Efficiently computed reduced-parameter input-aided MMSE equalizers for ML detection: a unified approach

The typical approach to radar target classification is to image the target with waveforms that provide high resolution and low sidelobes, and then to compare the target images to a template library. In this chapter, we reconsider whether imaging-based metrics for waveform design are best for target classification, and develop alternative design strategies that result in waveforms with improved classification ability, but not necessarily a good ambiguity function by traditional notions. After presenting waveform design strategies based on optimizing signal-to-noise ratio or mutual information from a wide-sense stationary (WSS) ensemble of target impulse responses, we apply the design methods to the problem of radar target classification through a two-step process. The first step is to modify the design methodology that was based on WSS targets to account for the finite duration of practical target responses. The second step is to use the target class probabilities and impulse response library to calculate a weighted power spectral variance over target classes, which is then substituted into the design equations. The use of target class probabilities enables the waveform to be adapted in response to previous transmissions. Waveform behaviour and performance are studied over several different clutter and noise scenarios. The target impulse response library for these studies is based on finite-difference time-domain (FDTD) simulation of a publically available CAD model of an F-16 aircraft.

Shallow-water horizontal underwater acoustic (UWA) channels are characterized by a time-varying multipath structure with a long delay spread. This causes significant signal distortion in phase coherent transmissions by introducing intersymbol interference (ISI), which can span several hundreds of symbols. The multipath structure is usually very sparse. This paper proposes an adaptive sparse partial response equalizer (SPRE) well matched with the channel characteristics to mitigate the ISI efficiently, and communicate reliably. Unlike the conventional equalizers that try to eliminate the ISI completely, the proposed structure performs equalization in two steps. In the first step, the channel is equalized to a judiciously chosen target impulse response (TIR), thereby leaving controlled residual ISI at the output of the SPRE. In the second step, the residual ISI is further mitigated by a near-optimal, graph-based, low-complexity symbol detection algorithm known as belief propagation (BP). We demonstrate that due to the sparse nature of the long ISI channel, and the well-matched adaptive TIR, this two-step equalization process is particularly useful. The idea here can be compared to what is done in the magnetic recording literature [i.e., partial response maximum-likelihood (ML) equalization] to avoid excessive noise enhancement, with the difference that the TIR needs to be designed adaptively using training symbols and that in the second step, instead of using a ML detector, a BP algorithm is used. The proposed SPRE algorithm is designed for a general multiple-input-multiple-output (MIMO) system and it provides soft outputs for the transmitted bits as a by-product of the BP-type equalization algorithm. Hence, it can be efficiently employed in coded systems (e.g., turbo or low-density-parity-check-coded, interleaved systems) with an iterative decoding/equalization scheme, providing significant improvements in achievable error rates. Finally, we note that the proposed SPRE scheme also incorporates a phase locked loop (PLL) structure so as to track the Doppler shift introduced by the channel. To evaluate the effectiveness of the proposed equalizer, we compare it with several decision feedback equalizers (DFEs) proposed by Stojanovic (J. Ocean. Eng. vol. 19, no. 1, pp. 100-111, Jan. 1994), Roy (Proc. MTS/IEEE TECHNO-OCEAN Conf., vol. 1, pp. 26-33, Nov. 2004), and Roy (J. Ocean. Eng., vol. 32, no. 3, pp. 663-688, Jul. 2004) both through simulations and experimental results. The results demonstrate that the SPRE receiver outperforms the decision-feedback-based receivers when the channel has long, yet sparse (possibly, nonminimum phase) structure, by reducing the frame error rates (FERs), improving the post-equalization signal-to-noise ratio (SNR), and decreasing the required number of turbo iterations (reduced latency).

A new criterion is proposed for solving the problem of channel shortening in multicarrier systems. In a discrete multitone receiver, a time-domain equalizer (TEQ) reduces intersymbol interference (ISI) by shortening the effective duration of the channel impulse response. Minimum mean square error (MMSE) method for TEQ does not give satisfactory results. In N. Al-Dahir and J. M. Cioffi (1996) a new criterion for partially equalizing severe ISI channels to reduce the cyclic prefix overhead of the discrete multitone transceiver (DMT), assuming a fixed transmission bandwidth, is introduced. Due to specific constrained (unit morm constraint on the target impulse response (TIR)) in their method, the freedom to choose optimum vector (TIR) is reduced. Better results can be obtained by avoiding the unit norm constraint on the target impulse response (TIR). We change the cost function proposed in N. Al-Dahir and J. M. Cioffi (1996) to the cost function of determining the maximum of a determinant subject to linear matrix inequality (LMI) and quadratic constraint and solve the resulting optimization problem. Usefulness of the proposed method is shown with the help of simulations.

