Finite dictionary techniques for MSER equalization in RKHS

Adaptive beamforming is capable of separating user signals transmitted on the same carrier frequency, and thus provides a practical means of supporting multiusers in a space-division multiple-access scenario. Moreover, for the sake of further improving the achievable bandwidth efficiency, high-throughput quadrature amplitude modulation (QAM) schemes have become popular in numerous wireless network standards, notably, in the recent WiMax standard. This contribution focuses on the design of adaptive beamforming assisted detection for the employment in multiple-antenna aided multiuser systems that employ the high-order QAM signalling. Traditionally, the minimum mean square error (MMSE) design is regarded as the state-of-the-art for adaptive beamforming assisted receiver. However, the recent work (Chen et al., 2006) proposed a novel minimum symbol error rate (MSER) design for the beamforming assisted receiver, and it was demonstrated that this MSER design provides significant performance enhancement, in terms of achievable symbol error rate, over the standard MMSE design. This MSER beamforming design is developed fully in this contribution. In particular, an adaptive implementation of the MSER beamforming solution, referred to as the least symbol error rate algorithm, is investigated extensively. The proposed adaptive MSER beamforming scheme is evaluated in simulation, in comparison with the adaptive MMSE beamforming benchmark.

Adaptive channel equalisation is a signal processing technique to mitigate inter-symbol interference (ISI) in a time dispersive channel. To this end, the use of least mean squares (LMS) algorithm and its variants is widespread since they minimise the minimum mean squared error (MMSE) criteria by online stochastic gradient algorithms and they asymptotically tend to the optimal Weiner solution for linearly separable channels. The kernel least mean squares (KLMS) algorithm and its variants are based on the MMSE based algorithms for non-linear channels. However, as has been pointed out in the literature, the minimum bit/symbol error rate (MBER/MSER) criterion is a better choice for adapting an equaliser as compared to the traditional approaches based on MMSE criterion. In this paper, we propose a novel equaliser that is inspired from the recently proposed MSER adaptation by Gong et al. using the kernel trick for non-linear channel equalisation.

The paper considers the problem of constructing adaptive minimum bit error rate (MBER) neural network equalisers for binary signalling. Motivated from a kernel density estimation of the bit error rate (BER) as a smooth function of training data, a stochastic gradient algorithm called the least bit error rate (LBER) is developed for adaptive nonlinear equalisers. This LBER algorithm is applied to adaptive training of a radial basis function (RBF) equaliser in a channel intersymbol interference (ISI) plus co-channel interference setting. A simulation study shows that the proposed algorithm has good convergence speed, and a small-size RBF equaliser trained by the LBER can closely approximate the performance of the optimal Bayesian equaliser. The results also demonstrate that the standard adaptive algorithm, the least mean square (LMS), performs poorly for neural network equalisers because the minimum mean square error (MMSE) is clearly suboptimal in the equalisation setting.

The multikernel adaptive filters based on the minimum mean square error (MMSE) criterion have been proposed to improve the performance of the kernel least mean square (KLMS), efficiently. However, these multikernel methods suffer from large computational burden as well as instability in impulsive noises. To address these issues, a novel multikernel method is proposed by replacing the trace operation of a matrix with the inner product of two vectors, thus leading to higher computational efficiency, significantly. Based on the maximum correntropy criterion, the multikernel maximum correntropy (MKMC) algorithm is therefore proposed. To further reduce the complexity, an online vector quantization strategy is presented for MKMC to generate the quantized MKMC (QMKMC) algorithm. Monte Carlo simulations on different nonlinear examples validate the superiorities of the proposed two algorithms.

The kernel adaptive filters (KAFs) based on the minimum mean square error (MMSE) criterion in reproducing kernel Hilbert space (RKHS) improve the performance of linear adaptive filters but result in instability issues and large burdens of computation and memory in impulsive noises. To this end, a novel Nystrom kernel recursive generalized maximum correntropy (NKRGMC) with probability density rank-based quantization (PRQ) sampling (NKRGMC-PRQ) algorithm is proposed to improve filtering performance, robustness, and computational efficiency of the traditional KAFs in this letter. In a fixed dimensional network structure, the proposed NKRGMC-PRQ algorithm can achieve a comparable performance to KAFs with low computational complexity. Monte Carlo simulations are conducted to validate the superiorities of NKRGMC-PRQ in terms of filtering accuracy, computational complexity, and robustness.

In orthogonal frequency division multiplexing (OFDM), Fourier Transform (FT) is used as a modulation technique. To avoid inter-symbol interference (ISI) in OFDM by a time dispersive channel, a cyclic prefix (CP) is used which also reduces its spectral efficiency. wavelet packet transform (WPT) as a modulation scheme has been proposed for wireless communication. In this paper, WPT based OFDM is presented and proposed using minimum mean square error (MMSE) equalizer. Equalization is a major factor in wavelets. MMSE is proposed for wavelet based OFDM (WOFDM) based on WPT and compared with zero forcing equalizer (ZFE). The performance is measured for arbitrary magnitude finite impulse response (FIR) channels in the presence of additive white Gaussian noise (AWGN) and impulse noise. Simulation results show a clear improvement in bit error rate (BER) for MMSE over ZFE equalization technique in the presence of noise.

