paper answers three questions: 1) how should a node divide its limited energy between the transmission of the self-information and the relay-information? 2) whether a single path or a combination of multiple paths should be used to route the information from a node to the BS? and 3) if multi-path routing is used, how should a single data stream be divided among the multiple paths? The answers to these questions are obtained by minimizing the energy per bit, or equivalently, by maximizing the amount of information delivered to the BS under certain energy constraints. Two different scheduling strategies are considered, the fair equal information strategy that requires all the nodes deliver the same amount of information to the BS, and the unfair maximum information strategy that maximizes the total amount of information delivered to the BS. The optimum MHTS for these two strategies are derived, with either convex optimization or analytical expressions, under a per node energy constraint and a total energy constraint, respectively.

This paper considers the precoder design for dual-hop amplify-and-forward relay networks and formulates the design from the standpoint of finite-alphabet inputs. In particular, the mutual information is employed as the utility function, which, however, results in a nonlinear and nonconcave problem. This paper exploits the structure of the optimal precoder that maximizes the mutual information and develops a two-step algorithm based on convex optimization and optimization on the Stiefel manifold. By doing so, the proposed algorithm is insensitive to initial point selection and able to achieve a near global optimal precoder solution. Besides, it converges fast and offers high mutual information gain. These advantages are verified by numerical examples, which also show the large performance gain in mutual information also represents the large gain in the coded bit-error rate.

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.

Two proportionate affine projection sign algorithms (APSAs) are proposed for system identification applications, such as network echo cancellation (NEC), where the impulse response is often real-valued with sparse coefficients and long filter length. The proposed proportionate-type algorithms can achieve fast convergence and low steady-state misalignment by adopting a proportionate regularization matrix to the APSA. Benefiting from the characteristic of Zi-norm algorithms, affine projection, and proportionate matrix, the new algorithms are robust to impulsive interferences and colored input, and achieve much faster convergence rate in sparse impulse responses than the original APSA, the normalized sign algorithm (NSA), and the proportionate least mean square (PNLMS) algorithm. The computational complexity of the new algorithms is lower than the affine projection algorithm (APA) family due to elimination of matrix inversion.

The turbo detection of a coded under-determined multiple-input multiple-output (UD-MIMO) system is studied in this paper. A UD-MIMO system with N transmit antennas and M <; N receive antennas has more unknowns than the observations. However, most existing low complexity detectors, such as the vertical Bell Laboratories Layered Space-Time (V BLAST) or the block decision feedback equalizer (BDFE), work only when M ≥ N. We propose a new turbo detector structure that combines the existing generalized parallel interference cancellation (GPIC) technique and a new generalized serial interference cancellation (GSIC) technique, with a soft-input soft output (SISO) BDFE. In the first iteration, the GPIC-BDFE equalization is adopted. From the second iteration and beyond, due to the availability of the a priori soft information, the UD MIMO system can be partitioned into multiple sub-systems by using a reliability-based partition scheme. Then, the GSIC-BDFE equalization, which has a much lower complexity than the GPIC BDFE equalization, can be used. Simulation results show that the new detection scheme achieves significant performance gain as the iteration progresses with a reasonable complexity.

Nonuniform random sampling is applied to a wideband 3D synthetic aperture radar (SAR) imaging system to reduce the number of measurement points in both frequency and space domains. Experimental tests were performed on a construction foam specimen using uniformly sampled Q-band frequencies in 35.04 GHz to 44.96 GHz and at a grid of two millimeter step sizes. Using discrete Fourier transform (DFT) or discrete cosine transform (DCT) sparse representations, the 3D images can be reconstructed from 7% random samples of the experimental data achieving comparable quality as the one from original full-set data. This can translate to significant time reduction of measurement from more than one hour to less than 20 minutes.

