Distributed detection in the presence of frequency offset and phase shift

In this paper, we study the problem of distributed detection in the presence of unknown carrier frequency offset (CFO) and initial phase, the issue we encounter in the emerging applications of wireless sensor networks (WSNs) due to hardware constraints on sensor nodes. Suboptimal fusion rules taking into account CFO and initial phase and non-data-aided methods of low complexity for CFO and initial phase shift estimation are developed. Instead of the estimation performance, the objective function is in terms of the final detection performance. In particular, a generalized likelihood ratio test is proposed first for distributed detection in the presence of unknown CFOs and phase shifts. Then computationally simplified algorithms are proposed under the high and low signal-to-noise ratio regimes, respectively. Specifically, under the high-SNR condition, a time-averaging autocorrelator is used for CFO estimation and the Chair-Varshney fusion rule is used for decision fusion; while under the low-SNR condition, maximum likelihood estimation can be realized by a fast Fourier transform. The simulation results show that the developed fusion schemes are robust to CFO and initial phase.