Improved Proportionate Normalized Least-mean-square Research Articles

Adaptive resource allocation in NOMA-enabled backscatter communications systems

The integration of NOMA with Backscatter communication (BackCom) is a promising solution for developing a green future wireless network. However, system performance degrades with the deployment of multiple backscatter devices (BDs) in a network. Hence, energy efficiency (EE) maximization with proper resource allocation is among the primary concerns. In this regard, this paper proposes an adaptive resource allocation method for maximizing EE by simultaneously optimizing the transmission power from the base station (BS), power allocation coefficients, and reflection coefficients under the constraints of maximum allowable transmission power and minimum achievable data rate. Specifically, an iterative method based on a parametric transformation approach is adopted for maximizing EE by jointly optimizing the coefficients, in which the power allocation problem to the BDs is solved by an adaptive method that is based on improved proportionate normalized least mean square (IPNLMS) algorithm. Then, the system performance is evaluated, and the impact of different parameters is also studied it is observed that EE is significantly improved as compared to the existing scheme, and maximum at <span>η</span>=-0.5.

Orthogonal time-frequency space (OTFS) modulation for underwater mobile acoustic communications

This paper investigates the Orthogonal Time-Frequency Space (OTFS) Modulation for Underwater Mobile Acoustic Communications where the communication channel suffers from severe multipath and Doppler effects simultaneously. Practical OTFS modulation schemes with different parameters are designed for acoustic transmission at a center frequency of 115 kHz and a bandwidth of 11.5 kHz. The schemes are tested in lake experiments where the transmitter was anchored and the receiver was towed by a boat at a speed of approximately 1 m/s or 3.6 km/h. The receiver utilizes low-complexity channel estimation and equalization algorithms, such as NLMS (Normalized Least Mean Squares) and IPNLMS (improved proportionate NLMS) algorithms. The results show some insights of the OTFS scheme for acoustic communications. First, the mobile acoustic channel characteristics are different in the 2D delay-Doppler domain than those in the 1D time and frequency domains for the Single-Carrier Coherent Modulation (SCCM) and the Orthogonal frequency division modulation (OFDM), respectively. Second, in mobile scenarios, the OTFS scheme receiver effectively and significantly reduces the accuracy requirements of the Doppler compensation algorithm and provides better frequency-selective fading suppression and Doppler effect robustness compared to SCCM and OFDM schemes. Third, the OTFS scheme has better anti-multipath performance and reduces multipath interference by effectively differentiating signals on different paths in the 2D delay-Doppler domain.

An Extended Version of the Proportional Adaptive Algorithm Based on Kernel Methods for Channel Identification with Binary Measurements

In recent years, kernel methods have provided an important alternative solution, as they offer a simple way of expanding linear algorithms to cover the non-linear mode as well. In this paper, we propose a novel recursive kernel approach allowing to identify the finite impulse response (FIR) in non-linear systems, with binary value output observations. This approach employs a kernel function to perform implicit data mapping. The transformation is performed by changing the basis of the data In a high-dimensional feature space in which the relations between the different variables become linearized. To assess the performance of the proposed approach, we have compared it with two other algorithms, such as proportionate normalized least-meansquare (PNLMS) and improved PNLMS (IPNLMS). For this purpose, we used three measurable frequency-selective fading radio channels, known as the broadband radio access Network (BRAN C, BRAN D, and BRAN E), which are standardized by the European Telecommunications Standards Institute (ETSI), and one theoretical frequency selective channel, known as the Macchi’s channel. Simulation results show that the proposed algorithm offers better results, even in high noise environments, and generates a lower mean square error (MSE) compared with PNLMS and IPNLMS.

A mixing regularization parameter IPNLMS for underwater acoustic MIMO channel estimation

Less sensitivity to the sparsity of the underwater acoustic (UWA) channel is a drawback of the improved proportionate normalized least-mean-square (IPNLMS) algorithm. To address this problem, we propose an IPNLMS algorithm with a mixing regularization parameter (MRP-IPNLMS) for the multiple-input multiple-output (MIMO) UWA channel estimation. Firstly, the proposed MRP-IPNLMS exploits the sparsity of the UWA channel and integrates an approximate L0 norm into the cost function of the IPNLMS method, achieving the fast convergence in the sparse UWA channel estimation. Furthermore, we adopt a time-varying mixing regularization parameter to dynamically adjust the cost function. The proposed MRP-IPNLMS algorithm adaptively combines the fast convergence of the small regularization parameter with the low steady-state misalignment of the large regularization parameter. In addition, we evaluate the performance of the proposed algorithm in terms of its convergence, steady-state misalignment, and output signal-to-noise ratio (OSNR). Finally, simulations and real-data experiments are also conducted to demonstrate the effectiveness of the proposed algorithm.