Two proportionate affine projection sign algorithms (APSAs) are proposed for network echo cancellation (NEC) applications where the impulse response is often real-valued with sparse coefficients and long filter length. The proposed proportionate-type algorithms can achieve fast convergence and low steady-state misalignment by adopting a proportionate regularization matrix to the APSA. Benefiting from the characteristics of l1-norm optimization, affine projection, and proportionate matrix, the new algorithms are more robust to impulsive interferences and colored input than the proportionate least mean squares (PNLMS) algorithm and the robust proportionate affine projection algorithm (Robust PAPA). The new algorithms also achieve much faster convergence rate in sparse impulse responses than the original APSA and the normalized sign algorithm (NSA). The new algorithms are robust to all types of NEC impulse response with different sparseness without the need to change parameters or estimate the sparseness of the impulse response. The computational complexity of the new algorithms is lower than the affine projection algorithm (APA) family due to the elimination of the matrix inversion.

A new oversampled orthogonal frequency division multiplexing (OOFDM) scheme is proposed for doubly selective fading environment. The proposed OOFDM scheme employs oversampling in the time domain and linear processing in the frequency domain, both at the receiver without changing the structure of conventional orthogonal frequency division multiplexing (OFDM) transmitters. The time-frequency processing enables a two dimensional Doppler-frequency grid of the fading channel, such that each data symbol is modeled equivalently as being transmitted at multiple subcarriers and various Doppler spreads simultaneously, while retaining the same spectral efficiency as conventional OFDM systems. Optimum combining ensures coherent combining of the data samples spread over the Doppler-frequency grid and non-coherent combining of inter-carrier interference (ICI) components caused by time varying fading. Theoretical error probabilities of the OOFDM systems are derived by analyzing the statistical properties of Doppler-frequency fading coefficients and noise sample correlations. Both theoretical analysis and computer simulation show that the new system with an oversampling factor of two outperforms the conventional OFDM system by as much as 7 dB.

This paper proposes a reliability-based turbo detection scheme for multiple-input multiple-output (MIMO) systems with frequency-selective fading. The proposed scheme performs iterative successive soft interference cancellation (SSIC) with a block decision-feedback equalizer (BDFE). To minimize the negative impacts of error propagation in SSIC, we propose a new group-wise reliability-based ordering scheme, where neighboring symbols that severely interfere with each other are clustered into the same group, and for each group, more "reliable" symbols are detected before less "reliable" ones. The symbol reliability is measured by using the symbol a priori probability, which is a unique byproduct of the turbo detection and can be obtained with little overhead. The reliability information is updated iteratively as the turbo detection progresses, and this leads to a dynamic ordering scheme that is unavailable in conventional ordered successive interference cancellation (OSIC) schemes. Simulation results show that extra performance gain is obtained at a very small ordering cost, and the reliability-based turbo detection can achieve a performance that is only 0.5 dB away from the optimum maximum a posteriori probability (MAP) detection.

This paper proposes a low-complexity frequency-domain turbo equalizer (FDTE) combined with phase rotation compensation and soft successive interference cancellation (SSIC) for single carrier multiple-input multiple-output (MIMO) underwater acoustic (UWA) communications. Different from existing time-domain turbo equalizers in MIMO UWA systems, the proposed receiver implements low-complexity turbo equalization in the frequency domain to combat severe inter-symbol interference (ISI) and employs a layered structure to cope with unbalanced MIMO channels. Soft, rather than hard, successive interference cancellation (SIC) is employed in the layered iterative turbo detection to alleviate co-channel interference (CCI), and phase compensation is utilized within the layered FDTE to mitigate phase rotation. The proposed scheme was evaluated by the SPACE08 experiment conducted in a shallow area of the Atlantic Ocean in October 2008. The 2-transducer 12-hydrophone MIMO system communicated with quaternary phase shift keying (QPSK) and 8-phase shift keying (8PSK) modulation schemes over 200 m and 1000 m ranges, where the proposed FDTE-SSIC scheme achieved low bit error rates (BERs) with only a few iterations. Simulation results also demonstrated that the proposed FDTE-SSIC receiver provided lower BER than one-layer FDTE receivers with comparable complexity.

