Complexity-Reduced Suboptimal Equalization with Monte Carlo Based MIMO Detectors

In this paper, we propose a low complexity graph-based linear minimum mean square error (LMMSE) equalizer in order to remove inter-symbol and inter-stream interference in multiple input multiple output (MIMO) communication. The proposed state space representation inflicted on the graph provides linearly increasing computational complexity with block length. Also, owing to the Gaussian assumption used in the presented cycle-free factor graph, the complexity of the suggested equalizer structure is not affected by the size of the signalling space. In addition, we introduce an efficient way of computing extrinsic bit log-likelihood ratio (LLR) values for LMMSE estimation compatible with higher order alphabets which is shown to perform better than the other methods in the literature. Overall, we provide an efficient receiver structure reaching high data rates in frequency selective MIMO systems whose performance is shown to be very close to a genie-aided matched filter bound through extensive simulations.

We generalize the multiuser (CDMA spread spectrum) communication systems to the fading environments. We first extend Verdu's (1986) conventional optimum receiver to Rayleigh-fading environments and then evaluate its performance. Having no knowledge of the received power at the receiving end, we therefore need an estimator to efficiently estimate the received signal strength of each user in fading environments. A linear minimum mean square error (LMMSE) unbiased estimator is proposed to attain this goal. By using the minimum mean square error (MMSE) Bayesian estimation, we further propose the LMMSE bit estimator for efficient demodulation. Its performance is close to the optimum multiuser receiver but with a much simpler polynomial complexity. To further reduce the complexity, we extend the LMMSE estimator to the sequential LMMSE estimator. In sequential estimation, we do not need to implement the matched filter banks and to perform the matrix inversion when estimating. In addition, it converges after approximately 2k iterations, where k is the number of users. With this fast convergence property and the simple structure, the sequential LMMSE estimator provides an attractive alternative to the implementation of a multiuser system.

In recent years, there has been an increased need for digital wireless applications to use high rate data transmission. OFDM (Orthogonal Frequency Division Multiplexing) offers an interesting solution that allows for the exploitation of the 60 GHz band with optimal spectral efficiency, a robustness to frequency selective fading, and a resistance to inter-symbol interference (ISI) that is a major problem in high speed data communications. Transmitted data in an OFDM system is divided on different subcarriers, after applying PSK (phase shift keying) or QAM (Quadrature Amplitude Modulation) modulation. The bandwidth of the obtained signal is converted to the time domain by using an IFFT (Inverse Fast Fourier Transform) in order to transmit it through a wireless channel. To recover the distorted data at the receiver, the effects of the channel must be estimated and compensated by the receiving system [1, 2]. In this paper, the 60 GHz channel estimation methods for OFDM systems based on comb-type pilot arrangement are investigated, as the algorithm of channel estimation based on comb-type is divided into pilot signal estimation and channel interpolation. The pilot signal estimation based on LS (Least Squares) or LMMSE (Linear Minimum Mean Square Error) criteria is studied along with the channel interpolation based on LI (linear interpolation). The performances of various estimation algorithms are evaluated and compared by measuring the Bit Error rate (BER) and Mean Square Error (MSE) where 16-QAM modulation scheme is applied.

Channel estimation (CE) is a challenging problem and one of the key technologies in Orthogonal Frequency Division Multiplexing (OFDM) systems. The Linear Minimum Mean Square Error (LMMSE) proposed for OFDM systems has excellent Mean Square Error (MSE) performance. However, the conventional method requires the statistical knowledge of the channel information in advance and the complicated inverse operation of large dimension matrices. In this case, an enhanced fast LMMSE channel estimation using Fast Fourier Transform (FFT) operation and the most significant taps (MST) algorithm for OFDM systems is proposed. This method has the advantage of low computational complexity and no requirement on the detailed channel information. In addition, simulation results demonstrate that the proposed algorithm outperforms other LMMSE methods in terms of bit error rate (BER) without the loss of MSE performance.

