Wei Liu received his B.Sc. in 1996 and L.L.B. in 1997, both from Peking University, China, M.Phil. from University of Hong Kong, in 2001, and Ph.D. in 2003 from the School of Electronics and Computer Science, University of Southampton, UK. Since September 2005, he has been with the Department of Electronic and Electrical Engineering, University of Sheffield, UK, first as a lecturer, and then a senior lecturer. His research interests are in sensor array signal processing, blind signal processing, multivariate signal processing and their various applications. An expanding and shift scheme for efficient fourth-order difference co-array construction is presented. It consists of two sparse subarrays, where one of them is modified and shifted according to the analysis provided. The number of consecutive lags of the new construction at the fourth order is consistently larger than two previously proposed methods. Simulations are performed to show the improved performance by the new construction in comparison with existing structures using cumulant-based methods for non-Gaussian stationary signals. As another way to exploit the increased degrees of freedom (DOFs) provided by the fourth-order different co-array, a new fourth-order DOA estimation method is introduced to deal with non-stationary signals, which may not necessarily be non-Gaussian. Simulation results are also provided to show that the method works well for non-stationary signals, extending the paradigm of fourth-order difference co-array applications.