Sensor fusion algorithms allow the combination of many heterogeneous data types to make sophisticated decisions. In many situations, these algorithms give increased performance such as better detectability and/or reduced false alarm rates. To achieve these benefits, typically some system or signal model is given. This work focuses on the situation where the event signal is unknown and a false alarm criterion must be met. Specifically, the case where data from multiple passive infrared (PIR) sensors are processed to detect intrusion into a room while satisfying a false alarm constraint is analyzed. The central challenge is the space of intrusion signals is unknown and we want to quantify analytically the probability of false alarm. It is shown that this quantification is possible by estimating the background noise statistics and computing the Mahalanobis distance in the frequency domain. Using the Mahalanobis distance as the decision metric, a threshold is computed to satisfy the false alarm constraint.

The goal of sensor fusion is to combine the information obtained by various sensors to make better decisions. By better, it is meant that the sensor fusion algorithm provides, for example, better detectability or lower false alarm rates compared to decisions based upon a single sensor. This work is motivated by combining the data gathered by multiple passive infrared (PIR) sensors to detect intrusions into a room. Optimal decision theoretic approaches typically include statistical models for both the background (non-event) data, and intrusion (event) data. Concurrent work by the author has shown that by appropriately processing multiple PIR data streams, a statistic can be computed which has a known distribution on the background data. If the distribution of the statistic during an event is known, optimal decision procedures could be derived to perform sensor fusion. It is shown, however, that it is difficult to statistically model the event data. This paper thus focuses on using minimax theory to derive the worst-case event distribution for minimizing Bayes risk. Because of this, using the minimax distribution as a surrogate for the unknown true distribution of the event data provides a lower bound on risk performance. The minimax formulation is very general and will be used to consider loss functions, the probability of intrusions events and consider nonbinary decisions.

The proportional fair sharing (PFS) algorithm has been used in multi-user systems as an attempt to balance fairness and performance of the system throughput. Motivated by the cellular downlink scheduling problem, it is shown that when the rates of each user are i.i.d., the performance of the PFS scheduling algorithms is asymptotically equivalent to a purely greedy scheduling algorithm. The mean asymptotic throughput of the PFS algorithm is characterized and the rate of convergence to this limit is derived under i.i.d. models. Additionally the asymptotic covariance matrix about the convergence point is stated.

Communication using mid-ultraviolet radiation between 200nm and 280nm has received renewed attention due to advancements in UV LED emitters and unique propagation characteristics at these wavelengths. Atmospheric gases absorb light at mid-UV so that receivers or sensors operating on the earth’s surface receive no interference from solar radiation. This so-called “solar-blind” region of the spectrum allows the use of single-photon detection techniques. Further, UV light is strongly scattered by molecules in the air, enabling non-line-of-sight (NLOS) communication. We extend previous work in this area by incorporating angle-dependent Mie scattering into one of the standard propagation models, in an effort to include the effects of aerosols. Experimental results from outdoor measurements using a fog generator are also presented.

To utilize the multi-user diversity in broadcast channels, the channel state information (CSI) of each user must be known at the transmitter. To reduce the overhead of CSI feedback under random beamforming the question of which receivers should feed back their CSI is investigated. Using the closed form expression for the SINR distribution, thresholding functions T(n) are designed to meet specific design criterion as a function of the number of receivers. Specifically three design criterion are proposed. The asymptotic limits of the successful thresholding functions T(n) are found. If T(n) scales slower than log n, asymptotically no performance is lost. If T(n) scales faster than log n, all multi-user diversity is lost.

Feedback of channel state information (CSI) in wireless systems is essential in order to exploit multi-user diversity and achieve the highest possible performace. When each spatially distributed user in the wireless system is assumed to have i.i.d. scalar CSI values, the optimal fixed-rate and entropy-constrained point density functions are established in the high-resolution regime for the quantization of the CSI feedback to a centralized scheduler under the mean square error (MSE) criterion. The spatially distributed nature of the users leads to a distributed functional scalar quantization approach for the optimal high resolution point densities of the CSI feedback. Under a mild absolute moment criterion, it is shown that with a greedy scheduling algorithm at the centralized scheduler, the optimal fixed-rate point density for each user corresponds to a point density associated with the maximal order statistic distribution. This result is generalized to monotonic functions of arbitrary order statistics. Optimal point densities under entropy-constrained quantization for the CSI are established under mild conditions on the distribution function of the CSI metric.

In this paper we analyze the performance of random beamforming schemes in a multi-user Gaussian broadcast channel. Each user will have N > 1 receive antennas allowing optimal combining to be performed. To notify the transmitter of its current channel state, each user feeds back their SINR after LMMSE combining. Two feedback schemes are analyzed. The first scheme allows each user to feedback the post-processed SINR for each of the random transmit beams. To analyze this scheme, the distribution of the post-processed SINR is found. The second scheme attempts to limit feedback by allowing each user to feedback only the largest observed post-processed SINR and the index of the associated transmit beam. Using the Fr´echet bounds, the throughput of the reduce feedback scheme is bounded and shown to have the same asymptotic scaling properties as the first scheme. Empirically, it is observed that as the number of users in the system increases, the reduced feedback scheme approaches the throughput of the scheme without thresholding.

A random beamforming scheme for the Gaussian MIMO broadcast channel with channel quality feedback is investigated and extended. Considering the case where the n receivers each have N receive antennas, the effects of feeding back various amounts of signal-to-interference-plus-noise ratio (SINR) information are analyzed. Using the results from order statistics of the ratio of a linear combination of exponential random variables, the distribution function of the maximum order statistic of the SINR observed at the receiver is found. The analysis from viewing each antenna as an individual user is extended to allow combining at the receivers, where it is known that the linear MMSE combiner is the optimal linear receiver and the CDF for the SINR after optimal combining is derived. Analytically, using the Delta Method, the asymptotic distribution of the maximum order statistic of the SINR with and without combining is shown to be, in the nomenclature of extreme order statistics, of type 3. The throughput of the feedback schemes are shown to exhibit optimal scaling asymptotically in the number of users. Finally, to further reduce the amount of feedback, a hard threshold is applied to the SINR feedback. The amount of feedback saved by implementing a hard threshold is determined and the effect on the system throughput is analyzed and bounded.

In this paper we analyze the performance of random beamforming schemes in a multi-user Gaussian broadcast channel utilizing SINR feedback. For generality, the receivers are allowed to have multiple receive antennas. The first scheme analyzed allows each receiver to feed back the largest SINR it observes for each transmit beam. The distribution function of the maximum SINR is derived and is noted to differ from previous work. In an effort to further reduce feedback, a scheme where each user feeds back the maximum SINR observed over its receive antennas and transmit beams. Using the Fr´echet bounds and properties of chi-squared random variables, the throughput of this system is bounded and empirically shown to approach the performance of the previous scheme as the number of users increases.