In this paper, we implement a real-time hardware triply selective Rayleigh fading simulator. This simulator incorporates the inter-tap and spatial correlation matrices into multiple uncorrelated frequency-flat Rayleigh fading waveforms (including temporal correlation) to simulate a multiple-input multiple-output (MIMO) triply selective Rayleigh fading channel. In the correlation incorporation procedure, this simulator uses a Kronecker product method to save a large amount of hardware memories. Occupying 34% hardware resources of one Stratix III FPGA chip, this simulator can simulate 4 × 4 MIMO fading channels with 10 correlated delay-taps per subchannel in real-time for a symbol rate of 3.69 μs. Accuracy of this simulator is proved by comparing the statistical properties of its outputs to corresponding theoretical values, and they match perfectly.

A variable step size normalized sign algorithm (VSS-NSA) is proposed, for acoustic echo cancelation, which adjusts its step size automatically by matching the L1norm of the a posteriori error to that of the background noise plus near-end signal. Simulation results show that the new algorithm combined with double-talk detection outperforms the dual sign algorithm (DSA) and the normalized triple-state sign algorithm (NTSSA) in terms of convergence rate and stability.

This paper proposes a low-complexity turbo block decision feedback equalizer (BDFE) with reliability-based successive soft interference cancellation (SSIC) for multiple-input multiple-output (MIMO) systems. Turbo equalization in MIMO systems needs to combat both intersymbol interference (ISI) due to frequency-selective fading and multiplexing interference (MI) among data streams transmitted by different antennas. The proposed MIMO BDFE performs SSIC on both ISI in the time-domain and MI in the space-domain. For an SSIC receiver, the order in which the symbols are detected and cancelled is critical to the system performance, yet it is often overlooked in the literature. We propose a new reliability-based detection ordering scheme, where symbols with higher a priori reliability are detected before those with lower a priori reliability. The reliability information can be obtained from the a priori probability at the input of the soft-decision equalizer. The reliability-based ordering scheme is enabled by the turbo equalization structure, and it yields an extra equalization gain that is unavailable in a conventional equalization system. Furthermore, the adoption of non-linear BDFE in MIMO systems enables a low-complexity sequence-based log-likelihood ratio (LLR) evaluation, which is superior to the symbol-based LLR evaluation method employed by most other low-complexity turbo equalizers.

A new layered frequency-domain turbo equalization (LFDTE) scheme is proposed for single carrier (SC) multiple-input multiple-output (MIMO) systems. The proposed scheme combines the respective advantages of layered detection and turbo equalization to further lower the bit error rate (BER) for high-data-rate communications. Different from the traditional frequency-domain turbo equalization (FDTE) method for MIMO systems, our new detection algorithm employs a layered structure in each turbo iteration, and at each layer a group of best data streams is detected in the form of soft symbols and then canceled from the received signals in frequency domain. The extrinsic information for the detected coded bits gleaned by the current layer is fed back to the previous layers as a-priori information utilized for equalization in the next iteration. Since the frequency-domain equalization (FDE) is performed in each frequency bin, the proposed receiver scheme has similar computational complexity compared to the traditional FDTE, but achieves better performance of BER. Simulation results demonstrate that the new proposed scheme outperforms the traditional FDTE without layered detection at the same number of iterations, and the performance becomes better if multiple layers are used in the detection.

This article proposes a hardware triply selective Rayleigh fading channel emulator which is implemented by incorporating spatial and inter-tap correlation matrices into uncorrelated frequency-flat Rayleigh fading waveforms with a Kronecker product method. The Kronecker product of square roots of three correlation matrices are computed in real time via serial, parallel, or mixed serial-parallel computational methods and then combined with uncorrelated flat fading waveforms. A 4×4 multiple-input multiple-output (MIMO) triply selective channel with 4 correlated delay-taps per subchannel is implemented on a Stratix III FPGA DSP development kit. We show that the three methods provide flexibility for designs in speed and resource utilization.

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.

A new affine projection sign algorithm (APSA) is proposed, which is robust against non-Gaussian impulsive interferences and has fast convergence. The conventional affine projection algorithm (APA) converges fast at a high cost in terms of computational complexity and it also suffers performance degradation in the presence of impulsive interferences. The family of sign algorithms (SAs) stands out due to its low complexity and robustness against impulsive noise. The proposed APSA combines the benefits of the APA and SA by updating its weight vector according to theL1-norm optimization criterion while using multiple projections. The features of the APA and theL1-norm minimization guarantee the APSA an excellent candidate for combatting impulsive interference and speeding up the convergence rate for colored inputs at a low computational complexity. Simulations in a system identification context show that the proposed APSA outperforms the normalized least-mean-square (NLMS) algorithm, APA, and normalized sign algorithm (NSA) in terms of convergence rate and steady-state error. The robustness of the APSA against impulsive interference is also demonstrated.

