Maximum Likelihood Channel Research Articles

Doubly iterative multiple‐input–multiple‐output‐bit‐interleaved coded modulation receiver with joint channel estimation and randomised sampling detection

In this study, the authors propose a lattice reduction (LR)-based doubly iterative receiver for joint channel estimation and detection in multiple-input–multiple-output (MIMO) bit-interleaved coded modulation systems. For the inner iteration loop of the receiver, LR-based randomised sampling detection is employed to enjoy the tradeoff between performance and complexity while for the outer iteration loop, the expectation–maximisation (EM)-based iterative channel estimation using sampling results is proposed to achieve the maximum likelihood channel estimation performance. Besides, a modified computational efficient EM-based channel estimation approach is also derived to reduce the complexity further. Simulation results demonstrate that the proposed doubly MIMO iterative receiver can have comparable bit-error rate performance with a reasonable computational complexity.

Near Maximum-Likelihood Detector and Channel Estimator for Uplink Multiuser Massive MIMO Systems With One-Bit ADCs

In massive multiple-input multiple-output (MIMO) systems, it may not be power efficient to have a pair of high-resolution analog-to-digital converters (ADCs) for each antenna element. In this paper, a near maximum likelihood (nML) detector for uplink multiuser massive MIMO systems is proposed where each antenna is connected to a pair of one-bit ADCs, i.e., one for each real and imaginary component of the baseband signal. The exhaustive search over all the possible transmitted vectors required in the original maximum likelihood (ML) detection problem is relaxed to formulate an ML estimation problem. Then, the ML estimation problem is converted into a convex optimization problem which can be efficiently solved. Using the solution, the base station can perform simple symbol-by-symbol detection for the transmitted signals from multiple users. To further improve detection performance, we also develop a two-stage nML detector that exploits the structures of both the original ML and the proposed (one-stage) nML detectors. Numerical results show that the proposed nML detectors are efficient enough to simultaneously support multiple uplink users adopting higher-order constellations, e.g., 16 quadrature amplitude modulation. Since our detectors exploit the channel state information as part of the detection, an ML channel estimation technique with one-bit ADCs that shares the same structure with our proposed nML detector is also developed. The proposed detectors and channel estimator provide a complete low power solution for the uplink of a massive MIMO system.

ML and MAP channel estimation for distributed one-way relay networks with orthogonal training

In this letter, we investigate the individual channel estimation for the classical distributed-space-time-coding (DSTC) based one-way relay network (OWRN) under the superimposed training framework. Without resorting to the composite channel estimation, as did in traditional work, we directly estimate the individual channels from the maximum likelihood (ML) and the maximum a posteriori (MAP) estimators. We derive the closed-form ML estimators with the orthogonal training designing. Due to the complicated structure of the MAP in-channel estimator, we design an iterative gradient descent estimation process to find the optimal solutions. Numerical results are provided to corroborate our studies.

Network Coded Multihop Wireless Communication Networks: Channel Estimation and Training Design

User-cooperation-based multihop wireless communication networks (MH-WCNs) as the key communication technological component of mobile social networks (MSNs) can be exploited to enhance data rates and extend coverage. As one of the most promising and efficient user cooperation techniques, network coding can increase the potential cooperation performance gains among selfishly driven users in MSNs. To take full advantages of network coding in MH-WCNs, a network coding transmission strategy and its corresponding channel estimation technique are studied in this paper. Particularly, a four-hop network coding transmission is presented first, followed by an extension strategy for the arbitrary $2N$ -hop scenario $(N\geq 2)$ . The linear minimum mean square error (LMMSE) and maximum-likelihood (ML) channel estimation methods are designed to improve the transmission quality in MH-WCNs. Closed-form expressions in terms of the mean square error (MSE) for the LMMSE channel estimation method are derived, which allows the design of the optimal training sequence. Unlike the LMMSE method, it is difficult to obtain closed-form MSE expressions for the nonlinear ML channel estimation method. In order to accomplish optimal training sequence design for the ML method, the Cramer–Rao lower bound is employed. Numerical results are provided to corroborate the proposed analysis, and the results demonstrate that the analysis is accurate and the proposed methods are effective.

