Collaborative Estimation in Distributed Sensor Networks

Networks of smart ultra-portable devices are already indispensable in our lives, augmenting our senses and connecting our lives through real time processing and communication of sensory (e.g., audio, video, location) inputs. Though usually hidden from the user\u27s sight, the engineering of these devices involves fierce tradeoffs between energy availability (battery sizes impact portability) and signal processing / communication capability (which impacts the smartness of the devices). The goal of this dissertation is to provide a fundamental understanding and characterization of these tradeoffs in the context of a sensor network, where the goal is to estimate a common signal by coordinating a multitude of battery-powered sensor nodes. Most of the research so far has been based on two key assumptions -- distributed processing and temporal independence -- that lend analytical tractability to the problem but otherwise are often found lacking in practice. This dissertation introduces novel techniques to relax these assumptions -- leading to vastly efficient energy usage in typical networks (up to 20% savings) and new insights on the quality of inference. For example, the phenomenon of sensor drift is ubiquitous in applications such as air-quality monitoring, oceanography and bridge monitoring, where calibration is often difficult and costly. This dissertation provides an analytical framework linking the state of calibration to the overall uncertainty of the inferred parameters. In distributed estimation, sensor nodes locally process their observed data and send the resulting messages to a sink, which combines the received messages to produce a final estimate of the unknown parameter. In this dissertation, this problem is generalized and called collaborative estimation , where some sensors can potentially have access to the observations from neighboring sensors and use that information to enhance the quality of their messages sent to the sink, while using the same (or lower) energy resources. This is motivated by the fact that inter-sensor communication may be possible if sensors are geographically close. As demonstrated in this dissertation, collaborative estimation is particularly effective in energy-skewed and information-skewed networks, where some nodes may have larger batteries than others and similarly some nodes may be more informative (less noisy) compared to others. Since the node with the largest battery is not necessarily also the most informative, the proposed inter-sensor collaboration provides a natural framework to route the relevant information from low-energy-high-quality nodes to high-energy-low-quality nodes in a manner that enhances the overall power-distortion tradeoff. This dissertation also analyzes how time-correlated measurement noise affects the uncertainties of inferred parameters. Imperfections such as baseline drift in sensors result in a time-correlated additive component in the measurement noise. Though some models of drift have been reported in the literature earlier, none of the studies have considered the effect of drifting sensors on an estimation application. In this dissertation, approximate measures of estimation accuracy (Cramer-Rao bounds) are derived as a function of physical properties of sensors -- namely the drift strength, correlation (Markov) factor and the time-elapsed since last calibration. For stationary drift (Markov factor less than one), it is demonstrated that the first order effect of drift is asymptotically equivalent to scaling the measurement noise by an appropriate factor. When the drift is non-stationary (Markov factor equal to one), it is established that the constant part of a signal can only be estimated inconsistently (with non-zero asymptotic variance). The results help quantify the notions that measurements taken sooner after calibration result in more accurate inference

Achievable Rate and Modulation for Bandlimited Channels with Oversampling and 1-Bit Quantization at the Receiver

