Low-complexity Channel Estimation Algorithm Research Articles

Doppler Shift and Channel Estimation for Intelligent Transparent Surface Assisted Communication Systems on High-Speed Railways

The critical distinction between the emerging intelligent transparent surface (ITS) and intelligent reflection surface (IRS) is that the incident signals can penetrate the ITS instead of being reflected, which enables the ITS to combat the severe signal penetration loss for high-speed railway (HSR) wireless communications. This paper thus investigates the channel estimation problem for an ITS-assisted HSR network where the ITS is embedded into the carriage window. We first formulate the channels as functions of physical parameters, and thus transform the channel estimation into a parameter recovery problem. Next, we design the first two pilot blocks within each frame and develop a serial low-complexity channel estimation algorithm. Specifically, the channel estimates are initially obtained, and each estimate is further expressed as the sum of its perfectly known value and the estimation error. By leveraging the relationship between channels for the two pilot blocks, we recover the Doppler shifts from the channel estimates, based on which we can further acquire other channel parameters. Moreover, the Cramer-Rao lower bound (CRLB) for each parameter is derived as a performance benchmark. Finally, we provide numerical results to establish the effectiveness of our proposed estimators.

Belief-Propagation-Based Low-Complexity Channel Estimation and Detection for Underwater Acoustic Communications With Moving Transceivers

Achieving reliable communications with low complexity is challenging for underwater acoustic communications with moving transceivers, where the time-varying channels need to be estimated and tracked accurately and data detection needs to be performed with low complexity. In this article, with the use of a superimposed training (ST) scheme, we address this challenge by developing a low-complexity channel estimation and tracking algorithm, which is then integrated with low-complexity data detection in the frequency domain. ST is used to acquire improved channel-tracking capability. Based on belief propagation, we design a message-passing-based low-complexity bidirectional channel estimation (LCE-MP) algorithm, where all computational intensive parts are handled by the fast Fourier transform (FFT) algorithm, thereby achieving very efficient implementation with logarithmic complexity. Specifically, a message-passing-based fast information collection algorithm is presented to acquire “local” channel estimates, followed by the fusion of local channel estimates to achieve a “global” estimate of the channel. It is shown that the computational complexity per channel tap is only in a logarithmic level for the channel estimation and tracking. Moreover, the ST-scheme-based LCE-MP algorithm is combined with FFT-based data detection and decoding, which are performed in an iterative manner. The overall complexity of channel estimation and data detection is in a logarithmic level, and the system delivers excellent performance thanks to the joint processing. Field experiments were carried out in Jiaozhou Bay in 2019, and the experimental results verify the effectiveness of the proposed technique.

Joint estimation and detection method based on turbo equalization framework and VAMP

In this letter, we consider the single-carrier frequency domain equalization (SC-FDE) system, and propose a low-complexity joint symbol detection and channel estimation algorithm based on the recently proposed vector approximate message passing (VAMP). Specifically, we leverage VAMP twice to estimate symbols and channels, respectively, in a turbo-like way. Moreover, this algorithm organically combines the gaussian mixture model (GMM), which can accurately simulate the sparse aggregation characteristics of the channel and effectively suppress inter symbol interference (ISI). The simulation results show that compared with the traditional linear minimum mean square error (LMMSE) estimation receiving algorithm and the existing generalized approximate message passing algorithm (GAMP), the designed receiving algorithm has significant advantages in channel estimation normalized mean square error (NMSE) and bit error ratio (BER) performance, where sharing the same order of complexity.

Low complexity channel estimation algorithm using paired spatial signatures for UAV 3D MIMO systems

This paper proposes a low complexity channel estimation algorithm for unmanned aerial vehicle three dimension multi-user multiple-input-multiple-output (3D MIMO) systems with the uniform planar array (UPA) at base station using paired spatial signatures. With the aid of antenna array theory and array signal processing, 3D channel is firstly modeled based on the angles between the direction of arrival along x- and y-axis of the UPA. And 3D MIMO channels can be projected onto the x- and y-directions, respectively. Then, channel estimation for multi-user uplinks using small amount of training resources is divided into two phases. At the first uplink preamble phase, each user is assigned the orthogonal pilot, and the paired spatial signatures and optimal rotation angle of each user through the same pilot sequence are obtained. We also propose a user grouping strategy based on three-dimension angle-division multiple access (3D-ADMA) to ensure that the user's spatial signatures do not overlap. At the second phase during several coherence times, the same pilot sequence within a group and orthogonal pilot sequences between groups are assigned, then, the channel state information of the user's x- and y-directions are recovered by the paired space signatures and optimal rotation angle of each user obtained in the preamble phase, respectively. And dynamically updating the user's paired spatial signatures and optimal rotation angle utilizes the obtained channel parameter of x- and y-directions. Finally, the channel parameter of the x- and y-directions are reconstructed by the updated user's space signatures and the optimal rotation angle, and the 3D MIMO channel estimation is obtained through the Kronecker product. Compared with the conventional channel estimation method of the 3D MIMO system under UPA using a low-rank model, the proposed methods reduce the computational complexity without degrading the estimated performance to a large extent. Furthermore, it is carried out with limited training resources, and the pilot resource overhead of the system is greatly reduced by the 3D-ADMA packet and the two-stage pilot allocation. Simulation results verified that the proposed algorithm is effective and feasible.