Finite-length delay-optimized multi-input multi-output (MIMO) equalizers that optimally shorten the impulse response memory of frequency-selective (MIMO) channels are derived. The MIMO equalizers are designed to minimize the average energy of the error sequence between the equalized MIMO channel impulse response (CIR) and a MIMO target impulse response (TIR) with shorter memory. Two criteria for optimizing the MIMO TIR are analyzed and compared. The presented analytical framework encompasses a multitude of previously-studied finite-length equalization techniques.

A new scheme based on Kalman filtering to optimize the waveforms of an adaptive multi-antenna radar system for target impulse response (TIR) estimation is presented. This work aims to improve the performance of TIR estimation by making use of the temporal correlation between successive received signals, and minimize the mean square error (MSE) of TIR estimation. The waveform design approach is based upon constant learning from the target feature at the receiver. Under the multiple antennas scenario, a dynamic feedback loop control system is established to real-time monitor the change in the target features extracted form received signals. The transmitter adapts its transmitted waveform to suit the time-invariant environment. Finally, the simulation results show that, as compared with the waveform design method based on the MAP criterion, the proposed waveform design algorithm is able to improve the performance of TIR estimation for extended targets with multiple iterations, and has a relatively lower level of complexity.

The use of information theory to design waveforms for the measurement of extended radar targets exhibiting resonance phenomena is investigated. The target impulse response is introduced to model target scattering behavior. Two radar waveform design problems with constraints on waveform energy and duration are then solved. In the first, a deterministic target impulse response is used to design waveform/receiver-filter pairs for the optimal detection of extended targets in additive noise. In the second, a random target impulse response is used to design waveforms that maximize the mutual information between a target ensemble and the received signal in additive Gaussian noise. The two solutions are contrasted to show the difference between the characteristics of waveforms for extended target detection and information extraction. The optimal target detection solution places as much energy as possible in the largest target scattering mode under the imposed constraints on waveform duration and energy. The optimal information extraction solution distributes the energy among the target scattering modes in order to maximize the mutual information between the target ensemble and the received radar waveform. >

This paper considers the problem of channel shortening in OFDM systems. More specifically, we propose non-blind shortening techniques with controlled target impulse response (TIR) quality. Compared to other existing channel shortening methods, the proposed solutions are computationally cheaper and lead to better BER performance. Simulation results are provided to illustrate this claim and to assess the performance of the proposed method.

The paper describes synthesis of the transfer function of a multistage wideband amplifier having the monotonic step response. The procedure is based on approximation of a specially chosen impulse response in the time domain. This target impulse response is constructed using a delayed and exponentially attenuated sin/sup 2/ t function. The Laplace transform of this pulse is a transcendental function, yet the real and imaginary parts of this transform may be approximated by the polynomials with alternating zeros. The approximation allows one to obtain a realizable transfer function. The design example shows that the step response of this transfer function is practically monotonic, and, in addition, has a superior delay-to-rise-time ratio.

This paper proposes two nonlinear blind equalizers: the nonlinear constant modulus algorithm (NCMA) and the nonlinear modified constant modulus algorithm (NCMA) by applying a nonlinear transfer function (NTF) into constant modulus algorithm (CMA) and modified constant modulus algorithm (MCMA), respectively. The effect of the NTF on CMA and MCMA is theoretically analyzed, which implies that the NTF can make their decision regions much sharper so that the proposed two nonlinear blind equalizers are more robust against the convergency error compared to their linear counterparts. The embedded single layer in NCMA and NMCMA simultaneously guarantees a comparably speedy convergency. On 16-quadrature amplitude modulation (QAM) symbols, computer simulations show that NCMA achieves an 8dB lower convergency mean square error (MSE) than CMA, and NMCMA achieves a 15dB lower convergency MSE than MCMA.

This research focuses on predicting stock closing prices for one day or the future in specific economic conditions. Today, Sri Lanka faces a financial crisis due to the COVID-19 pandemic. Therefore, lots of investors are bankrupt due to unpredictable stock prices. This work mainly focuses on predicting stock prices in banking sector shares such as Commercial Bank (COMB.N), Hatton National Bank (HNB.N), Seylan Bank (SEYB.N), and Sampath Bank (SAMP.N) on Colombo Stock Exchange (CSE) in Sri Lanka. According to the hypothesis, All Share Price Index (ASPI) and Banking Sector indices have been taken as a numerical sentiment parameter other than the historical prices from each bank. Since ASPI shows overall market performance and Banking sector indices show banking sector capitalization changed over time. There can be a positive and negative sentiment when the ASPI and Sector Indices increase and decrease, respectively. Finally, a dataset is divided into 70% for training and 30% for testing. This study has used Recurrent Neural Networks (RNNs) such as Long short-term memory (LSTM) and Gated Recurrent Unit (GRU) using 25, 50, 100, 150, and 200 epochs. LSTM model has given the lowest Mean Squared Error (MSE) and Root Mean Square Error (RMSE). According to the LSTM model, COMB.N, HNB.N, and SAMP.N were given the lowest MSE, and RMSE for 100 epochs, and SEYB.N was given the lowest MSE and RMSE value for the 150 epochs.