In this paper, carrier frequency offsets (CFOs) are considered in a layered frequency-domain equalization (LFDE) architecture for a single carrier (SC) broadband wireless multiple-input multiple-output (MIMO) system. At each layer of detection, a group of best data streams are selected to be equalized and reliably detected via removing the phase and amplitude distortion caused by the multiple CFOs. The estimated phase rotations and amplitude scalers are required to be compensated to the detected data streams in order to reconstruct the interference signals which are canceled out from the received signals. Instead of direct estimation of CFOs, our algorithm is to estimate the phase rotations and amplitude scalars in a group-wise fashion, which dramatically reduces the computational complexity at receiver. Simulation results demonstrate that the proposed LFDE with phase compensation architecture can provide good performance for a MIMO system impaired by CFOs over unbalanced multi-path channels with long delay spread. We also show that the performance will be improved if more layers are used at receivers.

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.

A low-complexity hardware implementation method is proposed for discrete-time frequency-selective Rayleigh fading channels. The proposed method first employs the sum-of-sinusoids method to generate multiple independent flat fading channel responses, then utilizes a simple weight-delay-sum filtering method to incorporate the fractionally-delayed multipath rays into inter-tap correlated tap gains. It thus achieves accurate correlation properties in both inter-tap correlation and temporal correlation (or Doppler spectrum). The proposed method is implemented by an Altera Stratix II FPGA development kit and the results show excellent performance match with those by Matlab software simulations.

A new variable step-size fractional lower-order moment (FLOM) algorithm is proposed for non-Gaussian interference suppression. The Normalized FLOM algorithm is a generalization of the normalized least mean square (NLMS) algorithm with a lower order p ≤ 2 and p = 2 corresponding to the NLMS algorithm. With a fixed step size, the smaller the order p, the faster the convergence of the NFLOM algorithm, but the higher the excess mean square errors (MSE) after convergence. The proposed VSS-FLOM provides a compromise solution to the two conflicting goals of low excess MSE and fast convergence. Simulation results for a system identification application in Gaussian and compound K interference environments show that the proposed VSS-FLOM algorithm outperforms the fixed step-size NFLOM and VSS-LMS algorithms in non-Gaussian interference environments.

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.

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.

A frequency-domain channel estimation method is proposed for time-varying multiple-input multiple output (MIMO) single-carrier frequency-domain equalization (SC-FDE). The proposed method uses frequency-domain interpolation to obtain channel frequency responses of data blocks from estimated responses of two adjacent pilot blocks. It takes the channel temporal-spatial correlation into account to achieve minimum mean squared error (MMSE) estimation, thus improving the accuracy and effectiveness in high Doppler scenarios. The simulation results of the bit error rate (BER) performances show that the proposed method works well for fast time-varying channels with Doppler spread as high as 300 Hz while maintaining over 70% data efficiency.

A computer simulation model is proposed for discrete-time doubly-selective compound-K fading channel. It first generates multiple independent mobile-to-mobile Rayleigh fading Channel Impulse Response (CIR) using the non-isotropic scattering model, then generates the cross- and auto-correlated gamma shadowing matrix using the combination of the memoryless nonlinear transformation (MNLT) method and the decomposition methods. It then combines the complex Rayleigh CIR with the gamma shadowing matrix to yield the doubly-selective fading channel CIR whose envelop follows the compound K distribution. Simulation examples demonstrate that the proposed method can effectively produce compound K fading channel responses with satisfactory statistical properties.

