A new numerical method is presented for the design and optimization of linear arrays of nonuniformly spaced longitudinal slots on the broad wall of rectangular waveguides, based on the Method of Least Squares (MLS). Elliott's design theory for travelling-wave-fed slot arrays is extended to nonuniformly spaced slots. As a common approach in MLS, an error function is formulated according to the design goals (namely the input impedance matching and pattern synthesis) and then minimized with respect to the design parameters (namely slot lengths, offsets, spacings and excitations). Having the slot parameters, one can design a linear slot array which accounts for the desired input impedance matching and array pattern. This approach has the advantage of combining the ``nonuniform pattern synthesis'', which includes the external mutual coupling and element pattern of slots, with ``impedance matching'' and ``calculation of the array parameters''. This procedure increases the design speed as well as synthesizing any desired pattern. The MLS design results and those obtained by HFSS simulation software are in good agreement and verify the accuracy of the proposed method.
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