Mutual Information and Minimum Mean-square Error in Gaussian Channels

This paper deals with arbitrarily distributed finite-power input signals observed through an additive Gaussian noise channel. It shows a new formula that connects the input-output mutual information and the minimum mean-square error (MMSE) achievable by optimal estimation of the input given the output. That is, the derivative of the mutual information (nats) with respect to the signal-to-noise ratio (SNR) is equal to half the MMSE, regardless of the input statistics. This relationship holds for both scalar and vector signals, as well as for discrete-time and continuous-time noncausal MMSE estimation. This fundamental information-theoretic result has an unexpected consequence in continuous-time nonlinear estimation: For any input signal with finite power, the causal filtering MMSE achieved at SNR is equal to the average value of the noncausal smoothing MMSE achieved with a channel whose signal-to-noise ratio is chosen uniformly distributed between 0 and SNR

Optimization of MLS receivers for multipath environments

A receiver is designed for aircraft (A/C), which, as a component of the proposed Microwave Landing System (MLS), is capable of optimal performance in the multipath environments found in air terminal areas. Topics discussed include: the angle-tracking problem of the MLS receiver; signal modeling; preliminary approaches to optimal design; suboptimal design; and simulation study

Power allocation and signal labelling on physical layer security

PhD ThesisSecure communications between legitimate users have received considerable attention recently. Transmission cryptography, which introduces secrecy on the network layer, is heavily relied on conventionally to secure communications. However, it is theoretically possible to break the encryption if unlimited computational resource is provided. As a result, physical layer security becomes a hot topic as it provides perfect secrecy from an information theory perspective. The study of physical layer security on real communication system model is challenging and important, as the previous researches are mainly focusing on the Gaussian input model which is not practically implementable. In this thesis, the physical layer security of wireless networks employing finite-alphabet input schemes are studied. In particular, firstly, the secrecy capacity of the single-input single-output (SISO) wiretap channel model with coded modulation (CM) and bit-interleaved coded modulation (BICM) is derived in closed-form, while a fast, sub-optimal power control policy (PCP) is presented to maximize the secrecy capacity performance. Since finite-alphabet input schemes achieve maximum secrecy capacity at medium SNR range, the maximum amount of energy that the destination can harvest from the transmission while satisfying the secrecy rate constraint is computed. Secondly, the effects of mapping techniques on secrecy capacity of BICM scheme are investigated, the secrecy capacity performances of various known mappings are compared on 8PSK, 16QAM and (1,5,10) constellations, showing that Gray mapping obtains lowest secrecy capacity value at high SNRs. We propose a new mapping algorithm, called maximum error event (MEE), to optimize the secrecy capacity over a wide range of SNRs. At low SNR, MEE mapping achieves a lower secrecy rate than other well-known mappings, but at medium-to-high SNRs MEE mapping achieves a significantly higher secrecy rate over a wide range of SNRs. Finally, the secrecy capacity and power allocation algorithm (PA) of finite-alphabet input wiretap channels with decode-and-forward (DF) relays are proposed, the simulation results are compared with the equal power allocation algorithm

Topics in Nonlinear Stochastic Control, Estimation, and Decision, Using a Measure Transformation Approach

We discuss topics in the theory of nonlinear stochastic control, estimation, and decision via a probabilistic approach using measure transformations and martingale theory. First, we investigate the problem of estimating a diffusion process using coordinate transformations and measure transformations, both locally and globally; this is the analog of nonlinear coordinate and state feedback transformations used to obtain exact linearization in nonlinear deterministic control problems. Our results are new in that we use a probabilistic approach rather than a purely geometric one, and also in that we derive representations when the processes are defined locally rather than just globally. A gauge transformation then leads to a Feynman-Kac formula that is related to the unnormalized conditional density and subsequent bounds of filter estimates, where some of these bounds are extensions of pre-existing results while others are presented here for the first time. Second, we present new methods and new results in obtaining a minimum principle for partially observed diffusions using calculus of variations when the control variable is present only in the drift coefficient and correlation exists between state and observation noise, and then when the control variable exists in both drift and diffusion coefficients and no correlation exists. Here the problem is formulated as one of complete information, but instead of considering the unnormalized conditional density as the new state, this density is decomposed into two measure-valued processes and leads to a separation principle reminiscent of the linear-quadratic-Gaussian problem and stochastic flows of Euclidean processes. Third, we study the decision problem using likelihood-ratio tests and evaluate the performance using Chernoff bounds. We present new results by expressing both likelihood-ratios and error-probabilities in terms of a ratio of two unnormalized conditional densities where each satisfies a stochastic differential equation that in some cases can be solved in closed form