Sparse identification of volterra models for power amplifiers without pseudoinverse computation

Article number 9178996We present a new formulation of the doubly orthogonal matching pursuit (DOMP) algorithm for the sparse recovery of Volterra series models. The proposal works over the covariance matrices by taking advantage of the orthogonal properties of the solution at each iteration and avoids the calculation of the pseudoinverse matrix to obtain the model coefficients. A detailed formulation of the algorithm is provided along with a computational complexity assessment, showing a fixed complexity per iteration compared with its previous versions in which it depends on the iteration number. Moreover, we empirically demonstrate the reduction in computational complexity in terms of runtime and highlight the pruning capabilities through its application to the digital predistortion of a class J power amplifier operating under 5G-NR signals with the bandwidth of 20 and 30 MHz, concluding that this proposal significantly outperforms existing techniques in terms of computational complexity

Homotopy based algorithms for ℓ0\ell_0-regularized least-squares

Sparse signal restoration is usually formulated as the minimization of a quadratic cost function $\|y-Ax\|_2^2$, where A is a dictionary and x is an unknown sparse vector. It is well-known that imposing an $\ell_0$ constraint leads to an NP-hard minimization problem. The convex relaxation approach has received considerable attention, where the $\ell_0$-norm is replaced by the $\ell_1$-norm. Among the many efficient $\ell_1$ solvers, the homotopy algorithm minimizes $\|y-Ax\|_2^2+\lambda\|x\|_1$ with respect to x for a continuum of $\lambda$'s. It is inspired by the piecewise regularity of the $\ell_1$-regularization path, also referred to as the homotopy path. In this paper, we address the minimization problem $\|y-Ax\|_2^2+\lambda\|x\|_0$ for a continuum of $\lambda$'s and propose two heuristic search algorithms for $\ell_0$-homotopy. Continuation Single Best Replacement is a forward-backward greedy strategy extending the Single Best Replacement algorithm, previously proposed for $\ell_0$-minimization at a given $\lambda$. The adaptive search of the $\lambda$-values is inspired by $\ell_1$-homotopy. $\ell_0$ Regularization Path Descent is a more complex algorithm exploiting the structural properties of the $\ell_0$-regularization path, which is piecewise constant with respect to $\lambda$. Both algorithms are empirically evaluated for difficult inverse problems involving ill-conditioned dictionaries. Finally, we show that they can be easily coupled with usual methods of model order selection.Comment: 38 page