2D MIMO Radar with Coprime Arrays

Abstract

In this contribution, a new class of planar coprime MIMO radar systems based on quadratic integers is proposed where the antenna locations are represented by lattice points generated by prime integers in quadratic number fields. By exploiting the coprimality of certain quadratic integers, the virtual coarrays of proposed structures enjoy a quadratic gain in parameter identifiability according to the Chinese Remainder Theorem (CRT). To avoid holes in the coarray, we present Hole-free CRT arrays with guaranteed full-rank autocorrelation matrices for subspace-based target estimation. The ring of Gaussian integers and the ring of Eisenstein integers are chosen as examples of designing coprime MIMO radar systems. It is shown that the proposed arrays achieve enhanced angular resolutions and improve the side lobe suppression. In the context of target estimation, simulations show the superior performance of the coprime MIMO structures based on CRT.

Time Division Multiplexing: From a Co-Prime Sampling Point of View

“…This is same as the locations for x 1 (t) hence the self difference matrix is same. The second sub-sampler with spacing M d has samples at [12,16,20]. The self difference matrix is given in Fig.…”

Coprime Sensing via Chinese Remaindering Over Quadratic Fields—Part II: Generalizations and Applications

“…Theorem 1: Let Z[q] denote a ring of integers with minimum polynomial X 2 +BX +C. Two quadratic integers m = m 1 + m 2 q and n = n 1 + n 2 q in Z[q] are coprime if and only if GCD(N(m), N(n), m 1 n 2 − m 2 n 1 ) = 1 or equivalently (1) GCD(N(m), N(n), m 1 n 1 − Bm 1 n 2 + Cm 2 n 2 ) = 1, (2) where GCD denotes the greatest common divisor and N(m) is the norm of m that is defined by…”

“…To begin with, let us assume (1) holds. By adding and subtracting m 2 n 2 q to the last term in (1), this condition can be rewritten as GCD(N(m), N(n), (m 1 n 2 +m 2 n 2 q)−(m 2 n 1 +m 2 n 2 q)) = 1, (44) Recalling that m = m 1 + m 2 q and n = n 1 + n 2 q, (44) can be simplified to GCD(N(m), N(n), n 2 m − m 2 n) = 1.…”