Ever since the adoption of the single carrier frequency division multiple access (SC-FDMA) scheme for the uplink in the Long Term Evolution (LTE) standard, there has been much interest in improved receiver algorithms for the same. Successive interference cancelation (SIC) based turbo receivers (Turbo SIC) have been proposed to tackle the multi-stream interference (MSI) for transmission modes such as spatial multiplexing (SM) and multiuser (MU) multiple input multiple output (MIMO). In addition, decision feedback equalizers (DFE) have been discussed as an alternative to the simple linear minimum mean square error (LMMSE) based receivers to suppress intersymbol interference (ISI) caused by the frequency selective multi-path channel. This paper proposes a DFE receiver variant based on parallel interference cancelation (PIC) with maximum likelihood detection (MLD) and ordered SIC (OSIC) principles to suppress ISI and MSI. Simulations show that the proposed receiver performs better than the existing SIC and DFE based receivers and achieves the matched filter bound (MFB) for both coded and uncoded systems.

The MIMO detector should output the log-likelihood ratio (LLR) of each coded bit to the channel decoder in order to achieve the desired bit error rate (BER) performance in a channel coded multiple-input multiple-output (MIMO) system, whereas channel estimation error which will result in performance degradation in the practical MIMO system. This paper proposes to divide the linear minimum mean square error(LMMSE) into two parts: white noise error and Wiener filter error (the error caused by the ideal channel after Wiener filtering). Based on the Wiener filter coefficients, noise, and channel response, we can derive channel estimation errors and incorporate them into the MMSE detector to improve system performance. The simulation results show that the proposed new method can improve system performance with negligible complexity increase.

Linear minimum mean square error (LMMSE) receivers are often applied in practical communication scenarios for single-input-multiple-output (SIMO) systems owing to their low computational complexity and competitive performance. However, their performance is only the best among all the linear receivers, as they minimize the bit mean square error (MSE) alone in linear space. To overcome this limitation, in this study, we propose an LMMSE receiver based on the measurements augmented by their nonlinear conversion for a photon-counting receiver, a photomultiplier tube, and an avalanche photodetector. The performance of the proposed LMMSE receiver is studied for different nonlinear conversions, numbers of receivers, and receiver types. The simulation results indicate that the Monte Carlo results are consistent with the analytical results and that the proposed LMMSE receiver outperforms the conventional one in terms of bit MSE and bit error rate. Accordingly, it can be concluded that to achieve a desired bit MSE, the proposed LMMSE-based nonlinear receiver not only reduces the need to increase the number of receivers but also reduces the bandwidth requirements.

In this paper we propose a novel turbo equalizer based on the expectation propagation (EP) algorithm. Optimal equalization is computationally unfeasible when high-order modulations and/or large memory channels are used. In these scenarios, low-cost and suboptimal equalizers, such as those based on the linear minimum mean square error (LMMSE), are commonly used. The LMMSE-based equalizer can be efficiently implemented with a Kalman smoother (KS), i.e., a forward and backward Kalman filtering whose predictions are merged in a posterior smoothing step. Recently, it was shown that applying EP at the forward and backward stages of a KS equalizer could significantly improve its performance. In this paper, we investigate applying EP at the smoothing level instead. Also, we propose some further modifications to better exploit the information coming from the channel decoder in turbo equalization schemes. Overall, we remarkably reduce the computational complexity while highly improving the performance in terms of bit error rate.

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.

A decision-directed (DD) channel estimation based on iterative linear minimum mean square error (LMMSE) is proposed for orthogonal frequency division multiplexing systems. Existing DD channel estimation is well known to have the problem of error propagation because of symbol-by-symbol detection. The proposed algorithm can estimate the correction term of current channel state information (CSI) according to the error vector of previous CSI by applying the orthogonality principle, and corrects the current CSI with this correction term. Analysis and simulation results have shown that this method has no error propagation problem. The performance of the proposed algorithm is much better than the conventional DD channel estimation, and close to the optimal LMMSE estimator, but with much less computational complexity compared with the optimal LMMSE estimator.

