A special coprime array configuration for increased degrees of freedom

Direction‐of‐arrival estimation based on difference‐sum co‐array of a special coprime array

“…The steering vector corresponding to the k ‐th source signal is $$$$\begin{equation} \bm {a}{\left(\theta _{k}\right)}={\left[1, e^{-j \frac{2 \pi }{\lambda } u_{2} d \sin {\left(\theta _{k}\right)}}, \ldots , e^{-j \frac{2 \pi }{\lambda } u_{i} d \sin {\left(\theta _{k}\right)}}\right]}^{T}, \end{equation}$$$$where $$u_i d,i \in \lbrace 2,3,\ldots ,M+N-1\rbrace$$ represents the position of the i ‐th sensor in the relative prime array. For the T samples, the time average function can be calculated by [13–15], $$$$\begin{equation} R_{x_1^* x_i } (\tau ) = \sum \limits _{k = 1}^K {a_1^* (\theta )_k a_i (} \theta )_k \cdot \left[{ {1 \over T}}\sum \limits _{t = 1}^T {s_k^* (t)s_k (t + \tau )} \right] + R_{n_1^* n_i } (\tau ), \end{equation}$$$$where τ is the time lag, T is the number of snapshots. When T is sufficiently large, (5) can be written as …”

“…, M + N − 1} represents the position of the i-th sensor in the relative prime array. For the T samples, the time average function can be calculated by [13][14][15],…”