Blind and semi-blind ML detection for space-time block-coded OFDM wireless systems

This paper investigates the joint maximum likelihood (ML) data detection and channel estimation problem for Alamouti space-time block-coded (STBC) orthogonal frequency-division multiplexing (OFDM) wireless systems. The joint ML estimation and data detection is generally considered a hard combinatorial optimization problem. We propose an efficient low-complexity algorithm based on branch-estimate-bound strategy that renders exact joint ML solution. However, the computational complexity of blind algorithm becomes critical at low signal-to-noise ratio (SNR) as the number of OFDM carriers and constellation size are increased especially in multiple-antenna systems. To overcome this problem, a semi-blind algorithm based on a new framework for reducing the complexity is proposed by relying on subcarrier reordering and decoding the carriers with different levels of confidence using a suitable reliability criterion. In addition, it is shown that by utilizing the inherent structure of Alamouti coding, the estimation performance improvement or the complexity reduction can be achieved. The proposed algorithms can reliably track the wireless Rayleigh fading channel without requiring any channel statistics. Simulation results presented against the perfect coherent detection demonstrate the effectiveness of blind and semi-blind algorithms over frequency-selective channels with different fading characteristics.

Joint Multiple-Access Channel Effective Order and CIR Estimation Algorithm for Multi-User OFDM/SDMA System

In this paper, a novel joint estimation of channel effective order and channel impulse response (CIR) is presented for multiuser orthogonal frequency division multiplexing/space-division multiple-access (OFDM/SDMA) systems. By exploiting Akaike’s Information Criterion (AIC) as the fitness function to search the optimal order, the proposed scheme performs the channel effective order and CIR estimation in a parallel way based on differential evolution (DE) algorithm. Simulation results demonstrate that the proposed scheme is capable of attaining a better mean square error performance than the fixed channel order scheme, and improving the performance of time-domain maximum likelihood (ML) channel estimator.

Channel Estimation for Relay-Based M2M Two-Way Communications Using Expectation-Maximization

The growing popularity of machine-to-machine (M2M) communications in wireless networks is driving the need to update the corresponding receiver technology based on the characteristics of M2M. In this paper, an expectation-maximization-based maximum likelihood cascaded channel estimation method is developed for relay-based M2M two-way communications. As the closed-form solution of maximum likelihood channel estimation does not exist, and the superimposed signal structure at the receiver is conducive to the expectation-maximization application, the expectation-maximization algorithm is utilized to provide the maximum likelihood solution in the presence of unobserved data through stable iterations. Even in the absence of the training sequence, the cascaded channel estimates are obtained through the expectation-maximization iterations. The Bayesian Cramér-Rao lower bounds are derived under random parameters for the channel estimation, and the simulation demonstrates the validity of the proposed studies.

Estimating Channel Parameters from the Syndrome of a Linear Code

In this letter, we analyse the properties of a maximum likelihood channel estimator based on the syndrome of a linear code. For the two examples of a binary symmetric channel and a binary input additive white Gaussian noise channel, we derive expressions for the bias and the mean squared error and compare them to the Cram\'er-Rao bound. The analytical expressions show the relationship between the estimator properties and the parameters of the linear code, i.e., the number of check nodes and the check node degree.

Optimized joint timing synchronization and channel estimation for communications systems with multiple transmit antennas

This paper proposes a joint timing synchronization and channel estimation scheme for communications systems with multiple transmit antennas based on a well-designed training sequence arrangement. In addition, a generalized maximum-likelihood (ML) channel estimation scheme is presented, and this one-shot scheme is applied to obtain all channel impulse responses (CIR) from different transmit antennas. The proposed approach consists of three stages at each receive antenna. First, coarse timing and frequency offset estimates are obtained. Then, an advanced timing, relative timing indices, and the corresponding CIR estimates at the second stage are obtained using the generalized ML estimation based on a sliding observation vector. Finally, the fine time adjustment based on the minimum mean squared error criterion is performed. From the simulation results, the proposed approach has excellent performance in timing synchronization under several channel models at signal-to-noise ratio smaller than 1dB.

Maximum likelihood channel estimation algorithm combines logarithm likelihood ratio decoding in the coal mine application

The environment of the wireless communication system in the coal mine has unique characteristics: great noise, strong multiple path interference, and the wireless communication of orthogonal frequency division multiplexing (OFDM) in underground coal mine is sensitive to the frequency selection of multiple path fading channel, whose decoding is separated from the traditional channel estimation algorithm. In order to increase its accuracy and reliability, a new iterating channel estimation algorithm combining the logarithm likelihood ratio (LLR) decode iterate based on the maximum likelihood estimation (ML) is proposed in this paper, which estimates iteration channel in combination with LLR decode. Without estimating the channel noise power, it exchanges the information between the ML channel estimation and the LLR decode using the feedback information of LLR decode. The decoding speed is very quick, and the satisfied result will be obtained by iterating in some time. The simulation results of the shortwave broadband channel in the coal mine show that the error rate of the system is basically convergent after the iteration in two times.

