Sanghyouk Choi¹, Joohwan Chun¹, Inchan Paek² and Jonghun Jang³, ¹KAIST, Korea,
²PGM Image Sensor Centre, Korea and ³Agency for Defense Development, Korea

We present the gradient and Hessian of the trace of the multivariate Cramér-Rao bound (CRB) formula for unknown impinging angles of plane waves with non-unitary beamspace measurements,. These gradient and Hessian can be used to find the optimal beamspace transformation matrix, i.e., the optimum beamsteering angles, using the Newton-Raphson iteration. These trace formulas are particularly useful to deal with the multiple source senario. We also show the mean squred error (MSE) performance gain of the optimally steered beamspace measurements compared with the usuall DFT steered measurements, when the angle of arrivals (AOAs) are estimated with stochastic maximum likelihood (SMLE) algorithm.

Cramér-Rao bound, beamspace transformation, correlated noise, DFT beams, subarray formation