Sound Source Localization (SSL) is critical in industrial environments for monitoring equipment status and ensuring operator safety. Current SSL methods face a trade-off between accuracy and model complexity. Therefore, developing precise and lightweight SSL methods for devices with limited computational resources remains an urgent necessity. This paper introduces Latent Space Kernel Least Mean Square (LS-KLMS), a novel lightweight online learning algorithm designed for accurate and efficient SSL. LS-KLMS integrates Latent Space Model (LSM) with the Kernel Least Mean Square (KLMS) framework, enabling the transformation of high-dimensional audio data into a low-dimensional latent space and subsequently mapping it into a Reproducing Kernel Hilbert Space (RKHS). Within RKHS, linear filtering establishes nonlinear relationships between multi-channel audio signals and source coordinates, maintaining the lightweight and online learning capabilities inherent to Kernel Adaptive Filtering (KAF). An SSL system utilizing eight <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$\mathbf{6 4}$</tex>-channel microphone arrays is deployed in a real-world hydropower station to evaluate the performance of LS-KLMS against popular existing SSL methods. Experimental results demonstrate that LS-KLMS achieves superior localization accuracy while maintaining a lightweight structure and exhibiting stable, rapid convergence. These attributes make LS-KLMS a promising solution for accurate and efficient SSL in resource-limited industrial applications.

This paper investigates the kernel entropy based extended Kalman filter (EKF) as the navigation processor for the Global Navigation Satellite Systems (GNSS), such as the Global Positioning System (GPS). The algorithm is effective for dealing with non-Gaussian errors or heavy-tailed (or impulsive) interference errors, such as the multipath. The kernel minimum error entropy (MEE) and maximum correntropy criterion (MCC) based filtering for satellite navigation system is involved for dealing with non-Gaussian errors or heavy-tailed interference errors or outliers of the GPS. The standard EKF method is derived based on minimization of mean square error (MSE) and is optimal only under Gaussian assumption in case the system models are precisely established. The GPS navigation algorithm based on kernel entropy related principles, including the MEE criterion and the MCC will be performed, which is utilized not only for the time-varying adaptation but the outlier type of interference errors. The kernel entropy based design is a new approach using information from higher-order signal statistics. In information theoretic learning (ITL), the entropy principle based measure uses information from higher-order signal statistics and captures more statistical information as compared to MSE. To improve the performance under non-Gaussian environments, the proposed filter which adopts the MEE/MCC as the optimization criterion instead of using the minimum mean square error (MMSE) is utilized for mitigation of the heavy-tailed type of multipath errors. Performance assessment will be carried out to show the effectiveness of the proposed approach for positioning improvement in GPS navigation processing.

In orthogonal frequency-division multiplexing (OFDM) systems, it is generally assumed that the channel response is static in an OFDM symbol period. However, the assumption does not hold in high-mobility environments. As a result, intercarrier interference (ICI) is induced and the system performance is degraded. A simple remedy for this problem is the application of the zero-forcing (ZF) and minimum mean square error (MMSE) equalizers. Unfortunately, the direct ZF method requires the inversion of an NxN ICI matrix, where N is the number of subcarriers. When N is large, the computational complexity can become prohibitively high. As for the direct MMSE method, in addition to an NxN matrix inverse, it requires an extra NxN matrix multiplication, making the required computational complexity higher compared to the direct ZF method. In this dissertation, we first propose a low-complexity ZF method to solve the problem in single-input-single-output (SISO) OFDM systems. The main idea is to explore the special structure inherent in the ICI matrix and to apply Newton's iteration for matrix inversion. With our formulation, fast Fourier transforms (FFTs) can be used in the iterative process, reducing the complexity from O(N^3) to O(Nlog_2 N) . Also, the required number of the iteration is typically one or two. We also analyze the convergence behavior of the proposed method and derive the theoretical output signal-to-interference-noise-ratio (SINR). For the MMSE method, we first reformulate the MMSE solution in a way that the extra matrix multiplication can be avoided. Similar to the ZF method, we then exploit the structure of the ICI matrix and apply Newton's iteration to reduce the complexity of the matrix inversion. For a multiple-input-multiple-output (MIMO) OFDM system, the required complexity of the ZF and MMSE methods becomes more intractable. We then manage to extend the proposed ZF and MMSE methods for SISO-OFDM systems to MIMO-OFDM systems. It turns out that the computational complexity can be reduced even more significantly. Simulation results show that the performance of the proposed methods is almost as good as that of the direct ZF and MMSE methods, while the required computational complexity is reduced dramatically. Finally, we explore the application of the proposed methods in mobility-induced ICI mitigation for OFDM multiple access (OFDMA) systems, and in carrier frequency offset (CFO) induced ICI mitigation for OFDMA uplink systems. As that in OFDM systems, the proposed methods can reduce the required computational complexity, effectively.