OTFS underwater acoustic communications based on passive time reversal

Orthogonal time-frequency-space (OTFS) is a new two-dimensional (2D) modulation technique that offers reliable communications over time-varying channels. Due to the characteristics of underwater acoustic (UWA) channels, the computational complexity of traditional OTFS receivers is too high to implement in practice. In this paper, a 2D passive time reversal (PTR) structure receiver is designed in the Delay-Doppler domain, achieving spatial, temporal, and frequency focusing. Compared with existing methods, the proposed method could achieve similar performance with a lower complexity. Meanwhile, we also propose an adaptive channel estimation method based on the improved proportionate normalized least mean squares (IPNLMS) algorithm to reduce the complexity of channel estimation for the OTFS UWA communications system. The performance is evaluated under statistical simulated channels and measured channels from real-world experiments. The results verify the proposed 2D PTR receiver and demonstrate it could achieve good BER performance with a lower complexity.

Filter proportionate normalized least mean square algorithm for a sparse system

SummaryIn this paper, the proportionate normalized least mean square (PNLMS) and its modifications, such as improved PNLMS (IPNLMS) and μ‐law PNLMS (MPNLMS) algorithms, developed for a sparse system, are analyzed for a compressed input signal. This analysis is based on a comparative study of the steady‐state error and convergence time for the original signal and the compressed signal. Further, in this paper, a filter PNLMS (FPNLMS) algorithm that is a modification of the IPNLMS algorithm is proposed. The FPNLMS algorithm uses a step size varying in time to adapt to the sparse system. Simulations are carried out to compare the proposed FPNLMS algorithm for different signal‐to‐noise ratio for a compressed input signal with existing algorithms, ie, PNLMS, MPNLMS, and IPNLMS algorithms. The FPNLMS algorithm achieves a better steady‐state and convergence time compared with other existing algorithms in both low and high SNRs. The FPNLMS algorithm is further simulated for a real transfer function to show its robustness compared with existing algorithms.

Time-Frequency Domain Turbo Equalization for Single-Carrier Underwater Acoustic Communications

Single-carrier frequency-domain equalization (SC-FDE) is a promising technique for coherent high-rate underwater acoustic (UWA) communications. In this paper, a time-frequency domain turbo equalization (TFD-TE) scheme is proposed for single-carrier modulation. The TFD-TE scheme is to couple a multi-channel frequency domain equalizer with phase rotation compensation and a low-order single-channel time-domain turbo equalizer. To mitigate the error propagation and further enhance receiver performance, a bidirectional equalizer that combined the soft outputs of a conventional equalizer and a backward equalizer is introduced into the proposed TFD-TE scheme (Bi-TFD-TF). The sparse channel is estimated by the improved proportionate normalized least mean squares (IPNLMS) algorithm block by block. Both the simulated and experimental results show the proposed TFD-TE can effectively improve system performance with acceptable complexity. The proposed TFD-TE scheme is evaluated using communication data collected from the DJK15 lake experiment. For the $1\times 4$ single-input multiple-output (SIMO) communication system using quadrature phase shift keying (QPSK) and 8-phase shift keying (8PSK) modulations, the proposed scheme achieves error-free transmission after a few iterations. Our receiver achieves a maximum raw data rate of 12 kbit/s and a reliable net data rate of 4 kbit/s within 4-kHz bandwidth at a range of 10.8 km. Compared with conventional frequency domain turbo equalization (FD-TE), the proposed TFD-TE scheme can enhance 0.8–1.3 dB in terms of output signal-to-noise ratio (OSNR). The related bi-TFD-TE provides an additional 0.8–1.7-dB OSNR improvements.

