Sparse Array Design Exploiting the Augmented Conjugate Correlation Statistics for DOA Estimation

With the augmentation of the non-zero conjugate correlation statistics of some modulating signals, enlarged degrees of freedom (DOFs) can be achieved with conventional sparse arrays as proposed by many literatures. But little research has been carried out on sparse array design with the augmented statistics. In this paper, a novel sparse array geometry which exploits both the correlation and conjugate correlation statistics is proposed. It stems from the prototype nested array with transposed subarrays. The sensor locations are determined systematically, and the closed-form expression for the achieved aperture under given number of physical sensors is derived. In our scheme, a new hole-free virtual array called the sum difference coarray is constituted with the proposed sparse array, in which all the lags are consecutive. Due to the output of the coarray is obtained by averaging the repeated lags generated by the addition and subtraction of the physical sensor location, the hole-free structure of the coarray enables all the lags engaged in averaging and makes the output of the coarray more stable. Moreover, the coarray has larger aperture than existing sparse arrays, so that bringing more degrees of freedom. In the end, simulations are conducted to demonstrate the superior performance of the proposed scheme over other existing structures.