Search

A powerful technique for the solution of a number of experimental inverse problems, described by an underlying first-kind Fredholm equation is presented. Such problems include, for example, diffraction-limited imaging and the analysis of laser light scattering data. The technique requires the construction of the 'singular system' of the problem which then provides exact orthonormal bases both for the description of sampled and truncated measured data and for the reconstructed continuous object 'solution' of the inversion. The singular-system approach may be regarded as a theory of information which generalizes in several directions the well known classical concepts of Shannon and Nyquist., SCOPUS: ar.j, info:eu-repo/semantics/published

In recent years, several algorithms for the iterative calculation of a polynomial matrix eigenvalue decomposition (PEVD) have been introduced. The PEVD is a generalisation of the ordinary EVD and uses paraunitary operations to diagonalise a parahermitian matrix. This paper addresses potential computational savings that can be applied to existing cyclic-by-row approaches for the PEVD. These savings are found during the search and rotation stages, and do not significantly impact on algorithm accuracy. We demonstrate that with the proposed techniques, computations can be significantly reduced. The benefits of this are important for a number of broadband multichannel problems.

Polynomial matrix singular value decomposition (PMSVD) plays a very important role in broadband multiple-input multiple-output (MIMO) systems. It can be used to decompose a broadband MIMO channel matrix in order to recover the transmitted signals corrupted by the channel interference (CI) at the receiver. In this contribution newly developed singular value decomposition (SVD) algorithm for polynomial matrices are analyzed and compared in the application of decomposing optical MIMO channels. The bit-error rate (BER) performance is evaluated and optimized by applying bit and power allocation schemes. For our simulations, the specific impulse responses of the (2x2) MIMO channel, including a 1.4 km multi-mode fiber and optical couplers at both ends, are measured for the operating wavelength of 1576 nm.

Recently a selection of sequential matrix diagonalisation (SMD) algorithms have been introduced which approximate polynomial eigenvalue decomposition of parahermitian matrices. These variants differ only in the search methods that are used to bring energy onto the zero-lag. Here we analyse the search methods in terms of their computational complexities for different sizes of parahermitian matrices which are verified through simulated execution times. Another important factor for these search methods is their ability to transfer energy. Simulations show that the more computationally complex search methods transfer a greater proportion of the off-diagonal energy onto the zero-lag over a selected range of parahermitian matrix sizes. Despite their higher cost per iteration experiments indicate that the more complex search algorithms still converge faster in real time.