Biorthogonal partners and applications

Two digital filters H(z) and F(z) are said to be biorthogonal partners of each other if their cascade H(z)F(z) satisfies the Nyquist or zero-crossing property. Biorthogonal partners arise in many different contexts such as filterbank theory, exact and least squares digital interpolation, and multiresolution theory. They also play a central role in the theory of equalization, especially, fractionally spaced equalizers in digital communications. We first develop several theoretical properties of biorthogonal partners. We also develop conditions for the existence of biorthogonal partners and FIR biorthogonal pairs and establish the connections to the Riesz basis property. We then explain how these results play a role in many of the above-mentioned applications

Discrete probability density estimation using multirate DSP models

We propose a model based approach for estimation of probability mass functions for discrete random variables. The model is based on tools from multirate signal processing. Similar in principle to the kernel based methods, the approach takes advantage of well-known results from multirate signal processing theory. Similarities to and differences from wavelet based approaches is also indicated where appropriate. In the final form, the probability estimates are obtained by filtering the square root of the histogram through a multirate system whose components are biorthogonal partners of each other

Discrete pdf estimation in the presence of noise

The problem of estimating a pdf from measurements has been widely studied by many researchers. However, most of the work was focused on estimating a probability density function of continuous random variables, especially in the absence of noise. In this paper, we consider a model for representing discrete probability density functions based on multirate dsp models. Using this model, we propose an efficient and stable scheme for pdf estimation when the measurements are corrupted by independent additive noise. This approach makes use of well-known results from multirate dsp theory, especially that of biorthogonal partners. Simulation results are given, which clearly show the advantage of the proposed method

Fractional biorthogonal partners in channel equalization and signal interpolation

The concept of biorthogonal partners has been introduced recently by the authors. The work presented here is an extension of some of these results to the case where the upsampling and downsampling ratios are not integers but rational numbers, hence, the name fractional biorthogonal partners. The conditions for the existence of stable and of finite impulse response (FIR) fractional biorthogonal partners are derived. It is also shown that the FIR solutions (when they exist) are not unique. This property is further explored in one of the applications of fractional biorthogonal partners, namely, the fractionally spaced equalization in digital communications. The goal is to construct zero-forcing equalizers (ZFEs) that also combat the channel noise. The performance of these equalizers is assessed through computer simulations. Another application considered is the all-FIR interpolation technique with the minimum amount of oversampling required in the input signal. We also consider the extension of the least squares approximation problem to the setting of fractional biorthogonal partners

Investigation, Design and Implementation of MIMO Antennas for Mobile Phones. Simulation and Measurement of MIMO Antennas for Mobile Handsets and Investigations of Channel Capacity of the Radiating Elements Using Spatial and Polarisation Diversity Strategies.

The objectives of this work were to investigate, design and implement Multiple-Input Multiple-Output (MIMO) antenna arrays for mobile phones. Several MIMO antennas were developed and tested over various wireless-communication frequency bands. The radiation performance and channel capacity of these antennas were computed and measured: the results are discussed in the context of the frequency bands of interest. A comprehensive study of MIMO antenna configurations such as 2 × 1, 3 × 1, 2 × 2 and 3 × 3, using polarisation diversity as proposed for future mobile handsets, is presented. The channel capacity is investigated and discussed, as applying to Rayleigh fading channels with different power spectrum distributions with respect to azimuth and zenith angles. The channel capacity of 2 × 2 and 3 × 3 MIMO systems using spatial polarisation diversity is presented for different antenna designs. The presented results show that the maximum channel capacity for an antenna contained within a small volume can be reached with careful selection of the orthogonal spatial fields. The results are also compared against planar array MIMO antenna systems, in which the antenna size considered was much larger. A 50% antenna size reduction method is explored by applying magnetic wall concept on the symmetry reference of the antenna structure. Using this method, a triple dual-band inverted-F antenna system is presented and considered for MIMO application. Means of achieving minimum coupling between the three antennas are investigated over the 2.45 GHz and 5.2 GHz bands. A new 2 2 MIMO dual-band balanced antenna handset, intended to minimise the coupling with the handset and human body was proposed, developed and tested. The antenna coupling with the handset and human hand is reported in terms the radiation performance and the available channel capacity. In addition, a dual-polarisation dipole antenna is proposed, intended for use as one of three collocated orthogonal antennas in a polarisation-diversity MIMO communication system. The antenna actually consists of two overlaid electric and magnetic dipoles, such that their radiation patterns are nominally identical but they are cross-polarised and hence only interact minimally

Biorthogonal partners and applications

Abstract. Two digital filters H(z) and F(z) are said to be biorthogonal partners of each other if their cascade H(z)F(z) satisfies the Nyquist or zero-crossing property. Biorthogonal partners arise in many different contexts such as filter bank theory, exact and least squares digital interpolation, and multiresolution theory. They also play a central role in the theory of equalization, especially, fractionally spaced equalizers in digital communications. In this paper we first develop several theoretical properties of biorthogonal partners. We also develop conditions for the existence of biorthogonal partners and FIR biorthogonal pairs, and establish the connections to the Riesz basis property. We then explain how these results play a role in many of the above mentioned applications. 1 1