Bayesian Iterative Channel Estimation for Multiple-Input Multiple-Output Underwater Acoustic Communications

This paper considers pilot-based channel estimation in large-scale multiple-input multiple-output (MIMO) communication systems, also known as “massive MIMO”. Unlike previous works on this topic, which mainly considered the impact of inter-cell disturbance due to pilot reuse (so-called pilot contamination), we are concerned with the computational complexity. The conventional minimum mean square error (MMSE) and minimum variance unbiased (MVU) channel estimators rely on inverting covariance matrices, which has cubic complexity in the multiplication of number of antennas at each side. Since this is extremely expensive when there are hundreds of antennas, we propose to approximate the inversion by an L-order matrix polynomial. A set of low-complexity Bayesian channel estimators, coined Polynomial ExpAnsion CHannel (PEACH) estimators, are introduced. The coefficients of the polynomials are optimized to yield small mean square error (MSE). We show numerically that near-optimal performance is achieved with low polynomial orders. In practice, the order L can be selected to balance between complexity and MSE. Interestingly, pilot contamination is beneficial to the PEACH estimators in the sense that smaller L can be used to achieve near-optimal MSEs.

In recent years, multiple-input multiple-output (MIMO) systems, which use several transmit and receive antennas, have attracted much attention for high performance radio systems. In MIMO systems, the channel estimation is important to distinguish transmit signals from multiple transmit antennas. While the space-alternating generalized expectation-maximization (SAGE) algorithm is known to offer good channel estimation and data detection. We proposed earlier the minimum mean square error (MMSE)-based SAGE algorithm for MIMO systems where the MMSE estimation is used for channel estimation. We showed that the proposed MMSE-based SAGE algorithm can achieve the better bit error rate (BER) than the maximum likelihood (ML) detection with training symbols. The MMSE channel estimation needs the knowledge of the maximum Doppler frequency F <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">d</sub> for deriving the covariance matrix of the channel and the variance sigma <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> of additive white Gaussian noise (AWGN). Additionally, the computation of the MMSE channel estimation requires O(L <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">3</sup> ) operations where L is the transmitted frame length. Thus, its computational complexity is high. In this paper, we propose a zero-forcing (ZF)-based SAGE algorithm for channel estimation and data detection in MIMO systems that does not need the knowledge of Fd and sigma <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> . Since the computation of the proposed ZF-based SAGE algorithm requires O(N <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">3</sup> ) operations where N is the number of transmit antennas, its computational complexity is low. We show that the proposed ZF-based tracking SAGE algorithm with less computational complexity can achieve almost the same BER as that of the MMSE-based tracking SAGE algorithm

In this study, various techniques of UWA (Underwater Acoustic, UWA) channel estimation for underwater MIMO-OFDM system are studied. Dual turbo channel estimation algorithm based on channel puncture technique is proposed. In order to judge the criteria of channel compensation, difference between the raw received signal and the re-coded information signal is carried out. The uncertain sub-channels are punched by using channel puncture technique and replaced by the responses estimated by MMSE (Minimum Mean Square Error, MMSE) or OMP (Orthogonal Matching Pursuit, OMP) algorithms. Compared with the conventional existing algorithms, the proposed algorithm can effectively reduce the occupancy of pilots, offer confined error propagation and significantly increase the stability of the system with Monte Caro simulation. The results of in-tank-experiment further indorse the reliable performance with improved efficiency of 1.51 bits/s/Hz.

This paper studies the effect of channel estimation in WiMAX system. The channel estimation is based on the principle of pilot-symbol-aided channel estimation (PACE) in frequency domain. The algorithms used here are based on the least squares (LS) and the minimum mean squares error (MMSE) approaches. Furthermore we propose a simple method to reduce the computation complexity of MMSE algorithm significantly which has a desirable performance. In the end, our result will quantitatively demonstrate the effect of LS, MMSE and proposed low complexity MMSE algorithms for uncoded IEEE802.16d standard of WiMAX system.

