## 1 Introduction  
In the context of wireless sensor networks (WSNs), the detection of unknown parameters by using a multitude of sensor nodes has been of significant interest over the past few decades (e.g., [1; 2; 3; 4; 5; 6; 7; 8; 9; 10; 11; 12; 13] and the references therein). The widely-deployed sensors are designated to provide measurements of a given physical process (temperature, humidity, _etc._), as well as to detect specific events (mobile target, acoustic source, _etc._) over a region of interest. An important strategy has been followed in many studies, where a fusion center (FC) is employed to make a global decision based on original observations from local sensors.  
In practice, especially to meet bandwidth/energy constraints, there is a need to reduce the dimension of raw measurements from each sensor to the FC by using one-bit quantization [1; 2; 3; 4; 5; 6; 7; 8; 9; 10; 11]. In [4], a fixed quantization (FQ) approach was examined for distributed estimation of a mean parameter (_i.e._, the mean of observations). It was shown that the optimum quantization threshold depends on the unknown parameter to be estimated and is thus practically infeasible. To overcome this difficulty, a distributed adaptive quantization (AQ) approach was proposed in [5; 6], where the threshold is dynamically regulated from one sensor to another, in such a way that the threshold converges to the optimum threshold. In [7], the design of the binary antisymmetric quantizer was studied by the minimization of the worst case of the Cramer-Rao bound (CRB). Using a generalized likelihood ratio test (GLRT) framework, joint estimation and detection of an unknown mean parameter based on one-bit quantization was considered in [8]. A one-bit Rao detector was introduced as a computationally-efficient alternative to the GLRT in [9]. Meanwhile, distributed estimation of both an unknown mean parameter and a scale parameter was considered in [10], where sensors are divided into two groups, each using a different threshold to generate binary observations. In situations with less stringent bandwidth/power constraints, multi-bit quantization strategies can be employed with enhanced estimation performance [11; 12; 13].  
In this paper, we consider the problem of quantization for change detection using one-bit quantized observations collected by distributed sensors and forwarded to a FC through distortive binary symmetric channels (BSCs). The change detection problem involves an unknown change of the power, _i.e._, a scale parameter, of the observed signals. To deal with the unknown parameter, we employ the GLRT approach to develop a fusion rule for the FC to solve the change detection problem. We propose a one-bit quantizer based on an asymptotic analysis of the GLRT. Our analysis demonstrates that the optimum quantization thresholds for local sensors for GLRT fusion rule are identical and unrelated to the unknown scale parameter. However, the optimum quantization threshold is dependent on the cross-over error probability of the BSCs.  
This paper is organized as follows. The problem is formulated in Section 2. In Section 3, the GLRT fusion rule is proposed. In Section 4, we present an asymptotic analysis of the GLRT, which is used to design the one-bit GLRT quantizers. In Section 5, the GLRT using unquantized observations in presented as a benchmark to the proposed quantization/detection schemes. Simulation results and comparisons are provided in Section 6. Finally, concluding remarks are given in Section 7.