A kernel based technique for MSER equalisation for non-linear channels

Adaptive channel equalization is a signal processing technique to mitigate inter-symbol interference in a time dispersive channel. For adaptive equalization, minimum mean square error (MMSE) criterion-based reproducing kernel Hilbert spaces (RKHS) approaches such as the kernel least mean squares (KLMS) algorithm and its variants have been suggested in the literature for nonlinear channels. Another optimality criterion, based on minimum bit/symbol error rate (MBER/MSER), is a better choice for adapting an equalizer as compared to MMSE criterion. A kernel-based minimum symbol error rate (KMSER) equalization algorithm combines minimum symbol error rate (MSER)-based approaches with RKHS techniques. However, most algorithms in RKHS such as KMSER/KLMS require infinite storage requirement and hence cannot be practically implemented. To curtail the infinite memory requirement, and make adaptive algorithm suitable for implementation with finite memory and processing power, we propose quantized KMSER (QKMSER) and fixed-budget quantized KMSER (FBQKMSER)-based equalizers in this paper. In this paper, we derive the dynamical equation for MSE evolution of the QKMSER and FBQKMSER and find their performance to be asymptotically close to the MSE behavior of the KMSER. Also, it is found via simulations that the tracking performance of FBQKMSER is better than all the compared algorithms in this paper which is particularly useful for non-stationary channels.

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.

In this paper, we use the minimum mean square error (MMSE) criterion to design the scaled and offset belief propagation (BP)-based decoding algorithms for short low-density parity-check (LDPC) codes on the fast Rayleigh fading channel. Based on the MMSE criterion, the theoretical formulas and numerical calculations on the optimum factors for these two improved BP-based algorithms are provided. The simulation results for several short (Chen et al., 2005 and Gallager, 1962) regular LDPC codes on the fast Rayleigh fading channel demonstrate that the scaled and offset BP-based algorithms with our proposed factors can achieve the performance better than that of the BP algorithm.

This paper address the problem of designing jointly the linear transmitters and receiver in a non-regenerative MIMO relay system, where linear processing is applied at the source, relay and destination node, using minimum mean square error (MMSE) criterion. Under the average power constraints at both the source and relay node, the iterative optimization method is presented and a low-complexity block optimization method is proposed. Simulation results show that the proposed methods perform better than other existing relaying schemes, and the performance gain is very significant when the signal-to-noise ratio (SNR) is high.

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.

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.

The kernel least mean square (KLMS) algorithm is the simplest algorithm in kernel adaptive filters. However, the network growth of KLMS is still an issue for preventing its online applications, especially when the length of training data is large. The Nystrom method is an efficient method for curbing the growth of the network size. In this paper, we apply the Nystrom method to the KLMS algorithm, generating a novel algorithm named kernel least mean square based on the Nystrom method (NysKLMS). In comparison with the KLMS algorithm, the proposed NysKLMS algorithm can reduce the computational complexity, significantly. The NysKLMS algorithm is proved to be convergent in the mean square sense when its step size satisfies some conditions. In addition, the theoretical steady-state excess mean square error of NysKLMS supported by simulations is calculated to evaluate the filtering accuracy. Simulations on system identification and nonlinear channel equalization show that the NysKLMS algorithm can approach the filtering performance of the KLMS algorithm by using much lower computational complexity, and outperform the KLMS with the novelty criterion, the KLMS with the surprise criterion, the quantized KLMS, the fixed-budget QKLMS, and the random Fourier features KLMS.

In recent years, a lot of attention has been drawn to the use of multiple antennas at both the transmitter and receiver sides. Such techniques are named here as space-time transmission and noted as STT. By their use of the available space dimension, STT techniques can achieve very high spectral efficiencies in Rayleigh fading channels with rich scattering. The use of STT techniques for indoor wireless systems with a huge number of antennas is considered. As a low complexity detection algorithm, ordered successive detection based schemes are considered. A scheme known as V-BLAST (vertical Bell Labs layered space-time) is proposed in the zero forcing (ZF) criterion (see Wolniansky, P.W. et al., Proc. ISSSE'98, 1998). In a previous work, it has been shown how this scheme can be much improved by the use of a backward iterative detection algorithm (see Benjebbour, A. et al., Proc. WPMC, p.819-24, 2000; Proc. VTC2001 Spring, 2001). An extension of the conventional V-BLAST algorithm to the minimum mean square error (MMSE) criterion is now proposed. For the proposed receiver, an ordering metric is defined. Then, the effect of ordering on both receivers is discussed. And finally, it is shown how the ordering metric in the MMSE criterion can be simplified.

