Fade depth scaling with channel bandwidth

The dependence of small-scale fading on bandwidth is quantified experimentally in the 3.1–10.6 GHz band for indoor channels. The fade depth converges to 4 dB at 1 GHz bandwidth, with little reduction for further increase in bandwidth. A simple yet accurate empirical fade depth model is developed, enabling convenient evaluation of the link budget for a channel with given bandwidth

Stochastic Modeling and Estimation of Wireless Channels with Application to Ultra Wide Band Systems

This thesis is concerned with modeling of both space and time variations of Ultra Wide Band (UWB) indoor channels. The most common empirically determined amplitude distribution in many UWB environments is Nakagami distribution. The latter is generalized to stochastic diffusion processes which capture the dynamics of UWB channels. In contrast with the traditional models, the statistics of the proposed models are shown to be time varying, but converge in steady state to their static counterparts. System identification algorithms are used to extract various channel parameters using received signal measurement data, which are usually available at the receiver. The expectation maximization (EM) algorithm and the Kalman filter (KF) are employed in estimating channel parameters as well as the inphase and quadrature components, respectively. The proposed algorithms are recursive and therefore can be implemented in real time. Further, sufficient conditions for the convergence of the EM algorithm are provided. Comparison with recursive Least-square (LS) algorithms is carried out using experimental measurements. Distributed stochastic power control algorithms based on the fixed point theorem and stochastic approximations are used to solve for the optimal transmit power problem and numerical results are also presented. A framework which can capture the statistics of the overall received signal and a methodology to estimate parameters of the counting process based on the received signal is developed. Furthermore, second moment statistics and characteristic functions are computed explicitly and considered as an extension of Rice’s shot noise analysis. Another two important components, input design and model selection are also considered. Gel’fand n-widths and Time n-widths are used to represent the inherent error introduced by input design. Kolmogorov n-width is used to characterize the representation error introduced by model selection. In particular, it is shown that the optimal model for reducing the representation error is a finite impulse response (FIR) model and the optimal input is an impulse at the start of the observation interval

Location-free Spectrum Cartography

Spectrum cartography constructs maps of metrics such as channel gain or received signal power across a geographic area of interest using spatially distributed sensor measurements. Applications of these maps include network planning, interference coordination, power control, localization, and cognitive radios to name a few. Since existing spectrum cartography techniques require accurate estimates of the sensor locations, their performance is drastically impaired by multipath affecting the positioning pilot signals, as occurs in indoor or dense urban scenarios. To overcome such a limitation, this paper introduces a novel paradigm for spectrum cartography, where estimation of spectral maps relies on features of these positioning signals rather than on location estimates. Specific learning algorithms are built upon this approach and offer a markedly improved estimation performance than existing approaches relying on localization, as demonstrated by simulation studies in indoor scenarios.Comment: 14 pages, 12 figures, 1 table. Submitted to IEEE Transactions on Signal Processin

Transceiver design and system optimization for ultra-wideband communications

This dissertation investigates the potential promises and proposes possible solutions to the challenges of designing transceivers and optimizing system parameters in ultra-wideband (UWB) systems. The goal is to provide guidelines for UWB transceiver implementations under constraints by regulation, existing interference, and channel estimation. New UWB pulse shapes are invented that satisfy the Federal Communications Commission spectral mask. Parameters are designed to possibly implement the proposed pulses. A link budget is quantified based on an accurate frequency-dependent path loss calculation to account for variations across the ultra-wide bandwidth of the signal. Achievable information rates are quantified as a function of transmission distance over additive white Gaussian noise and multipath channels under specific UWB constraints: limited power spectral density, specific modulation formats, and a highly dispersive channel. The effect of self-interference (SI) and inter-symbol interference (ISI) on channel capacity is determined, and modulation formats that mitigate against this effect is identified. Spreading gains of familiar UWB signaling formats are evaluated, and UWB signals are proved to be spread spectrum. Conditions are formulated for trading coding gain with spreading gain with only a small impact on performance. Numerical results are examined to demonstrate that over a frequency-selective channel, the spreading gain may be beneficial in reducing the SI and ISI resulting in higher information rates. A reduced-rank adaptive filtering technique is applied to the problem of interference suppression and optimum combining in UWB communications. The reduced-rank combining method, in particular the eigencanceler, is proposed and compared with a minimum mean square error Rake receiver. Simulation results are evaluated to show that the performance of the proposed method is superior to the minimum mean square error when the correlation matrix is estimated from limited data. Impact of channel estimation on UWB system performance is investigated when path delays and path amplitudes are jointly estimated. Cramér-Rao bound (CRB) expressions for the variance of path delay and amplitude estimates are formulated using maximum likelihood estimation. Using the errors obtained from the CRB, the effective signal-to-noise ratio for UWB Rake receivers employing maximum ratio combining (MRC) is devised in the presence of channel path delay and amplitude errors. An exact expression of the bit error rate (BER) for UWB Rake receivers with MRC is derived with imperfect estimates of channel path delays and amplitudes. Further, this analysis is applied to design optimal transceiver parameters. The BER is used as part of a binary symmetric channel and the achievable information rates are evaluated. The optimum power allocation and number of symbols allocated to the pilot are developed with respect to maximizing the information rate. The optimal signal bandwidth to be used for UWB communications is determined in the presence of imperfect channel state information. The number of multipath components to be collected by Rake receivers is designed to optimize performance with non-ideal channel estimation

Approximation of L\"owdin Orthogonalization to a Spectrally Efficient Orthogonal Overlapping PPM Design for UWB Impulse Radio

In this paper we consider the design of spectrally efficient time-limited pulses for ultrawideband (UWB) systems using an overlapping pulse position modulation scheme. For this we investigate an orthogonalization method, which was developed in 1950 by Per-Olov L\"owdin. Our objective is to obtain a set of N orthogonal (L\"owdin) pulses, which remain time-limited and spectrally efficient for UWB systems, from a set of N equidistant translates of a time-limited optimal spectral designed UWB pulse. We derive an approximate L\"owdin orthogonalization (ALO) by using circulant approximations for the Gram matrix to obtain a practical filter implementation. We show that the centered ALO and L\"owdin pulses converge pointwise to the same Nyquist pulse as N tends to infinity. The set of translates of the Nyquist pulse forms an orthonormal basis or the shift-invariant space generated by the initial spectral optimal pulse. The ALO transform provides a closed-form approximation of the L\"owdin transform, which can be implemented in an analog fashion without the need of analog to digital conversions. Furthermore, we investigate the interplay between the optimization and the orthogonalization procedure by using methods from the theory of shift-invariant spaces. Finally we develop a connection between our results and wavelet and frame theory.Comment: 33 pages, 11 figures. Accepted for publication 9 Sep 201