Single‐symbol decodable space‐time block code for multi‐input–multi‐output systems with four transmit antennas

This study presents an orthogonal design of space-time block code (STBC) that is single symbol decodable and enables full diversity and full rate transmission in a quasi-static channel environment. In the proposed scheme, full diversity is achieved by use of constellation rotation and co-ordination interpolation as is the case for the co-ordinate interleaved orthogonal design, whereas the transmission matrix of the proposed code consists of orthogonal columns with all non-zero elements, alleviating the concern about high peak-to-average power ratio. In particular, the proposed code offers lower complexity of channel estimation, and exhibits lower symbol error rate than the conventional quasi-orthogonal STBC when an maximum-likelihood decision-directed channel estimator is assumed. The advantages of the proposed code over the conventional codes are demonstrated through computer simulations. In addition, the selection of the angle of rotation for the proposed design is also presented, regarding the impact of channel estimation error.

Linear Frequency Domain Equalization of SOQPSK-TG for Wideband Aeronautical Telemetry Channels

This work explores multipath interference mitigation for a single transmit antenna, single receive antenna system with SOQPSK-TG using a linear single-carrier frequency domain equalization (SCFDE) technique. Linear SCFDE with maximum likelihood (ML) channel estimation is shown to greatly improve system Bit Error Rates (BER). Simulation results also demonstrate that three samples per bit at the receiver are adequate to achieve the best BER performance.

Joint CFO and Channel Estimation for Asynchronous Cooperative Communication Systems

This letter addresses the joint maximum likelihood carrier frequency offset (CFO) and channel estimation for asynchronous cooperative communication systems. We first present a space-alternating generalized expectation-maximization (SAGE) based iterative estimator (SAGE-IE). Then a low-complexity approximate SAGE-IE (A-SAGE-IE) is developed. Our proposed algorithms decouple the multi-dimensional optimization problem into many one-dimensional optimization problems where the CFO and channel coefficients of each relay-destination link can be determined separately. Simulations indicate that, even though timing offsets are present, the proposed estimators can asymptotically achieve the Cramer-Rao bround (CRB) for the perfectly timing synchronized case.

SIMO Channel Estimation Using Space-Time Signal Subspace Projection and Soft Information

We consider the channel estimation of a time-slotted wireless communication system with a mobile user and a base station, where the base station employs an M-element (M >; 1) antenna array. The uplink single-input multiple-output (SIMO) channel is usually estimated by training sequence within each time slot. To improve the estimation performance, the channel estimate is often refined by projecting it to the corresponding spatial signal subspace. However, this projection will not work when the number of resolvable multipath rays is larger than that of the antenna array elements, which makes the channel matrix full row rank. In this paper, we formulate the channel estimation under the space-time signal model for this full-row-rank case, and propose a new method by space-time signal subspace projection using both training and unknown data sequences. To further improve the accuracy of the channel estimate, the soft information fed back from the decoder can be used. By involving this soft information, we propose another new channel estimation method. This method approximately follows the maximum likelihood (ML) criterion and is therefore referred to as the approximated ML channel estimation. Numerical results show that these methods can be performed separately or jointly to improve the performance of channel estimation by training sequences.

Performance analysis of decision directed maximum likelihood MIMO channel tracking algorithm

SUMMARYIn this paper, the performance of decision directed (DD) maximum likelihood (ML) channel tracking algorithm is analyzed. The ML channel tracking algorithm presents efficient performance especially in the decision directed mode of the operation. In this paper, after introducing the method for analysis of DD algorithms, the performance of ML MIMO channel tracking algorithm in the DD mode of operation is analyzed. In this method channel tracking error is evaluated for a given decision error rate. Then, the decision error rate is approximated for a given channel tracking error. By solving these two derived equations jointly, both the decision error rate and the channel tracking error are computed. The presented analysis is compared with simulation results for different channel ranks, Doppler frequency shifts, and signal‐to‐noise ratios, and it is shown that the analysis is a good match for simulation results especially in high rank MIMO channels and high Doppler shifts. Copyright © 2012 John Wiley & Sons, Ltd.