A major complaint of individuals with normal hearing and hearing impairments is a reduced ability to understand speech in a noisy environment. This paper is proposed to remove the noise from the speech signal in various real time environments and to make the hearing impaired to understand the information by transforming speech in to text format. The quality of audio signal can be improved by filtering the degraded speech signal through adaptive filters. For Noise cancellation widrow & hoff’s Least Mean Square (LMS) algorithms are being used for simplicity in implementation. The LMS algorithm was simple in it's derivation and robust in a number of applications but it also have limitation in selection of a certain values such as step size and results in computational complexity. Hence to overcome all the limitations and to present an enhanced speech signal, a novel approach named VSSNDLMS algorithm is proposed. The performance of algorithms like Variable Step Size Normalised LMS , Normalised Differential LMS with proposed VSSNDLMS with different input signals are analysed in this paper . Finally, through simulation results the proposed VSSNDLMS algorithm converges fastly with minimum mean square error and it is useful in predicting the adaptive filter performance of various algorithms and the implementation indicate the improvement in quality of the speech signal and it appears to be favourable for hearing impaired. Keywords: VSSNDLMS, LMS Algorithm, Noise Cancellation, Speech Processing, Adaptive Filter

Adaptive beamforming for binary phase shift keying communication systems

For decreasing intersymbol interference (ISI) due to band-limited channels in digital communication, the uses of equalization techniques are necessary. Among adaptive equalization techniques, because of their ease of implementation and nonlinear capabilities, the neural networks have been used as an alternative for effectively dealing with the channel distortion, especially the nonlinear distortion. The complex backpropagation (BP) neural networks are proposed as nonlinear adaptive equalizers that can deal with both QAM and PSK signals of any constellation size (e.g. 32-QAM, 64-QAM and MPSK), and the complex BP algorithm for the new node activation functions having multi-output values and multi-saturation regions is presented. We also show that the proposed complex BPN provides, compared with the linear equalizer using the least mean squares (LMS) algorithm, an interesting improvement concerning bit error rate (BER) when channel distortions are nonlinear.

In the Molecular Communication (MC), molecules are utilized to encode, transmit, and receive information. Transmission of the information is achieved by means of diffusion of molecules and the information is recovered based on the molecule concentration variations at the receiver location. The MC is very prone to intersymbol interference (ISI) due to residual molecules emitted previously. Furthermore, the stochastic nature of the molecule movements adds noise to the MC. For the first time, we propose four methods for a receiver in the MC to recover the transmitted information distorted by both ISI and noise. We introduce sequence detection methods based on maximum a posteriori (MAP) and maximum likelihood (ML) criterions, a linear equalizer based on minimum mean-square error (MMSE) criterion, and a decision-feedback equalizer (DFE) which is a nonlinear equalizer. We present a channel estimator to estimate time varying MC channel at the receiver. The performances of the proposed methods based on bit error rates are evaluated. The sequence detection methods reveal the best performance at the expense of computational complexity. However, the MMSE equalizer has the lowest performance with the lowest computational complexity. The results show that using these methods significantly increases the information transmission rate in the MC.

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.

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.

Prediction of two dimensional hand trajectories from cortical surface recordings entails finding a functional mapping from spectral modulations in multidimensional channels to instantaneous hand positions. Such studies thus far have been conducted through linear adaptive filters, even though, the functional mapping from the cortical activity to behavior might be nonlinear. Herein, we employ a nonlinear adaptive filter, kernel least mean square (KLMS), which nonlinearly map inputs to a higher dimensional feature space in which inner products can be efficiently computed. The methodology is a simple and effective nonlinear extension of the least mean square (LMS) algorithm. Preliminary results show significant improvements in mean squared error (MSE) values of reconstructed trajectories compared to linear methods (LMS) at a confidence level of 95% in the axis of highest excursion.