In order to establish the optimal receiver strategy, in terms of error rate for Single Input Multi Output (SIMO) wireless channels, the Maximum Likelihood (ML) detection should be performed following a multi-dimensional matched filter. However, the implementation of the matched filter and the ML detection both need the estimation of the channel impulse response in advance. In this work, we propose a novel method to establish the matched filters of the SIMO channel blindly alongside a three-step technique for the blind and adaptive ML detection of the symbol vector. With the use of the novel method, the system will benefit from the bandwidth efficiency point of view due to the use of blind schemes. The constant modulus algorithm is utilized to perform the blind matched filtering operation and later Least Mean Squared algorithm is introduced for further correction on the matched filter estimate. The blindly estimated matched filters are incorporated into the ML detector so that the transmitted symbols are found and therefore the channel is equalized. Simulations are provided to present the equalization performance and convergence speed of the novel technique.

In this paper, a new optimization on windowing technique based on finite impulse response (FIR) filters is proposed for revealing and evaluating the Influence of filters position in cascaded filter tested on the ECG signal de-noising. baseline wander (BLW), power line interference (PLI) and electromyography (EMG) noises are getting removed. The performance of the adopted method is evaluated on the PTB diagnostic database. Subsequently, the comparisons are based on signal to noise ratio (SNR) improvement and mean square error (MSE) minimization. Where the Rectangular, and Kaiser windows have been used for the more potent performances. The disparity average (DA) of SNR values is detected; in both Kaiser and Rectangular windows are assessed by ±0.38046dB and ±0.70278dB respectively, while the MSE values were constant. The excellent configuration or filters position (H-B-L) of the filtration system is selected according to high measurements of SNR and low MSE too, to de-noise the ECG signals. First of all, this applied approach has led to 31.30 dB SNR improvement with MSE minimization of 26. 43%. This means that there is a significant contribution to improving the field of filtration.

This paper describes the study and development of a linear, variable-pass network system which is controlled by the Fano short-time autocorrelation function of the input. Given an input function, the message, whose short-time power spectrum varies in an unpredictable manner with time, and to which there has been added a different function, the disturbance, whose short-time power spectrum is either time-invariant or varies in a completely known manner, a linear, input-controlled, variable-pass network can be specified which minimizes the mean-square error between the message input and the total output, taking network delay into account. Methods for mathematical computation of the mean-square error have been devised. The linear, input-controlled, variable-pass network has been found to have a lower mean-square error than that attainable with an optimum-mean-square, linear, fixed, selective network, for certain types of input messages.

The El Niño-Southern Oscillation (ENSO) is the dominant mode of climate variability on interannual time scales, and its temporal evolution can be summarized using the Niño 3.4 index. Here we used EOF analysis to construct low-dimensional representations of the 12-month evolution of Niño 3.4 during different times of the year. The leading EOF explains more than 90% of the variance of the Niño 3.4 evolution from June to May, which means that the differences in evolution from one year to another are essentially differences in amplitude. Two EOFs explained 94% or more of the evolution variance for other 12-month periods of the year. The two-dimensional nature of the Niño 3.4 trajectories is a direct expression of the spring persistence barrier since the first EOF describes wintertime ENSO events, and the second EOF describes independent behavior during the antecedent spring. A periodic second-order autoregressive (AR2) model reproduced the observed properties, but a first-order model did not. Niño 3.4 EOFs in ocean-atmosphere coupled model forecasts matched observed EOFs with varying levels of fidelity depending on model and time of year. Forecast models with more accurate climatological covariance also have lower mean-squared error (MSE). Low-dimensional EOF-based statistical corrections reduced forecast MSE.

In cellular systems, deploying a large number of antennas at the base station (BS), also called massive multiple-input multiple-output (MIMO), can offer a huge improvement in system throughput. This performance gain achieved through coherent beamforming highly depends on having accurate channel state information (CSI) at the BS. Initially, massive MIMO was considered promising only for time division duplexing (TDD) systems because the downlink training overhead in frequency division duplexing (FDD) systems could be large. To reduce the overhead in FDD systems, we propose efficient eigenspace training and precoding. In the downlink training, the prebeamforming matrix is designed based on the spatial fading correlation to probe the channel and minimize the mean squared error (MSE) in channel estimation. In data transmission, the precoding matrix is designed based on instantaneous CSI to manage the inter-user interference. Our algorithms achieve significant savings in the downlink training because the overhead is associated with the dimension of prebeamforming matrix and no longer limited by the number of BS antennas. Compared with joint spatial division and multiplexing, our algorithms offer much lower MSE and, under some conditions, higher sum rates.