With the increasing rate of wireless devices and high bandwidth operations, wireless networking and communications are becoming over crowded. To cope with such crowded and messy situation, massive MIMO is designed to work with hundreds of low-cost serving antennas at a time as well as improve the spectral efficiency at the same time. Time Division Duplexing (TDD) has been used for gaining beamforming which is a major part of massive MIMO, to gain its best improvement to transmit and receive pilot sequences. All the benefits are only possible if the channel state information or channel estimation is gained properly. Least Square (LS), Minimum Mean Square Error (MMSE) and Linear Minimum Mean Square Error (LMMSE) are the estimators commonly used for estimating channel matrices. We have optimized these methods using genetic algorithm to minimize the mean squared error and finding the best channel matrix from existing algorithms with less computational complexity. Our simulation result has shown that the use of Genetic Algorithm (GA) worked well on existing algorithms in a Rayleigh slow fading channel and existence of Additive White Gaussian Noise. We found that the GA optimized LS is better than existing algorithms. GA provides optimal result in some few iterations in terms of Mean Square Error (MSE) with respect to SNRand computational complexity.

An orthogonal frequency division multiplexing (OFDM) is one of the effective techniques used in wireless communications. In OFDM systems, channel impairments due to multipath dispersive wireless channels can cause deep fades in wireless channels. The OFDM receiver also requires an accurate and computationally efficient channel state information when coherent detection is involved. Therefore, it needs a good robust estimation method of the channel in wireless communication for OFDM systems. And one of these channel estimation methods is minimum mean square error (MMSE) channel estimation. MMSE channel estimation one most used method in OFDM systems. In this work we enhanced robustness of MMSE channel estimation by using it in base of quasi-cyclic low density parity check (QC-LDPC) coded OFDM system.

In cellular communications, recently Multi In Multi Out (MIMO) and Massive MIMO research is getting attention for the need of high data rates in Long Term Evolution Advanced(LTE-A) and 5G Communications. In MIMO baseband signal processing at physical layer, both the channel estimation and the detection algorithms play a crucial role. In this paper it is discussed the estimation algorithms least square (LS) and minimum mean square error (MMSE) and the channel detection algorithms Zero Forcing (ZF) and MMSE. Currently none of the channel estimation algorithms of LTE-A offers twin advantages of low battery consumption and very low latency, which is a key requirement of 5G. It is expected the massive MIMO with 128 or more antennas will be a norm at 5G base stations. To achieve the ultra-low latency, the matrix computations for massive MIMO are the very big bottleneck in realizing the channel estimation and massive MIMO detection algorithms. For the optimization of the 5G Massive MIMO channel estimation and detection algorithms, the prerequisite is massive complex matrix inversion speed. In this paper, a parallel processing based coding scheme is proposed by using Gauss-Jordan elimination kernel algorithm on a single instruction multiple data (SIMD) stream vector processor to realize a complex matrix inverse with optimum speed which is the need of 5G channel estimation and detection.

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

In this paper, we propose a joint channel estimation and symbol detection (JCESD) algorithm relying on message-passing algorithms (MPA) for orthogonal frequency division multiple access (OFDMA) systems. The channel estimation and symbol detection leverage the framework of expectation propagation (EP) and belief propagation (BP) with the aid of Gaussian approximation, respectively. Furthermore, to reduce the computation complexity involved in channel estimation, the matrix inversion is transformed into a series of diagonal matrix inversions through the Sherman-Morrison formula. Simulation experiments show that the proposed algorithm can reduce the pilot overhead by about 50%, compared with the traditional linear minimum mean square error (LMMSE) algorithm, and can approach to the bit error rate (BER) performance bound of perfectly known channel state information within 0.1 dB.

This paper investigates intercarrier interference (ICI) suppression and channel estimation for the uplink of an orthogonal frequency-division multiple-access (OFDMA) system in a time- and frequency-selective fading channel. In such a doubly selective channel, channel variations within each OFDMA block disrupt the orthogonality among subcarriers and leads to ICI. We develop an appropriate signal model for the OFDMA uplink in a doubly selective fading channel and propose a minimum mean square error (MMSE) scheme and an MMSE successive detection (MMSE-SD) scheme to suppress ICI. It is shown that the MMSE scheme is the optimal linear scheme in terms of maximizing achievable data rate and that the MMSE-SD scheme is able to further remove ICI and exploit the Doppler diversity embedded in time-varying channels. As an essential component in ICI suppression, channel estimation is also considered. A basis expansion model (BEM) is formulated for the OFDMA uplink channel, and a pilot-aided channel-estimation algorithm is developed to track users' channels in the time domain. Simulation results are presented to illustrate the overall performance improvements that can be obtained from using the proposed ICI suppression and channel-estimation schemes.

