Maximum Likelihood DOA Estimation and Detection Without Eigendecomposition

Most popular techniques f o r t h e narrowband direct ion of arrival ( D O A ) problem rely on a n eigendecomposi t ion ( E V D ) compu ta t i o n t o de t e rmine both the n u m b e r of s ignals and the i r respective D O A s . In t h i s paper, a n al ternat ive algori thm i s presented tha t solves both t h e D O A detect ion and e s t ima t ion problems w i thou t resort ing t o an E V D . T h e algori thm i s s h o w n t o be asymptot ical ly equivalent t o t h e ( s tochas t i c ) m a x i m u m likelihood me thod , and hence yields asymptot ical ly m i n i m u m variance D O A es t ima tes . I n addi t ion, t he asympto t i c dis tr ibut ion of t he algori thm’s cost f u n c t i o n i s derived, and i s s h o w n t o be composed of t he s u m of t w o di f ferent ly scaled chi-squared r a n d o m variables. A hypothesis tes t f o r de t e rmin ing t h e n u m b e r of signals based on this result i t t hen presented.