Performance analysis of adaptive lattice filters for FM signals and alpha-stable processes

The performance of an adaptive filter may be studied through the behaviour of the optimal and adaptive coefficients in a given environment. This thesis investigates the performance of finite impulse response adaptive lattice filters for two classes of input signals: (a) frequency modulated signals with polynomial phases of order p in complex Gaussian white noise (as nonstationary signals), and (b) the impulsive autoregressive processes with alpha-stable distributions (as non-Gaussian signals). Initially, an overview is given for linear prediction and adaptive filtering. The convergence and tracking properties of the stochastic gradient algorithms are discussed for stationary and nonstationary input signals. It is explained that the stochastic gradient lattice algorithm has many advantages over the least-mean square algorithm. Some of these advantages are having a modular structure, easy-guaranteed stability, less sensitivity to the eigenvalue spread of the input autocorrelation matrix, and easy quantization of filter coefficients (normally called reflection coefficients). We then characterize the performance of the stochastic gradient lattice algorithm for the frequency modulated signals through the optimal and adaptive lattice reflection coefficients. This is a difficult task due to the nonlinear dependence of the adaptive reflection coefficients on the preceding stages and the input signal. To ease the derivations, we assume that reflection coefficients of each stage are independent of the inputs to that stage. Then the optimal lattice filter is derived for the frequency modulated signals. This is performed by computing the optimal values of residual errors, reflection coefficients, and recovery errors. Next, we show the tracking behaviour of adaptive reflection coefficients for frequency modulated signals. This is carried out by computing the tracking model of these coefficients for the stochastic gradient lattice algorithm in average. The second-order convergence of the adaptive coefficients is investigated by modeling the theoretical asymptotic variance of the gradient noise at each stage. The accuracy of the analytical results is verified by computer simulations. Using the previous analytical results, we show a new property, the polynomial order reducing property of adaptive lattice filters. This property may be used to reduce the order of the polynomial phase of input frequency modulated signals. Considering two examples, we show how this property may be used in processing frequency modulated signals. In the first example, a detection procedure in carried out on a frequency modulated signal with a second-order polynomial phase in complex Gaussian white noise. We showed that using this technique a better probability of detection is obtained for the reduced-order phase signals compared to that of the traditional energy detector. Also, it is empirically shown that the distribution of the gradient noise in the first adaptive reflection coefficients approximates the Gaussian law. In the second example, the instantaneous frequency of the same observed signal is estimated. We show that by using this technique a lower mean square error is achieved for the estimated frequencies at high signal-to-noise ratios in comparison to that of the adaptive line enhancer. The performance of adaptive lattice filters is then investigated for the second type of input signals, i.e., impulsive autoregressive processes with alpha-stable distributions . The concept of alpha-stable distributions is first introduced. We discuss that the stochastic gradient algorithm which performs desirable results for finite variance input signals (like frequency modulated signals in noise) does not perform a fast convergence for infinite variance stable processes (due to using the minimum mean-square error criterion). To deal with such problems, the concept of minimum dispersion criterion, fractional lower order moments, and recently-developed algorithms for stable processes are introduced. We then study the possibility of using the lattice structure for impulsive stable processes. Accordingly, two new algorithms including the least-mean P-norm lattice algorithm and its normalized version are proposed for lattice filters based on the fractional lower order moments. Simulation results show that using the proposed algorithms, faster convergence speeds are achieved for parameters estimation of autoregressive stable processes with low to moderate degrees of impulsiveness in comparison to many other algorithms. Also, we discuss the effect of impulsiveness of stable processes on generating some misalignment between the estimated parameters and the true values. Due to the infinite variance of stable processes, the performance of the proposed algorithms is only investigated using extensive computer simulations.

The design and testing of a daylighting device : optimising the energy and optical performance of Australian commercial buildings

The effective daylighting of multistorey commercial building interiors poses an interesting problem for designers in Australia’s tropical and subtropical context. Given that a building exterior receives adequate sun and skylight as dictated by location-specific factors such as weather, siting and external obstructions; then the availability of daylight throughout its interior is dependant on certain building characteristics: the distance from a window façade (room depth), ceiling or window head height, window size and the visible transmittance of daylighting apertures. The daylighting of general stock, multistorey commercial buildings is made difficult by their design limitations with respect to some of these characteristics. The admission of daylight to these interiors is usually exclusively by vertical windows. Using conventional glazing, such windows can only admit sun and skylight to a depth of approximately 2 times the window height. This penetration depth is typically much less than the depth of the office interiors, so that core areas of these buildings receive little or no daylight. This issue is particularly relevant where deep, open plan office layouts prevail. The resulting interior daylight pattern is a relatively narrow perimeter zone bathed in (sometimes too intense) light, contrasted with a poorly daylit core zone. The broad luminance range this may present to a building occupant’s visual field can be a source of discomfort glare. Furthermore, the need in most tropical and subtropical regions to restrict solar heat gains to building interiors for much of the year has resulted in the widespread use of heavily tinted or reflective glazing on commercial building façades. This strategy reduces the amount of solar radiation admitted to the interior, thereby decreasing daylight levels proportionately throughout. However this technique does little to improve the way light is distributed throughout the office space. Where clear skies dominate weather conditions, at different times of day or year direct sunlight may pass unobstructed through vertical windows causing disability or discomfort glare for building occupants and as such, its admission to an interior must be appropriately controlled. Any daylighting system to be applied to multistorey commercial buildings must consider these design obstacles, and attempt to improve the distribution of daylight throughout these deep, sidelit office spaces without causing glare conditions. The research described in this thesis delineates first the design optimisation and then the actual prototyping and manufacture process of a daylighting device to be applied to such multistorey buildings in tropical and subtropical environments.