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

Reduced Complexity Optimal Hard Decision Fusion under Neyman-Pearson Criterion

Distributed detection is an important part of many of the applications like wireless sensor networks, cooperative spectrum sensing in the cognitive radio network. Traditionally optimal non-randomized hard decision fusion rule under Neyman Pearson(NP) criterion is exponential in complexity. But recently [4] this was solved using dynamic programming. As mentioned in [4] that decision fusion problem exhibits semi-monotonic property in a special case. We use this property in our simulations and eventually apply dynamic programming to solve the problem with further reduced complexity. Further, we study the e�ect of using multiple antennas at FC with reduced complexity rule

Estimation in Phase-Shift and Forward Wireless Sensor Networks

We consider a network of single-antenna sensors that observe an unknown deterministic parameter. Each sensor applies a phase shift to the observation and the sensors simultaneously transmit the result to a multi-antenna fusion center (FC). Based on its knowledge of the wireless channel to the sensors, the FC calculates values for the phase factors that minimize the variance of the parameter estimate, and feeds this information back to the sensors. The use of a phase-shift-only transmission scheme provides a simplified analog implementation at the sensor, and also leads to a simpler algorithm design and performance analysis. We propose two algorithms for this problem, a numerical solution based on a relaxed semidefinite programming problem, and a closed-form solution based on the analytic constant modulus algorithm. Both approaches are shown to provide performance close to the theoretical bound. We derive asymptotic performance analyses for cases involving large numbers of sensors or large numbers of FC antennas, and we also study the impact of phase errors at the sensor transmitters. Finally, we consider the sensor selection problem, in which only a subset of the sensors is chosen to send their observations to the FC.Comment: 28 pages, 5 figures, accepted by IEEE Transactions on Signal Processing, Apr. 201

Distributed Detection over Gaussian Multiple Access Channels with Constant Modulus Signaling

A distributed detection scheme where the sensors transmit with constant modulus signals over a Gaussian multiple access channel is considered. The deflection coefficient of the proposed scheme is shown to depend on the characteristic function of the sensing noise and the error exponent for the system is derived using large deviation theory. Optimization of the deflection coefficient and error exponent are considered with respect to a transmission phase parameter for a variety of sensing noise distributions including impulsive ones. The proposed scheme is also favorably compared with existing amplify-and-forward and detect-and-forward schemes. The effect of fading is shown to be detrimental to the detection performance through a reduction in the deflection coefficient depending on the fading statistics. Simulations corroborate that the deflection coefficient and error exponent can be effectively used to optimize the error probability for a wide variety of sensing noise distributions.Comment: 30 pages, 12 figure