Photon-counting detectors are greatly improving the resolution and image quality in computed tomography (CT) technology. The drawback is, however, that the reconstruction becomes more challenging. This is because there is a considerable increment of the processing data due to the multiple energy bins and materials in the reconstruction analysis, as well as improved resolution. Yet efficient material decomposition and reconstruction methods tend to generate noisy images that do not completely satisfy the expected image quality. Therefore, there is a need for efficient denoising of the resulting material images. We present a new and fast denoiser that is based on a linear minimum mean square error (LMMSE) estimator. The LMMSE is very fast to compute, but not commonly used for CT image denoising, probably due to its inability to adapt the amount of denoising to different parts of the image and the difficulty to derive accurate statistical properties from the CT data. To overcome these problems we propose a model-based deep learning strategy, that is, a deep neural network that preserves an LMMSE structure (model-based), providing more robustness unseen data, as well as good interpretability to the result. In this way, the solution adapts to the anatomy in every point of the image and noise properties at that particular location. In order to asses the performance of the new method, we compare it to both to a conventional LMMSE estimator and to a “black-box” CNN in a simulation study with anthropomorphic phantoms.

LMMSE and MAP estimators for reduction of multiplicative noise in the nonsubsampled contourlet domain

The author proposed soft decision feedback equalisation for orthogonal frequency division multiplexing (OFDM) transmission over doubly selective channels which is used for turbo equalisation. The doubly selective channel is approximated using the basis expansion model (BEM). The decision feedback equaliser (DFE) is obtained and updated for every sub-carrier which results in a per-tone DFE. On the basis of the Gaussian approximation, expressions for the a priori, the a posteriori and the extrinsic information have been derived for quadrature phase shift keying (QPSK) modulation. For turbo equalisation, where iterative joint channel equalisation and channel decoding is executed, in the first iteration, estimates are based on the feed-forward filter which are fed to the channel decoder. These estimates are not reliable and may incur error propagation and poor turbo equalisation performance. For more reliable estimates in the first iteration, the DFE is initialised as a linear minimum mean square error (LMMSE) equaliser. The per-tone LMMSE soft-output equaliser is also derived, and expressions for the a priori, a posteriori and extrinsic information are obtained viewing the LMMSE equaliser as a special case of the DFE. The extrinsic information in both cases was derived based on the Gaussian approximation. Numerical results for bit-error rate performance assuming the BEM channel model and Jakes' channel model are shown to confirm our findings.

The basic idea of this letter is concerned with the large Peak-to-Average Power Ratio (PAPR) problem in multi-carrier Under-Water Acoustic (UWA) communication systems that implement Orthogonal Frequency Division Multiplexing (OFDM). A Tangent Rooting (TanhR) companding technique is presented in this paper to reduce the PAPR in UWA communication systems. This technique achieves a noticeable reduction of the PAPR in UWA systems, while maintaining a good Bit Error Rate (BER) performance . Channel equalisation with Linear Minimum Mean Square Error (LMMSE) and Zero-Forcing (ZF) equalisers is considered in this paper. Simulation results ensure superiority of the proposed technique compared to the Selected Mapping (SLM) and the Partial Transmit Sequence (PTS) techniques from both the PAPR and BER perspectives.

In a code-division multiple-access system, multiuser detection (MUD) can exploit the information of signals from other interfering users to increase system capacity. However, the optimum MUD can be characterized as an NP-hard combinatorial optimization problem such that the computational complexity increases exponentially with the number of users. In this paper, we apply a new evolutionary algorithm, called particle swarm optimization (PSO), to develop a suboptimal MUD strategy. The decorrelating detector (DD) or linear minimum mean square error (LMMSE) detector is used as the first stage to initialize the PSO-based MUD. Then, the PSO algorithm is applied to detect the received data bit by optimizing an objective function incorporating the linear system of the DD or LMMSE detector. Simulation results show that the performance of our proposed decorrelating PSO and LMMSE-PSO MUD are promising and outperform the decorrelating and LMMSE MUD with a slight increase in computation.