Tone-in-noise detection has been studied for decades; however, it is not completely understood what cue or cues are used by listeners for this task. Model predictions based on energy in the critical band are generally more successful than those based on temporal cues, except when the energy cue is not available. Nevertheless, neither energy nor temporal cues can explain the predictable variance for all listeners. In this study, it was hypothesized that better predictions of listeners' detection performance could be obtained using a nonlinear combination of energy and temporal cues, even when the energy cue was not available. The combination of different cues was achieved using the logarithmic likelihood-ratio test (LRT), an optimal detector in signal detection theory. A nonlinear LRT-based combination of cues was proposed, given that the cues have Gaussian distributions and the covariance matrices of cue values from noise-alone and tone-plus-noise conditions are different. Predictions of listeners' detection performance for three different sets of reproducible noises were computed with the proposed model. Results showed that predictions for hit rates approached the predictable variance for all three datasets, even when an energy cue was not available.

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We consider the distributed estimation of a Gaussian vector with a linear observation model in an inhomogeneous wireless sensor network, in which a fusion center (FC) reconstructs the unknown vector using a linear estimator. Sensors employ uniform multi-bit quantizers and binary PSK modulation, and they communicate with the FC over orthogonal power-and bandwidth-constrained wireless channels.We study transmit power and quantization rate (measured in bits per sensor) allocation schemes that minimize the mean-square error (MSE). In particular, we derive two closed-form upper bounds on the MSE in terms of the optimization parameters and propose "coupled" and "decoupled" resource allocation schemes that minimize these bounds. We show that the bounds are good approximations of the simulated MSE and that the performance of the proposed schemes approaches the clairvoyant centralized estimation when the total transmit power or bandwidth is very large. We investigate how the power and rate allocations are dependent on the sensors' observation qualities and channel gains and on the total transmit power and bandwidth constraints. Our simulations corroborate our analytical results and demonstrate the superior performance of the proposed algorithms. Index TermsDistributed estimation, Gaussian vector, upper bounds on MSE, power and rate allocation, ellipsoid method, quantization, linear estimator, linear observation model.

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