LDPC Codes for Compressed Sensing

We present a mathematical connection between channel coding and compressed sensing. In particular, we link, on the one hand, channel coding linear programming decoding (CC-LPD), which is a well-known relaxation of maximum-likelihood channel decoding for binary linear codes, and, on the other hand, compressed sensing linear programming decoding (CS-LPD), also known as basis pursuit, which is a widely used linear programming relaxation for the problem of finding the sparsest solution of an underdetermined system of linear equations. More specifically, we establish a tight connection between CS-LPD based on a zero-one measurement matrix over the reals and CC-LPD of the binary linear channel code that is obtained by viewing this measurement matrix as a binary parity-check matrix. This connection allows the translation of performance guarantees from one setup to the other. The main message of this paper is that parity-check matrices of “good” channel codes can be used as provably “good” measurement matrices under basis pursuit. In particular, we provide the first deterministic construction of compressed sensing measurement matrices with an order-optimal number of rows using high-girth low-density parity-check codes constructed by Gallager.

Joint communication and positioning based on soft channel parameter estimation

A joint communication and positioning system based on maximum-likelihood channel parameter estimation is proposed. The parameters of the physical channel, needed for positioning, and the channel coefficients of the equivalent discrete-time channel model, needed for communication, are estimated jointly using a priori information about pulse shaping and receive filtering. The paper focusses on the positioning part of the system. It is investigated how soft information for the parameter estimates can be obtained. On the basis of confidence regions, two methods for obtaining soft information are proposed. The accuracy of these approximative methods depends on the nonlinearity of the parameter estimation problem, which is analyzed by so-called curvature measures. The performance of the two methods is investigated by means of Monte Carlo simulations. The results are compared with the Cramer-Rao lower bound. It is shown that soft information aids the positioning. Negative effects caused by multipath propagation can be mitigated significantly even without oversampling.

Bit error rate minimising pilot symbol arrangement in closed-loop orthogonal frequency division multiplexing systems

The use of a feedback link in wireless orthogonal frequency division multiplexing (OFDM) systems is analysed. Although open-loop scenarios have been rigorously investigated in the literature, closed-loop scenarios, in which there is a feedback link from a strong to a weak user, have not been thoroughly studied. The study mainly focus on the recently proposed dynamic pilot symbol arrangement strategy. It was shown in a recent paper that for coherent OFDM transmission, this strategy is capable of delivering substantial gains in the performance. Pilot symbols are used to sample channel behaviour so that data symbols can be decoded correctly. However, these pilots do not need to be arranged so as to estimate the channel in the best possible way. In this work, the authors propose a pilot symbol arrangement strategy that minimises the bit error rate, we analyse the solution in detail and propose a low complexity search that maintains most of the quality of an exhaustive search. This low complexity search makes the pilot symbol method viable for medium to large-scale OFDM systems. The authors also analyse the use of a Wiener filter for channel estimation combined with the dynamic pilot symbol strategy and show that it delivers good gains in comparison to a simple maximum likelihood channel estimate.

Operational Duality Between Lossy Compression and Channel Coding

We explore the duality between lossy compression and channel coding in the operational sense: whether a capacity-achieving encoder-decoder sequence achieves the rate-distortion function of the dual problem when the channel decoder [encoder] is the source compressor [decompressor, resp.], and vice versa. We show that, if used as a lossy compressor, the maximum-likelihood channel decoder of a randomly chosen capacity-achieving codebook achieves the rate-distortion function almost surely. However, operational duality does not hold for every capacity achieving encoder-decoder sequence, or rate-distortion achieving compressor-decompressor sequence. We show that there exist optimal channel coding [lossy compression] schemes, which fail when used for the dual lossy compression [channel coding resp.] problem.

Effect of source kurtosis on MIMO information rate

We consider how information rate in a Multiple-Input Multiple-Output (MIMO) wireless communication system is affected by the use of non-Gaussian source distributions. Of particular interest is the comparison of information rate for a legitimate receiver with that available to an eavesdropping receiver, as the source distribution becomes less Gaussian or, equivalently, as the magnitude of the source kurtosis increases. A legitimate receiver will usually be able to perform maximum likelihood channel estimation using knowledge of a symbol training sequence embedded in the transmitted data. An eavesdropper however may not have this prior knowledge and will therefore be unable to directly estimate the channel. We compare, via simulations, the performance of a well-known Blind Source Separation (BSS) algorithm with theoretically derived results and where the source distributions are taken from the discrete digital constellations: Quadrature Amplitude Modulation (QAM), Phase Shift Keying (PSK). By incorporating a sample timing offset in the simulations we show how the kurtosis of these digital sources is altered. We also show how the legitimate user and eavesdropper information rates are affected as the source kurtosis is varied.