Null space method for tap value initialization in constant modulus algorithm for mode division multiplexing systems

In this paper, we propose a constant modulus algorithm (CMA) for mode division multiplexing (MDM) systems with improved convergence performance. In order to adapt to sparse channels with large differential mode group delay (DMGD) in MDM systems, the CMA adopts a variable step size similar to the improved proportionate normalized least-mean-square (IPNLMS) algorithm. In additional to that, when a singularity problem is encountered or the tap values fail to converge, it reinitializes the tap coefficients according to the tap vectors of the successfully de-multiplexed data tributaries. The proposed initialization approach is based on the fact that the channel matrix is unitary in the frequency domain in the absence of mode dependent loss (MDL), which means the channel coefficient vectors for each data tributary should be orthogonal to each other. By limiting the initial values of the taps within the null space of the complex conjugate vectors of the successfully de-multiplexed channels, singularity can be effectively avoided and the convergence of the taps is guaranteed. When the number of modes is two, the proposed algorithm becomes the constrained CMA, which has been commonly implemented in polarization division multiplexing (PDM) systems. Although the algorithm has been derived under zero MDL assumption, it is found that the proposed CMA can be quite resilient to MDL. No singularity/tap convergence failure problem occurs when the MDL is below 4 dB at both the input and the output ports.

Improving Passive Time Reversal Underwater Acoustic Communications Using Subarray Processing.

Multichannel receivers are usually employed in high-rate underwater acoustic communication to achieve spatial diversity. In the context of multichannel underwater acoustic communications, passive time reversal (TR) combined with a single-channel adaptive decision feedback equalizer (TR-DFE) is a low-complexity solution to achieve both spatial and temporal focusing. In this paper, we present a novel receiver structure to combine passive time reversal with a low-order multichannel adaptive decision feedback equalizer (TR-MC-DFE) to improve the performance of the conventional TR-DFE. First, the proposed method divides the whole received array into several subarrays. Second, we conduct passive time reversal processing in each subarray. Third, the multiple subarray outputs are equalized with a low-order multichannel DFE. We also investigated different channel estimation methods, including least squares (LS), orthogonal matching pursuit (OMP), and improved proportionate normalized least mean squares (IPNLMS). The bit error rate (BER) and output signal-to-noise ratio (SNR) performances of the receiver algorithms are evaluated using simulation and real data collected in a lake experiment. The source-receiver range is 7.4 km, and the data rate with quadrature phase shift keying (QPSK) signal is 8 kbits/s. The uncoded BER of the single input multiple output (SIMO) systems varies between and for the conventional TR-DFE, and between and for the proposed TR-MC-DFE when eight hydrophones are utilized. Compared to conventional TR-DFE, the average output SNR of the experimental data is enhanced by 3 dB.

A novel gain distribution policy based on individual-coefficient convergence for PNLMS-type algorithms

This paper introduces a new gain distribution policy for proportionate normalized least-mean-square (PNLMS)-type algorithms. In the proposed approach, gains assigned to the coefficients that have achieved the vicinity of their optimal values are transferred to other coefficients. To estimate such a vicinity, a metric based on the variation rate of the adaptive filter coefficient magnitude is devised, which is used as a way for assessing the individual-coefficient convergence. Then, the proposed approach is applied to the PNLMS, improved PNLMS (IPNLMS), and individual-activation-factor PNLMS (IAF-PNLMS), leading to enhanced versions of these algorithms. Simulation results show that the proposed approach (and the corresponding enhanced algorithms) performs well for different operating scenarios.

Formula omitted] optimality and a posteriori output estimate of the forgetting factor NLMS algorithm

The normalized least mean squares (NLMS) algorithm is widely used for adaptive filtering. The NLMS algorithm may be extended using a variety of weight parameters that improve its performance. One such extension involves appropriately introducing a forgetting factor into the NLMS algorithm using the H∞ framework. The resultant forgetting factor NLMS (FFNLMS) algorithm may be regarded as a special case of the improved proportionate NLMS (IPNLMS) algorithm. This work reveals that the FFNLMS algorithm is H∞-optimal, and the a posteriori output estimate is identical to the observation signal for sufficiently large times.

A Sparsity Managed Adaptive MIMO Equalization for Few-Mode Fiber Transmission With Various Differential Mode Delays