Channel Estimation for Underwater Acoustic Communications Based on Orthogonal Chirp Division Multiplexing

Orthogonal chirp division multiplexing (OCDM) is a recently proposed multiplexing scheme and has drawn increasing attention in underwater communications. In an OCDM system, a series of orthogonal chirp signals carry the data information. However, the time variation feature of underwater acoustic (UWA) channels is rarely considered in the existing OCDM systems. In this paper, a particular transmission structure is proposed for the OCDM system to process the signal block-by-block at the receiver. Moreover, a low complexity channel estimation algorithm and the corresponding equalizers are derived. The proposed structure has a better ability to track time-varying channels. The simulation results show that the proposed method achieves promising performance under time-varying channels.

Millimeter Wave Channel Estimation Based on Subspace Fitting

We consider the channel estimation of millimeter wave (mmWave) multiple-input multiple-output systems, where both the transmitter and receiver adopt hybrid beamforming structure. Due to the spatial sparsity of the mmWave channel, it can be reconstructed by estimating the direction and gain of the paths. Leveraging this feature, we propose a channel estimation algorithm based on subspace fitting to estimate the path directions, and the path gains are obtained using the least squares method. However, similar to the most existing mmWave channel estimation schemes, the proposed algorithm requires a two-dimensional search in candidate angle space, which is very complicated. In order to reduce the computational complexity, we develop a low-complexity channel estimation algorithm using the orthogonal matching pursuit (OMP) method, which significantly reduces the computational complexity. However, when the paths are strongly correlated, the channel estimation accuracy will decrease. To overcome this defect, we further develop a low-complexity method based on subspace fitting. This algorithm makes a trade-off between the computational complexity and channel estimation accuracy. Furthermore, the pilot beam pattern for different hybrid beamforming structure is designed using infinitely and quantized phase shifters to improve the signal-to-noise ratio of the pilot signals. In addition, the proposed channel estimation methods can also be used in the multi-user scenario. Simulation results demonstrate that the proposed subspace fitting method outperforms the existing methods when the angular resolution is the same. Meanwhile, the low-complexity OMP and subspace fitting methods have a good performance in single path scenario when compared to subspace fitting method, even if the computation complexity is lower. Moreover, the performance of the low-complexity subspace fitting method is close to the subspace fitting method.

BEM-Based Low-Complexity Analytical Channel Estimation with Optional Iterative Interference Cancellation Over Rapidly Time-Varying Channels for MIMO OFDM Systems

A BEM-based low-complexity channel estimation algorithm with analytical solution is proposed over rapidly time-varying channels for multiple-input multiple-output (MIMO) orthogonal frequency division multiplexing (OFDM) systems. The time-varying channel taps are estimated with the aid of the designed clustered frequency-multiplexed pilots across different antennas along with basis expansion model (BEM). The proposed approach is specifically designed for MIMO OFDM systems over doubly selective channels. For each subchannel, the derived BEM coefficients can be expressed by explicit analytical solution, whose calculations are partitioned into two steps. During the two steps, two different basis functions such as the critically sampled complex exponential (CCE)-BEM and P-BEM are adopted, respectively. For a MIMO system with $$N_T$$NT transmit antennas, $$N_R$$NR receive antennas and $$L$$L channel taps, the complexity order of the proposed channel estimation is $$O(N_T N_R L\log L)$$O(NTNRLlogL), whereas the complexity order of least squares (LS) estimation is $$O((N_T N_R L)^3)$$O((NTNRL)3). Additionally, the proposed channel estimation can be iteratively improved in conjunction with hybrid interference cancelation, with only requiring one iteration. Simulation results corroborate the performance advantages of the proposed solution over CCE-BEM based LS scheme under different normalized Doppler spreads.

