Determining the quality of sensing devices exhibiting minimal digitization complexity is addressed. Measurements of such sensor systems are characterized by multivariate binary distributions and assessing sensitivity via the Cramér-Rao lower bound turns out to be intractable. In this context, the Fisher matrix of the exponential family and a lower bound for arbitrary probabilistic models are discussed. The conservative approximation for Fisher’s information matrix rests on a surrogate exponential family distribution connected to the actual data-generating system by two compact equivalences. Without characterizing the likelihood and its support, this probabilistic notion enables designing estimators that consistently achieve the sensitivity level defined by the inverse of the conservative information matrix. For hard-limited multivariate Gaussian signal models, a quadratic exponential surrogate distribution tames statistical complexity such that a quantitative and conservative assessment of Fisher information becomes possible. This result is exploited for the Fisherian quantization loss analysis of an array with low-complexity binary sensors in comparison to an ideal system featuring infinite amplitude resolution. Additionally, data-driven assessment by estimating a conservative approximation for the Fisher matrix under recursive binary sampling as implemented in ΣΔ-modulating analog-to-digital converters is demonstrated.

We consider the problem of making a quick decision in favor of one of two possible physical signal models while the numerical measurements are acquired by sensing devices featuring minimal digitization complexity. Therefore, the digital data streams available for statistical processing are binary and exhibit temporal and spatial dependencies. To handle the intractable multivariate binary data model, we first consider sequential tests for exponential family distributions. Within this generic probabilistic framework, we identify adaptive approximations for the log-likelihood ratio and the Kullback-Leibler divergence. The results allow designing sequential detectors for binary radio systems and analyzing their average run-time along classical arguments of Wald. In particular, the derived tests exploit the spatio-temporal correlation structure of the analog sensor signals engraved into the binary measurements. As an application, we consider the specification of binary sensing architectures for cognitive radio and GNSS spectrum monitoring where our results characterize the sequential detection latency as a function of the temporal oversampling and the number of antennas. Finally, we evaluate the efficiency of the proposed algorithms and illustrate the accuracy of our analysis via Monte-Carlo simulations.

This work considers detecting the presence of a band-limited random radio source using an antenna array featuring a low-complexity digitization process with single-bit output resolution. In contrast to high-resolution analog-to-digital conversion, such a direct transformation of the analog radio measurements to a binary representation can be implemented hardware and energy-efficient. However, the probabilistic model of the binary receive data becomes challenging. Therefore, we first consider the Neyman-Pearson test within generic exponential families and derive the associated analytic detection rate expressions. Then we use a specific replacement model for the binary likelihood and study the achievable detection performance with 1-bit radio array measurements. As an application, we explore the capability of a low-complexity GPS spectrum monitoring system with different numbers of antennas and different observation intervals. Results show that with a moderate amount of binary sensors it is possible to reliably perform the monitoring task.

Analog-to-digital (A/D) conversion plays a crucial role when it comes to the design of energy-efficient and fast signal processing systems. As its complexity grows exponentially with the number of output bits, significant savings are possible when resorting to a minimum resolution of a single bit. However, then the nonlinear effect which is introduced by the A/D converter results in a pronounced performance loss, in particular for the case when the receiver is operated outside the low signal-to-noise ratio (SNR) regime. By trading the A/D resolution for a moderately faster sampling rate, we show that for time-of-arrival (TOA) estimation under any SNR level it is possible to obtain a low-complexity 1-bit receive system which features a smaller performance degradation then the classical low SNR hard-limiting loss of 2/π (-1.96 dB). Key to this result is the employment of a lower bound for the Fisher information matrix which enables us to approximate the estimation performance for coarsely quantized receivers with correlated noise models in a pessimistic way.