It is often observed that various differential mode delays (DMDs) coexist in single multi-core fiber (MCF) and/or few-mode fiber (FMF) transmission. From a multi-input and multi-output (MIMO) equalization perspective, this indicates optimum equalization tap length for each multi-core and/or multi-mode signal varies according to its DMD. Correspondingly, complex calculation of finding each optimum tap length is necessary to obtain satisfactory performance. This paper presents a new adaptive MIMO equalization method to deal with various DMDs while avoiding such complex calculation. The method uses the same tap length for all multi-core and/or multi-mode signals according to the maximum DMD to reduce the calculation cost. To rectify negative effects such as noise enhancement due to the non-optimum tap length setting, the method applies the improved proportionate normalized least mean square (IPNLMS) with leveraged equalization coefficients update on the basis of the overall sparsity of coefficients. IPNLMS inherently updates equalization coefficients by proportionately promoting the previous coefficients in order that the coefficients of signal part are promoted while those of noise part are suppressed. To determine the IPNLMS parameters that govern the amount of the promotion, the presented method uses a simple sparsity metric that calculates the overall sparsity of coefficients. Then, the sparsity metric is mapped to IPNLMS parameters in a manner that the overall sparsity of coefficients is progressively facilitated as adaptation. Evaluations using experimental data of FMF transmission over 527 km end-to-end with 33.2 ns maximum DMD show the presented method effectively deals with various DMDs to suppress the noise and obtains 0.7 dB of Q-factor performance enhancement comparing to the conventional method.

On the Steady-State Analysis of PNLMS-Type Algorithms for Correlated Gaussian Input Data

This letter presents model expressions describing the steady-state behavior of proportionate normalized least-mean-square (PNLMS)-type algorithms, taking into account both complex- and real-valued correlated Gaussian input data. Specifically, based on energy-conservation arguments, general expressions for the excess mean-square error (EMSE) in steady state and misadjustment are obtained. Such general expressions are then applied to two well-known PNLMS-type algorithms, namely the improved PNLMS (IPNLMS) and the individual-activation-factor PNLMS (IAF-PNLMS). Simulation results are shown confirming the accuracy of the proposed model expressions under different operating conditions.

On Regularization in Adaptive Filtering

Regularization plays a fundamental role in adaptive filtering. An adaptive filter that is not properly regularized will perform very poorly. In spite of this, regularization in our opinion is underestimated and rarely discussed in the literature of adaptive filtering. There are, very likely, many different ways to regularize an adaptive filter. In this paper, we propose one possible way to do it based on a condition that intuitively makes sense. From this condition, we show how to regularize four important algorithms: the normalized least-mean-square (NLMS), the signed-regressor NLMS (SR-NLMS), the improved proportionate NLMS (IPNLMS), and the SR-IPNLMS.

A PNLMS Algorithm With Individual Activation Factors

This paper presents a proportionate normalized least-mean-square (PNLMS) algorithm using individual activation factors for each adaptive filter coefficient, instead of a global activation factor as in the standard PNLMS algorithm. The proposed individual activation factors, determined in terms of the corresponding adaptive filter coefficients, are recursively updated. This approach leads to a better distribution of the adaptation energy over the filter coefficients than the standard PNLMS does. Thereby, for impulse responses exhibiting high sparseness, the proposed algorithm achieves faster convergence, outperforming both the PNLMS and improved PNLMS (IPNLMS) algorithms.

Adaptive Combination of Proportionate Filters for Sparse Echo Cancellation

Proportionate adaptive filters, such as those based on the improved proportionate normalized least-mean-square (IPNLMS) algorithm, have been proposed for echo cancellation as an interesting alternative to the normalized least-mean-square (NLMS) filter. Proportionate schemes offer improved performance when the echo path is sparse, but are still subject to some compromises regarding their convergence properties and steady-state error. In this paper, we study how combination schemes, where the outputs of two independent adaptive filters are adaptively mixed together, can be used to increase IPNLMS robustness to channels with different degrees of sparsity, as well as to alleviate the rate of convergence versus steady-state misadjustment tradeoff imposed by the selection of the step size. We also introduce a new block-based combination scheme which is specifically designed to further exploit the characteristics of the IPNLMS filter. The advantages of these combined filters are justified theoretically and illustrated in several echo cancellation scenarios.

A Low Delay and Fast Converging Improved Proportionate Algorithm for Sparse System Identification

A sparse system identification algorithm for network echo cancellation is presented. This new approach exploits both the fast convergence of the improved proportionate normalized least mean square (IPNLMS) algorithm and the efficient implementation of the multidelay adaptive filtering (MDF) algorithm inheriting the beneficial properties of both. The proposed IPMDF algorithm is evaluated using impulse responses with various degrees of sparseness. Simulation results are also presented for both speech and white Gaussian noise input sequences. It has been shown that the IPMDF algorithm outperforms the MDF and IPNLMS algorithms for both sparse and dispersive echo path impulse responses. Computational complexity of the proposed algorithm is also discussed.