The standard approaches to solving overdetermined linear systems Ax ≈ b construct minimal corrections to the vector b and/or the matrix A such that the corrected system is compatible. In ordinary least squares (LS) the correction is restricted to b, while in data least squares (DLS) it is restricted to A. In scaled total least squares (Scaled TLS) [15], corrections to both b and A are allowed, ...

The digital Fourier transform (DFT) and the adaptive least mean square (LMS) algorithm have existed for some time. This paper establishes a connection between them. The result is the “LMS spectrum analyzer,” a new means for the calculation of the DFT. The method uses a set of N periodic complex phasors whose frequencies are equally spaced from dc to the sampling frequency. The phasors are weigh...

In this article the computation of FIR filter weights in adaptive channel equalization tasks in quasi stationary environments is considered. The problem is formulated as a system of equations. It can be solved via direct matrix inversion (DMI) or iteratively via the LMS or RLS algorithm. Thereby suitable criteria such as least squares (LS) or mean square error (MSE) are minimized. By using thes...

The Lasso achieves variance reduction and variable selection by solving an 1-regularized least squares problem. Huang (2003) claims that ‘there always exists an interval of regularization parameter values such that the corresponding mean squared prediction error for the Lasso estimator is smaller than for the ordinary least square estimator’. This result is correct. However, its proof in Huang ...

3rd generation partnership project (3GPP) long term evolution (LTE) uses single carrier-frequency division multiple access (SC-FDMA) in uplink transmission and orthogonal frequency division multiple access (OFDMA) scheme for the downlink. One of the most important challenges for a transceiver design is channel estimation (CE) and equalization. In this paper, a training based least mean square (...

This paper compares performance of finite impulse response (FIR) adaptive linear equalizers based on the recursive least-squares (RLS) and least mean square (LMS) algorithms in nonstationary uncorrelated scattering wireless channels. Simulation results, in terms of steady-state mean-square estimation error (MSE) and average bit-error rate (BER) metrics, are found for the frequency-selective Ray...

The optimum and many suboptimum iterative soft-input soft-output (SISO) multiuser detectors require a priori information about the multiuser system, such as the users’ transmitted signature waveforms, relative delays, as well as the channel impulse response. In this paper, we employ adaptive algorithms in the SISO multiuser detector in order to avoid the need for this a priori information. Firs...

A simple model characterizing the convergence properties of an adaptive digital lattice filter using gradient algorithms has been reported [ 11. This model is extended to the least mean square (LMS) lattice joint process estimator [SI, and to the least squares (LS) lattice and “fast” Kalman algorithms [9] -[16]. The models in each case are compared with computer simulation. The single-stage LMS...

Quantitative analysis of CaO in limestone mining is mandatory, not only for ore exploration, but also for grade control. A partial least squares regression (PLSR) CaO estimation technique was developed for limestone mining. The proposed near-infrared spectroscopy (NIR)-based method uses reflectance spectra of the rock sample surface in the visible to short-wave infrared wavelength regions (350–...