Optimal linear minimum mean square error (MMSE) transceiver design techniques are proposed for Bayesian learning (BL)-based sparse parameter vector estimation in a multiple-input multiple-output (MIMO) wireless sensor network (WSN). Our proposed transceiver designs rely on majorization theory and hyperparameter estimates obtained from the BL module for minimizing the mean square error (MSE) of parameter estimation at the fusion center (FC). The linear transceiver design framework is initially proposed for the general scenario with arbitrary SNR sensor observations, followed by a special case with high-SNR sensor observations scenario. Our analysis also incorporates the channel correlation. The MMSE channel estimates are determined for the sensors (SNs), followed by a robust transceiver design procedure that is resilient to the channel state information (CSI) uncertainty arising due to the channel estimation error, an aberration that is unavoidable in practical implementations. Our simulation results demonstrate the improved performance of the proposed BL framework and optimal MMSE transceiver design in sparse parameter estimation relyingon realistic imperfect channel estimates over the benchmarks.

In this paper, IQ based imbalance as well as channel estimation using hybrid ML-MMSE Equalizer is used to limit the errors in demodulated signal. The IQ based signal has a intrinsic-esteemed type. Thus, the combination of in phase quadrature as well as cordless pass of the channel is well maintained as the productive pass of the channel. Evolved from the intrinsic-esteemed type. After the execution of Minimum Mean Square Error (MMSE) measure, the productive pass in the channel is estimated. By applying hybrid ML-MMSE (Maximum likelihood Minimum mean square error) equalizer to minimize the pilot overhead which occurred over the passage and verify that the MMSE of the constructive channel coarse grain can be diminished by the pilot phase shifts correspondingly. After instigating a pilot phase shift then standardize the system to set covariance matrices for constructive passage for transmitting the signal. Considering the channel assessment act might be corrupted because of using Hybrid ML-MMSE equalizer, therefore advancing an MMSE pattern allocated data detection scheme was used for the channel assessment fault. The illustration of the channel assessment with Hybrid ML-MMSE Equalizer is showed via broad numerical results.

This paper reports on investigations into the effects of spatial correlation on channel estimation and capacity of a multiple input multiple output (MIMO) system. Minimum mean square error (MMSE) method is applied for channel estimation under a correlated channel scenario. Simulation results for a 4 times 4 MIMO system with the Jakes model describing a channel between a base station and a mobile station demonstrate a trade-off between the effects of spatial correlation, channel estimation and capacity. For low values of signal to noise ratio (SNR), spatial correlation decreases channel estimation errors and improves capacity. For high values of SNR, spatial correlation has a less pronounced effect on improving channel estimation and thus the MIMO capacity is adversely affected by the decreased channel matrix rank.

Multipath channels often exhibit sparse structures in multicarrier underwater acoustic (MC-UWA) communication systems. Conventional linear channel estimators, such as least squares (LS) and minimum mean square error (MMSE) are considered as optimal solutions under the assumption of rich multipath. However, they often result in low spectral efficiency due to neglect of the sparsity in multipath channels. In this paper, we propose a novel sparse channel estimation method with compressive sensing. The proposed estimator has better estimation performance and low complexity when compared with the LS estimator. Simulations verified the proposed method with respect to the mean square error (MSE) and the computational complexity. Key words: Underwater acoustic (UWA), orthogonal frequency division multiplexing (OFDM), sparse multipath, compressive sensing (CS), sparse channel estimator.

In this paper, we evaluate the computational complexity and the performance of the RAKE receivers for the Direct Sequence---Ultra Wideband (DS-UWB) with considering the accuracy of channel estimation in a multipath channel. As RAKE receivers for DS-UWB, we consider the maximal-ratio combining (MRC)-RAKE, the minimum mean square error (MMSE)-RAKE, and the MRC-RAKE-Equalizer that is the MRC-RAKE followed by a liner equalizer. Generally, if the channel estimation is perfect, as the number of fingers or taps increases, the performance of each receiver is improved, however the computational complexity of each receiver increases. In practice, the channel estimation is not perfect. The channel estimation error makes their performances degraded. Therefore, the performances of the RAKE receivers depend on the accuracy of channel estimation. Consequently, we evaluate the computational complexities and the Bit Error Rates (BERs) of MRC-RAKE, MMSE-RAKE, and MRC-RAKE-Equalizer with considering the accuracy of channel estimation for DS-UWB. We show that the accuracy of channel estimation affects the BER of each receiver significantly. We also show that when the accuracy of channel estimation is high, MRC-RAKE-Equalizer can achieve the better BER than MMSE-RAKE with less computational complexity, while MMSE-RAKE can achieve the better BER than MRC-RAKE-Equalizer when the accuracy of channel estimation is low.