A novel fast and accurate full-wave approach to the analysis of a wide class of slotted waveguide arrays and finite multi-layer waveguide arrays with dielectric cover is presented. The numerical-analytical solution is based on Galerkin method with weighted Chebyshev and Gegenbauer polynomials as basis functions explicitly accounting for the field asymptotic at the edges. An extremely fast convergence of the method is achieved due to proper basis functions. The other key point of the solution is the computational acceleration of double series and integrals which are the matrix elements of a final system of linear algebraic equations.

The results for traveling-wave array with shunt slots for radar applications are considered. A parametric study of waveguide antenna arrays with finite multi-layer dielectric cover is presented, which includes the effect of dielectric cover on impedance matching, array efficiency and directivity.