A low complexity soft-input soft-output (SISO) block decision feedback equalizer (BDFE) is presented for turbo equalization. The proposed method employs a sub-optimum sequence-based detection, where the soft-output of the equalizer is calculated by evaluating an approximation of the sequence-based a posteriori probability (APP) of the data symbol. The sequence-based APP approximation is enabled by the adoption of both soft a priori information and soft decision feedback, and it leads to better performance and faster convergence compared to symbol-based detection methods as used by most other low complexity equalizers. The performance and convergence property of the proposed algorithm is analyzed by using extrinsic information transfer (EXIT) chart. Both analytical and simulation results show that the new equalizer can achieve a performance similar to that of trellis-based equalization algorithms, with a complexity similar to linear SISO minimum mean square error equalizers.

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.

A low complexity soft-input soft-output block decision feedback equalization (BDFE) algorithm is presented for Turbo equalization. Based on minimum mean square error criterion, the feedforward filter and feedback filter of BDFE are adaptively formulated by extracting symbol statistics from soft a priori information. The adoption of a priori information during filter design greatly benefit system performance. Unlike most other low complexity equalization algorithms with symbol-based detection, the proposed algorithm adopts a sub-optimum sequence-based method to evaluate an approximation of data symbol a posteriori probability (APP). The sequence-based APP approximation is enabled by hard a priori information from previous iteration, and it outperforms symbol-based detection method adopted by most other low complexity algorithms.

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.

A robust adaptive beamformer is proposed using the near field regionally constrained adaptive approach that designs a set of linear constraints by filtering on a low rank subspace of the near field signal over a spatial region and a wide frequency band. This method can accurately control the beamformer response over the designed spatial-temporal region using a small number of linear constraint vectors and improve the robustness against target location errors. Meanwhile, this method enhances the capability of the near field beamformer in distance discrimination without additional constraints so that interference impinging at the same direction as the desired signal but at a different distance can be effectively suppressed

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

Iterative equalization using optimal multiuser detector and trellis-based channel decoder in coded CDMA systems improves the bit error rate (BER) performance dramatically. However, given large number of users employed in the system over multipath channels causing significant multiple-access interference (MAI) and intersymbol interference (ISI), the optimal multiuser detector is thus prohibitively complex. Therefore, the sub-optimal detectors such as low-complexity linear and non-linear equalizers have to be considered. In this paper, a novel low-complexity block decision feedback equalizer (DFE) is proposed for the synchronous CDMA system. Based on the conventional block DFE, the new method is developed by computing the reliable extrinsic log-likelihood ratio (LLR) using two consecutive received samples rather than one received sample in the literature. At each iteration, the estimated symbols by the equalizer is then saved as a priori information for next iteration. Simulation results demonstrate that the proposed low-complexity block DFE algorithm offers very good performance gain over the conventional block DFE.

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

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.

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.

This paper proposes a robust near-field adaptive beamformer for microphone array applications in small rooms. Robustness against location errors is crucial for near-field adaptive beamforming due to the difficulty in estimating near-field signal locations especially the radial distances. A near-field regionally constrained adaptive beamformer is proposed to design a set of linear constraints by filtering on a low rank subspace of the near-field signal over a spatial region and frequency band such that the beamformer response over the designed spatial-temporal region can be accurately controlled by a small number of linear constraint vectors. The proposed constraint design method is a systematic approach which guarantees real arithmetic implementation and direct time domain algorithms for broadband beamforming. It improves the robustness against large errors in distance and directions of arrival, and achieves good distance discrimination simultaneously. We show with a nine-element uniform linear array that the proposed near-field adaptive beamformer is robust against distance errors as large as /spl plusmn/32% of the presumed radial distance and angle errors up to /spl plusmn/20/spl deg/. It can suppress a far field interfering signal with the same angle of incidence as a near-field target by more than 20 dB with no loss of the array gain at the near-field target. The significant distance discrimination of the proposed near-field beamformer also helps to improve the dereverberation gain and reduce the desired signal cancellation in reverberant environments.

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.

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.

This paper discusses eigenvector constraint design for broadband adaptive array beam forming. The constraint equations are constructed using the real and imaginary parts of the steering vectors and the response vectors, thus perm its real arithmetic and guarantees real outputs. A simple and elegant structure is developed for implementing the designed beam former by a Generalized Sidelobe Canceler (GSC). This structure reduces the computational complexity from O (N2) to O (N), where N being the dimension of the weight vector.

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.

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.