Faster, stabler, and simpler - A recursive-least-squares algorithm exploiting the Frisch-Waugh-Lovell theorem

We propose a novel recursive least squares (RLS) algorithm that exploits the Frisch-Waugh-Lovell theorem to reduce digital complexity and improve convergence speed and algorithmic stability in fixed-point arithmetic. We tested the new algorithm in the digital background calibration section of a four-channel time-interleaved analog-to-digital converter, obtaining better stability and faster convergence. The digital complexity of the new algorithm in terms of multiplications and divisions is 33% lower asymptotically than that of the conventional Bierman algorithm if the model parameters need not be computed at each update; otherwise, it is the same. Memory requirements are also the same. Because, in calibration, the distance between the ideal and calibrated outputs of the system is to be minimized, the actual value of the model parameters is usually not of interest. Convergence time can be up to 10 or 20 times better in fixed-point arithmetic, and stability for large models is also better in our simulations. In our simulations, when the conventional Bierman RLS algorithm is stable, the steady-state accuracy of the new algorithm is either comparable or better, depending on the simulation setup

Methods for Model Complexity Reduction for the Nonlinear Calibration of Amplifiers Using Volterra Kernels

Volterra models allow modeling nonlinear dynamical systems, even though they require the estimation of a large number of parameters and have, consequently, potentially large computational costs. The pruning of Volterra models is thus of fundamental importance to reduce the computational costs of nonlinear calibration, and improve stability and speed, while preserving accuracy. Several techniques (LASSO, DOMP and OBS) and their variants (WLASSO and OBD) are compared in this paper for the experimental calibration of an IF amplifier. The results show that Volterra models can be simplified, yielding models that are 4–5 times sparser, with a limited impact on accuracy. About 6 dB of improved Error Vector Magnitude (EVM) is obtained, improving the dynamic range of the amplifiers. The Symbol Error Rate (SER) is greatly reduced by calibration at a large input power, and pruning reduces the model complexity without hindering SER. Hence, pruning allows improving the dynamic range of the amplifier, with almost an order of magnitude reduction in model complexity. We propose the OBS technique, used in the neural network field, in conjunction with the better known DOMP technique, to prune the model with the best accuracy. The simulations show, in fact, that the OBS and DOMP techniques outperform the others, and OBD, LASSO and WLASSO are, in turn, less efficient. A methodology for pruning in the complex domain is described, based on the Frisch–Waugh–Lovell (FWL) theorem, to separate the linear and nonlinear sections of the model. This is essential because linear models are used for equalization and cannot be pruned to preserve model generality vis-a-vis channel variations, whereas nonlinear models must be pruned as much as possible to minimize the computational overhead. This methodology can be extended to models other than the Volterra one, as the only conditions we impose on the nonlinear model are that it is feedforward and linear in the parameters

Under the different sectors: the relationship between low-carbon economic development, health and GDP

Developing a modern low-carbon economy while protecting health is not only a current trend but also an urgent problem that needs to be solved. The growth of the national low-carbon economy is closely related to various sectors; however, it remains unclear how the development of low-carbon economies in these sectors impacts the national economy and the health of residents. Using panel data on carbon emissions and resident health in 28 province-level regions in China, this study employs unit root tests, co-integration tests, and regression analysis to empirically examine the relationship between carbon emissions, low-carbon economic development, health, and GDP in industry, construction, and transportation. The results show that: First, China’s carbon emissions can promote economic development. Second, low-carbon economic development can enhance resident health while improving GDP. Third, low-carbon economic development has a significant positive effect on GDP and resident health in the industrial and transportation sector, but not in the construction sector, and the level of industrial development and carbon emission sources are significant factors contributing to the inconsistency. Our findings complement existing insights into the coupling effect of carbon emissions and economic development across sectors. They can assist policymakers in tailoring low-carbon policies to specific sectors, formulating strategies to optimize energy consumption structures, improving green technology levels, and aiding enterprises in gradually reducing carbon emissions without sacrificing economic benefits, thus achieving low-carbon economic development