Channel Estimation and Hybrid Precoding for Millimeter Wave Cellular Systems

Millimeter wave (mmWave) cellular systems will enable gigabit-per-second data rates thanks to the large bandwidth available at mmWave frequencies. To realize sufficient link margin, mmWave systems will employ directional beamforming with large antenna arrays at both the transmitter and receiver. Due to the high cost and power consumption of gigasample mixed-signal devices, mmWave precoding will likely be divided among the analog and digital domains. The large number of antennas and the presence of analog beamforming requires the development of mmWave-specific channel estimation and precoding algorithms. This paper develops an adaptive algorithm to estimate the mmWave channel parameters that exploits the poor scattering nature of the channel. To enable the efficient operation of this algorithm, a novel hierarchical multi-resolution codebook is designed to construct training beamforming vectors with different beamwidths. For single-path channels, an upper bound on the estimation error probability using the proposed algorithm is derived, and some insights into the efficient allocation of the training power among the adaptive stages of the algorithm are obtained. The adaptive channel estimation algorithm is then extended to the multi-path case relying on the sparse nature of the channel. Using the estimated channel, this paper proposes a new hybrid analog/digital precoding algorithm that overcomes the hardware constraints on the analog-only beamforming, and approaches the performance of digital solutions. Simulation results show that the proposed low-complexity channel estimation algorithm achieves comparable precoding gains compared to exhaustive channel training algorithms. The results illustrate that the proposed channel estimation and precoding algorithms can approach the coverage probability achieved by perfect channel knowledge even in the presence of interference.

A Low Complexity Channel Estimation Algorithm for Massive MIMO System

Massive MIMO can boost the capacity and increase the coverage, however the pilot overhead of its channel estimation will linearly increase with the antenna increasing. In order to reduce pilot overhead and improve the quality of channel estimation, a multi-dimension Wiener filtering channel estimation algorithm was put forward. First we analyzed Massive MIMO system model and channel model in which Base station configured a two-dimension antenna array; then accomplished channel estimation applying the correlation function of time, frequency, the row and column of the antenna array, and presented a simple closedform solution of the space-time-frequency correlation function to reduce the complexity of the algorithm. The proposed algorithm extends one-dimension space filtering to two-dimension, so doesn’t need to transmit pilots in every raw of the two-dimension antenna array contrast with 3D-Wiener and can reduce beyond 50% pilot overhead. Based on the simulation results, this algorithm can achieve 8dB performance gain over 2D-Winner and 3dB over 3D-Wiener with same pilot overhead and can acquires the optimal throughput with considering both the channel estimation quality and pilot overhead.

Low complexity PARAFAC‐based channel estimation for non‐regenerative MIMO relay systems

In this study, the authors present a novel channel estimation scheme for a two-hop non-regenerative multiple-input multiple-output relay system. The proposed scheme has two stages. In the first stage, the source node transmits channel training sequence to the relay node. The relay node amplifies the received signal and forwards it to the destination node. During the second stage, the relay node amplifies the pre-received signal with another amplification matrix, and forwards it to the destination node. Based on the proposed scheme, by using parallel factor (PARAFAC) analysis, they further propose a low complexity channel estimation algorithm, where full knowledge of all channel matrices involved in the communication can be estimated at the destination node. Compared with existing algorithms, the proposed algorithm yields smaller channel estimation error with lower complexity. Numerical examples are shown to demonstrate the effectiveness of the low complexity PARAFAC-based channel estimation algorithm.

Low‐complexity channel estimation and turbo equalisation for high frequency channels

A low-complexity channel estimation algorithm is proposed to improve performance of two high frequency standardised waveforms: MIL-STD-188-110B Appendix C standard and STANAG 4285. In the proposed estimation algorithm, the channel impulse response is modelled as a linear-time function within a frame and the least square criterion is adopted. With the estimated CIRs, the authors study and compare bit-error-rate (BER) performance and complexity of three turbo equalisation (TEQ) schemes, including the minimum mean-square error (MMSE), the MMSE with decision feedback equalisation (DFE) (MMSE-DFE) and the soft-feedback interference-cancellation (SFIC) turbo receivers. The authors then propose a hybrid TEQ scheme that uses the MMSE-DFE equaliser for the first iteration and the SFIC equaliser for the rest. Simulation results show that the proposed channel estimation algorithm performs well and the TEQ schemes realise a significant performance improvement as compared with a non-iterative receiver. Moreover, the proposed hybrid TEQ scheme achieves the best trade-off between BER and complexity for the MIL-STD-188-110B Appendix C standard, whereas the SFIC-TEQ scheme is optimal for the STANAG 4285 standard.