J. Brewer

Bio: J. Brewer is an academic researcher from University of California, Davis. The author has contributed to research in topics: Multivariable calculus & Matrix calculus. The author has an hindex of 1, co-authored 1 publications receiving 1861 citations.

Kronecker products and matrix calculus in system theory

Abstract: The paper begins with a review of the algebras related to Kronecker products. These algebras have several applications in system theory including the analysis of stochastic steady state. The calculus of matrix valued functions of matrices is reviewed in the second part of the paper. This calculus is then used to develop an interesting new method for the identifiication of parameters of lnear time-invariant system models.

Tutorial on higher-order statistics (spectra) in signal processing and system theory: theoretical results and some applications

Abstract: A compendium of recent theoretical results associated with using higher-order statistics in signal processing and system theory is provided, and the utility of applying higher-order statistics to practical problems is demonstrated. Most of the results are given for one-dimensional processes, but some extensions to vector processes and multichannel systems are discussed. The topics covered include cumulant-polyspectra formulas; impulse response formulas; autoregressive (AR) coefficients; relationships between second-order and higher-order statistics for linear systems; double C(q,k) formulas for extracting autoregressive moving average (ARMA) coefficients; bicepstral formulas; multichannel formulas; harmonic processes; estimates of cumulants; and applications to identification of various systems, including the identification of systems from just output measurements, identification of AR systems, identification of moving-average systems, and identification of ARMA systems. >

Deconstructing multiantenna fading channels

Abstract: Accurate and tractable channel modeling is critical to realizing the full potential of antenna arrays in wireless communications. Current approaches represent two extremes: idealized statistical models representing a rich scattering environment and parameterized physical models that describe realistic scattering environments via the angles and gains associated with different propagation paths. However, simple rules that capture the effects of scattering characteristics on channel capacity and diversity are difficult to infer from existing models. We propose an intermediate virtual channel representation that captures the essence of physical modeling and provides a simple geometric interpretation of the scattering environment. The virtual representation corresponds to a fixed coordinate transformation via spatial basis functions defined by fixed virtual angles. We show that in an uncorrelated scattering environment, the elements of the channel matrix form a segment of a stationary process and that the virtual channel coefficients are approximately uncorrelated samples of the underlying spectral representation. For any scattering environment, the virtual channel matrix clearly reveals the two key factors affecting capacity: the number of parallel channels and the level of diversity. The concepts of spatial zooming and aliasing are introduced to provide a transparent interpretation of the effect of antenna spacing on channel statistics and capacity. Numerical results are presented to illustrate various aspects of the virtual framework.

Linear transmit processing in MIMO communications systems

Abstract: We examine and compare the different types of linear transmit processing for multiple input, multiple output systems, where we assume that the receive filter is independent of the transmit filter contrary to the joint optimization of transmit and receive filters. We can identify three filter types similar to receive processing: the transmit matched filter, the transmit zero-forcing filter, and the transmit Wiener filter. We show that the transmit filters are based on similar optimizations as the respective receive filters with an additional constraint for the transmit power. Moreover, the transmit Wiener filter has similar convergence properties as the receive Wiener filter, i.e., it converges to the matched filter and the zero-forcing filter for low and high signal-to-noise ratio, respectively. We give closed-form solutions for all transmit filters and present the fundamental result that their mean-square errors are equal to the errors of the respective receive filters, if the information symbols and the additive noise are uncorrelated. However, our simulations reveal that the bit-error ratio results of the transmit filters differ from the results for the respective receive filters.