Filtered multitone (FMT) modulation divides the communication band into several subbands to shorten the span of symbols affected by multipath in underwater acoustic (UWA) communications. However, there is still intersymbol interference (ISI) in each subband of FMT modulation degrading communication performance. Therefore, ISI suppression techniques must be applied to FMT modulation UWA communications. The suppression performance of traditional adaptive equalization methods often exploited in FMT modulation UWA communications is limited when the effect of ISI spans tens of symbols or large constellation sizes are used. Turbo equalization consisting of adaptive equalization and channel decoding can improve equalization performance through information exchanging and iterative processes. To overcome the shortcoming of traditional minimum mean square error (MMSE) equalization and effectively suppress the ISI with relatively low computation complexity, an FMT modulation UWA communication using low-complexity channel-estimation-based (CE-based) MMSE turbo equalization is proposed in this paper. In the proposed method, turbo equalization is first exploited to suppress the ISI in FMT modulation UWA communications, and the equalizer coefficients of turbo equalization are adjusted using the low-complexity CE-based MMSE algorithm. The proposed method is analyzed in theory and verified by simulation analysis and real data collected in the experiment carried out in a pool with multipath propagation. The results demonstrate that the proposed method can achieve better communication performance with a higher bit rate than the FMT modulation UWA communication using traditional MMSE adaptive equalization.

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 present days, there has been a race among the communication systems in different schemes and generations. Gradually the transmission rate of data is increasing tremendously and breaking the previous generation's record. Now people are thinking of transmitting data beyond imagination. Using multiple antennas both at transmitter and receiver side, MIMO wireless technology efficiently provides very high spectral efficiency, boost the data transmission rate, enhance link reliability and improve system coverage. While transmitting data over mobile radio channels at high bit rates, the impulse response of the channel can be extended over a lot of symbol periods, leading fading and Inter-symbol interference (lSI). Equalizers are used to minimize Fading and interference effects. The analysis of the paper is studying the performance of Minimum mean square error method in terms of BER for MIMO (2×2) and (3×3) wireless channels. Binary Phase Shift Keying (BPSK) modulation technique was used in Rayleigh flat fading channel. Simulating in MATLAB results show that Minimum mean square error (MMSE) receivers is good for noise free channel and is successful in removing ISI. Successive interference method with optimal ordering outperforms the MMSE however a few problems arise because of iterative nature of the algorithm.

Multiple-input multiple-output (MIMO) systems can achieve high data-rate and high capacity transmission. In MIMO systems, the scheme that weight substreams based on minimum mean square error (MMSE) criterion at the transmitter using feedback channel state information (CSI) achieves good performance (denoted hereafter as MMSE precoder). However, if the optimum number of substreams is not selected based on CSI and methods for reducing the performance degradation due to feedback delay is not used, MMSE precoder cannot achieve the full performance possible. In this paper, we propose an MMSE precoder with mode selection for MIMO systems, which selects both the number of substreams and the modulation scheme for each substream to minimize the average BER at a fixed rate. We evaluate the BER of the proposed MMSE precoder with two methods for reducing performance degradation due to feedback delay, channel prediction and receive weight robust to feedback delay. We also evaluate the BER of the proposed MMSE precoder with the method that combines channel prediction with receive weight robust to feedback delay. Simulation results show that the BER of the proposed MMSE precoder is improved compared to that of the conventional MMSE precoder using the fixed number of substreams. We also show that the method that combines channel prediction with receive weight robust to feedback delay can achieve good BER even when the large feedback delay exists.

The performance of linear filters degrade drastically when applied to mitigate intersymbol interference caused by channels with frequent nulls in their spectral characteristics like, e.g., time-dispersive radio channels. In such cases, the well-known decision feedback equalizer (DFE) is one possible nonlinear approach to improve the quality of the receiver. However, adapting the DFE filter coefficients to equalize time-varying channels is computationally intense, especially if the dimension of the observation vector is very high. In this paper, we apply the conjugate gradient (CG) algorithm to a conventional minimum mean square error (MMSE) DFE in order to reduce its computational complexity. Moreover, we compare its performance to the one of MMSE DFE versions which are based on the computationally efficient least-mean-square (LMS) or recursive least-squares (RLS) algorithm, respectively. The analysis additionally includes a detailed investigation of computational complexity with respect to the required number of floating point operations (FLOPs). Simulation results when applied to a digital communications system show the ability of the CG based MMSE DFE to outperform either the LMS and the RLS based MMSE DFE although its computational complexity is even smaller in most of the cases.

Differential Evolution (DE) is a novel but powerful optimizer. It has been proved that the DE is superior to Genetic Algorithm (GA) in many real life applications. This paper proposed a memetic Differential Evolution assisted Minimum Bit Error Rate (MBER) linear detector for Multiple-input and multiple-output (MIMO) multi-user system. Compared with GA based MBER and other linear MIMO detectors such as minimum mean square error (MMSE) and zero forcing(ZF)detectors, the proposed scheme shows a better performance in terms of the bit error rate.