Distributed Detection over Fading MACs with Multiple Antennas at the Fusion Center

A distributed detection problem over fading Gaussian multiple-access channels is considered. Sensors observe a phenomenon and transmit their observations to a fusion center using the amplify and forward scheme. The fusion center has multiple antennas with different channel models considered between the sensors and the fusion center, and different cases of channel state information are assumed at the sensors. The performance is evaluated in terms of the error exponent for each of these cases, where the effect of multiple antennas at the fusion center is studied. It is shown that for zero-mean channels between the sensors and the fusion center when there is no channel information at the sensors, arbitrarily large gains in the error exponent can be obtained with sufficient increase in the number of antennas at the fusion center. In stark contrast, when there is channel information at the sensors, the gain in error exponent due to having multiple antennas at the fusion center is shown to be no more than a factor of (8/pi) for Rayleigh fading channels between the sensors and the fusion center, independent of the number of antennas at the fusion center, or correlation among noise samples across sensors. Scaling laws for such gains are also provided when both sensors and antennas are increased simultaneously. Simple practical schemes and a numerical method using semidefinite relaxation techniques are presented that utilize the limited possible gains available. Simulations are used to establish the accuracy of the results.Comment: 21 pages, 9 figures, submitted to the IEEE Transactions on Signal Processin

Distributed detection, localization, and estimation in time-critical wireless sensor networks

In this thesis the problem of distributed detection, localization, and estimation (DDLE) of a stationary target in a fusion center (FC) based wireless sensor network (WSN) is considered. The communication process is subject to time-critical operation, restricted power and bandwidth (BW) resources operating over a shared communication channel Buffering from Rayleigh fading and phase noise. A novel algorithm is proposed to solve the DDLE problem consisting of two dependent stages: distributed detection and distributed estimation. The WSN performs distributed detection first and based on the global detection decision the distributed estimation stage is performed. The communication between the SNs and the FC occurs over a shared channel via a slotted Aloha MAC protocol to conserve BW. In distributed detection, hard decision fusion is adopted, using the counting rule (CR), and sensor censoring in order to save power and BW. The effect of Rayleigh fading on distributed detection is also considered and accounted for by using distributed diversity combining techniques where the diversity combining is among the sensor nodes (SNs) in lieu of having the processing done at the FC. Two distributed techniques are proposed: the distributed maximum ratio combining (dMRC) and the distributed Equal Gain Combining (dEGC). Both techniques show superior detection performance when compared to conventional diversity combining procedures that take place at the FC. In distributed estimation, the segmented distributed localization and estimation (SDLE) framework is proposed. The SDLE enables efficient power and BW processing. The SOLE hinges on the idea of introducing intermediate parameters that are estimated locally by the SNs and transmitted to the FC instead of the actual measurements. This concept decouples the main problem into a simpler set of local estimation problems solved at the SNs and a global estimation problem solved at the FC. Two algorithms are proposed for solving the local problem: a nonlinear least squares (NLS) algorithm using the variable projection (VP) method and a simpler gird search (GS) method. Also, Four algorithms are proposed to solve the global problem: NLS, GS, hyperspherical intersection method (HSI), and robust hyperspherical intersection (RHSI) method. Thus, the SDLE can be solved through local and global algorithm combinations. Five combinations are tied: NLS2 (NLS-NLS), NLS-HSI, NLS-RHSI, GS2, and GS-N LS. It turns out that the last algorithm combination delivers the best localization and estimation performance. In fact , the target can be localized with less than one meter error. The SNs send their local estimates to the FC over a shared channel using the slotted-Aloha MAC protocol, which suits WSNs since it requires only one channel. However, Aloha is known for its relatively high medium access or contention delay given the medium access probability is poorly chosen. This fact significantly hinders the time-critical operation of the system. Hence, multi-packet reception (MPR) is used with slotted Aloha protocol, in which several channels are used for contention. The contention delay is analyzed for slotted Aloha with and without MPR. More specifically, the mean and variance have been analytically computed and the contention delay distribution is approximated. Having theoretical expressions for the contention delay statistics enables optimizing both the medium access probability and the number of MPR channels in order to strike a trade-off between delay performance and complexity

Noncoherent Decision Fusion over Fading Hybrid MACs in Wireless Sensor Networks

In this paper, we consider the problem of decision fusion for noncoherent detection in a wireless sensor network. Novel to the current work is the integration of the hybrid multi-access channel (MAC) in the fusion rule design. We assume that sensors transmit their local binary decisions over a hybrid MAC which is a composite of conventional orthogonal and nonorthogonal MACs. Under Rayleigh fading scenario, we present a likelihood ratio (LR)-based fusion rule, which has been shown to be optimal through theoretical analysis and simulation. However, it requires a large amount of computation, which is not easily implemented in resource-constrained sensor networks. Therefore, three sub-optimal alternatives with low-complexity are proposed, namely the weighed energy detector (WED), the deflection-coefficient-maximization (DCM), and the two-step (TS) rules. We show that when the channel signal-to-noise ratio (SNR) is low, the LR-based fusion rule reduces to the WED rule; at high-channel SNR, it is equivalent to the TS rule; and at moderate-channel SNR, it can be approached closely by the DCM rule. Compared with the conventional orthogonal and nonorthogonal MACs, numerical results show that the hybrid MAC with the proposed fusion rules can improve the detection performance when the channel SNR is medium