Sustainably realizing applications of the future with high performance demands requires that energy efficiency becomes a central design criterion for the entire system. For example, the power consumption of the analog-to-digital converter (ADC) can become a major factor when transmitting at large bandwidths and carrier frequencies, e.g., for ultra-short range high data rate communication. The consumed energy per conversion step increases with the sampling rate such that high resolution ADCs become unfeasible in the sub-THz regime at the very high sampling rates required. This makes signaling schemes adapted to 1-bit quantizers a promising alternative. We therefore quantify the performance of bandlimited 1-bit quantized wireless communication channels using techniques like oversampling and faster-than-Nyquist (FTN) signaling to compensate for the loss of achievable rate. As a limiting case, we provide bounds on the mutual information rate of the hard bandlimited 1-bit quantized continuous-time – i.e., infinitely oversampled – additive white Gaussian noise channel in the mid-to-high signal-to-noise ratio (SNR) regime. We derive analytic expressions using runlength encoded input signals. For real signals the maximum value of the lower bound on the spectral efficiency in the high-SNR limit was found to be approximately 1.63 bit/s/Hz. Since in practical scenarios the oversampling ratio remains finite, we derive bounds on the achievable rate of the bandlimited oversampled discrete-time channel. These bounds match the results of the continuous-time channel remarkably well. We observe spectral efficiencies up to 1.53 bit/s/Hz in the high-SNR limit given hard bandlimitation. When excess bandwidth is tolerable, spectral efficiencies above 2 bit/s/Hz per domain are achievable w.r.t. the 95 %-power containment bandwidth. Applying the obtained bounds to a bandlimited oversampled 1-bit quantized multiple-input multiple-output channel, we show the benefits when using appropriate power allocation schemes. As a constant envelope modulation scheme, continuous phase modulation is considered in order to relieve linearity requirements on the power amplifier. Noise-free performance limits are investigated for phase shift keying (PSK) and continuous phase frequency shift keying (CPFSK) using higher-order modulation alphabets and intermediate frequencies. Adapted waveforms are designed that can be described as FTN-CPFSK. With the same spectral efficiency in the high-SNR limit as PSK and CPFSK, these waveforms provide a significantly improved bit error rate (BER) performance. The gain in SNR required for achieving a certain BER can be up to 20 dB.Die nachhaltige Realisierung von zukünftigen Übertragungssystemen mit hohen Leistungsanforderungen erfordert, dass die Energieeffizienz zu einem zentralen Designkriterium für das gesamte System wird. Zum Beispiel kann die Leistungsaufnahme des Analog-Digital-Wandlers (ADC) zu einem wichtigen Faktor bei der Übertragung mit großen Bandbreiten und Trägerfrequenzen werden, z. B. für die Kommunikation mit hohen Datenraten über sehr kurze Entfernungen. Die verbrauchte Energie des ADCs steigt mit der Abtastrate, so dass hochauflösende ADCs im Sub-THz-Bereich bei den erforderlichen sehr hohen Abtastraten schwer einsetzbar sind. Dies macht Signalisierungsschemata, die an 1-Bit-Quantisierer angepasst sind, zu einer vielversprechenden Alternative. Wir quantifizieren daher die Leistungsfähigkeit von bandbegrenzten 1-Bit-quantisierten drahtlosen Kommunikationssystemen, wobei Techniken wie Oversampling und Faster-than-Nyquist (FTN) Signalisierung eingesetzt werden, um den durch Quantisierung verursachten Verlust der erreichbaren Rate auszugleichen. Wir geben Grenzen für die Transinformationsrate des Extremfalls eines strikt bandbegrenzten 1-Bit quantisierten zeitkontinuierlichen – d.h. unendlich überabgetasteten – Kanals mit additivem weißen Gauß’schen Rauschen bei mittlerem bis hohem Signal-Rausch-Verhältnis (SNR) an. Wir leiten analytische Ausdrücke basierend auf lauflängencodierten Eingangssignalen ab. Für reelle Signale ist der maximale Wert der unteren Grenze der spektralen Effizienz im Hoch-SNR-Bereich etwa 1,63 Bit/s/Hz. Da die Überabtastrate in praktischen Szenarien endlich bleibt, geben wir Grenzen für die erreichbare Rate eines bandbegrenzten, überabgetasteten zeitdiskreten Kanals an. Diese Grenzen stimmen mit den Ergebnissen des zeitkontinuierlichen Kanals bemerkenswert gut überein. Im Hoch-SNR-Bereich sind spektrale Effizienzen bis zu 1,53 Bit/s/Hz bei strikter Bandbegrenzung möglich. Wenn Energieanteile außerhalb des Frequenzbandes tolerierbar sind, können spektrale Effizienzen über 2 Bit/s/Hz pro Domäne – bezogen auf die Bandbreite, die 95 % der Energie enthält – erreichbar sein. Durch die Anwendung der erhaltenen Grenzen auf einen bandbegrenzten überabgetasteten 1-Bit quantisierten Multiple-Input Multiple-Output-Kanal zeigen wir Vorteile durch die Verwendung geeigneter Leistungsverteilungsschemata. Als Modulationsverfahren mit konstanter Hüllkurve betrachten wir kontinuierliche Phasenmodulation, um die Anforderungen an die Linearität des Leistungsverstärkers zu verringern. Beschränkungen für die erreichbare Datenrate bei rauschfreier Übertragung auf Zwischenfrequenzen mit Modulationsalphabeten höherer Ordnung werden für Phase-shift keying (PSK) and Continuous-phase frequency-shift keying (CPFSK) untersucht. Weiterhin werden angepasste Signalformen entworfen, die als FTN-CPFSK beschrieben werden können. Mit der gleichen spektralen Effizienz im Hoch-SNR-Bereich wie PSK und CPFSK bieten diese Signalformen eine deutlich verbesserte Bitfehlerrate (BER). Die Verringerung des erforderlichen SNRs zur Erreichung einer bestimmten BER kann bis zu 20 dB betragen

Tuning-free one-bit covariance estimation using data-driven dithering

We consider covariance estimation of any subgaussian distribution from finitely many i.i.d. samples that are quantized to one bit of information per entry. Recent work has shown that a reliable estimator can be constructed if uniformly distributed dithers on $[-\lambda,\lambda]$ are used in the one-bit quantizer. This estimator enjoys near-minimax optimal, non-asymptotic error estimates in the operator and Frobenius norms if $\lambda$ is chosen proportional to the largest variance of the distribution. However, this quantity is not known a-priori, and in practice $\lambda$ needs to be carefully tuned to achieve good performance. In this work we resolve this problem by introducing a tuning-free variant of this estimator, which replaces $\lambda$ by a data-driven quantity. We prove that this estimator satisfies the same non-asymptotic error estimates - up to small (logarithmic) losses and a slightly worse probability estimate. Our proof relies on a new version of the Burkholder-Rosenthal inequalities for matrix martingales, which is expected to be of independent interest