Parameter estimation using quantized observations is of importance in many practical applications. Under a symmetric 1-bit setup, consisting of a zero-threshold hard-limiter, it is well known that the large sample performance loss for low signal-to-noise ratios (SNRs) is moderate (2/Π or -1.96dB). This makes low-complexity analog-to-digital converters (ADCs) with 1-bit resolution a promising solution for future wireless communications and signal processing devices. However, hardware imperfections and external effects introduce the quantizer with an unknown hard-limiting level different from zero. In this paper, the performance loss associated with pilot-based channel estimation, subject to an asymmetric hard limiter with unknown offset, is studied under two setups. The analysis is carried out via the Cramér-Rao lower bound (CRLB) and an expected CRLB for a setup with random parameter. Our findings show that the unknown threshold leads to an additional information loss, which vanishes for low SNR values or when the offset is close to zero.

Energy-efficient signal processing systems require estimation methods operating on data collected with low-complexity devices. Using analog-to-digital converters (ADC) with 1-bit amplitude resolution has been identified as a possible option in order to obtain low power consumption. The 1-bit performance loss, in comparison to an ideal receiver with ∞-bit ADC, is well-established and moderate for low SNR applications (2/π or -1.96 dB). Recently it has been shown that for parameter estimation with state-space models the 1-bit performance loss with Bayesian filtering can be significantly smaller (√2/π or -0.98 dB). Here we extend the analysis to Bayesian smoothing where additional measurements are used to reconstruct the current state of the system parameter. Our results show that a 1-bit receiver performing smoothing is able to outperform an ideal ∞-bit system carrying out filtering by the cost of an additional processing delay Δ.

The problem of optimum analog receive filtering for digital signal detection and parameter estimation is considered. Here the case of a signal source with bandwidth Btand a receiver with fixed sampling rate fsis discussed under the assumption that 2Bt> fs. We investigate the impact of adjusting the receive bandwidth Brof the analog pre-filter, which is applied prior to the sampler, with respect to the deflection coefficient or the Fisher information measure. This reveals that the design rule 2Brs, known as the sampling theorem, does not necessarily lead to optimum system performance. Studying the two analytical information measures under a fix sampling rate fsand an arbitrary choice of Br, we provide an example where receive setups with 2Br> fsachieve higher detection and parameter estimation performance.

The problem of parameter estimation from large noisy data is considered. If the observation size N is large, the calculation of efficient estimators is computationally expensive. Further, memory can be a limiting factor in technical systems where data is stored for later processing. Here we follow the idea of reducing the size of the observation by projecting the data onto a subspace of smaller dimension M ≪ N, but with the highest possible informative value regarding the estimation problem. Under the assumption that a prior distribution of the parameter is available and the output size is fixed to M, we derive a characterization of the Pareto-optimal set of linear transformations by using a weighted form of the Bayesian Cramér-Rao lower bound (BCRLB) which stands in relation to the expected value of the Fisher information measure. Satellite-based positioning is discussed as a possible application. Here N must be chosen large in order to compensate for low signal-to-noise ratios (SNR). For different values of M, we visualize the information-loss and show by simulation of the MAP estimator the potential accuracy when operating on the reduced data.

The problem how to approximately determine the value of the Fisher information measure for a general parametric probabilistic system is considered. Having available the first and second moment of the system output in a parametric form, it is shown that the information measure can be bounded from below through a replacement of the original system by a Gaussian system with equivalent moments. The presented technique is applied to a system of practical importance and the potential quality of the bound is demonstrated.

Using coarse resolution analog-to-digital conversion (ADC) offers the possibility to reduce the complexity of digital receive systems but introduces a loss in effective signal-to-noise ratio (SNR) when comparing to ideal receivers with infinite resolution ADC. Therefore, here the problem of signal parameter estimation from a coarsely quantized receive signal is considered. In order to increase the system performance, we propose to adjust the analog radio front-end to the quantization device in order to reduce the quantization-loss. By optimizing the bandwidth of the analog filter with respect to a weighted form of the Cramér-Rao lower bound (CRLB), we show that for low SNR and a 1-bit hard-limiting device it is possible to significantly reduce the quantizationloss of initially -1.96 dB. As application, joint carrier-phase and time-delay estimation for satellite-based positioning and synchronization is discussed. Simulations of the maximum-likelihood estimator (MLE) show that the optimum estimator achieves the same quantization-loss reduction as predicted by the performance bound of the optimized system.